Estudo teórico e experimental sobre ebulição convectiva no interior ...

Taye stephen Mogaji

Estudo teórico e experimental sobre

ebulição convectiva no interior de

tubos com fitas retorcidas

Tese apresentada à Escola de Engenharia

de São Carlos, Departamento de Engenharia

Mecânica, da Universidade de São Paulo, como

parte dos requisitos para obtenção do título de

Doutor em Engenharia Mecânica.

Área de Concentração: Térmica e Fluidos

Orientador: Prof. Dr. Gherhardt Ribatski

SÃO CARLOS-SP

2014

ESTE EXEMPLAR TRATA-SE DA VERSÃO CORRIGIDA. A VERSÃO ORIGINAL ENCONTRA-SE

DISPONÍVEL JUNTO AO DEPARTAMENTO DE ENGENHARIA MECANICA DA EESC-USP.

DEDICATION

This research work is dedicated to the Almigthy God, the author and finisher of my

faith and in memory of my late father Pa David Kolawole Mogaji.

ACKNOWNLEDGEMENT

This study has been carried out at Laboratory of Thermal and Fluids Engineering,

Department of Mechanical Engineering, School of Engineering of São Carlos (EESC-

USP) under the direction of Prof. Gherhardt Ribatski. The Doctoral scholarship has

been funded by the CAPES (Coordination for the Improvement of Higher Level - or

Education-Personnel, Brazil) under Contract Number 00011/07-0, and the financial

support to this study under Contract Number 474403/2008-4 given by CNPq (The

National Council for Scientific and Technological Development, Brazil), which are

gratefully acknowledge.

I would like to thank my University, Federal University of Technology Akure (FUTA),

Ondo State, Nigeria, for giving me the opportunity to carry out my Doctoral degree

study here in Brasil through study leave with pay support received from the

University.

I would like to thank Professor Gherhardt Ribatski for giving me the opportunity to

carry out this research work in his laboratory, for his excellent supervision, academic

training and guidance during this period. Finally, I would like to thank him for his

careful reading of this thesis.

To my family, my lovely wife, Mrs Josephine Bukola Mogaji, and my children, Favour

Emmanuela and Pedro Ayodeji Mogaji for their ultimate support and understanding

during this period.

Encouragement and prayer support from my twins brother and his family (Mr and Mrs

K.A. Mogaji), the entire family members of Mogaji’s, Fasina’s and Omoreige’s, my

Pastor and adviser (Dr.Engr.S. P. Ayodeji) are appreciated and recognized.

The technical support given to this investigation by Mr. Jose Roberto Bogni for

successful construction and maintenance of the experimental bench is also

appreciated and deeply recognized.

I also acknowledge my colleagues of the Laboratory of Refrigeration (EESC-USP),

Cristiano Bigonha Tibiriça, Daniel Sempertegui Tapia, Francisco Julio Nascimento,

Hugo Leonardo Leo, Jacqueline Diniz da Silva, Gustavo Rodriguez de Souza,

Anderson Ubices de Moraes, Francisco Loyola, Cristian Alfredo Chávez Toro, Thiago

Augosto Moreira, Felipe, Nourjane Namaca, Karime Barbarasanto Caminoto for their

helps and specially Kanizawa Fabio Toshio for his collaboration during this period.

To Professor Antonio Moreira, Oscar Rodriguez, Daniel Verala Mogalhães, for their

excellent academic training given to me during my course work period, technical

Jorge Nicolau do santo and Roberto for your collaboration during this period.

To Professor Enio Pedone Bandarra Filho for his candid contribution to this research

work and presentation of part of the results obtained in this study at ECI 8th

International Conference on Boiling and Condensation Heat Transfer, 2012,

Lausanne, Switzerland.

To friends and colleagues of the group Núcleo de Engenharia Térmica e Fluidos

(NETeF) for your contributions in terms of important discussions and suggestions

during this period: Marcelo Souza Castro, Marcia Regina Osaki, Evelise Corbalan,

Hugo Fernando Velasco Pena, Adriana Bonilla Riano,Iara Hernande Rodriguez,

Jonas Laerte Ansoni, Luis Enrique Ortiz-Vidal, Ricardo Pereria de Avila, Marlon

Mauricio Hernandez Cely, Glauber Cruz , Serginho and Daniela Andresa Mortari.

ABSTRACT

MOGAJI, Taye Stephen (2014). THEORETICAL AND EXPERIMENTAL STUDY ON

CONVECTIVE BOILING INSIDE TUBES CONTAINING TWISTED-TAPE INSERTS.

258 pages. Thesis (PhD) - Escola de Engenharia de São Carlos, University of São

Paulo, São Carlos.

This research comprises an experimental and theoretical study on convective boiling

inside tubes containing twisted-tape inserts. The demand for more compact and

efficient thermal systems, in which the heat exchangers plays an important role, has

led to the development and use of various heat transfer enhancement techniques.

Among them twisted-tape insert as a swirl flow device is one of the most used.

Twisted-tape inserts have been used for over more than one century ago as a

technique of heat transfer enhancement applied to heat exchangers. However, the

heat transfer augmentation comes together with pressure drop increment, impacting

the pumping power and, consequently, the system efficiency. Moreover, until now it

is not clear, the operational conditions under which the heat transfer coefficient

augmentation by the use of twisted-tape inserts overcomes pressure drop penalty. In

the present study, initially, extensive investigations of the literature concerning

convective boiling inside plain tubes with and without twisted-tape inserts were

performed. This literature review covers pressure drop, heat transfer coefficient and

the leading frictional pressure drop gradient and heat transfer coefficient predictive

methods during convective boiling inside tubes with and without twisted-tape inserts.

Then, pressure drop and heat transfer coefficient results acquired in the present

study were obtained in an experimental apparatus of 12.7 and 15.9 mm ID tubes

during flow boiling of R134a for twisted-tape ratios of 3, 4, 9, 14 and tubes without

inserts, mass velocities ranging from 75 to 200 kg / m2 s, saturation temperatures of 5

and 15 °C and heat fluxes of 5 and 10 kW / m2. The experimental results were

parametrically analyzed and compared against the predictive methods from literature.

An analysis of the enhancement of the heat transfer coefficient and the pressure drop

penalty is presented. Heat transfer coefficient increments up to 45 % keeping the

same pumping power and pressure drop penalty of about 35 % were obtained by

using twisted-tape relative to tubes without inserts. Additionally, through comparison

of the present study experimental results with the predictive methods from the

literature for heat transfer coefficient during two-phase flow inside tube containing

twisted-tape inserts, it was verified that non of these methods predict satisfactory well

the experimental results. However, a new method was develop for predicting the heat

transfer coefficient during flow boiling inside tubes containing twisted-tape inserts

based on the experimental results obtained in the present study. The predictive

method takes into account the physical picture of the swirl flow phenomenon by

including swirl flow effects promoted by the twisted-tape inserts. The proposed

method predicts satisfactorily well the data obtained in the present study, predicting

89.1% of the experimental data within an error band of ±30 % and absolute mean

deviation of 15.7 %.

Keywords: Convective boiling, twisted-tape, heat transfer enhancement, pressure

drop, swirl flow.

RESUMO

MOGAJI, Taye Stephen (2014). Estudo teórico e experimental sobre a ebulição

convectiva no interior de tubos com fitas retorcidas. 258 páginas. Tese (Doutorado) -

Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos.

A presente pesquisa trata-se de um estudo teórico e experimental sobre a ebulição

convectiva no interior de tubos com fitas retorcidas. A crescente demanda por

sistemas térmicos mais compactos e eficientes, nos quais os trocadores de calor

apresentam elevada relevância, tem motivado o desenvolvimento de inúmeras

técnicas de intensificação de troca de calor, sendo que a utilização de fitas

retorcidas é uma das técnicas mais adotadas. Fitas retorcidas são utilizadas como

técnicas de intensificação de troca de calor há mais de um século. Entretanto o

incremento da transferência de calor é acompanhado do aumento da perda de

pressão, que por sua vez implica em aumento da potência de bombeamento, e

consequentemente afeta a eficiência global do sistema. Adicionalmente, até os dias

de hoje não há consenso sobre as condições operacionais em que o ganho com o

incremento do coeficiente de transferência de calor é superior à perda devido ao

aumento da perda de pressão. Neste estudo, inicialmente foi realizada uma extensa

revisão da literatura sobre a ebulição convectiva no interior de tubos com e sem fitas

retorcidas. Esta revisão aborda aspectos relacionados à perda de pressão e ao

coeficiente de transferência de calor, juntamente com os métodos de previsão

destes parâmetros. Foram realizados experimentos para determinação experimental

de perda de pressão e coeficiente de transferência de calor, em aparato

experimental contando com tubos horizontais com diâmetros internos iguais a 12,7 e

15,9 mm, para escoamento bifásico de R134a, razões de retorcimento iguais a 3, 4,

9, 14 e tubo sem fita, velocidades mássicas entre 75 e 200 kg/m²s, temperaturas de

saturação iguais a 5 e 15 °C, e flux de calor iguais a 5 e 10 kW/m². Os resultados

experimentais foram analisados e comparados com estimativas segundo métodos

disponíveis na literatura. Uma análise do aumento do coeficiente de transferência de

calor e da perda de pressão friccional é apresentada. Foram verificados incrementos

do coeficiente de transferência de calor de até 45% para a mesma potência de

bombeamento, e aumento de perda de pressão de aproximadamente 35% para

tubos com fitas retorcidas em relação aos tubos sem fita. Adicionalmente, através da

comparação dos resultados experimentais com os métodos de previsão para

coeficiente de transferência de calor, foi verificado que nenhuma metodologia

apresentava previsões satisfatórias dos resultados. Portanto um novo método para

previsão do coeficiente de transferência de calor durante ebulição convectiva no

interior de tubos com fitas retorcidas foi desenvolvido com base nos resultados

experimentais obtidos durante o presente estudo. O método proposto é função de

parâmetros geométricos e do escoamento, e também de parâmetros físicos do

escoamento rotacional induzido pela fita. A metodologia desenvolvida apresenta

previsões satisfatórias dos resultados experimentais, prevendo 89,1% dos

resultados experimentais com erro inferior a ±30% e erro médio absoluto igual a

15,7%.

Palavras-chave: Ebulição convectiva, fitas retorcidas, intensificação de transferência

de calor, perda de pressão, escoamento rotacional.

LIST OF SYMBOLS

Latin Letters

di Internal diameter, m

E Electrical power, W

e Tape thickness,m

Fe Fin effect multiplier, dimensionless

fw Surface material parameter, dimensionless

F Convective enhancement factor, dimensionless

Fr Froude Number, dimensionless

g Acceleration due to gravity, m2 / s

G Mass velocity, kg / m2 s

Gr Grashof Number, dimensionless

h Heat transfer coefficient, W / m2 K

H Length of 180° tape turn, m

i Enthalpy, kJ / kg

k Thermal conductivity, W / m K

L Length, m

M Molecular mass, kg / kmol

Mass flow rate, kg / s

pr Reduced pressure, dimensionless

Pr Prandtl number, dimensionless

Heat transfer, W

Re Reynolds Number, dimensionless

Ra Peak-to-valley surface roughnesses, µm

V Velocity, m / s

T Temperature, oC

x Vapor quality, dimensionless

xdi Dryout completion quality, dimensionless

xde Dryout inception quality, dimensionless

We Weber Number, dimensionless

y Twist ratio

z Distance from inlet, m

Greek symbols

∆p Pressure drop, Pa

Liquid film thickness, m

Superficial void fraction, dimensionless

Surface roughness, µm

Enhancement parameter, dimensionless

Geometric parameter define by Eq.(2.132), dimensionless

Dynamic viscosity, kg / m s

η Absolute mean error, %

ζ Percentage of exp. data within an error band of ±30 %, dimensionless

ϕ Heat flux, kW / m2

Two phase multiplier for liquid, dimensionless

Two phase multiplier for vapor, dimensionless

Angle, rad

Density, kg / m3

Surface tension, N / m

Subscripts

acc Accelerational

env Heat transfer to the environment

fric Frictional

grav Gravitational

Hydraulic

Homogeneous

In Inlet

l Liquid

v Vapor

lv Liquid-vapor

Out Outlet

PH Pre-Heater

PT Plain tube

TS Test section

TT With twisted tape

w Wall

2φ Two–phase

V0 Mixture as vapor

L0 Mixture as Liquid

Dimensionless

Boiling Number

Convective Number

Froude Number

Grashof – Number

Nulsset Number

Reynolds Number

Weber Number

Martineli Parameter

LIST OF FIGURES Figure 2.1 - Two-phase flow (liquid-vapor) in a tube (Kanizawa, 2011). ................... 32

Figure 2.2 - Flow patterns observed in horizontal tubes, Cheng et al. (2008)........... 37

Figure 2.3 - Flow pattern map for horizontal flow (Baker 1954). ............................... 38

Figure 2.4 - Flow pattern map for R134a at Tsat = 30 oC in a 10 mm internal diameter

tube for ϕ = 10 kW / m2 using G = 100 kg / m2 s (Kattan et al. 1998)....................... 39

Figure 2.5 - Flow pattern map evaluated for R22 at Tsat = 5 oC in a 13.84 mm internal

diameter tube for ϕ = 2.1 kW/m2 using G = 100 kg / m2 s to calculate the void

fractions. (Wojtan et al. 2005). .................................................................................. 40

Figure 2.6 - Simplified stratified flow configuration, Kattan et al. (1998). .................. 41

Figure 2.7 – Comparison among the predictive methods for Nusselt Number during

during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C,

p=692 kPa Tsub =19.08 oC......................................................................................... 95

Figure 2.8 – Comparison among the predictive methods for Nusselt Number during

during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C,

p=692 kPa Tsub =19.08 oC......................................................................................... 95

Figure 3.1 - Photograph of the experimental bench................................................ 108

Figure 3.2 - Schematic diagram of the refrigerant circuit. ....................................... 109

Figure 3.3 - Thermodynamic process of the refrigerant along the refrigerant test

circuit. ..................................................................................................................... 110

Figure 3.4 - Schematic diagram of the test section and the thermocouples

distribution. ............................................................................................................. 111

Figure 3.5 - Positioning of thermocouples for each cross section along the test

section. ................................................................................................................... 112

Figure 3.6 - Visualisation section at the test section outlet. .................................... 112

Figure 3.7 - Illustration of fitting of differential pressure transducers....................... 113

Figure 3.8 - Photograph of the Pre-heater. ............................................................. 114

Figure 3.9 - Schematic diagram of the acquisition system and terminals. .............. 117

Figure 3.10 - Image of the program implemented for data acquisition.................... 118

Figure 3.11 - Photograph of the twisted-tape inserts used during the experimental

compaign. ............................................................................................................... 119

Figure 3.12 - Comparison between experimental friction factors and estimated friction

factors, for single-phase flow in tubes with 12.7 mm ID (filled symbols) and 15.9 mm

ID (empty symbols). ................................................................................................127

Figure 3.13 - Comparison of experimental and estimated heat transfer coefficient for

liquid single-phase flow, for 12.7 mm ID tube. Estimatives according to Dittus and

Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols). ..................127

Figure 3.14 - Comparison of experimental and estimated heat transfer coefficient for

liquid single-phase flow, for 15.9 mm ID tube. Estimatives according to Dittus and

Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols). ..................128

Figure 3.15 - Variation with mass velocity of the heat exchanged between the test

section and the surroundings. .................................................................................129

Figure 3.16 - Variation with mass velocity of the heat exchanged between the pre-

heater and the surroundings....................................................................................129

Figure 4.1 - Variation of frictional pressure drop gradient with vapor quality for

adiabatic two-phase flow in 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols)

and Tsat = 15 °C (filled symbols). .............................................................................133


adiabatic two-phase flow in 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols)

and Tsat = 15 °C (filled symbols). .............................................................................133

Figure 4.3 - Variation of frictional pressure drop gradient with vapor quality for R134a,

12.7 mm ID tube, G = 75 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C

(filled symbols). .......................................................................................................134



(filled symbols). .......................................................................................................135



(filled symbols). .......................................................................................................135



(filled symbols). .......................................................................................................136



(filled symbols). .......................................................................................................136



(filled symbols). ....................................................................................................... 137

Figure 4.9 - Variation of frictional pressure drop gradient with vapor quality fo R134a,


(filled symbols). ....................................................................................................... 137


R134a 15.9 mm ID tube, G = 200 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat =

15 °C (filled symbols). ............................................................................................. 138

Figure 4.11 - Comparison between estimated and experimental frictional pressure

drop, for 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C

(filled symbols). ....................................................................................................... 139


drop, for 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C

(filled symbols). ....................................................................................................... 139

Figure 4.13- Comparison of the trends of the frictional pressure drop according to

predictive methods and experimental data for plain tube without twisted-tape,for 15.9

mm ID plain tube, Tsat = 15 °C and G = 100 kg / m² s. ............................................ 140


drop gradient, for 12.7 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3,

4, 9 and 14.............................................................................................................. 142


drop gradient, for 15.9 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3,

4, 9 and 14.............................................................................................................. 142

Figure 4.16 - Comparison of the trends of the frictional pressure drop according to

predictive methods and experimental data for plain tube with twisted-tape, for 12.7

mm ID tube Tsat = 15 °C. ......................................................................................... 144

Figure 4.17 - Comparison of the trends of the frictional pressure drop according to


mm, ID tube, Tsat = 15 °C. ....................................................................................... 144

Figure 4.18 – Illustration of the variation of pressure drop penalty with vapor quality,

for ID = 12.7 mm and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols)........ 145

Figure 4.19 - Illustration of the variation of pressure drop penalty with vapor quality

for ID = 15.9 mm, and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols)....... 146

Figure 4.20 – Variation of heat transfer coefficient with vapor quality during flow

boiling in tube without twisted-tape inserts, ϕ = 10 kW / m², Tsat = 5 °C, di = 12.7 mm

(empty symbols) and di = 15.9 mm (filled symbols).................................................148

Figure 4.21 - Variation of heat transfer coefficient with vapor quality during flow

boiling in tube without twisted-tape inserts, ϕ = 10 kW / m², di = 15.9 mm , Tsat = 5 °C

(empty symbols) and Tsat = 15 °C (filled symbols). ..................................................148

Figure 4.22 - Variation of heat transfer coefficient with vapor quality during flow

boiling in tube without twisted-tape inserts, Tsat = 15 °C ,di = 15.9 mm ,ϕ = 10 kW /

m² (empty symbols) and ϕ = 5 kW / m², (filled symbols).........................................149

Figure 4.23- Comparison between estimated and experimental heat transfer

coefficients for the12.7 mm ID tube without inserts according to Kandlikar (1990). 150

Figure 4.24 - Heat transfer coefficient variation with vapor quality during flow boiling

in 12.7 mm ID, .........................................................................................................151


in 12.7 mm ID, G = 150 kg / m2 s, φ = 10 kW / m², Tsat =5 oC. ................................152


in 15.9 mm ID, G = 75 kg / m2 s, φ = 10 kW / m², Tsat = 5 oC. .................................152


in 15.9 mm ID, G = 150 kg / m2 s,φ = 10 kW / m², Tsat = 5 oC. ................................153

Figure 4.28 - Illustration of the effect of heat flux on heat transfer coefficient for plain

tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 12.7

mm ID Tsat = 5 oC.....................................................................................................154

Figure 4.29 - Illustration of the effect of heat flux on heat transfer coefficient for plain

tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 15.9

mm ID Tsat = 5 oC.....................................................................................................154


in 15.9 mm ID, φ = 10 kW / m², Tsat = 15 oC; y = 14 (filled symbol) and y = 3 (empty

symbol)....................................................................................................................155

Figure 4.31 – Illustration of the effect of tube diameter on the heat transfer coefficient

with vapor quality inside tubes with twisted-tape inserts, G = 100 kg / m2 s, φ = 10

kW / m², Tsat = 15 oC................................................................................................156

Figure 4.32 - Effect of the saturation temperature on the heat transfer coefficient

during flow boiling in 15.9 mm ID, G = 75 kg / m2 s, φ = 10 kW / m², y = 14 (filled

symbol) and y = 4 (empty symbol). ......................................................................... 157

Figure 4.33 - Effect of the saturation temperature on the heat transfer coefficient for

during flow boiling in 15.9 mm ID, G = 150 kg / m2 s, φ = 10 kW / m², y = 14 (filled

symbol) and y = 4 (empty symbol). ......................................................................... 157

Figure 4.34 - Comparison between estimatives according to Akhavan-Behabadi et al.

(2009b) and experimental heat transfer coefficients. .............................................. 159

Figure 4.35 - Comparison of the trends of the heat transfer coefficient according to


mm ID tube, Tsat = 5 °C, φ = 10 kW/m². ................................................................... 160

Figure 4.36 - Comparison of the trends of the heat transfer coefficient according to


mm ID tube, Tsat= 5 °C, φ = 10 kW/m²..................................................................... 160

Figure 4.37 - Variation of enhancement factor 1ε for unit pumping power, for G = 75

kg/m²s, ϕ = 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).

................................................................................................................................ 163

Figure 4.38 – Variation of enhancement factor 2ε for the same pumping power, for G

= 75 kg/m²s, ϕ = 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled

symbols). ................................................................................................................ 164

Figure 4.39 – Variation of enhancement factor 2ε for the same pumping power, for G

= 200 kg/m²s, ϕ = 10 kW/m², Tsat = 15 °C, d = 12.7 mm (empty symbols) and di =

15.9 mm (filled symbols). ........................................................................................ 164

Figure 5.1 - Comparison of the experimental vapor quality data for the dryout

inception in plain tubes and the predictions according to the method of Wojtan et al.

(2005), Tsat = 15 oC and φ = 10 kW / m2 . ............................................................... 168

Figure 5.2 - Comparison between the experimental and predicted values of the heat

transfer coefficient during single-phase flows inside tube with twisted-tape insert, ID

=12.7 mm................................................................................................................ 170

Figure 5.3 - Flow images. (a) Stratified flow (y = 14, G = 75 kg / m2 s, x = 0.25, Tsat =

5 oC); (b) stratified wavy flow (y =14,G = 100 kg / m2 s, x = 0.20, Tsat = 5 oC); (c)

Anular flow ( y = 3, G = 150 kg / m2 s, x = 0.35, Tsat = 5 oC); (d) Dryout (y = 3, G =

200 kg / m2 s, x = 0.45, Tsat = 5 oC). ........................................................................172

Figure 5.4 - Flow pattern Schematic diagram..........................................................173

Figure 5.5 - Comparison between the method proposed in the present study and the

experimental heat transfer results for tubes with twisted-tape inserts. ....................175

Figure 5.6 - Results of the statistical analyses of the comparison between

experimental and predicted results according to the present method for different

experimental conditions, G = 75-200 kg / m² s, y=3-14, Tsat = 5 and 15°C, φ = 5 and

10 kW / m². ..............................................................................................................176

Figure 5.7 - Evolution of the heat transfer coefficient with vapor quality according to

the experimental results (symbols) and predictions according to the proposed method

(lines), ϕ = 10 kW / m², Tsat= 5 °C, G = 75 kg / m2 s and ID = 12.7 mm..................177

Figure 5.8 – Evolution of the heat transfer coefficient with vapor quality according to


(lines) , ϕ= 10 kW/m², Tsat= 15 °C, G = 75 kg / m2 s and ID = 15.9 mm..................178



(lines) , ϕ = 10 kW/m², Tsat= 5 °C, G = 100 kg / m2 s and ID = 12.7 mm.................178



(lines) , ϕ = 10 kW/m², Tsat= 15 °C, G = 100 kg / m2 s and ID = 15.9 mm...............179

Figure 5.11– Evolution of the heat transfer coefficient with vapor quality according to


(lines), ϕ = 10 kW / m²,Tsat = 5 °C, G = 150 kg / m2 s and ID = 12.7 mm................179



(lines) , ϕ = 10 kW/m², Tsat =15 °C, G = 150 kg / m2 s and ID = 15.9 mm...............180



(lines) , ϕ = 10 kW/m², Tsat = 5 °C, G = 200 kg / m2 s and ID = 12.7 mm................180



(lines) , ϕ = 10 kW/m², Tsat = 15 °C, G = 200 kg / m2 s and ID = 15.9 mm. ............ 181

Figure 5.15 - Comparism between experimental heat transfer data from Agrawal et

al. (1986) and the prediction by the present study proposed model. ...................... 182

Figure 5.16 - Comparism between experimental heat transfer data from Akhavan-

Behabadi et al. (2009b) and the prediction by the present study proposed model. 182

LIST OF TABLES

Table 2.1 – Coeficients for estimating two phase flow multipliers of Lockhart and

Martinelli (1949) apud Thome (2008)........................................................................ 49

Table 2.2 - Values of fluid dependent parameter . ............................................. 69

Table 2.3 - Values of the empirical constants of the Kandlikar (1990) method. ........ 69

Table 2.4 - Summary of predictive methods for the heat transfer coefficient during

flow boiling ................................................................................................................ 76

Table 2.5 - Variation of heat transfer coefficient estimated by the predictive methods

based on different experimental operating conditions............................................... 81

Table 2.6 - Summaries of some studies in the literature concerning single-phase

flows inside tubes containing twisted-tape inserts .................................................... 88

Table 2.7 - Description of the experimental studies concerning two-phase flow inside

tubes containing twisted-tape inserts........................................................................ 96

Table 3.1 - Uncertainty of the measured parameters.............................................. 130

Table 3.2 - Uncertainty of the calculated parameters ............................................. 130

Table 4.1 - Experimental conditions covered in the present study.......................... 131

Table 4.2 - Physical, chemical and thermodynamic properties of R134a ............... 132

Table 4.3 - Results of the statistical analysis of the comparison between experimental

data and predictive methods for frictional pressure drop in plain tubes. ................. 141

Table 4.4 – Results of the statistical analysis of the comparison between

experimental and predicted pressure drop data during two-phase flow in tubes with

twisted-tape inserts. ................................................................................................ 143

Table 4.5 – Results of the statistical analysis of the comparison between

experimental results for heat transfer coefficient during two-phase flow in plain tubes

and predictive methods from literature.................................................................... 150

Table 4.6 - Results of the statistical analysis of the comparison between experimental

results and predictive methods for heat transfer coefficient in tubes with twisted tape

inserts......................................................................................................................159

Table 5.1 - Results of the statistical analysis of the comparison between the

proposed method and the heat transfer experimental results, G = 75-200 kg / m² s,

Tsat = 5 and 15 °C, φ = 5 and 10 kW / m²................................................................175

Table A.1 - Coefficients of the equation for the pressure transducers and uncertainty

................................................................................................................................197

Table A.2 - Features of the thermometers used during calibration of the acquisition

system channel for temperature. .............................................................................198

Table A.3 - Coefficients for the reading temperature and estimated uncertainties for

the thermocouples channels....................................................................................198

Table A.4 - Characteristics of the multimeters used during the calibration of power

transducers..............................................................................................................200

Table A.5 - Coefficients and calculated uncertainty results of the active power

transducers..............................................................................................................200

Table B.1 – Flow boiling pressure drop experimental results for Tsat = 5oC under

adiabatic conditions inside 12.7 mm internal diameter tube ....................................202

Table B.2 - Flow boiling pressure drop experimental results for Tsat = 15oC under


Table B.3 - Flow boiling pressure drop experimental results for Tsat = 5oC under


Table B.4 - Flow boiling pressure drop experimental results for Tsat =15 oC under


Table B.5 - Flow boiling heat transfer coefficient experimental results with local

saturation temperature Tsat = 5 oC measured at each section of the of the test section

inside 12.7 mm internal diameter tube ....................................................................230


saturation temperature Tsat = 15 oC measured at each section of the of the test

section inside 12.7 mm internal diameter tube ........................................................242


saturation temperature Tsat = 5 oC measured at each section of the of the test section

inside 15.9 mm internal diameter tube.................................................................... 247


saturation temperature Tsat = 15 oC measured at each section of the of the test

section inside 15.9 mm internal diameter tube........................................................ 258

SUMMARY _Toc387378716

1INTRODUCTION ..........................................................................................27

1.1 Objectives..............................................................................................29

1.2 Thesis structure .....................................................................................30

2 LITERATURE REVIEW ...............................................................................31

2.1 Introduction............................................................................................31

2.2 Definitions of terms used in two-phase flows.........................................31

2.3 Two-phase flow parameters ..................................................................32

2.4 Two-phase flow patterns during convective boiling ...............................35

2.4.1 Flow patterns in horizontal two-phase flows....................................35

2.4.2 Flow pattern predictive methods......................................................37

2.5 Fundamentals of convective boiling.......................................................43

2.6 Pressure drop ........................................................................................45

2.6.1 Correlations to predict single-phase frictional pressure drop inside

plain tube..................................................................................................46

2.6.2 Methods to predict two-phase flow pressure drop in plain tubes.....48

2.7 Comparisons from the literature of the two-phase frictional pressure drop

predictive methods ......................................................................................57

2.8 Heat transfer during convective boiling..................................................60

2.8.1 Introduction .....................................................................................60

2.8.2 Predictive methods for flow boiling heat transfer coefficient............61

2.9 Studies concerning twisted-tapes. .........................................................83

2.9.1 Introduction .....................................................................................83

2.9.2 Single-phase flow studies................................................................84

2.9.3 Flow boiling in tube contaninig twisted-tape insert ..........................97

2.9.4 Conclusions based on the literature review...................................106

3 EQUIPMENT, EXPERIMENTAL PROCEDURE AND DATA REDUCTION108

3.1 Introduction ......................................................................................... 108

3.2 Experimental bench ............................................................................ 109

3.2.1 Test section .................................................................................. 110

3.2.2 Visualization sections ................................................................... 112

3.2.3 Pressure drop measurement instruments..................................... 112

3.2.4 Temperature measurements......................................................... 113

3.2.5 Pre-Heater Section ....................................................................... 114

3.2.6 Flow Stabilization section.............................................................. 114

3.2.7 Sub-Cooler.................................................................................... 115

3.2.8 Condenser .................................................................................... 115

3.2.9 Reservoir ...................................................................................... 115

3.2.10 Micro Pump................................................................................. 116

3.2.11 Flow meter .................................................................................. 116

3.3 Ethylene-Glycol/Water Solution Circuit ............................................... 116

3.4 Control and Data Acquisition System.................................................. 116

3.5 Twisted-tape inserts ............................................................................ 118

3.6 Experimental procedure...................................................................... 120

3.6.1 Single-phase flow tests ................................................................. 120

3.6.2 Two-phase flow test...................................................................... 121

3.7 Data reduction Procedures ................................................................. 122

3.7.1 Pressure drop ............................................................................... 123

3.7.2 Heat Exchange with environment ................................................. 124

3.7.3 Heat transfer coefficient ................................................................ 125

3.8 Validation of the experimental bench and determination of the

uncertainty ................................................................................................ 126

3.8.1 Single-phase pressure drop experimental data validation ............ 126

3.8.2 Single-phase flow heat transfer experimental data validation....... 126

3.9 Uncertainty analysis ............................................................................129

4 EXPERIMENTAL RESULTS......................................................................131

4.1 Pressure drop results ..........................................................................132

4.1.1 Pressure drop for tubes without twisted-tape inserts.....................132

4.1.2 Pressure drop for tubes with twisted-tape inserts..........................134

4.1.3 Comparison between the experimental frictional pressure drop

results and the predictive methods.........................................................138

4.1.4 Evaluation of the pressure drop penalty due to twisted-tape inserts

..........................................................................................................................144

4.2 Heat transfer coefficient results ...........................................................146

4.2.1 Results for tubes without twisted-tape...........................................147

4.2.2 Comparison between the experimental heat transfer coefficients

results for tubes without twisted-tape inserts and the predictive methods.

...............................................................................................................149

4.2.3 Results for tubes with twisted-tape inserts ....................................150

4.2.4 Comparison between the experimental heat transfer coefficient

results for tubes with twisted-tape inserts and the predictive methods...157

4.2.5 Overall Performance of the heat transfer enhancement technique160

5 PREDICTIVE METHOD FOR HEAT TRANSFER COEFFICIENT DURING

FLOW BOILING INSIDE TUBES CONTAINING TWISTED-TAPE INSERTS166

6 CONCLUSIONS AND RECOMMENDATIONS..........................................183

6.1 Conclusions.........................................................................................183

6.2 Recommendations for future studies ...................................................185

REFERENCES .............................................................................................187

Appendix A – Calibration of the Experimental measuring equipments .........195

A.1 Uncertainty analysis ............................................................................195

A.2 Absolute pressure transducers............................................................196

A.3 Flowmeter ...........................................................................................197

A.4 Calibration of thermocouples channels ...............................................197

A.5 Calibration of the active power transducers........................................ 199

A.6 Characteristics of differential pressure transducers............................ 201

Appendix B – Experimental Data.................................................................. 202

Appendix C – Publications ........................................................................... 263

Introduction 27

1INTRODUCTION

The convective boiling mechanism has been under intense research over the

last three decades. This is initially result of the fact that most of refrigerants used in

the refrigeration and air-conditioning sectors until the 80’s were related to the

depletion of the ozone layer. During the 1980’s, the refrigerant R134a came up as

the solution and its use spreads rapidly, because its impact on the ozone layer is

negligible. From the mid-90’s, attention has been devoted to the global warming.

Therefore, based on the fact that R134a presents a high global warming potential,

researchers have started to focus on the development of new refrigerants, parallel to

the revival of natural fluids, e.g. ammonia and hydrocarbons.

Independently of the refrigerant choice, results have shown that the refrigerant

leakages, relative to the total refrigerant inventory in the system, increase with

increasing the refrigerant total charge. Ribatski (2008) have shown that leaks are

inevitable and can only be minimized. Most of the refrigerant inventory is located in

the heat exchangers. So, by minimizing the heat exchanger size, both the refrigerant

inventory and the material used for its manufacture are reduced resulting in lower

initial and operational costs. Moreover, the environmental impact during the system

lifetime is also reduced, since, as pointed out by Ribatski (2008), decreasing the

refrigerant inventory implies that the amount of refrigerant leakage decreases in both

relative and absolute values. Under this scenario, several researches have been

developed focusing on new refrigerants and heat transfer enhancement without

major pressure drop penalties in order to reduce the refrigerant inventory and

improving the system efficiency. One of the alternatives to achieve such an objective

is the use of twisted-tape inserts.

Bergles (1999) defines twisted-tape inserts as passive heat transfer

enhancement technique, i.e. it does not require external energy source to increase

the heat transfer coefficient. Sarviya and Veeresh (2012) reported twisted-tape

inserts as one of the important swirl flow devices for passive heat transfer

augmentation. The implementation of this technique occurs through the twisting of a

metal tape which is then fixed internally inside a smooth tube.

28 Introduction

According to Manglik and Bergles (1993), twisted-tape inserts have been used for

over a century, dating from 1896. This technique presents advantage over other

techniques due to the low manufacturing costs, easy installation and maintenance,

and according to Thome and Ribatski (2005) the possibility of being used to retrofit

heat exchangers already in use.

Similarly to most of the heat transfer enhancement techniques, the heat

transfer coefficient enhancement given by twisted-tape inserts is accompanied by a

drastic increase in the pressure drop, impacting the pumping power and,

consequently, the system efficiency. Bandarra-Filho and Saiz-Jabardo (2006) have

pointed out that the use of inserting devices especially in dry expansion evaporator

coils are in fact efficient in upgrading the heat transfer coefficient but at the cost of

significant pressure drop augmentation. However, Shatto and Peterson (1996)

highlighted the fact that the negative result of increasing the pressure drop gradient

by the use of inserts can be overcome by a reduction in the heat exchanger size due

to the heat transfer enhancement. Therefore, to effectively estimate the net benefits

of enhancing heat transfer rates through the use of this device in practical heat

exchangers, both the heat transfer and pressure drop characteristics must be known.

Moreover, since the results of the comparison among the predictive methods

from the literature for heat transfer coefficient during two-phase flow inside tube

containing twisted-tape inserts revealed notable discrepancies. Therefore, an

accurate heat transfer predictive method taken into account the swirl effects

promoted by the tape on the heat transfer coefficient inside horizontal tubes

containing twisted-tapes inserts is still necessary and is one of the objectives of the

present study.

The present study was developed in order to determine when the effect on the

heat exchanger efficiency of this heat transfer enhancement technique overcomes

pressure drop penalties. For this purpose, an experimental investigation has been

conducted to evaluate the effect of twisted-tape inserts on the heat transfer

coefficient and pressure drop augmentations during flow boiling inside horizontal

tubes. The experiments were performed for R134a in 12.7 and 15.9 mm ID tubes.

The overall performance was evaluated according to the following parameters: the

ratio between the heat transfer coefficients per unit of pumping power of the tube with

and without twisted-tape; and the ratio of heat transfer coefficients of the tube with

Introduction 29

and without twisted-tape for the same pumping power keeping the same tube

diameter, vapor quality, saturation temperature and heat flux.

1.1 Objectives

The present study has the general objective of investigating pressure drop and

heat transfer during convective boiling under saturated conditions inside tubes with

twisted-tape inserts.

The specific objectives are the following:

i. Perform an extensive review of the literature concerning flow boiling inside

horizontal plain tubes with and without twisted-tape inserts;

ii. Obtain a broad database for flow boiling inside horizontal tubes with and

without twisted-tapes including pressure drop and heat transfer coefficient

results and based on this database evaluate, the accuracy of heat transfer and

pressure drop predictive methods available in the literature;

iii. Characterize conditions under which the use of twisting tape is favourable,

considering the following parameters: the ratio between the heat transfer

coefficients per unit of pumping power of the tube with and without twisted-

tape and the ratio of heat transfer coefficients of the tube with and without

twisted-tape for the same pumping power. These parameters are given by the

following equations, respectively:

(1.1)

(1.2)

iv. Perform a parametric analysis of the experimental results;

v. Develop a heat transfer predictive method taken into account the swirl effects

promoted by the tape on the heat transfer coefficient.

30 Introduction

1.2 Thesis structure

The structure of this text is composed of literature review, description of the

experimental setup and procedures, presentation and discussion of the experimental

results, development of a new heat transfer model and conclusions.

Below, the chapters of this thesis are briefly described and contextualized.

Chapter 2 presents the review of the literature concerning this study. Definition

of terms applied to two-phase flows and fundamental aspects of convective boiling

are presented. A section is devoted to two-phase flow patterns during convective

boiling inside tubes without twisted-tape. A study of literature concerning flow boiling

pressure drop and heat transfer coefficient with and without twisted-tape is

presented. Description of twisted-tape and models to predict heat transfer coefficient

and pressure drop are also presented.

Chapter 3 presents a description of the apparatus used for the experimental

campaing. The experimental conditions tested are defined and data reduction

procedures are detailed. Validation of the experimental bench and the analyses of

experimental uncertainties are also presented in this chapter.

Chapter 4 presents the heat transfer coefficient and pressure drop

experimental results for convective boiling inside a horizontal tube for plain tubes with

and without twisted-tape inserts. This chapter also presents comparisons of the

experimental results against predictive methods from literature. Moreover, an

analysis of the experimental results given in terms of heat transfer enhancements

and pressure drop penalty factors is also presented.

Chapter 5 is dedicated to the development of a new predictive method based

on the experimental results obtained in present study for estimating the heat transfer

coefficient during convective boiling inside horizontal tubes containing twisted-tape

inserts.

Finally, in Chapter 6 conclusions from the present study are presented.

Suggestions and recommendations for future studies are also provided.

Literature review 31

2 LITERATURE REVIEW

2.1 Introduction

This chapter reviews the main aspects of the literature related to the present

study. Two-phase flow terms are defined and the fundamentals of convective boiling

are presented. A section is devoted to the literature concerning flow patterns,

pressure drop and heat transfer during convective boiling inside horizontal tubes

without twisted-tape. Leading correlations and models to predict heat transfer

coefficient and pressure drop for plain tubes without twisted-tapes are described.

Finally, a section dealing with the literatures concerning heat transfer and pressure

drop during flow boiling and single-phase flow inside horizontal tubes containing

twisted-tape inserts is also presented.

2.2 Definitions of terms used in two-phase flows

The term “phase” is a thermodynamic definition of a state of matter. Generally

the following three states of matter are defined: solid, liquid and gas. Thus, the

simplest case of multiphase flow in which two phases are present for a pure

component is reffered to as two-phase flow.

The following three analytical parameters are considered in the definition of

terms for two-phase flows:

1. Primary parameters:

• Thermal: power;

• Hydraulics: pressure, mass flow rate, fluid temperature, pressure drop;

• Geometry: flow and heated areas, hydraulic and equivalent diameters;

2. Calculated parameters:

• Mass velocity, heat flux, vapor quality and void fraction;

3. Fluid properties:

• Density, viscosity, enthalpy, surface tension, thermal conductivity and

heat capacity.

Below, the definitions of the calculated parameters in two-phase flow from the

primary parameters are given.

32 Literature review

2.3 Two-phase flow parameters

Consider the flow of liquid and vapor in a tube as shown in Fig. 2.1, the total

mass flow rate along the tube is equal to the sum of the mass flows of the liquid, ,

and vapor, phases as follows:

(2.1)

Figure 2.1 - Two-phase flow (liquid-vapor) in a tube (Kanizawa, 2011).

Vapor quality is defined as the ratio of vapor mass flow rate and the total mass

flow rate given as follows:

(2.2)

Thermodynamic equilibrium vapor quality can be deduced from an energy

balance along a tube length and is given as follows:

( ) Lth

LV

i z ix

i

−=

(2.3)

where Li is the enthalpy of the saturated liquid,

LVi is the latent heat of evaporation,

both estimated at the saturation temperature at the position z along the tube length.

In Eq. (2.3) ( )zi is the average local fluid enthalpy in a given cross section at

position z and th

x is the thermodynamic equilibrium vapor quality.


In case of thermodynamic equilibrium the mass based vapor quality becomes

similar to the thermodynamic equilibrium vapor quality. Usually studies concerning

flow boiling of pure fluids assumes thermodynamic equilibrium and xxth = . So, in the

present study thermodynamic equilibrium will be assumed and thxx = .

The mass velocity of each phase is defined as the ratio between the

correspondent mass flow rate of the phase and the total cross-sectional area of the

tube. Therefore the mass velocity for the liquid phase and vapor phase are given by

the following equations, respectively:

( )A

xmGL

−=

1&

(2.4)

A

xmGV

&=

(2.5)

Hence, the mass velocity of the mixture is given by the sum of the mass

velocity of the two phases:

VL GGG += (2.6)

The mean velocity (insitu velocity) of each phases are the mean velocities at

which the phases actually travel. The mean cross-sectional velocities of the phases

are determined by the ratio of volumetric flow rates and the respective cross-

sectional areas occupied by each phase given as:

(2.7)

(2.8)

where is the superficial void fraction defined as the cross-sectional area occupied

by the vapor relative to the total area of the channel cross-section. This is an

important parameter used to determine the flow pattern transition, heat transfer

coefficient and two-phase pressure drop. The void fraction is defined as:

(2.9)


where is the time averaged cross sectional area of the channel occupied by

vapor.

From the equation of continuity, it is possible to define liquid and vapor phase

means velocities as follows:

(2.10)

(2.11)

The superficial velocities L

j and Vj are defined as the ratio of the volumetric

flow rate of each phase and the total cross-sectional area of the channel. The

superficial velocities are given as follows:

(2.9)

(2.10)

The two-phase superficial velocity is the sum of the liquid and vapor superficial

velocities and is given as follows:

L Vj j j= + (2.11)

The local drift velocities are defined as the velocity of each phase relative to

the two-phase superficial velocity as follows:

Lj LV V j= − (2.12)

Vj VV V j= − (2.13)

The drift fluxes and are defined as follows:

(2.14)

(2.15)


2.4 Two-phase flow patterns during convective boiling

Liquid-vapor flows inside tubes present different two-phase flow topologies as

the liquid phase evaporates. These topologies are commonly referred to as flow

pattern. The predominant mechanisms defining the heat transfer coefficient and

pressure drop are influenced by the flow pattern. So, to predict accurately heat

transfer and pressure drop, it is necessary that the prediction methods incorporate

flow pattern characteristics. The flow pattern depends on many parameters such as

liquid and vapor velocities, void fraction, tube inclination and geometry, surface

roughness, pressure and fluid properties. Different nomenclature and classifications

are adopted for flow patterns by distinct authors.

During convective boiling, different flow patterns occur and consequently

different heat transfer mechanisms may be dominant depending on the operating

conditions such as mass velocity, vapor quality and heat flux. Distinct two-phase flow

patterns can be observed depending on the orientation of the tube, whether vertical

or horizontal. One of the main differences is often a tendency to stratification that

occurs in horizontal flows and convectional tubes due to gravitational forces.

The settings of flow patterns in horizontal tubes are more complex than those

observed in vertical tubes. In vertical tubes, the annular flow pattern is almost

symmetrical and the distribution of the average liquid film thickness along the tube

perimeter is almost uniform. For horizontal tubes and reduced mass velocities,

gravitational force determines the two-phase distribution. For low mass velocities and

moderate vapor qualities, gravitational force pulls the liquid downward and makes the

vapor buoyant. Under these conditions, the lower region of the tube presents a

thicker liquid film, while in the upper part of tube the liquid is absent. In the present

study, emphasis is given to two-phase flow patterns occurring for horizontal flows.

2.4.1 Flow patterns in horizontal two-phase flows

The flow patterns observed in horizontal two-phase flows are asymmetrical due

to the influence of gravity. The generally accepted flow pattern are shown in Fig. 2.2

and characterized as follows:

• Bubbly flow: The gas (or vapor phase) is distributed as discrete

bubbles in a continuous liquid phase. The average size of bubbles is


usually small compared with the tube diameter. At high mass velocities,

the bubbles distribution tend to be more uniform within the liquid.

• Stratified flow: This flow pattern is characterized by segregation of

liquid phase at the tube bottom (under normal gravity conditions) and

vapor at the top. Some authors subdivided this flow pattern into

stratified smooth and stratified wavy. The stratified smooth occurs for

lower vapor velocities. The stratified wavy is also known as wavy flow.

• Wavy flow: This flow pattern is also characterized by the liquid phase

flowing in the bottom and the vapor in the upper part of the tube and

occurs when the vapor velocity is high enough to induce waves on the

liquid-vapor interface. The amplitude of the waves depends on the

relative velocity between the phases and the properties of the fluids,

such as their density and surface tension.

• Plug flow: This is an intermittent flow that occurs at low vapor flow

rates and moderate liquid flow rates. For this flow pattern, liquid plugs,

free of entrained gas bubbles, are separated by zones of elongated

vapor bubbles. The coalescence of the small bubbles rise to larger

bubbles, elongated and occupying the top portion of the tube. Plug flow

is also termed as elongated bubbles.

• Slug flow: When the vapor velocity increases from plug flow, the liquid

slugs become aerated and contain small bubbles. The two-phase

distribution for slug flow is more chaotic compared with plug flow and

the interface between vapor and liquid is not clearly defined.

• Annular flow: Annular flow pattern is characterized by the presence of

a continuos liquid film along the inner surface of the tube and the vapor

phase in the core. For horizontal tubes, the film is asymmetric, with the

thicker liquid film at the bottom of the tube. This behavior is due to the

gravitational effects that tends to reduce the film thickness at the top of

the tube and increases its value on the lower part of the tube.

• Dryout (Not shown in Fig. 2.2): This flow pattern occurs when an

evaporating annular film progressively dries out from the upper part of

the tube with increasing vapor quality


• Mist flow: This flow pattern occurs when all the liquid is entrained in the

vapor core under high vapor velocity conditions. The vapor phase flows

as a continuous phase and the liquid in the form of droplets is

continued.

In general, these flow patterns can be grouped according to the following:

(1) Dispersed flows: One phase is dispersed in the other that flows as a continuous

phase. The main flow patterns associated are bubbly and mist flows.

(2) Separated-phases: as the denomination suggests, the liquid-vapor interface is

well defined. Such flows are typical of stratified and annular patterns, which

include most of the applications in refrigeration.

(3) Mixed flows: The flow pattern are characterized by the combination of the groups

mentioned. This group includes the slug pattern where bubbles of reasonable

dimension flow intermittently, separated by liquid plugs containing small bubbles

dispersed within the liquid.

Figure 2.2 - Flow patterns observed in horizontal tubes, Cheng et al. (2008).

2.4.2 Flow pattern predictive methods

In the 50’s, two dimensional maps to predict flow pattern began to appears in

the literature. They are attempts to characterize flow patterns based on two-

dimensional plots containing transition lines segregating regions corresponding to the

different flow patterns. Generally, these maps were developed for adiabatic and

isotherm conditions and are based on liquid and gas velocities as coordinate axis.

Superficial velocities and dimensionless groups containing superficial and insitu

velocities of both phases are also used.


In case of diabatic conditions, generally, the mass velocity and vapor quality are used

in the vertical and horizontal axis, respectively. This procedure allows to follow the

flow pattern transitions with vapor quality variation as the liquid evaporates.

The flow pattern maps available in literature were first developed for nuclear and

petrochemical industries, in this case for flow of oil and gas in large diameter pipes.

Figure 2.3 illustrates the map developed by Baker (1954), based on data for air-water

and oil-water flows.

Figure 2.3 - Flow pattern map for horizontal flow (Baker 1954).

Taitel and Dukler (1976) were the pioneers to develop a method for prediction

of flow patterns based on physical mechanisms present in two-phase flows. In this

method, all parameters of interest are dimensionless and compared with

phenomenological grounded transition curves. The method of Taitel and Duker

(1976) is based on the equations of conservation of mass and momentum assuming

equilibrium stratified flow in slightly inclined pipes. They transformed these equations

to dimensionless form and obtained their solution based on phenomenological

transition criterions. According to Taitel and Duker, transitions are based on the

following physical mecanisim i) Transition between stratified and intermittent or

annular flow patterns: it takes place when the interface becomes unstable as a result

of Kelvin-Helmholtz instability and a finite amplitude wave on the liquid surface

grows; ii) Transition between intermittent and dispersed regimes: taking place when

the turbulent flunctuations are strong enough to overcome buoyant forces acting in

the gas; iii) Transition beteewn intermittent and annular regimes: from the stratified


flow pattern depending on the liquid level either intermittent or annular flow will

develop, 0.5 being the threshold value of the ratio between the liquid level and the

tube diameter.

In the late 90’s, Kattan et al. (1998) based on Steiner (1993) proposed two-

phase flow pattern predictive method for evaporation of halocarbon refrigerants in

horizontal tubes. A flow pattern map based on the predictive method of Kattan et al.

(1998) is illustrated in Fig. 2.4. This predictive method was developed based on flow

pattern data for five refrigerants covering a wide range of mass velocities and vapor

qualities containing about 700 data points. The method of Kattan et al. (1998)

characterizes the following flow patterns: fully stratified, stratified-wavy, intermittent,

annular flow and mist flow. Their new method predicted correctly 96.2 % of their

experimental data.

Figure 2.4 - Flow pattern map for R134a at Tsat = 30 oC in a 10 mm internal diameter tube for ϕ = 10 kW / m2 using G = 100 kg / m2 s (Kattan et al. 1998).

Zücher et al. (1999) modified the flow pattern transitions proposed by Kattan et

al. (1998) based on new observation for ammonia: stratified to stratified-wavy and

stratified-wavy to intermittent and annular. These modifications were based on the

fact that the authors noted that the heat flux effects according to Kattan et al. (1998)

method were over estimated by predicting the transition from annular to stratified-

wavy flow at too low vapor qualities. Later on, in order of obtaining better predictions

of their data , Zücher et al. (2000) and Zücher et al. (2002) proposed the use of Taitel

and Dukler (1976) void fraction models for fully stratified flow and the Rouhani and

Mas

s ve

loci

ty [

kg/m

2 s]

Vapor quality [-]


Axelsson (1992) void fraction model for intermittent and annular flows and the

interpolations between both models for stratified-wavy flows. However, the gain of

accuracy by using this void fraction prediction procedure is neglible compared to the

gain of complexity for its implementation. As a practical option, a new and easier to

implement version of the method were proposed by Thome and El Hajal (2002).

These authors introduced the Rouhani and Axelsson (1993) correlation for the void

fraction instead of using Taitel and Dukler (1976) approach.

Wojtan et al. (2005) working with an optical procedure to measure the void

fraction, noted that the stratified/wavy region of the Kattan et al. (1998) method

should be divided into three sub-regions corresponding to the following flow patterns:

slug, slug-stratified/wavy and stratified/wavy. These regions occur at lower vapor

qualities than the intermittent-annular transition. Moreover new dryout and mist flow

patterns were also developed based on their experimental data. By adding these new

flow patterns Wojtan et al. (2005) modified the previous method of Kattan et al.

(1998), for determining flow patterns in conventional horizontal pipes. This method,

whose flows pattern are illustrated in the map shown in Fig. 2.5, is based on

experimental results for R22 and R410A gathered for tubes with internal diameters

between 8.00 and 13.84 mm.

In the method of Wojtan et al. (2005) and Kattan et al. (1998), the parameter

that defines the flow structure and the parcels of the tube perimeter in contact with

the liquid and gas is the dry angle defined as shown in Fig. 2.6:

Figure 2.5 - Flow pattern map evaluated for R22 at Tsat = 5 oC in a 13.84 mm internal diameter tube for

ϕ = 2.1 kW/m2 using G = 100 kg / m2 s to calculate the void fractions. (Wojtan et al. 2005).


Figure 2.6 - Simplified stratified flow configuration, Kattan et al. (1998).

Wojtan et al. (2005) kept the equation proposed by Kattan et al. (1998) to

determine the stratified to stratified-wavy flow transition boundary given as follows:

(2.16)

The same equation proposed by Kattan et al. (1998) for the transition between

stratified-wavy to intermittent and annular flow was kept by Wojtan et al. (2005) and

is given as follow:

(2.17)

where the liquid Froude number and the liquid Weber number are defined

as:

(2.18)

(2.19)

The dimensionless geometrical parameters , and in Eqs. (2.19)

and (2.20) are determined as follows:

(2.20)


(2.21)

(2.22)

The void fraction is calculated using the same equation proposed by

Rouhani and Axelsson (1970) and modified by Steiner (1993) given as follow:

(2.23)

where the stratified angle is calculated with the equation proposed by Biberg

(1999) given as follow:

(2.24)

Wojtan et al. (2005) obtained the new flow patterns: slug, slug-stratified/wavy

and stratified/wavy shown in Fig. 2.5 by modified the stratified-wavy flow patterns

proposed by Thome-El Hajal (2002) as follows:

1. A new transition line is added at Gstrat = Gstrat(xIA) at x < xIA (this creates a

new horizontal transition line to the left of xIA and modifies the boundary of the

stratified (S) regime).

2. The stratified-wavy region is divided into three subzones:

• For G > Gwavy(xIA) , this becomes the slug zone.

• For Gstrat < G < Gwavy(xIA) and x < xIA, this becomes the slug/stratified-

wavy zone.

• For x ≥ xIA, this remains as the stratified wavy zone.

Wojtan et al. (2005) developed correlations to predict dryout inception and

completion vapor qualities based on their experimental data keeping the same

dimensionless equations proposed by Mori et al. (2000). The dryout inception and

completion vapor qualities equations are given as follows:

( ) ( )[ ]70.0crit

25.0LV

37.0V

17.0V FrW235.052.0

di e58.0xφφρρ−= (2.25)


( ) ( )[ ]27.0crit

.09.0LV

15.0V

38.0V

3FrW10.8.557.0

de e61.0xφφρρ −−−= (2.26)

where the is calculated using the same equation proposed by Kutateladze

(1948) given as follow:

(2.27)

After isolating the mass velocity as function of vapor quality in Eqs. (2.29) and

(2.30), the following flow pattern transitions equations were proposed by Wojtan et al.

(2005) for predicting dryout and mist flow pattern curves, respectively:

(2.28)

(2.29)

2.5 Fundamentals of convective boiling

According to Collier and Thome (1994), convective boiling also named in the

literature as flow boiling is defined as the addition of heat to a forced flow of liquid

such that vapor is generated. Convective boiling often combines high heat transfer at

low mass flow rates, as well as a nearly constant temperature along the heat

exchanger length due to the thermally saturated nature of a liquid-vapor mixture.

Convective boiling can occur under sub-cooled and saturated conditions, depending

on the fluid temperature. In case of sub-cooled condition, the bubble nucleation

occurs with the liquid average temperature lower than the saturation temperature. In

saturated condition, convective boiling occurs with liquid average temperature higher

than the liquid saturation temperature.

Figure 2.7 shows how the temperature, heat transfer coefficient and heat

transfer mechanisms varies with the flow pattern during the evaporation process.

Whilst the liquid is being heated up to the saturation temperature and the wall


temperature remains below that necessary for nucleation, the process of heat

transfer is single phase convective heat transfer to the liquid phase (region A). At

some point along the tube, the wall superheat is enough such that the formation of

vapor from nucleation sites can occur. Initially vapor formation takes place in the

presence of subcooled liquid (region B). From the subcooled boiling region, the

variation of the wall temperature along the tube length is reduced when compared

with single-phase flow. As the vapor quality increases through the saturated nucleate

boiling region (region C) a point may be reached where the predominant heat

transfer mechanism changes from nucleate boiling to conduction through a thin film

and evaporation at the liquid-vapor interface. This transition is preceded by a change

in the flow pattern from bubbly or slug flow to annular flow (region D). In the latter

regions, the thickness of the thin liquid film on the heating surface is such that its

temperature gradient is high and bubble nucleation is suppressed. At some critical

value of the vapor quality the complete evaporation of the liquid film occurs. This

transition is known as ' dryout ' and is accompanied by a drastic rise in the wall

temperature for channels operating with a controlled surface heat flux. In this region

mist flow can occur due to entrainment and deposition of liquid droplets on the tube

surface in (region E). The region comprising the surface dryout and the transition to

dry saturated vapor (region F) is termed as the liquid deficient region. These effects,

and drying of the wall, are the mechanisms that limit the maximum heat transfer rate

for a given flow in a tube.


Figure 2.7 - Heat transfer and flow pattern behavior during convective boiling (Collier and Thome, 1994).

2.6 Pressure drop

The accurate prediction of the pressure drop in direct expansion and flooded

evaporator as well as in tube-side and shell-side condensers is an important design

parameters for the optimization of refrigeration, air-conditioning and heat pump

systems. The pressure drop along heat exchangers may dramatically affects the

pumping power and the efficiency of the system.

The pressure drop during convective boiling inside a tube is made up of the

following parcels:

Gravitational pressure drop due to the pressure head ;

Accelerational pressure drop due to the variation of kinetic flow energy, which

may result from phase changes, compressibility and of cross section variation;

Frictional pressure drop due to viscous dissipation of the fluids at the tube wall

and between the phases, (interface).

The total pressure drop gradient is given by the sum of these parcels as

follows:

fricaccgravtotal dz

dp

dz

dp

dz

dp

dz

dp

+

+

=

(2.30)


In horizontal flows, the gravitational parcel is null. The accelerational pressure drop

gradient for two-phase flows in tubes of constant cross-section and for constant mass

velocity is given by:

(2.31)

where for halocarbon refrigerant and convectional tubes can be

calculated from Steiner version of the Rouhani and Axelson drift flux model given by

Eq. (2.26) as suggested by Wojtan et al. (2005).

2.6.1 Correlations to predict single-phase frictional pressure drop inside plain

tube

In several methods from the literature the two-phase flow pressure drop is

generally given as a function of the single-phase flow of liquid or gas. So, in this item

a brief review on the predictive methods for single-phase frictional pressure drop

inside tubes is provided.

The frictional pressure drop gradient for single-phase flow is given as a

function of the friction factor as follows:

(2.32)

where f is the friction factor of Fanning Type.

For developed laminar flow regime inside circular tubes, characterized by

Reynolds number less than 2300, the frictional factor is given by:

Re

16f = (2.33)

where the Reynolds number is defined as follows:

µiGd

Re = (2.34)


For fully developed turbulent flow characterize by Reynolds number higher

than 4000, the friction factor can be estimated through the Blasius’ equation for

smooth tube given by:

25.0Re

079.0f = (2.35)

The limiting values for using Eq. (2.38) is Reynolds number less than .

In case of tubes with rough surface, pressure drop predictive methods were

proposed based on the tube relative roughness given by ratio of the surface peak-to-

valley roughness and the characteristic dimension of the channel cross section.

Based on experimental data, Colebrook (1939) apud White (1998), adjusted the

following correlation for prediction of the friction factor in a tube with rough surface

during turbulent flow:

+−=

2/1

ir

2/1)4/fRe(

51.2

7.3

d/log0.2

)4/f(

1 ε (2.36)

According to White (1998), Eq. (2.39) is recommendable for Reynolds number

higher than 4000. In this method, the friction factor is obtained through iterative

process. Based on this, Haaland apud White (1998) proposed an alternative explicit

form to obtain the friction factor based on Colebrook, given by:

+−=

11.1

ir

2/17.3

d/

Re

9.6log8.1

)4/f(

1 ε (2.37)

Presenting maximum error less than 2 %, when compared against the original

correlation.

Churchill (1977) proposed the following correlation to estimate the friction

factor in rough surface tubes, valid for both laminar and turbulent flow regimes:

12/12/3

1616

9.0

ir

12

Re

37530

Re

7d27.0log457.2

Re

82f

+

++

=

−

ε (2.38)


It is worth noting that the methodology proposed by Churchill is explicit, in the

sense that the method does not required iteration to determine the friction factor.

2.6.2 Methods to predict two-phase flow pressure drop in plain tubes

2.6.2.1 Separate-phase methods

The majority of predictive methods for two-phase frictional pressure drop in the

literature were proposed based on separate-phase flow approach. This method

considers that phases are artificially separated into two streams flowing in its own

pipe. The first of these analyses was performed by Lockhart and Martinelli (1949)

and then followed by many others.

Lockhart and Martinelli (1949)

Lockhart and Martinelli (1949) performed pioneering work to evaluate two-

phase friction pressure drop gradient using two-phase multipliers for adiabatic air-

water mixtures at atmospheric pressure. The two-phase multipliers were defined

according to the following equations:

L

22

L

dz

dp

dz

dp

= ΦΦ (2.39)

V

22

V

dz

dp

dz

dp

= ΦΦ (2.40)

In Eqs. (2.42) and (2.43), Φ is reffered to as a two-phase multiplier, 2

dp

dz Φ

is the

two-phase flow frictional pressure drop gradient, L

dp

dz

and V

dp

dz

are frictional

pressure drop gradients assuming that each phase flows alone in a tube of the same

diameter where occurs the two-phase flow.


The single-phase pressure drop gradients L

dp

dz

and V

dp

dz

are estimated

according to Eq. (2.35) with the frictional factor given by Eq. (2.38).

The two phase flow multipliers are given by:

,X

1

X

C1

2

tttt

2

L ++=Φ for LRe < 4000 (2.41)

,XCX12

tttt

2

V ++=Φ for LRe > 4000 (2.42)

where ttX is the Martinelli parameter for both phases assumed as turbulent flow,

given as follows:

1.0

V

L

5.0

L

V

9.0

ttx

x1X

−=

µ

µ

ρ

ρ (2.43)

The values of the parameter C adjusted experimentally by Chisholm (1967)

are defined according to the flow regime of each phase as shown in Tab. 2.1

Table 2.1 – Coeficients for estimating two phase flow multipliers of Lockhart and Martinelli (1949) apud Thome (2008)

Liquid Gas C

Turbulent Turbulent 20

Laminar Turbulent 12

Turbulent Laminar 10

Laminar Laminar 5

Friedel (1979)

Friedel (1979) proposed an empirical correlation based on a two-phase

multiplier assuming the two-phase mixture flowing as liquid in a tube with the same

diameter for vertical upward and horizontal flows in round tubes given by:

035.0

0L

045.0

H

Fr

0L

22

0LWeFr

FH24.3C

dz

dp

dz

dp

+=

= ΦΦ (2.44)


In which the parameters FrC , F and H are given by:

( )0L

0V

V

L22

Frf

fxx1C

+−=

ρ

ρ (2.45)

( ) 224.078.0 x1xF −= (2.46)

( )0.91 0.19 0.7

0.240.78 1 1V VL

V L L

H x xµ µρ

ρ µ µ

= − −

(2.47)

It can be noted that the term is a modified Martinelli parameter and so

correlates similar effect as turbulent flow.

The friction factor 0Lf and 0V

f are estimated according to Eq. (2.38) assuming

the two-phase mixture flowing as liquid in a tube of the same diameter. H

Fr is the

homogeneous Froude number relating inertial and gravitational effects and is given

by:

i

2

H

2

Hdg

GFr

ρ= (2.48)

The homogeneous density that takes into account vapor quality effects is

given by the equation below:

1

LV

H

x1x−

−+=

ρρρ (2.49)

The Froude number and Weber number of the two-phase mixture flowing as

liquid contemplate the inertial and surface tension effects related to the interface

disturbances and consequently related to the flow pattern transition. The Weber

number is calculated according to Eq. (2.22).

Friedel (1979) used an experimental database containing 25,000 data points

in order to adjust his method. He obtained a standard deviation of approximate 30 %

when comparing his method against his database. The correlation is recommended

for fluids with (µL / µV) < 1000.


It is interesting to highlight that the methodology proposed by the Friedel

(1979) contemplates the two extreme values of the vapor quality, corresponding to

single-phase flows of liquid and vapor.

Grönnerud (1979)

In this method, the two-phase multiplier was adjusted based on experimental

results for R12 and ammonia. The two-phase multiplier is given as follows:

−

+=

= 1dz

dp1

dz

dp

dz

dp

25.0

V

L

V

L

Fr

0L

22

0L

µ

µ

ρ

ρ

Φ Φ (2.50)

In which 0L

dp

dz

is estimated according to Eq. (2.38) assuming the two-phase

mixture flowing as liquid in a tube with the same diameter.

The pressure drop term in the right hand side of Eq. (2.53) is a function of the

frictional factor and is defined by Grönnerud (1979) as follows:

( )[ ]5.0

Fr

108.1

Fr

Fr

fxx4xfdz

dp−+=

(2.51)

where the friction factor is given by:

2

0.3

0

10.0055 ln

Fr L

L

f FrFr

= +

(2.52)

The Froude number is calculated assuming the two-phase mixture flowing as

liquids according to Eq. (2.52) by replacing the homogeneous density by the liquid

density.

The Froude number was introduced in the correlation in order to capture the

flow pattern effects, in the sense that with increasing Froude number, the inertia

effects suppress the gravitational effect and the annular flow pattern will be prevalent

while a reduction of Froude number makes the gravitational effect to be prevalent

and hence favouring the occurrence of stratified flow.


Grönnerud (1979) correlation is developed especially for refrigerants and is

applicable to the entire vapor quality range.

Whalley (1987)

Whalley (1987) has proposed a correlation based on homogeneous model for

determining the two phase multipliers, 2

0VΦ as follows:

2

H

V

0V

H

0V

22

0Vx

1

f

f

dz

dp

dz

dp

ρ

ρΦ Φ =

= (2.53)

where Hf is the friction factor according to the homogeneous model and 0Vf is the

friction factor assuming the two-phase mixture as vapor in a tube with the same

diameter. Two-phase dynamic viscosity is estimated as proposed by Beattie and

Whalley (1981) as follows:

(2.54)

Jung and Radermacher (1989)

Jung and Radermacher (1989) developed a correlation based on the work of

Martinelli and Nelson (1948) and Lockhart and Martinelli (1949) that consist in a

curve fitting of their data, based on the Martinelli parameter. Their correlation is given

as follows:

,X58.3

dz

dp

dz

dp

735.0

tt

0L

22

0L

−=

= ΦΦ for 1X tt ≤ (2.55)

The empirical exponent and multiplicative constant were obtained based on

convective boiling pressure drop data in horizontal tubes for R22, R12, R114 and

R152A. This database includes more than 600 experimental data points covering

saturation pressures from 200 to 800 kPa and mass velocity from 230 to 720 kg/m2 s.

The correlation presented an average deviation of 8.4 % in relation to the

experimental data used for its development.


Bandarra Filho (2002)

Bandarra Filho (2002) proposed a correlation for the two-phase multiplier 2

0LΦ

based on data for horizontal plain tube for R134a evaporating at a saturature

temperature of 5 oC, mass velocities from 25 to 500 kg / m2 s and tube diameters of

7.0, 7.93, 9.52 and 17.4 mm. In his method as in Jung and Radermacher (1989), the

two-phase multiplier 2

0LΦ is given as a function of the Martinelli parameter. However,

Bandarra Filho (2002) has proposed a more consistent physical format by taking into

consideration the asymptotic condition corresponding to, ∞→ttX , that is related to

only liquid flow, 0=x . The correlation adjusted according to his data is given as:

,X6.21

dz

dp

dz

dp

85.0

tt

0L

22

0L

−+=

= ΦΦ for 1X tt ≤ and 200G ≥ smkg2 (2.56)

This correlation provided an absolute average deviation value of 6.4 % when

compared against the data used for its development.

2.6.2.2 Extrictly empirical method

Müller-Steinhagen and Heck (1986)

Müller-Steinhagen and Heck (1986) proposed a two-phase frictional pressure

drop correlation that is in essence an empirical interpolation as a function of the

vapor quality between all liquid and all vapor flows. Their method is given as follows:

( )1

33

2

1dp

S x Bxdz Φ

= − +

(2.57)

where the factor S is given as:

( )xAB2AS −+= (2.58)

A and B is calculated as follows:

2

0

0

2L

L L i

dp GA f

dz dρ

= =

(2.59)


2

0

0

2V

V V i

dp GB f

dz dρ

= =

(2.60)

where 0Lf and 0Vf are estimated according to Blasius, Eq. (2.38)

Müller-Steinhagen and Heck (1986) method was developed based on a

comprehensive database including about 9300 experimental data points obtained for

air-water, vapor-water, water-oil and several refrigerants.

2.6.2.3 Flow pattern based predictive method

Moreno Quiben and Thome (2007)

Moreno Quiben and Thome (2007) proposed a method for predicting frictional

pressure drop during two-phase flows based on a phenomenological approach,

taking explicitly into account the flow patterns effects. The frictional pressure drop is

estimated taken into account the phases distribution based on the flow pattern

prediction method proposed by Wojtan et al. (2005). The method was developed

based on a database comprising 2543 experimental data points covering the

refrigerants R134a, R410A and R22, tubes with internal diameters of 8 and 13.8 mm,

mass velocities from 70 to 700 kg / m2 s and vapor qualities between 0 and 1.

For annular flow, the two-phase frictional pressure drop gradient is estimated

from the interfacial shear stress based on the relative velocity between the liquid and

vapor phases derived from the conservation of momentum considering that the

pressure drop gradients is similar for both phases. The pressure drop gradient is

given as follows:

i

iannular

d4

L

p τ∆= (2.61)

where the interfacial shear stress represents the shear stress exerted by the vapor

on the liquid phase calculated according to the following equation:

( )2

LVVii VV2

1f −= ρτ (2.62)

The terms LV and VV are the average velocities of the liquid and vapor phase,

given by Eqs. (2.9) and (2.10), respectively.


The interfacial friction factor if is estimated by a correlation proposed by the

authors based on their two-phase frictional pressure drop database for annular flow.

The correlation is given by:

( ) [ ] 034.0

0L

08.0

L

V

4.02

VL

2.1

i Weg

R267.0f

−

−

−

=

µ

µ

σ

δρρδ (2.63)

where the liquid film thickness is estimated as follows:

(2.64)

The void fraction is calculated through Eq. (2.26).

The first term in Eq. (2.66) scales the interfacial friction factor to the ratio of the

film thickness to the tube diameter while the second term comes from the

manipulation of the Helmholtz instability equation using as the scaling factor for

the most dangerous wavelength for the formation of interfacial waves. The liquid

Weber is determined by Eq. (2.22).

For slug and intermittent flow pattern, the two-phase flow pressure drop

gradient is calculated considering an interpolation between the single-phase frictional

pressure drop and the two-phase frictional pressure drop for annular flow complying

within the limit of vapor quality tending to zero and , according to the following

equation:

(2.65)

where 0Lp∆ is the the single-phase frictional pressure drop (evaluated at x=0), is

the void fraction at the intermittent to annular transition boundary and ( )annularp∆ is

the two-phase frictional pressure drop evaluated at assuming annular flow and

using the Eqs. (2.64) to (2.68) with to calculate the corresponding film

thickness. The exponent 0.25 was estimated based on the authors’ experimental

results.


For stratified-wavy flows, the composition of the friction factor for the dry

region and the region of the wall in contact with liquid was taken into account as a

function of the dry angle shown in Fig. 2.6.

So, the stratified-wavy flows frictional pressure drop is calculated from:

( )2

242

V V

stratified wavy stratified wavy

i

VLp f

d

ρ− Φ −

∆ =

(2.66)

The friction factor for stratified-wavy flow in Eq. (2.69) is obtained by a

proration around the perimeter of the tube taken into account wet and dry parcels, as

follows:

( ) ( )( )annulari

*

dryV

*

drywavystratified2 f1ff θθΦ −+=−

(2.67)

where πθθ 2*

drydry = , Vf is the single-phase friction factor for the vapor phase given by

Eq. (2.38), and the interfacial friction factor,i

f , is given by Eq. (2.66) for annular flow.

The dry angle is given by:

strat

61.0

stratwavy

wavy

dryGG

GGθθ

−

−= (2.68)

where stratθ is calculated according to Eq. (2.27)

For Slug+SW flow, the two-phase flow pressure drop gradient is calculated

considering an interpolation between the single-phase frictional pressure drop and

the two-phase frictional pressure drop . The interpolation was

obtained using as parameter the superficial void fraction as follows:

(2.69)

The exponent 0.25 was estimated based on the authors’ experimental results.

For mist flow, all the liquid is assumed flowing as droplet entrained in a continuous

vapor phase with the droplets travelling at nearly the same velocity as the vapor. So,

the authors adopted the homogeneous flow theory to predict two-phase frictional

pressure drop as follows:


( )H

2

i

Hmist

G

d

Lf2p

ρ∆

= (2.70)

where Hρ is the homogeneous density given by Eq. (2.52)

The friction factor is given by Blasius correlation, according to Eq. (2.38)

with the viscosity estimated according to Cicchitti et al. (1960):

( ) LVH x1x µµµ −+= (2.71)

The process of dryout starts at the top of the tube, where the liquid film is

thinner, and takes place over a range of vapor quality (from the inception of dryout at

dix at the top of the tube to the completion of dryout at dex at the bottom of the tube)

and thus ends when the fully developed mist flow regime is reached. Based on this

behavior, the authors proposed a linear interpolation relation that captures pressure

drop variations between the annular and mist flows without jump in the frictional

pressure drop gradient. So, for dryout region, the pressure drop is given according to

the following equation:

( ) ( ) ( ) ( ) ( ) ( ) ( )[ ]demistditp

dide

di

ditpdryoutxpxp

xx

xxxpp ∆∆∆∆ −

−

−−= (2.72)

where dix and dex are calculated according to Eqs. (2.28) and (2.29) respectively.

2.7 Comparisons from the literature of the two-phase frictional pressure drop

predictive methods

Tribbe and Müller-Steinhagen (2000) reported an extensive comparison of 35

two-phase pressure drop predictive methods against a large database containing

experimental results for air-oil, cryogenics, steam-water, air-water fluid combinations

and several refrigerants. They observed that statistically, Müller-Steinhagen and

Heck (1986) method provides accurate predictions of the pressure drop data when

compared to the other methods. Ould-Didi et al (2002) compared seven of the most

quoted methods in the literature to their database (788 data points). They observed

that the method of Müller-Steinhagen and Heck (1986) and Grönnerud (1979)

consistently gave the best predictions while that of Friedel (1979) was only the third

best. They also mapped their experimental data using Kattan, Thome and Farvat’s


flow pattern map (1998) and observed that the Müller-Steinhagen and Heck (1986)

correlation provides the best predictions for annular flow and Grönnerud (1979)

correlation for intermittent and stratified wavy flows.

Bandarra Filho (2002) presented a pressure drop study of R134a under flow

boiling conditions in horizontal smooth and microfin copper tubes. He observed that

the method by Jung and Radermacher (1989) was found to provide the best

prediction of his plain tube data.

Mauro et al. (2007) carried out pressure drop measurements for different

refrigerants (R22, R134a, R404A, R407C, R410A, R507A), mass velocities between

190 and 1100 kg / m2 s in horizontal tubes. They obtained 1160 experimental

pressure drop data. According to Mauro et al. (2007), the method proposed by

Friedel (1979) is statistically accurate but fails to capture the pressure drop trends

with changing of the flow patterns. The method underestimate the pressure drop for

intermittent flows and overestimate the values for annular flow and in the dryout

region. Müller-Steinhagen and Heck (1986) correlation gives better predictions than

Friedel (1979) for intermittent flow and under dryout conditions. The model by

Moreno-Quibén and Thome (2007) predicted 77 % of the pressure drop data within

error band of ±30 % and hence presented the best predictions.

Park and Hrnjak (2007) investigated experimentally flow boiling pressure drops

in a horizontal smooth tube of 6.10 mm inner diameter for R744, R410A and R22 and

saturation temperatures from -30 and -15 oC. The method of Müller-Steinhagen and

Heck (1986) was the best for predicting their data. According to Thome et al. (2008),

the method proposed by Friedel (1979) is unsatisfactory for the estimation of

pressure drop for ammonia in tube with diameter of 10 mm providing only 29 % of the

estimation within error band of ±30 %. The method of Müller-Steinhagen and Heck

(1986) gives better results, presenting 48 % of the prediction within error band of ±30

%. Moreno-Quiben and Thome (2007) predictive method poorly predicted the

pressure drop data, predicting only 17 % of the data correctly. According to Revellin

and Haberschill (2009), the method of Friedel (1979) presents satisfactory

predictions of the database gathered by them, predicting 63 % of their data within

error band of ±30 %. In general, Friedel (1979) provided the best prediction of the

high pressure drop data. The method of Müller-Steinhagen and Heck (1986),

presented an almost similar result predicting 62.9 % of the pressure drop data within

error band of ±30 %. In general, this method worked best for low pressure drop data.


Hernandes (2010) performed a comparison between the leading plain-tube frictional

pressure drop predictive methods and a database gathered from literature containing

experimental results from independent laboratories. From his study, he found that the

predictive method by Müller-Steinhagen and Heck (1986) provided the best

agreement with his database.

Kanizawa (2011) carried out an experimental study on two-phase flow patterns

and pressure drop of R134a inside a 15.9 mm ID. The frictional pressure drop data

obtained from his experiment were compared against the predictions of Grönnerud

(1979), Müller-Steinhagen and Heck (1986), Friedel (1979) Lockhart and Martinelli

(1949) and Moreno-Quibén and Thome (2007). From his study, he found that the

predictive method by Grönnerud (1979) was the best predicting 90 % of the

experimental data within error band of ±30 %.

Grauso et al. ( 2013) investigated experimentally and assessment of predictive

methods available in literature focusing on flow pattern map, heat transfer and

pressure drops during evaporation of R1234ze (E) and R134a in a horizontal, circular

smooth tube. The authors observed that adiabatic frictional pressure gradients of the

two refrigerants were found to be very similar for all the investigated operating

conditions, showing the same trends with vapor quality. Also their results revealed

that the adiabatic frictional pressure gradients of R1234ze(E) is slightly higher than

those obtained for R134a at the same operating conditions. The frictional pressure

drop data obtained from their experiments were compared against the predictions of

Friedel (1979), Grönnerud (1979), Jung and Radermacher (1989), Müller-Steinhagen

and Heck (1986) and the phenomenological model by Moreno-Quibén and Thome

(2007). According to Grauso et al. (2013), the method proposed by Müller-

Steinhagen and Heck (1986) provided best prediction of their database, predicting

89.6 % of the experimental data within error band of ±30 %.

Several studies in the literature have compared experimental two-phase

pressure drop data and predictive methods. Based on the abovementioned

comparisons and according to the authors, it seems that the predictive methods work

better for certain databases. However, the predictive methods of Müller-Steinhagen

and Heck (1986) and Grönnerud (1979) are found to provide the best predictions of

various experimental databases obtained by authors from independent laboratories.


2.8 Heat transfer during convective boiling

2.8.1 Introduction

Flow boiling heat transfer is a very complex process in which numerous

phenomenons are superimposed, i.e. the saturated liquid generates vapor, which

flows with higher velocity than the liquid phase. The two-phase topology flow

geometry varies due to the shear forces of accelerating vapor; nucleate boiling

generates bubbles that agitates the flow and the liquid film in the case of annular

flows.

Figure 2.8 illustrates qualitatively the typical behavior of the heat transfer

coefficient during in-tube flow boiling for high flow rates. In this figure, we observe

that the flow pattern and the heat transfer mechanisms varies along the evaporation

process with increasing vapor quality. Generally speaking, for vapor qualities below

30 %, the nucleate boiling mechanism is dominant and the heat transfer coefficient

increases with increasing heat flux and saturation pressure as occurs in pool boiling.

With increasing the amount of vapor, the void fraction increases and the annular flow

pattern is established for vapor quality of approximately 40 % then the process of

evaporation in the liquid-vapor interface becomes predominant for 40% <x < 80 %.

Heat transfer mechanism in horizontal flows is affected by the formation of an

asymmetric liquid film during annular flow. For annular flow, the liquid film thickness

reduce progressively due to the liquid evaporation in the liquid-vapor interface. This

results in the reduction of the liquid thermal resistance promoting an increase of heat

transfer coefficient as displayed in Fig. 2.8. The heat transfer coefficient increases

with vapor quality until a condition where occurs the wall dryout. When the inner

surface of the tube is partially dry, the heat transfer rate on the dry regions is much

lower compared to that of the wet portions reducing the perimeter average heat

transfer coefficient. Even after the complete evaporation of the liquid film, under

certain conditions, liquid droplets detached from the liquid film in the annular flow

region are kept flowing within the vapor phase, characterizing the mist flow. In this

region the heat transfer coefficient decreases with increasing vapor quality and after

entrainment deposition of the liquid droplets, the rate of heat transfer tends to be

reduced.


Figure 2.8 - Schematic representation of the variation of the heat transfer coefficient during flow boiling.

Based on the brief analyses abovementioned, it can be concluded that

obtaining accurate and general methods for calculating heat transfer coefficient is a

difficult task. The heat transfer coefficient is a result of the influence of several

parameters such as the channel dimensions, the flow orientation, surface roughness

and material, mass velocity, fluid properties, saturation pressure, vapor quality, heat

flux and components of each phase in case of mixtures. Usually the methods to

estimate the heat transfer coefficient are based on dimensionless numbers relating

the properties of the fluid, the characteristics of the flow and the heat transfer rate.

The dimensionless numbers of Reynolds, Prandtl and Nusselt are generally used for

correlating single-phase flow inside tubes. Modified versions of these dimensionless

numbers are also considered for flow boiling heat transfer predictive methods plus

additional dimensionless numbers such as Weber and Froude. An approach used to

develop flow boiling heat transfer predictive methods that has been successful is the

superposition of nucleate boiling and forced convection effects and the method

based on the parcels of flow patterns. In the next item, some heat transfer predictive

methods available in the open literature are described.

2.8.2 Predictive methods for flow boiling heat transfer coefficient

Generally, the methods developed to predict the heat transfer coefficient

during flow boiling are based on the combination of the mechanisms of nucleate and


convective boiling as initially proposed by Chen (1966). The nucleate boiling effect

depends strongly on the heat flux and saturation temperature while the convective

boiling contribution depends strongly on the mass velocity and vapor quality. As

identified and analyzed by Bandara Filho (1997) and Wojtan et al. (2005), the

methods for correlating the heat transfer coefficient under flow boiling conditions can

be classified into the following groups:

2.8.2.1 Convective correlations

Convective correlations: these methods are simple correlations given in terms

of dimensionless numbers such as Martineli parameter. Such correlations are

obtained by assuming annular flow pattern. Under this flow pattern condition,

convective effects are dominant and the Martineli parameter is appropriate to predict

them.

2.8.2.2 Superposition effects

Methods based on superposition effects: these predictive methods assume

that the flow boiling heat transfer coefficient is the superposition of nucleate and

convective boiling effects. The convective effects are given through the product

between the heat transfer coefficient for forced convection inside the tube and a

factor related to intensification of convective effects. Nucleate boiling effects are

correlated through the product between the heat transfer coefficient using a pool

boiling correlation and a factor related to nucleate boiling suppression.

2.8.2.3 Pure empirical methods

Pure empirical correlations: these type of correlations are based on

adjustment of dimensionless numbers based on experimental databases. This type

of predictive method was proposed by Shah (1982), Kandlikar (1990) and Bandarra

Filho (1997). The results provided by these correlations are accurate for the

experimental conditions considered in their development. They are not

recommended for conditions different than the database used for their development.

2.8.2.4 Flow pattern based methods

Flow pattern based predictive methods: these are flow pattern oriented

methods developed for flow boiling heat transfer predictions. These methods take


into account the effect of the two-phase flow structure on the heat transfer coefficient

mechanisms.

Superposition effects based Group

Chen 1966

In convective boiling, different heat transfer mechanisms are dominant

according to the vapor quality range, heat flux, saturation temperature and mass

velocity levels. At low vapor qualities, nucleate boiling effects prevail while at high

vapor qualities, the heat transfer coefficient is controlled mainly by convective effects.

The predominance of these mechanisms was considered by Chen (1966) when

developing a method for prediction of convective boiling heat transfer coefficient

under condition of vertical flows. He postulated that both convective and nucleate

boiling heat transfer mechanisms play a role in flow boiling heat transfer and they are

additive such that the convective boiling heat transfer coefficient is calculated as

follows:

2 L NBh Fh ShΦ = + (2.73)

The first term on the right-hand side, LFh is the forced convective contribution

where Lh is the liquid-only heat transfer coefficient calculated according to Dittus and

Boelter (1930) correlation with only the liquid phase flowing in the same channel

given as follows:

i

L4.0

L

8.0

LLd

kPrRe023.0h = (2.74)

The second term, NBSh is the nucleate boiling contribution where NBh , is the

pool boiling heat transfer coefficient which is calculated from the Foster and Zuber

(1955) pool boiling correlation. The parameters F and S were defined by Chen

(1966) as the forced convective heat transfer enhancement and suppression factors,

respectively. The parameter F takes into account the increment of convective effects

relative to that of single-phase flow of the liquid. The enhancement of convective

effects is promoted by the flow acceleration due to the evaporation process itself and

in Chen’s method is a function of Martinelli parameter. The parameter S is the

nucleate boiling suppression factor that takes into account steeper temperature


gradients near the wall due to the fluid motion which tends to suppress the number of

nucleation active sites and was assumed to be a function of the two-phase Reynolds

number,2Re Φ

.

The terms F and S are estimated according to the following equations:

1F = , for 1.0X1 tt < (2.75)

( ) 736.0

tt 213.0X135.2F += , for 1.0X1 tt ≥ (2.76)

where ttX is calculated by Eq. (2.46)

( )Φ2

6 Re10.53.211S −+= (2.77)

where the two-phase Reynolds number is defined as follows:

L

25.1

2 ReFRe =Φ (2.78)

Chen (1966) method was based on a database of 665 experimental data from

six different data sources.

Gungor and Winterton (1986)

Based on a study of the literature, Gungor and Winterton (1986) pointed out

the absence of procedures for determining the flow boiling heat transfer coefficient

that covers the whole range from subcooled to saturated flow boiling. So, they

developed a new method for subcooled and saturated flow boiling under conditions

of horizontal and vertical flows based on the same approach of Chen (1966) using

their experimental database containing more than 4300 data points including water,

refrigerants and ethylene glycol. On contrary to Chen (1966), Gungor and Winterton

(1986) took into account the effect of heat flux on the convective enhancement factor

by including the dimensionless Boiling Number in the equation for its prediction.


Using the same approach of Chen (1966), Gungor and Winterton (1986)

estimated the liquid-only heat transfer coefficient Lh according to Eq. (2.77). The

Foster and Zuber (1955) pool boiling correlation adopted by Chen (1966) was

replaced by the correlation of Cooper (1984). The method of Cooper (1984) was

considered because of its simplicity and accuracy. The Cooper (1984) pool boiling

correlation is given as follows:

( )0.550.12 0.5 0.67

1055 logNB red redh P P M φ−= − (2.79)

The new convective enhancement factor is given as:

86.0

tt

16.1

X

137.1Bo240001F

++= (2.80)

where is calculated by:

(2.81)

The suppression factor is correlated as a function of convective enhancement

factor and the liquid only Reynolds number, LRe as follows:

17.1

L

26ReF10.15.11

1S

−+= (2.82)

According to the author, for horizontal flow, if the Froude number FrL0, (Eq.

2.21) is lower than 0.05, the values of the parameter as convective enhancement and

suppression factors, must be multiplied by the factors 1F and 1S respectively,

in order to capture flow stratification effects on the heat transfer coefficient present in

horizontal flows and low mass velocities. The factors 1F and 1S are given as follows:

( )0.1 2. 0

1 0

FrL

LF Fr−

= (2.83)

1 0LS Fr= (2.84)

Gungor and Winterton (1987)


Later on, Gungor and Winterton (1987) modified this method in order of

making it simpler while keeping its accuracy. The modified method is given as

follows.

Fhh L2 =Φ (2.85)

The modified convective enhancement factor in Eq. (2.76) is given as:

0.410.75

0.861 3000 1.121

l

v

xF Bo

x

ρ

ρ

= + +

− (2.86)

where Lh is estimated according to Eq. (2.77).

Jung and Radermacher (1989)

Jung and Radermacher (1989) modified Chen (1966) method based on their

experimental database containing more than 3000 data points covering thirteen

halogenated refrigerants. In their method, the flow boiling heat transfer coefficient is

estimated according to Eq. (2.76) as proposed by Chen (1966). The liquid-only heat

transfer coefficient is calculated according to Dittus and Boelter (1930) correlation

given by Eq. (2.77).

The nucleate boiling heat transfer coefficient NBh is calculated through the

correlation of Stephan and Abdelsalam (1980) given as follows:

( ) 533.0

581.0745.0

Pr207 L

L

V

satL

b

b

LNB

Tk

D

D

kh

=

ρ

ρφ (2.87)

where,

( )

0.5

20.0146

b

L V

Dg

σϑ

ρ ρ

=

− and 35oϑ = (2.88)

The modified convective enhancement factor proposed by Jung and

Radermacher (1989) based on the regression analysis of their experimental data is

given as follows:


85.0

ttX

129.037.2F

= (2.89)

A new correlation for the suppression factors was also developed by the

authors through the regression analysis of their experimental data. The suppression

factors is given as follow:

1.22 1.134048 ttS X Bo= for 1X tt ≤ (2.93)

0.28 0.332.0 0.1 ttS X Bo− −= − for 5X1 tt ≤< (2.94)

From Eqs. (2.93) and (2.94), it can be noticed that the author did not take into

account the Froude number to capture the effects of two-phase flow stratification due

to gravitational effects in horizontal flows.

Liu and Winterton (1991)

Based on the approach of Chen (1966) and on the method of Gungor and

Winterton (1986), Liu and Winterton (1991) developed a new method to predict

saturated and subcooled flow boiling heat transfer. They observed that predictive

methods for saturated flow boiling without an explicit nucleate boiling term, that rely

only on Boiling Number corrections, do not work for subcooled flow boiling.

Therefore, they proposed a method based on an explicit nucleate boiling term rather

than an empirical Boiling Number dependence. The authors used a database with

over 4200 experimental data points for saturated flow boiling and 991 experimental

data points for subcooled flow boiling. They proposed their method based on a

nonlinear superposition of nucleate boiling and convective effects as suggested by

Kutateladze (1961) using an assympotic exponent of 2. Their method is given as

follows:

( ) ( )2

1pool

2

10L

2

2 SShFFhh +=Φ (2.95)

where 0Lh is calculated from Dittus and Boelter (1930) correlation with the entire

mass flow rate flowing as liquid in the same channel and is given according to Eq.

(2.77) by replacing ReL with ReL0.


The pool boiling heat transfer coefficient is estimated using Cooper (1984)

correlation given by Eq. (2.82).

The authors modified the enhancement factors proposed by Chen (1966) by

introducing the Prandtl Number, LPr , and the ratio between liquid and vapor densities.

This approach is physically consistent, since with increasing Prandtl Number, the

thickness of the laminar boundary sub-layer decreases, increasing the heat transfer

coefficient. The density ratio was introduced to capture the fact that the greater this

ratio, the greater the speed of the vapor-phase for a fixed mass velocity and vapor

quality, improving vaporization effects on the liquid-vapor interface. The

enhancement factor was defined by them as:

0.35

1 Pr 1LL

V

F xρ

ρ

= + −

(2.96)

The suppression factor was correlated based on the Reynolds number for the

two-phase mixture flowing as liquid in the same channel and the convective

enhancement parameter given by Eq. (2.96). The suppression factor is given as

follows:

( )0.1 0.160

1

1 0.055 ReL

SF

=+

(2.97)

In order to correct the gravity effects associated with the reduced mass

velocities responsible for stratification of the two-phase flow, the authors incorporate

the Froude number such that if 0 0.05L

Fr < , the enhancement and suppression factors

F and S must be multiplied by factor 1F and 1S respectively as, defined in Eqs.

(2.86) and (2.87).

Pure empirical based Group

Kandlikar (1990)

Kandlikar (1990) has pointed out that the correlations proposed until that time

were not suitable to new fluids and therefore, he proposed a new method including a

parameter characterizing the pair fluid-surface as proposed by Rohsenow (1952) for


pool boiling. His predictive method was developed based on 5246 experimental data

from the literature is given according to the following equation as follows:

( ) ( ) LfL

D

L0L

B

2 hFCBohFr25ACoh +=Φ (2.98)

where 0LFr and Lh are given by Eqs.(2.21) and (2.77), respectively.

In the method of Kandlikar (1990), the convective enhancement and boiling

suppression factors were replaced by the Convective Number Co, and Boiling

Numbers Bo, respectively. As above mentioned, this method can be extended to

different fluids by evaluating only the fluid-dependent parameter fLF , for a specific

fluid based solely on one data point obtained from experiments for flow or pool

boiling. The values of the fLF , for different fluids as proposed by Kandlikar (1990),

are presented in Tab. 2.2.

Table 2.2 - Values of fluid dependent parameter .

Fluid Fluid

Water 1.00 R152a 1.10

R11 1.30 Nitrogen 4.70

R12 1.50 Neon 3.50

R13B1 1.31 R134a 1.63

R22 2.20 R404A 1.55

R113 1.30 R407C 1.50

The values of the constants A, B, C, D and E in Eq. (2.95) are given in Tab.

2.3. The values in the column corresponding to convective boiling dominant

mechanism are used if Co is less than 0.65 , while the value corresponding to

nucleate boiling dominant mechanism are used if Co is greater than 0.65.

Table 2.3 - Values of the empirical constants of the Kandlikar (1990) method.

Constant Convective boiling Nucleate boiling

A 1.1360 0.6683

B -0.9 -0.2

C 667.2 1058.0

D 0.7 0.7

E* 0.3 0.3

*The value of E should be fixed equal to 0 if 04.00 >LFr

Jabardo’s Group


Based on dimensionless parameters Bandarra Filho (1997) proposed a simple

method to predict flow boiling heat transfer coefficients of halocarbon refrigerants.

The model was developed using experimental data obtained in the Laboratory of Air

Conditioning and Refrigeration Center of University of Illinois at Urban-Champaign,

USA. To capture convective effects and the influence of refrigerant properties such

as liquid and vapor viscosity and densities, Bandarra Filho included the Martinelli

Parameter in its correlation. The Boiling Number was also incorporated to capture

nucleate boiling effects associated with high heat flux under reduced vapor quality

conditions. The author finally included the Froude number to correlate the

experimental results obtained at reduced mass velocities capturing effects related to

the occurrence of both stratified and stratified wavy flow pattern. The proposed

method is given as follow:

(2.99)

(2.100)

In a subsequent study Bandarra Filho (2002) based on his experimental data

proposed different correlations for predicting heat transfer coefficients in horizontal

tubes according to mass velocities ranges and adopting a mass velocity threshold of

200 kg / m2 s. For mass velocity higher than this threshold, the heat transfer

coefficient is correlated as a function of the Martinelli Parameter and Boiling Number

while for lower mass velocities, the heat transfer coefficient is correlated as a function

of the dimensionless number and Froude Number. The dimensionless number

takes into account the heat flux applied to the tube wall and the conduction

through the liquid film. The method is given as follows:

( )23.066.0

ttL2 BoX201hh−+=Φ for 200≥G kg / m2 s (2.101)

+=

−3

1

0L3

2

L2 FrBj74.01hh Φ

for 200<G kg / m2 s (2.102)

where Lh is determined by Eq. (2.77) and the dimensionless Bj is given as follows:

satL

i

Tk

dBj

φ= (2.103)


In Eq. (2.103) the saturation temperature, Tsat, should be in Kelvin

Barbieri (2005) based on Bandarra Filho (2002) has also proposed different

correlation according to the ranges of mass velocity, tube diameter and Martinelli

Parameter for estimating the heat transfer coefficient during flow boiling inside

horizontal tubes. The method is based on his results and previous data obtained by

Bandarra Filho (2002). The predictive method is given by the following equations:

( )0.76 0.172 1 2.62L tth h X Bo

−Φ = + for 1≤ttX , 150≥G kg / m2 s and 4.172.6 ≤≤ id mm (2.104)

( )0.56 0.702 1 7.35L tth h X Bo

−Φ = + for 1≤ttX , 100=G kg / m2 s and 4.172.6 ≤≤ id mm (2.105)

( )0.36 0.682 00.65L Lh h Fr Bj

−Φ = for 1≤ttX , 100<G kg / m2 s and 4.176.12 ≤≤ id mm (2.106)

where Lh is determined by Eq. (2.77) and Bj by Eq. (2.103).

Thome’s Group

Kattan et al. (1998) has pointed out that the flow boiling predictive methods

proposed until that time neglect mist flow and partial dryout flow pattern by

erroneously assuming conditions for evaporation under these conditions. Based on

this Statuo Quo, the authors developed a heat transfer predictive method for

horizontal flows that incorporates mist flow and dryout flow patterns besides

stratified, intermittent and annular flows. To estimate the flow boiling heat transfer

coefficients, Kattan et al. (1998) assumed that, the mean heat transfer around the

periphery of a evaporator tube in stratified, stratified-wavy and annular flow with

partial dryout regions of the tube is a direct proration of the liquid and vapor heat

transfer coefficients for wet and dry perimeter segments. Therefore, they proposed to

calculate the heat transfer coefficient a method that takes into account the relative

parcels of wet and dry perimeter given as follows:

2

(2 )

2

dry V dry weth hh

θ π θ

πΦ

+ −= (2.107)

where the dry angle, dryθ in Eq. (2.107) and schematically shown in Fig. 2.6, defined

the flow structures and the ratio of the tube perimeter in contact with liquid and vapor.


For stratified flow, dryθ is equals to the stratified angle stratθ and is calculated

according to the following equation:

strat

stratwavy

wavy

dryGG

GGθθ

−

−= (2.108)

where stratθ is calculated by Eq. (2.27)

For annular (A), and intermittent (I) flows, dryθ = 0. For stratified-wavy flow,

dryθ varies from zero up to its maximum value, stratθ .

The vapor heat transfer coefficient Vh is calculated according to Dittus and

Boelter (1930) correlation, Eq. (2.77), for the vapor only. Reynolds Number given as

follows:

(2.109)

where is calculated through Eq. (2.26)

The heat transfer coefficient on the wet perimeter is calculated with an

asymptotic model that combines the nucleate boiling and convective boiling heat

transfer contributions using an asymptotic exponent of 3 as follows:

( ) ( )[ ] 313

NB

3

CBwet hhh += (2.110)

The convective boiling heat transfer coefficient CBh is calculated from the

following equation:

δδ

L4.0

L

69.0

CB

kPrRe0133.0h = (2.111)

where δ is calculated by Eq. (2.67).

The nucleate boiling heat transfer coefficient NBh is determined from Copper’s

pool boiling correlation given by Eq. (2.82).


Wojtan et al. (2005) have proposed a flow pattern based method to predict

heat transfer coefficient during flow boiling inside horizontal tubes through

modification of the method proposed initially by Kattan et al. (1998). They observed

that the heat transfer coefficients predicted for stratified-wavy flow were not as

accurate as for annular flow and thereby developed a model to improve the accuracy

of predicting flow boiling heat transfer coefficient in stratified, dryout and mist flow

patterns. This new approach shows a good improvement in the heat transfer

prediction and extends the application of the model to vapor qualities below 0.15.

They kept the same procedure as proposed by Kattan et al. (1998) to calculate the

heat transfer coefficient for wet and dry perimeter of the tube given by Eqs. (2.107) to

(2.111)

For stratified-wavy flow, dryθ varies from zero up to its maximum value, stratθ .

The authors subdivided stratified-wavy flow into three sub zones (slug, slug/stratified-

wavy and stratified-wavy) to determine dryθ . For slug zone (slug), the high frequency

slugs maintain a continuous thin liquid layer on the upper tube perimeter. Thus,

similar to the intermittent and annular flow regimes, dryθ =0

For stratified-wavy zone (SW), the Eq. (2.71) was proposed.

For slug-stratified wavy zone (Slug + SW), the following interpolation between

the other two regimes is proposed forIA

xx < :

strat

61.0

stratwavy

wavy

IA

dryGG

GG

x

xθθ

−

−= (2.112)

The heat transfer coefficient for mist flow is calculated by a new correlation

developed in their study based on their experimental data which is a modification of

the correlation proposed by Groeneveld (1973). The mist flow heat transfer

correlation is given as follows :

i

V83.106.1

V

79.0

Hmistd

kYPrRe0117.0h −= (2.113)


where the homogeneous Reynolds number HRe is given as:

( )

−+= x1x

GdRe

L

V

V

i

Hρ

ρ

µ (2.114)

and the multiplier factor Y is defined as:

4.0

V

L )x1(11.01Y

−

−−=

ρ

ρ (2.115)

As observed by the authors, the heat transfer coefficient fall sharply in the

dryout region and becomes nearly constant for mist flow. So, they proposed for the

heat transfer coefficient in the dryout region using the following linear interpolation

given as follows:

( ) ( ) ( )[ ]demistdi2

dide

didi2dryout xhxh

xx

xxxhh −

−

−−= ΦΦ (2.116)

where ( )2 dih xΦ is the two-phase heat transfer coefficient calculated from Eq. (2.107)

at the dryout inception quality dix , and ( )demist xh is the mist flow heat transfer

coefficient calculated with Eq. (2.113) at the dryout completion quality dex . Dryout

inception quality dix and dryout completion quality dex are respectively calculated by

Eqs. (2.28) and (2.29). According to the author, if dex is not defined at the considered

mass velocity, it should be assumed that, dex = 0.999.


Presented in Tab. 2.4, is the summary of the predictive methods for the heat

transfer coefficient during flow boiling for plain tubes described in this Chapter.

76

Literature review

Table 2.4 - Summary of predictive methods for the heat transfer coefficient during flow boiling

Authors Fluids Tube

Orientation

G [kg/m2s]

φ [kW/m2]

i

d [mm] Comments

Chen

(1966)

Water, Methanol,

Cyclo hexane, pentane

Vertical G = 500 – 3600

Mean deviations of 12 % with data of six investigators. Large deviations observed for halocarbon refrigerants.

Gungor and Winterton

(1986)

Water, R11,

R12, R22

R113and R114

Vertical and

Horizontal

G = 60 – 8180

φ =1 - 2.6 3 – 32

The correlation gives mean deviation of 21.4 and 25.0 % for saturated and saturated flow boiling respectively relative to its database. The new correlation is simpler to apply and gives a closer fit to the data used in its development.

Gungor and Winterton

(1987)

Water, R11,

R12, R22

R113and R114

Vertical and

Horizontal

G = 60 – 8180

φ =1 - 2.6 3 – 32

The correlation was recommended as the best when compared with the flow boiling data of R134a of Thome (1997a).

Jung and Radermacher

(1989)

R11, R12, R13, R22, R32, R114, R123, R124, R134a, R141b, R142b,

R143a, R152a.

Horizontal G = 100 – 700

φ =5 - 40 8

The proposed method gives standard deviation in the order of 3 % while Chen (1966) of 70 % when compared to the authors’ database.

Kandlikar (1990)

Water, R11, R12, R22, R13B1, R113,R 114, R152a ,Nitrogen and

Neon

Horizontal G = 15 – 8180

φ =1.2 - 2.0 4.6 – 32

Mean deviation of 15.9 % for water and 18.8 % for the overall database. A fluid dependent parameter Ffl was introduced.

Liu and Winterton

(1991)

Water, R11, R12, R22, R113, R114 and Etileno-

glicol

Vertical and

Horizontal

G = 12.4 – 8180

φ =0.4 - 2.62 3 – 32 The new method can be used for saturated

subcooled boiling data.

Kattan et al. (1998)

R123, R134a, R402a, R404a and R502, Horizontal

G = 100 – 500

φ =0.44 – 7.83 10.92 – 12

This is a flow pattern based method. The method is better than the existing methods at high vapor qualities (x > 85 %) and for stratified types of flows.

Literature review

77

Table 2.4(Continuation) - Summary of predictive methods for the heat transfer coefficient during flow boiling

Authors Fluids Tube

Orientation

G [kg/m2s]

φ [kW/m2]

i

d [mm] Comments

Bandarra Filho (1997) R12, R22 andR134a Horizontal

G = 25 -500

φ =1.9-40 7.04- 10.92

The proposed method provide an absolute average deviation in the order of 12 % relative to the experimental data and the correlation is simpler to apply

Bandarra Filho (2002)

R22, R134a, R404a, R407C and R417A Horizontal

G = 25 -1100

φ =5 – 30 7.93- 17.4

The proposed method provide an absolute average deviation of 15 % and 5.9 % for high and reduced range of mass velocity, respectively.

Barbieri (2005) R134a Horizontal

G = 25 – 500

φ =5 and 10 6.2 - 17.4 The proposed models provided best predictions of the

experimental data obtained in his study

Wojtan et al. (2005b) R22 and R410A Horizontal

G = 70 – 700

φ =2.0 - 57.5 8.00 and 13.84

The new model reasonably predict most of the experimental data used in their study, extends the application of the model to vapor qualities below 0.15 and the heat transfer coefficients in the dryout and mist flows regions.


2.8.2.5 Comparison between some of the predictive methods for heat transfer coefficient during two-phase flow

Figures 2.9 and 2.10 display comparisons among the predictive methods for

the heat transfer coefficient in plain tubes described in this Chapter. These figures

reveals notable discrepancies among the methods.

As shown in Fig. 2.9 for mass flow of 75 kg / m2 s, when stratified flow is

expected, Bandarra Filho (1997) method presented almost constant heat transfer

coefficient with increasing vapor qualities until the onset of dryout indicating a typical

behavior of stratified flow pattern. On the other hand, in Fig. 2.10 for mass velocity of

150 kg / m2 s, heat transfer coefficient initially increases with increasing vapor quality,

up to around 50 %, further vapor quality augmentation causes a progressive

reduction of the heat transfer coefficient. This behavior is significantly different from

those trends displayed by the other predictive methods.

Bandarra Filho (2002) and Barbieri (2005) methods display similar trends for

the heat transfer coefficient with increasing vapor quality as illustrated in Figs. 2.9

and 2.10, their methods provide an unexpected behavior according to which the heat

transfer coefficient keeps increasing with vapor quality even for x close to the unity.

The augmentation of the heat transfer coefficient with increasing vapor quality is a

typical behavior of annular flows in which the evaporation of liquid film and

convective effects are predominant. Such behavior is generally captured by the

predictive methods available in the literature as well as Bandarra Filho (2002) and

Barbieri (2005) by the Martineli Parameter.

Jung and Radermacher (1989) and Liu and Winterton (1991) correlations also

display that the heat transfer coefficient increases with increasing vapor quality.

However, in case of these authors the increment of the heat transfer coefficient with

vapor quality is less stepper than according to the methods of Bandarra Filho (2002)

and Barbieri (2005). Here, it is important to highlight that Jung and Radermacher

(1989), Liu and Winterton (1991), Bandarra Filho (2002) and Barbieri (2005) have

considered in the development of their methods, data obtained under electrical

heating conditions. Therefore, their methods does not include results for dryout and

mist flows and, so, these methods are not recommendable for vapor qualities close

to 1


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

x [-]

h [

kW /

m2

oC

]

Jung and Radermacher (1989)Kandlikar (1990)Liu and Winterton (1991)Bandarra Filho (1997)Bandarra Filho (2002)Barbieri (2005)Wojtan et al. (2005b)

Figure 2.9 - Comparison among of the predictive method for heat transfer coefficient during convective

boiling of R245fa, ϕ = 7.5 kW / m², Tsat = 5 °C, G=75 kg / m2, and di = 6 mm.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

x [-]

h [

kW /

m2 o

C]

Jung and Radermacher (1989)Kandlikar (1990)Liu and Winterton (1991)Bandarra Filho (1997)Bandarra Filho (2002)Barbieri (2005)Wojtan et al. (2005b)

Figure 2.10 - Comparison among of the predictive method for heat transfer coefficient during

convective boiling R245fa, ϕ = 7.5 kW / m², Tsat = 5 °C, G=150 kg / m2, and di = 6 mm.

As shown in Figs. 2.9 and 2.10, it is interesting to note that according to

method of Kandlikar (1990) the heat transfer coefficient first decreases with

increasing vapor qualities up to 10 % and then the heat transfer coefficient

progressively increases up to a vapor quality of approximately 80 % with increasing

vapor qualities. These behaviors characterize the predominance of nucleate boiling

effect under low vapor quality conditions followed by annular flow and the


predominance of convective effects under moderate and intermediary vapor quality

conditions. For vapor qualities higher than 80 %, the onset of dryout occurs drying

the tube wall internal surface and resulting in reduction of heat transfer coefficient.

The method of Wojtan et al. (2005b) seems to capture these behaviors as well but in

this case the flow patterns effect is more drastic.

Table 2.5 presents variation of heat transfer coefficient estimated by the

predictive methods based on different experimental operating conditions.

Table 2.5 - Variation of heat transfer coefficient estimated by the predictive methods based on different experimental operating conditions

G=75 kg / m2 s G=75 kg / m2 s

x=0.1 x=0.7 Predictive methods

R1=R134a R2=R245fa

Tsat1 =5o C Tsat2 =15o C

D1=6 mm D2=15 mm

=7.5 kW/m2

=20 kW/m2 R1=R134a

R2= R245fa Tsat1 =5o C Tsat2 =15o C

D1=6 mm D2=15 mm

=7.5 kW/m2

=20 kW/m2

Jung and Radermacher (1989) 12.7 16.9 -13.7 52.6 21.8 10.1 -16.7 2.3

Kandlikar (1990) - 5.6 -16.8 91.1 - 7.2 -16.7 26.8

Liu and Winterton (1991) 51.3 9.6 -31.8 43.6 52.8 10.1 -31.9 17.9

Bandarra Filho (1997) 19.4 0.4 -38.8 13.4 14.5 0.6 -42.3 19.2

Bandarra Filho (2002) 23.7 2.1 76.7 90.4 23.6 2.1 90.8 91.3

Barbieri (2005) 12.4 1.4 -16.7 7.2 8.0 6.4 -16.8 15.2

Wojtan et al. (2005b) 54.0 16.3 -4.1 91.2 15.7 7.7 -23.2 72.7

G=150 kg / m2 s G=150 kg / m2 s

x=0.1 x=0.7 Predictive methods

R1=R134a R2=R245fa

Tsat1 =5o C Tsat 2=15o C

D1=6 mm D2=15 mm

=7.5 kW/m2

=20 kW/m2 R1=R134a

R2= R245fa Tsat1 =5o C Tsat2 =15o C

D1=6 mm D2=15 mm

=7.5 kW/m2

=20 kW/m2

Jung and Radermacher (1989) 0.8 10.8 -15.5 33.1 22.2 9.9 -16.7 0.6

Kandlikar (1990) - 5.3 -16.8 86.7 - 8.8 -16.7 18.4

Liu and Winterton (1991) 49.9 9.3 -16.8 38.2 51.3 9.8 -16.7 21.6

Bandarra Filho (1997) 15.9 0.3 -25.5 17.5 11.3 1.4 -44.0 23.1

Bandarra Filho (2002) 23.8 2.1 64.6 89.3 23.7 2.1 82.7 90.8

Barbieri (2005) 13.7 1.1 -16.8 6.7 7.3 6.2 -16.8 14.9

Wojtan et al. (2005b) 41.9 14.1 -16.9 86.9 32.8 2.8 -28.6 50.2

*When not specified the calculations of, , were made for R134a based on the following conditions: Tsat=5 oC, , and di =9.5 mm

* ( ) %100*112 hhhh −=

* 1h refers to the condition characterized by subscript 1 and * 2h to the condition characterized by subscript 2

Literature review

77


As can be noticed in Tab. 2.5, the effect of saturation temperature on heat

transfer coefficient increases with increasing saturation temperature under low vapor

quality condition. This effect becomes only marginal under high vapor quality

conditions. These behaviors are captured by the predictive methods of Jung and

Radermacher (1989) and Wojtan et al. (2005b). The predictive methods of Liu and

Winterton (1991), Kandlikar (1990), Bandarra Filho (1997), Bandarra Filho (2002)

and Barbieri (2005) were not able to capture these effects.

According to Tab. 2.5, the fact that the heat transfer coefficient increases with

decreasing tube diameter is well captured by the predictive methods of Jung and

Radermacher (1989), Bandarra Filho (1997), Barbieri (2005), Wojtan et al. (2005b),

Kandlikar (1990) and Liu and Winterton (1991). The predictive method of Bandarra

Filho (2002) fails to capture the effect of the tube diameter on the heat transfer

coefficient.

Considering the influence of fluid refrigerants on the heat transfer coefficient

increase, according to Tab. 2.5, the predictive methods of Wojtan et al. (2005b) and

Liu and Winterton (1991) shows highest effect among other predictive methods like

Jung and Radermacher (1989), Bandarra Filho (1997), Bandarra Filho (2002) and

Barbieri (2005) independent of the conditions displayed in Tab. 2.5. This effect is not

accertaing for predictive method of Kandlikar (1990) since the value of fluid

dependent parameter for R245fa is not provided by the author.

The effect of heat flux on heat transfer coefficient increases with increasing

heat flux under low vapor quality condition. For higher vapor quality conditions, this

effect causes heat transfer coefficient decreases independent of mass velocity. As

shown in Tab. 2.5, these behaviors are captured by the the predictive methods of

Kandlikar (1990), Liu and Winterton (1991), Wojtan et al. (2005b) and Jung and

Radermacher (1989). The predictive methods of Bandarra Filho (1997), Bandarra

Filho (2002) and Barbieri (2005) fails to capture the effect of the heat flux on the heat

transfer coefficient.

It is interesting to highlight that in Tab.2.5, the discrepancies among the results

provided by the different predictive methods characterized the perculiarity of each

method with respect to its mode of development.


2.9 Studies concerning twisted-tapes.

2.9.1 Introduction

The process of improving the thermo hydraulic performance of heat

exchangers is referred in the literature as heat transfer enhancement. The

engineering cognisance of the need to increase the thermal performance of heat

exchanger, thereby effecting energy, material and cost savings, as well as a

consequential mitigation of environmental degradation, has led to the development

and use of many heat transfer enhancement techniques (Dalkilic and Wongwises,

2009). In general, enhancement techniques can be divided into two groups named by

Bergles (1999) as active and passive techniques. A detailed description of these

techniques is given by Webb (1994). Active techniques are heat transfer

augmentation methods which requires the addition of external energy to enhance the

heat transfer flux for a fixed wall superheating. An example of such a technique is the

vibration of tubes. Passive techniques are generally based on surface and

geometrical modifications by incorporating inserts and additional devices. Generally,

passive techniques promote higher heat transfer coefficients by disturbing and

altering the existing flow behavior. Passive techniques hold the advantage over the

active techniques due to the fact that they do not require any direct input of external

power to sustain the enhancements characteristics.

The use of heat transfer enhancement techniques lead to increase in heat

transfer coefficient but at the cost of increasing pressure drop. So, while designing a

heat exchanger using any of these techniques, analyses of both heat transfer

coefficient and pressure drop have to be done. Apart from this, issues like long term

performance and detailed economic analysis of heat exchanger has to be studied.

Bandarra Filho and Saiz-Jabardo (2006) reported that the use of devices for

intensification of heat transfer is not new in the refrigeration and air conditioning

industry, especially in the evaporators such as flooded or direct expansion type

among others. Twisted-tape is one of the passive techniques used for more than a

century and they are widely used due to the possibility of being used in a new and to

retrofit heat exchangers already in use. Twisted-tapes inserts have provided

significant heat transfer enhancement in past studies. However, until now it is not

clear, the operational conditions under which the heat transfer coefficient


augmentation by the use of twisted-tape inserts overcomes pressure drop penalty

and its use is really brings benefits to the heat exchanger.

The twisted-tape insert, schematically presented in Fig. 2.12, is geometrically

characterized by the twist-ratio, defined as the ratio between 180° turn length H and

the internal diameter as follows:

i

Hy

d= (2.117)

Figure 2.11 - Schematic view of twisted-tape insert inside a tube (Kanizawa and Ribatski 2012).

2.9.2 Single-phase flow studies

An early evaluation of the status of swirl flow studies was presented by

Gambill and Bundi (1962). According to them, a large amount of data was collected

over a broad range of working fluids, Reynolds numbers and Nusselt numbers.

The emphasis of the present study was directed towards convective boiling inside

tubes containing twisted-tape inserts. However, single-phase flow heat transfer

research with twisted-tape inserts is the ground work for the development of a study

on convective boiling heat transfer in tubes with twisted-tape inserts. Therefore, this

item is initially dedicated to single-phase flow inside tubes containing twisted-tape

inserts.Then, the literature concerning twisted-tape during convective boiling in tubes

is critically described. Heat transfer and pressure drop predictive methods for single

and two-phase flow are also described.

2.9.2.1 Experimental studies concerning single-phase flow in tubes containing twisted-tape

Table 2.6 describes schematically the studies from the literature concerning

single-phase flows inside tubes containing twisted-tape inserts. According to this

table, experiments were performed for twist-ratios between 1.81 and 12 using the


heating methods: (i) Joule effect by applying a direct current to the test section

surface; (ii) counter current flow (water glycol water mixture and steam). Test

sections made of stainless steel, Aluminium and Inconel.

Several researches have been carried out regarding augmentation of heat

transfer with twisted-tapes inserts for single-phase flow. Smithberg and Landis (1964)

analytically and experimentally studied pressure drop, velocity distribution and heat

transfer characteristics for fully developed turbulent flows in tubes containing twisted-

tape swirl generators. They observed that the use of twisted-tapes increases the

Heat transfer coefficients. Heat transfer coefficients increases especially for low twist-

ratios, but not without an increase in the friction factor. They concluded that twisted-

tapes is an inexpensive and efficient heat transfer enhancement technique

recommendable for tubular heat exchangers already in use.

The investigation of subcooled boiling by Gambill et al. (1968) yielded useful

information dealing with heat transfer and pressure drop for water flowing in tubes

with twisted-tape inserts. The results of their study showed that, the swirl flow

produced heat transfer coefficient enhancement as much as two times larger than for

axial flow of the same fluid in some ranges of Reynolds number and twist-ratios.

Lopina and Bergles (1969) found heat transfer coefficient enhancements above 20 %

for a given pumping power during both cooling and heating processes by using

twisted-tape compared to plain tubes without twisted-tape. They also proposed a

correlation for predicting single-phase flow heat transfer coefficient and the friction

factor inside tubes containing twisted-tape insert based on their experimental data.

The proposed correlations agree reasonably well with their experimental data points.

Date (1974) has investigated the twisted-tape performance for laminar single-

phase flows. Their experimental results revealed that, for high Reynolds and Prandtl

Numbers and low twist-ratios, the twisted-tape inserts increases the heat transfer

coefficients by a factor of 1.5 compared to tubes without twisted-tape at the same

experimental conditions. The study of Hong and Bergles (1976) on augmentation of

heat transfer during laminar flow in tubes containing twisted-tape inserts showed, as

expected, that the Nusselt Number is a function of the twist-ratio, and the Reynolds

and Prandtl Numbers. They observed that the heat transfer coefficient can be

improved by a factor of two to three by insertion of twisted-tapes when compared to

the flow through an empty tube at the same flow conditions


Agrawal and Varma (1991) observed that the improvement of the heat transfer

coefficient by using twisted-tape is accompanied by a drastic increase of pressure

drop, impacting the system pumping power. They found heat transfer coefficient

enhancement from 27-133% for the tube with twisted-tape relative to the same tube

without twisted-tape inserts.

Manglik and Bergles (1993a, b) observed heat transfer and pressure drop

enhancements for laminar and turbulent single-phase flow inside tubes with twisted-

tape inserts. The following mechanisms were suggested by them as responsible for

this behavior: (i) partial cross-section obstruction; (ii) hydraulic diameter reduction;

(iii) augmentation of the flow effective length; (iv) swirl flow induced by the tape; and

(v) fin effect, if a good contact between the tape and the tube wall is attained.

Chakroun and Al-Fahed (1996) have investigated the effects of twisted-tape

width on the heat transfer and friction-factor performance for laminar flow in circular

tubes containing twisted-tapes. Their results revealed that the presence of twisted-

tape inserts inside the tubes caused the friction factor and heat transfer coefficient to

increase by factors of 3 to 7 times and 1.5 to 3 times, respectively, compared to the

data for the tube without twisted-tape. The authors recommended using loose-fit

tapes for low Reynolds numbers instead of tight-fit because they are easier to install

and remove for cleaning purposes.

Agarwal and Raja Rao (1996) obtained friction factor increments from 3.13 to

9.71 times compared to values for plain tubes without twisted-tapes. Nusselt

Numbers were found to be 2.28 to 5.35 and 1.21 to 3.70 times the values for plain

tubes without twisted-tape respectively based on similar flow rate and similar

pumping power for the twist-ratio of 2.41. They concluded that lower twist-ratios are

preferable to obtain maximum heat transfer enhancement. Maximum Nusselt

Numbers for the smallest twist-ratio were also obtained by Promvonge et al. (2006).

These authors have focused their study on heat transfer and friction factor

characteristics for tubes containing twisted-tape insert and Reynolds Number from

2000 to 12000.

Naphon (2006) observed higher heat transfer coefficients for tube with twisted-

tape insert compared to those obtained for tubes without twisted-tape insert at the

same Reynolds Number. He also found that the heat transfer coefficient increases

with decreasing the twist-ratio. Joshi et al. (2011) observed an increase in heat


transfer coefficient accompany by an increase of friction factor. with decreasing the

twist-ratios.

Wongcharee and Eiamsa-Ard (2010) investigated friction and heat transfer

characteristics of laminar swirl flow for tubes inserted with alternate segment of

clockwise and counter-clockwise twisted-tapes. The experimental results revealed

that the heat transfer coefficient and friction factor associated by alternating

clockwise and counter-clockwise twisted-tapes are higher than those associated with

a single twisted-tape and plain tube without twisted-tape. They also observed that

friction factor and heat transfer coefficient increase with decreasing twist-ratio due to

the higher intensity of swirl flow and the longer flowing path.

Hata and Masuzaki (2011) have performed experiments for twisted-tape-

induced swirl flow in a short circular tube. The authors analysed the influence of the

twist-ratio, on swirl velocity, fanning friction factor and heat transfer coefficient. Their

results revealed that the friction factor and heat transfer coefficient for the tube

without twisted-tape are lower than those for the tube with twisted-tape. Moreover,

they found that this difference increases with decreasing twist-ratio for wide ranges of

Reynolds Number and swirl velocities.

Bas and Ozceyhan (2012) investigated the heat transfer enhancement for

tubes with twisted-tape inserts loosely placed in the tube. In their study, the effects of

twist-ratios and clearance ratios (ratio between the difference of the tube diameter

and the tape width and the tube diameter) on heat transfer coefficient and friction

factor. Their experimental results revealed that using twisted-tape losely positioned in

the tube instead of tightly fitted is advantageous to the heat transfer performance.

Moreover, they suggested that the best operating condition occurs for low Reynolds

Number.

Sarviya and Veeresh (2012) investigated heat transfer and friction factor

characteristics for tubes fitted with twisted casted screen. The authors found that the

heat transfer coefficient and friction factor increases with decreasing twist-ratio.

Moreover, the performance evaluation for tube with twisted casted screen is

observed to be greater than unity. They concluded that higher heat transfer rates can

be achieved using porous inserts at the expense of a reasonable pressure drop.

88

Literature review

Table 2.6 - Summaries of some studies in the literature concerning single-phase flows inside tubes containing twisted-tape inserts

Authors Fluids Tube

Orientation Internal Diameter

(mm) Twist-Ratio Material Heating Method

Objective of the Study

Smithberg and Landis (1964) Water and Air Horizontal 35.1 1.81, 2.17 and 22 -- -- f

Lopina and Bergles (1969) Water Vertical 4.92 2.48, 3.15, 3.52, 5.26 and

9.2 Inconel Direct DC

Agrawal and Varma (1991) R12 Horizontal 10 3.76, 5.58, 7.37, 10.15 and

∞ SS Direct AC ,f

Manglik and Bergles (1993 a, b)

Water and etiline-Glycol Horizontal 14 3.0; 4.5 and 6.0 -- Direct AC ,f

Agarwal and Raja Rao (1996). Oil Horizontal 25 2.41 and 4.84 SS Direct AC ,f

Chakroun and Al-Fahed (1996) Oil Horizontal 14 3.6, 5.4 and 7.1 Aluminium -- ,f

Naphon (2006) Water Horizontal 8.10 2.5 and 3 Aluminium Hot water ,f

Wongcharee and Eiamsa-Ard (2010) Water Horizontal 19 3,4 and 5 Aluminium Direct AC ,f

Joshi et al. (2011) Water Horizontal 20 9, 9.5, and 12 Aluminium Direct AC ,f

Hata and Masuzaki (2011) Water Vertical 6 2.39, 3.39 and 4.55 SUS304. Direct AC ,f

Bas and Ozceyhan (2012) Air Horizontal 56 2, 2.5, 3, 3.5 and 4 Aluminium Direct AC ,f

Sarviya and Veeresh (2012) Water Horizontal 9.5 5 and 7 Aluminium Hot water ,f


2.9.2.2 Predictive methods for single-phase flow in tubes containing twisted-tape inserts

Friction factor

Lopina and Bergles (1969) based on their data described in Tab. 2.6

developed a method for predicting friction factor during single-phase flow inside

tubes containing twisted-tape inserts. The proposed method is given as follows:

406.0

ha

s

y

75.2

f

f=

(2.118)

where is the fanning friction factor for the plain tube and is calculated by:

2.0Re046.0=af

(2.119)

Chakroun and Al-Fahed (1996) explically included Swirl Number Sw in their

method and proposed a correlation for friction factor based on their experimental

data given as follows:

( ) ( )1 62 6 2.5515.767 2 2 4 1 10

i if e d e d Swπ π − = + − − + (2.120)

The Swirl Number describes the intensity of the secondary motion induced by

the twisted-tape and is given as follows:

y

ReS Sw

W = (2.121)

where,

L

iLs

Sw

dVRe

µ

ρ= (2.122)

The swirl velocity sV is given as follows:

( )[ ] 212

as y21VV π+= (2.123)


where aV is the axial velocity given as:

c

aA

mV

ρ

&= (2.124)

cA is the axial cross-sectional area given as :

2( 4)c i iA d edπ = − (2.125)

Later on, Naphon (2006) based on his experimental data described in Tab. 2.6

and taken into account twist-ratio effects proposed a correlation for predicting friction

factor during single-phase flow inside tubes containing twisted-tape inserts. The

correlation predicted their friction factor experimental data within an error band of

±10 .The proposed correlation is given as follows:

[ ] 045.11414.0 y1Re517.3f −− += (2.126)

Wongcharee and Eiamsa-Ard (2010) developed also an empirical correlation

for the friction factor based on their experimental data given as follows:

0.304 0.89612.886Ref y− −= (2.127)

The proposed correlations agree quiet well with their experimental data and

predicted their friction factor experimental data within an error band of ±5 .

Similarly, based on their own experimental results Bas and Ozceyhan (2012)

propose a correlation for the friction factor given as follows:

( ) 65.0

i

45.0dyRe32.12f

−−= (2.128)

Hata and Masuzaki (2011) based on their experimental results proposed a

correlation for the prediction of single-phase friction factor. In their method, they took

into account twisted-tape-induced axial velocity created by the presence of twisted-

tape inserts. The proposed correlation is given as follows:

( )125.0 y17.41Re126.0f −− += (2.129)


where, µ

ρ ia dV=Re with aV calculated through Eq. (2.124)

Figures 2.12 and 2.13 display comparisons of the friction factor versus the

Swirl Reynolds Number estimated according to the predictive methods described in

this Chapter, the comparison are perfomed for single-phase flow of R134a in a 12.7

ID tube for twist-ratios of 14 and 3. Except for the predictive method of Chakroun and

Al-Fahed (1996), it is observed that the friction factor decreases with increasing Swirl

Reynolds Number for all twist-ratios as expected. This behavior is also observed for

the plain tube without twisted-tape according to Blasius (1913).

The predictive method of Chakroun and Al-Fahed (1996) provides an

unrealistic results according to which the friction factor increases with increasing

Swirl Reynolds Number. It is important to highlight in Figs. 2.12 and 2.13, the

discrepancies among the results provided by the different predictive methods

achieving differences higher than one order of magnitude.

2,500 5,000 10,000 20,000 40,0002.5x10-3

1.0x10-2

1.0x10-1

1.0x100

1.0x101

Resw [-]

f [-

]

Hata and Masuzaki (2011)

Naphon (2006)Wongcharee and Eiamsa-Ard (2010)

Chakroun and Al-Fahed (1996)

Blasius (1913)

y=14Lopina and Bergles (1969)

Figure 2.12 – Comparison among predictive methods for friction factor during single-phase flow inside tube with twisted-tape insert for R134a, Tsub =10 oC.


2,500 5,000 10,000 20,000 40,0002.5x10-3

1.0x10-2

1.0x10-1

1.0x100

1.0x101

4.0x101

Resw [-]

f [-

]

Lopina and Bergles (1969)

Wongcharee and Eiamsa-Ard (2010)Naphon (2006)Chakroun and Al-Fahed (1996)

Hata and Masuzaki (2011)

y=3

Blasius (1913)

Figure 2.13 – Comparison among predictive methods for friction factor during single-phase flow inside tube with twisted-tape insert for R134a, Tsub =10 oC.

Heat transfer coefficient (Nusselt Numbers)

Based on their experimental data Lopina and Bergles (1969) proposed a

correlation for the heat transfer taken into account swirl flow effects created by the

presence of twisted-tape inserts. The proposed correlation is given as follows:

( ) 4.08.0PrRe023.0 hd FeNu

iα=

(2.130)

where is the fin effect multiplier and Reh is the Reynolds number based on the

hydraulic diameter , hd

( )24 4

2

i i

hi i

d d ed

d d

π

π

−=

+ (2.131)

The geometric parameter α in Eq. (2.130) is defined as:

y

y

2

4 22 πα

+= (2.132)

Later on, Manglik and Bergles (1993b) have proposed a new predictive

method based on the ratio of Nusselt Numbers of the tube with twisted-tape and with


straight tape inserts (y= ∞).Their method was developed for turbulent flow and is

given as follows:

+

−

−+

−∞=

y

769.01

de4

de22

de4PrRe023.0Nu

18.0

w

b

2.0

i

i

8.0

i

4.08.0

dy i µ

µ

π

π

π

π (2.133)

where, the exponent of the viscosity ratio 0.18 is a correction factor that takes into

account the effects on large temperature differences between the fluid and the tube

wall on the transport properties estimated based solely on the bulk temperature.

Chakroun and Al-Fahed (1996) based on their experimental results have also

proposed a correlation for the Nusselt Number during single-phase flow inside tubes

containing twisted-tape inserts given as follows:

( ) 14.0

wb

3.0569.0

d PrSw318.0Nui

µµ= (2.134)

where, the Swirl Number Sw is calculated through Eq. (2.121).

Naphon (2006) proposed a correlation for prediction of the Nusselt Number

based on his experimental data described in Tab. 2.6. The proposed correlation is

valid for 5.51.3 ≤≤ y and predicted their Nusselt Number data within an error band of

±15 . The proposed correlation is given as follows:

[ ] 31475.2136.0

dd Pry1Re648.0Nuii

−+= (2.135)

Wongcharee and Eiamsa-Ard (2010) developed an empirical correlation for

prediction of single-phase Nusselt Number inside tubes containing twisted-tape

inserts based on their experimental data given as follows:

594.04.0968.0

dd yPrRe032.0Nuii

−= (2.136)

The proposed correlation agree quiet well with their experimental data and

predicted their heat transfer coefficient experimental data within an error band of

±8 .

Bas and Ozceyhan (2012), using a procedure somewhat similar to

Wongcharee and Eiamsa-Ard (2010) proposed a correlation for prediction of single-

phase Nusselt Number based on their experimental data . The proposed correlation

is given as follows:


( ) 4.045.0

i

57.0

dd PrdyRe6.0Nuii

−= (2.137)

Hata and Masuzaki (2011) proposed a correlation for the prediction of

turbulent heat transfer inside the tube containing twisted-tape by introducing the swirl

velocity swV instead of the flow velocity, V. The effects of tube diameter and length

were also take into account in the proposed correlation given as follows:

14.0

w

b

08.0

i

4.085.0

Swdd

LPrRe02.0Nu

ii

=

−

µ

µ (2.138)

where,the Swirl Reynolds Number is calculated through Eq. (2. 122)

Figures 2.14 and 2.15 illustrate comparisons of the Nusselt Numbers versus

Swirl Number estimated according to the the predictive methods described in this

Chapter for single-phase flow for R134a in 12.7 mm ID tube and twist-ratios of 14

and 3.

In general the methods proposed by Lopina and Bergles (1969) and

Wongcharee and Eiamsa-Ard (2010) provide higher Nusselt Numbers than the

methods of Manglik and Bergles (1993b), Chakroun and Al-Fahed (1996) and

Naphon (2006). The highest Nusselt Number are provided by the method of

Wongcharee and Eiamsa-Ard (2010), behavior that is intensified for the twist-ratio of

3. Additionally, unlike Lopina and Bergles (1969) and Wongcharee and Eiamsa-Ard

(2010) that present pronunced increment of Nusset Numbers with increasing Swirl

numbers, the methods of Manglik and Bergles (1993b), Chakroun and Al-Fahed

(1996) and Naphon (2006) present marginal increment of Nusselt Number with

increasing Swirl Number. It is interesting to note that in Figs. (2.14) and (2.15), the

results provided by the different predictive methods varies from one another

signifying notable descripancies among the methods.


0 500 1000 1500 2000 2500 3000 35000

1000

2000

3000

4000

Sw [-]

Nu

[-]


Manglik and Bergles (1993b)

Chakroun and Al-Fahed (1996)

Naphon (2006)

Wongcharee and Eiamsa-Ard (2010)

y=14

Figure 2.7 – Comparison among the predictive methods for Nusselt Number during during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C, p=692 kPa Tsub =19.08 oC.

0 4000 8000 12000 160000

2000

4000

6000

8000

Sw [-]

Nu

[-]

Wongcharee and Eiamsa-Ard (2010)Naphon (2006)Chakroun and Al-Fahed (1996)

Lopina and Bergles (1969)Manglik and Bergles (1993b)

y=3

Figure 2.8 – Comparison among the predictive methods for Nusselt Number during during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C, p=692 kPa Tsub =19.08 oC.

Table 2.7 describes schematically the studies from the literature concerning

two-phase flows inside tubes containing twisted-tape inserts.

96

Literature review

Table 2.7 - Description of the experimental studies concerning two-phase flow inside tubes containing twisted-tape inserts.

Authors Fluids Tube

Orientation Internal Diameter

(mm) Twisted Tape Ratio

Tape

Material Heating Method

Objective of Study

Blatt and Adt (1963) Water Horizontal 3.81,6.35 and 12.7 2.5,5.0,7.5 S S Hot water and condensing Steam ,∆p

Cumo et al.(1974) R12 Vertical 7.56 4.4 -- Hot water

Agrawal et al.(1982) R12 Horizontal 10 3.76,5.58,7.37,10.15 S S Direct AC ∆p

Jensen et al. (1985) R113 Vertical 8.10 3.94,8.94,13.92 S S Direct DC ∆p

Agrawal et al. (1986) R12 Horizontal 10 3.76,5.58,7.3710.15 S S Direct AC

Jensen and Bensler (1986) R113 Vertical 8.10 3.94,8.94,13.92 S S Direct DC

Reid et al.(1991) R113 Horizontal 10.92 11.6 SS Direct DC ,∆p

Kedzierski and Kim(1998)

R12,R22,R152a,

R134a,R290,R32/R134a,R32/R152a,

R290/

R134a, R134a/

R600a

Horizontal 9.64 4.15 Aluminium Glycol/

Water mixture

Akhavan-Behabadi et al. (2009a) R134a Horizontal 12.6 6, 9, 12, and 15 Aluminium Direct AC ,∆p

Akhavan-Behabadi et al. (2009b) R134a Horizontal 7.5 6, 9, 12, and 15 Aluminium Direct AC ,∆p

Kanizawa and Ribatski (2012) R134a Horizontal 15.9 3, 4, 9, and 14 Aluminium Direct AC ∆p


2.9.3 Flow boiling in tube contaninig twisted-tape insert

2.9.3.1 Experimental studies of two phase flow in tubes containing twisted-tape inserts.

Blatt and Adt (1963) based on the experimental conditions given in Tab. 2.7

investigated the effect of twisted-tape swirl generators on the heat transfer coefficient

and pressure drop during flow boiling inside horizontal tubes. They found that

twisted-tapes inserts improve significantly heat transfer only at low heat fluxes, low

vapor qualities and small radial accelerations and always increases substantially the

pressure drop. Cumo et al. (1974) found that the insertion of twisted-tape doubles

heat transfer coefficient. Agrawal et al. (1982) and Agrawal et al. (1986) studies

revealed that the smallest twisted-tape ratio outperformed the others, achieving

enhancement ratios up to 3.2 but at expense of pressure drop increment which

increases as the twisted-tape ratio decreases. Jensen et al. (1985) found that the

two-phase pressure drop increases from 1.2 to 3.5 times compared to empty tube for

the same flow conditions. A significant increase of the heat transfer coefficient in tube

with twisted-tape as compared to the plain tube counterpart was found by Jensen

and Bensler (1986). In the same study, they observed that the heat transfer

coefficient increase up to 2 times compared to the empty plain tube counterpart by

inserting twisted-tape. Additionally, they found that the increase in the heat transfer

coefficient is higher at high vapor qualities and mass velocities and for smaller twist-

ratios.

On contrary of Jensen and Bensler (1986) results, Kedzierski and Kim (1998)

observed an earlier falloff in the heat transfer coefficient at high vapor qualities due to

formation of partial dryout in the tube. The results from Reid et al. (1991) revealed

that the heat transfer enhancement factor decreases with increasing mass velocity.

Akhavan-Behabadi et al.(2009a) investigated the effect of twisted-tape inserts

on heat transfer enhancement and pressure drop in horizontal tubes. Their results

show that the insertion of twisted-tapes inside the tube enhances the heat transfer

coefficient by as much as 57 % above the results for plain tube without twisted-tape.

These authors also observed as much as 180 % pressure drop augmentation

compared to empty tube at low vapor quality region and mass velocity of 54 kg / m2 s

for the smallest twist-ratio. This behavior occurred due the fact that, flow pattern

changed to annular and as a result, the pressure drop increases relative to the plain


tube in which the flow pattern is stratified-wavy. Moreover, contrary to Kedzierski and

Kim (1998) finding, Akhavan-Behabadi et al.(2009a) revealed that twisted-tapes are

more beneficial to the evaporator performance when installed at the end part of the

tube, preventing the formation of partial dryout and increasing the heat transfer

coefficient.

Highest enhancement in heat transfer coefficient for lowest twist-ratio of 6 was

obtained by Akhavan-Behabadi et al. (2009b). On performance evaluation basis for

similar pumping power, for low mass velocity conditions, best performance were

observed for highest twist-ratio of 15 while twist-ratios of 9 and 12 provided best

performance under high mass velocity conditions.

Kanizawa and Ribatski (2012) experimentally studied two-phase flow patterns

and pressure drop inside horizontal tubes containing twisted-tape inserts. The

authors observed that the frictional pressure drop penalty (defined as the ratio

between the experimental frictional pressure drop for the tube with twisted-tape insert

and its corresponding value for the plain tubes without inserts) due to the twisted-

tape is highly influenced by vapor quality and that this effect is more prominent for

reduced twist-ratios. The authors also found that the variation of the saturation

temperature from 5 to 15 °C have almost negligible effects on the pressure drop

penalty.

2.9.3.2 Predictive methods for two-phase flow and flow boiling inside tubes containing twisted-tape inserts.

This section presents some of the few available predictive methods from the

literature for the prediction of two-phase flow pressure drop and heat transfer

coefficient during flow boiling inside tubes containing twisted-tape inserts.

Pressure drop.

Most of the methods for predicting the frictional pressure drop during two-

phase flows inside tubes containing twisted-tape inserts are based on multipliers of

either pressure drop or friction factors for tubes without twisted-tape.


Agrawal et al. (1982)

Based on the database described in Tab. 2.7, Agrawal et al. (1982) proposed

a method to estimate the pressure drop for two-phase flow inside tubes with twisted-

tapes. The proposed method is given as follows:

509.0

PT2

TT

y

12.5

p

p=

Φ∆

∆ (2.139)

where TT and PT indicates the pressure drop for the same tube with and without

twisted-tape, respectively. In this method, the pressure drop for two-phase flow in a

tube without twisted-tape inserts is calculated according to the Lockhart-Martinelli

and Nelson (1949), described in section 2.6.2.1 considering the internal diameter of

the tube.

Jensen et al. (1985)

These authors proposed a method to estimate the pressure drop for two-

phase flow inside tubes with twisted-tapes using a procedure somewhat similar to

Agrawal et al. (1982). In their method, the ratio of the friction factor for the same tube

with and without twisted-tape is given as a function of the twist-ratio. The method

proposed by Jensen et al. (1985) is given by the following equations:

(2.140)

(2.141)

where, the subindex h corresponds to the estimative of the friction factor based on

hydraulic diameter calculated according to Eq. (2.132).

The friction factor for tube without twisted-tape insert is estimated according to

correlation of Reddy et al. (1983) apud Jensen et al. (1985), and is given as follows:

(2.142)

where is the friction factor for the two-phase mixture as liquid calculated

according to Eq. (2.38). The two-phase multiplier in Eq. (2.142) is given by:


(2.144)

where,

(2.144)

(2.145)

In Eqs. (2.144) and (2.145), is the reduced pressure.

Akhavan-Behabadi et al. (2009a)

Akhavan-Behabadi et al. (2009a) adopted a procedure similar to Agrawal et al.

(1982) in order of developing a new predictive method. Based on their data, they

proposed the following correlation to calculate the pressure drop inside tubes with

twisted-tape inserts:

28.0

PT2

TT

y

1.5

p

p=

Φ∆

∆ (2.146)

In the method of Akhavan-Behabadi et al. (2009a), the pressure drop during

two-phase flow in tubes without twisted-tape inserts is calculated according to the

method of Friedel (1979) described in section 2.6.2.1 considering as characteristic

dimension the internal diameter of the tube.

Kanizawa and Ribatski (2012)

Kanizawa and Ribatski (2012) have proposed a flow pattern based method to

predict pressure drop during two-phase flow in tubes with twisted-tape inserts. The

effect of vapor quality which is not contemplated by the aforementioned predictive

methods is capture by the proposed correlation. Their predictive method is given as

follows:

( )( )

1/55

5(1 )

0.65 1.88 2.10 0.1361.04 8.94 (1 )

6.68 1 19.381

m x

TT

xx m xPT L

ep

p y ey e Fr e

− −

− −

− ∆ − = + ∆ Π +

(2.147)

where the liquid Froude Number is given as follows:


( )

h

2

L

2

Lgd

x1GFr

ρ

−=

(2.148)

The dimensionless Π in Eq. (2.147) corresponds to the ratio of inertial effects

according to the axial and radial directions. This dimensionless is given as follows:

( )VL

H

2y2

ρρ

ρΠ

−= (2.149)

where ρH is the density of the two-phase mixture estimated according to the

homogeneous model.

The value of the exponent m was imposed by the authors equal to 40 in order

of fitting single-phase flow conditions. The plain tube pressure drop is evaluated

based on the Grönnerud (1979) method described in section 2.6.2.1 and is

calculated based on the hydraulic diameter h

d defined according to Eq. (2.131).

Figures 2.16 to 2.17 illustrate comparisons among the pressure drop

predictive methods described in this Chapter for two-phase flow for R134a in tube

diameter of 15.9 mm, mass velocities of 75 and 150 kg / m² s, saturation temperature

of 5 oC and twist-ratios of 14 and 4. These figures reveals notable descripancies

among the methods.

As shown in Figs 2.16 and 2.17, predictive methods of Jensen et al. (1985),

Agrawal et al. (1982), Akhavan-Behabadi et al. (2009a) and Kanizawa and Ribatski

(2012) present pressure drop gradient increases with increasing vapor quality and

decreasing twist-ratio, independently of the mass velocity.

Agrawal et al. (1982) presents discontinuity in pressure drop gradient for high

vapor quality region according to Figs 2.16 and 2.17. This behavior is significantly

different from those trends displayed by the other predictive methods and is related

to change in flow pattern transitions with the increasing vapor qualities.

Additionally, unlike the other methods, the influence of flow pattern on

pressure drop is well captured by Kanizawa and Ribatski (2012) method, capturing

the pressure drop inflection related to the transition from stagnant flow to intermittent

flow patterns at low vapor quality region shown in Fig. 2.16, and pressure drop

gradient peak for high vapor quality region. This is due to the fact that this method is

a flow pattern based method.


However, the predictive method of Kanizawa and Ribatski (2012) is observed

to be the best among other predictive methods abovementioned because, it

considered in details the influence of flow pattern on pressure drop gradient for both

low and high mass velocities conditions. Additionally, the effect of vapor quality, a

significant factor in the estimate of the increase in pressure drop was taken into

account by Kanizawa and Ribatski (2012) method what was absent in the predictive

methods of Agrawal et al. (1982) and Akhavan-Behabadi et al. (2009a).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.5

1.0

1.5

[-]

∆∆ ∆∆p

/

L

[kP

a/m

]





G=75 kg/m2s, y=4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.5

1.0

[-]

∆∆ ∆∆p

/

L

[kP

a/m

]


Agrawal et al. (1982)Jensen et al. (1985)Akhavan-Behabadi et al. (2009a)

G=75 kg/m2s, y=14

Figure 2.16 – Comparison among predictive methods for pressure drop during two-phase flow inside tube with twisted-tape insert for R134a, Tsat =5 oC, di = 15.9 mm.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

[-]

∆∆ ∆∆p

/

L

[kP

a/m

]





G=150 kg/m2s, y=4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

1.0

2.0

3.0

4.0

[-]

∆∆ ∆∆p

/

L

[kP

a/m

]





G=150 kg/m2s, y=14

Figure 2.17 – Comparison among predictive methods for pressure drop during two-phase flow inside tube with twisted-tape insert for R134a, Tsat =5 oC, di = 15.9 mm.

Heat transfer coefficient


These authors based on their experimental data described in Tab. 2.7 found

that the heat transfer coefficient enhancement depends on the effect of twist-ratio,

heat flux and mass velocity. Based on this fact, they proposed a method according to


which the ratio of the flow boiling heat transfer coefficients for the tube with and

without twisted-tapes inserts is correlated as a function of the Reynolds Number,

Boiling Number and twist-ratio. Their method is given as follows:

5219.0624.1247.2

2

TT yBoRe002944.0h

h −=Φ

(2.150)

where, Φ2h is the heat transfer coefficient for plain tube estimated according to Bo

Pierre (1964) correlation. Bo Pierre (1964) is a correlation for predicting average heat

transfer coefficient during flow boiling of refrigerant in a horizontal evaporator and is

given by:

n

LV2

L

i

L

2L

xhRe

d

kBh

=

∆Φ (2.151)

where for 9.0≤outx , B=0.0009 and n=0.5, for 9.0>outx , B=0.0082 and n=0.4.

Jensen and Bensler (1986)

Based on their data described in Tab.2.7, Jensen and Bensler (1986)

developed a predictive method for heat transfer coefficient during flow boiling in

tubes containing twisted-tape inserts according to the following procedure (i) Obtain a

reasonable prediction of plain tube data using well-established correlation from the

literature; (2) modify the plain tube correlation to predict the data for tubes with

twisted-tape.The method proposed by Jensen and Bensler (1986) is given as follows:

( ) 4.0

L

8.0

h

h

L

TT PrRe02.0d

kh α= (2.152)

where,

( )

l

h25.1

h

dx1GFRe

µ

−= (2.153)

1F = for 1.0X

1tt

< (2.154)


736.0

tt

213.0X

135.2F

+= for 1.0

X1

tt

≥ (2.155)

α and hd are estimated using Eqs. (2.132) and (2.131) respectively

Akhavan-Behabadi et al. (2009b)

Akhavan-Behabadi et al. (2009b) proposed a method to estimate heat transfer

coefficient during flow boiling in tubes containing twisted-tape inserts. using a

procedure somewhat similar to Agrawal et al. (1986). Based on this fact, they

proposed a method according to which the ratio of the flow boiling heat transfer

coefficients for the tube with and without twisted-tapes inserts can be correlated as a

function of the Reynolds Number, Boiling Number and twist-ratio. The proposed

method is given as follows:

2156.1yBoRe0056.0h

h 5.0532.1214.2

2

TT += −

Φ

(2.156)

where, Φ2h is estimated using Eq. (2.88)

Figures 2.18 to 2.21 show comparisons among the heat transfer coefficient

methods described in Tab. 2.7 for the refrigerant R134a, tube diameters of 12.7 and

15.9 mm, mass velocities of 75 and 150 kg / m² s, saturation temperature of 5 oC and

twist-ratios of 9 and 4.

Generally speaking, according to the predictive methods described in this item

the heat transfer coefficient increases with decreasing twist-ratio and increasing

mass velocity and vapor quality.

According to Figs. 2.18 to 2.21, the methods of Akhavan-Behabadi et al.

(2009b) and Agrawal et al. (1986) reveals that the heat transfer coefficient decreases

with increasing vapor quality independent of the tube diameter. According to the

predictive method of Jensen and Bensler (1986), the heat transfer coefficient

increases with increasing vapor quality until a peak at vapor qualities close to 1. This

peak is relate to the onset of dryout that is responsible for a drastic falloff of heat

transfer coefficient. It can also be noted, according to the methods of Akhavan-

Behabadi et al. (2009b) and Agrawal et al. (1986) that, the heat transfer coefficient in

a 15.9 mm ID tube is higher than that in smaller 12.7 mm ID tube. On the other hand,


Jensen and Bensler (1986) estimated higher heat transfer coefficients in the 12.7 mm

ID tube compared to the 15.9 mm ID tube, as expected. However, the predictive

method of Jensen and Bensler (1986) is observed to present best performance

among other predictive methods abovementioned, predicting the increase of heat

transfer coefficient with increasing vapor quality, decreasing tube diameter and twist

ratios, independently of the mass velocity.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

x [-]

h [

kW /

m2 o

C ]



Agrawal et al. (1986) y=4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

x [-]

h [

kW /

m2

oC

]

Akhavan-Behabadi et al. (2009b)Jensen and Bensler (1986) Agrawal et al. (1986) y=9

Figure 2.18 - Variation of the heat transfer coefficient with vapor quality according to predictive methods for heat transfer coefficient during flow boiling inside tubes containing twiste-tape, di = 12.7

mm, φ = 10 kW / m2, G = 75 kg / m² s, Tsat =5 oC

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

2.0

4.0

6.0

8.0

x [-]

h [

kW /

m2

oC

]




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

1.0

2.0

3.0

4.0

5.0

x [-]

h [

kW /

m2

oC

]



mm,φ = 10 kW / m2, G = 150 kg / m² s, Tsat = 5 oC.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

x [-]

h [

kW /

m2

oC

]

Akhavan-Behabadi iet al. (2009b)

Jensen and Bensler (1986) Agrawal et al. (1986) y=4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

1.0

2.0

3.0

4.0

x [-]

h [

kW /

m2

oC

]


Jensen and Bensler (1986) Agrawal et al. (1986) y=9


mm, φ = 10 kW / m2, G = 75 kg / m² s, Tsat = 5 oC.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

2.0

4.0

6.0

8.0

10.0

12.0

x [-]

h [

kW /

m2

oC

]




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

x [-]

h [

kW /

m2 o

C ]


Figure 2.21 - Variation of the heat transfer coefficient with vapor quality according to predictive

methods for heat transfer coefficient during flow boiling inside tubes containing twiste-tape, di = 15.9 mm,φ = 10 kW / m2 ,

G = 150 kg / m² s, Tsat = 5 oC.

2.9.4 Conclusions based on the literature review.

Studies from the open literature revealed that flow boiling in tubes containing

twisted-tape inserts present higher heat transfer coefficients than plain tubes without

inserts. In general, the heat transfer coefficient increases with decreasing twist-ratio

due to high velocity of fluid in the vicinity of the tube wall generated by the twisted-

tape. It is also observed in the literature that the increase of the heat transfer

coefficient by the tape is always accompanied by a drastic increase in the pressure

drop and consequently augmentation of the pumping power of the system.

Comparison among the predictive methods from literature for heat transfer coefficient

during two-phase flow inside tube containing twisted-tape inserts presented in

section 2.9.3 have revealed notable discrepancies. Therefore, an accurate heat


transfer predictive method taken into account the swirl effects promoted by the tape

on the heat transfer coefficient inside horizontal tubes containing twisted-tapes

inserts is still necessary and is one of the objectives of the next Chapters.

108 Equipment, experimental procedure and data reduction

3 EQUIPMENT, EXPERIMENTAL PROCEDURE AND

DATA REDUCTION

3.1 Introduction

This chapter describes the experimental bench and procedures adopted in the

present study. The data reduction procedures are detailed. Finally, the experimental

uncertainties of the measured and calculated parameters are presented.

The experimental apparatus is located at the Department of Mechanical

Engineering of the School of Engineering of São Carlos (EESC-USP) and was built

for the previous study of Kanizawa (2011). In the present study, results were

obtained for the heat transfer coefficient and pressure drop using two test sections

with internal diameters of 12.7 and 15.9 mm. In the study of Kanizawa (2011) flow

pattern and pressure drop results were obtained for the 15.9 mm ID test section for

R134a and the same twist-ratios considered in the present study. The photograph of

the experimental set up is presented in Fig. 3.1.

Figure 3.1 - Photograph of the experimental bench.

Equipment, experimental procedure and data reduction 109

3.2 Experimental bench

The experimental setup is comprised of refrigerant and ethylene-glycol/water

circuits, named also as primary and secondary circuits, respectively. Figure 3.2

presents schematically the refrigerant closed loop that globally comprises a micro-

pump to drive the working fluid through the test circuit, a sub-cooler, a pre-heater to

establish the experimental conditions at the inlet of the test section, a flow

stabilization section, a test section, two visualization sections, a heat exchanger to

condense the vapor generated in the heated sections and a refrigerant tank. The

secondary circuit, partially shown in Fig. 3.2, is responsible for the cooling effects in

the condenser and in the sub-cooler. This circuit contains a vapor compression

refrigeration cycle responsible for cooling the mixture of 60% of ethylene glycol in

water. This anti-freezing solution is driven by a centrifugal pump through the

condenser and the sub-cooler. The refrigeration cycle rejects heat to the external

environment through an evaporative cooling tower.

Figure 3.2 - Schematic diagram of the refrigerant circuit.

Figure 3.3 shows schematically the thermodynamic processes of the test fluid

along the refrigerant circuit. The numbers shown in Fig. 3.2 correspond to the

thermodynamic states indicated in Fig. 3.3.

The process 7-1 on the P - h diagram shown in Fig.3.3 corresponds to the

pumping process of the test fluid through the circuit by the micro-pump, increasing its

2

6

5

4

3

7 1


pressure until the state 1. The process 1-2 is the local pressure drop of the fluid

across the Coriolis type flowmeter. The process 2-3 corresponds to sub-cooling of

the working fluid in the sub-cooler to ensure that the fluid is sub-cooled at the pre-

heater inlet. During process 3-4, the vapor quality at the pre-heater outlet is adjusted

by adding electrical power to the system, heating the fluid and establishing the

experimental conditions at the inlet of the test section of the state 4. The process

between states 4 and 5 is to supply heat to the refrigerant in the pre-heater and the

test sections. The change in slope of the process between states 4 and 5 from the

saturated liquid line is related to the higher pressure drop gradient in processes

involving evaporation when compared to single-phase flow. The evaporation process

continues until state 5 corresponding to the output of the test section. Expansion of

the fluid at the entrance of the condenser resulting in decreasing of the refrigerant

temperature and consequently, its pressure occurs during process 5-6. Finally, from

state 6, the condensation of the fluid occurs until it arrive at state 7 in a subcooled

liquid state .

-50 0 50 100 150 200 250 300 350101

102

103

104

105

h [kJ/kg]

15°C

5°C

0°C

0.2 0.4 0.6 0.8

0

0.2

0.5

0.7

0.9

kJ/

kg-K

P [

kPa]

15°C

5°C

0°C

0.2 0.4 0.6 0.8

0

0.2

0.5

0.7

0.9

kJ/

kg-K

R134a

1

23 4

7

5

6

Figure 3.3 - Thermodynamic process of the refrigerant along the refrigerant test circuit.

3.2.1 Test section

The test sections are 2 m long brass and copper tubes with nominal internal

diameter of 12.7 and 15.9 mm, respectively. Both tubes have the same wall

thickness of 3.2mm with peak-to-valley roughnesses of 7.65 and 9.5 µm for the 12.7

and 15.9 mm internal diameter, respectively. In the test section were installed a total


of 16 thermocouples, evenly distributed in four cross sections. The first section is

positioned 460 mm from the test section inlet. The distances between neighbour

temperature measurement cross sections are 460 mm. Figure 3.4 shows the

schematic diagram of the test section and the thermocouples distribution.

Figure 3.4 - Schematic diagram of the test section and the thermocouples distribution.

In each section, the thermocouples were distributed at 90° apart, as indicated

in Fig. 3.5. The use of four thermocouples has the following objectives (i) obtain a

cross-sectional average heat transfer coefficient representative of the tube perimeter;

(ii) validate the measurements through comparison between the results given at the

sides; and (iii) to investigate the differences among local heat transfer coefficient

along the perimeter of the test section, related to stratification flow effects.

The test section heating effect was obtained by five electric heaters (tape type)

with nominal power of 624 W each, manufactured by Amptek, models AWH-052-

080D-Duo-Tape with width of 12 mm and length of 2400 mm. These resistors are

powered by a variable autotransformers (Variac) with maximum power of 3kW/220V.

The supplied electrical power is measured through active power transducers, model

2285A of Yokogawa. This heating system allows heat fluxes up to 30 kW / m². The

test section is insulated thermally with three layers of ceramic fibre with a density of

64 kg / m³ and nominal thickness of 50 mm, covered with a layer of Armaflex brand of

25 mm thickness rubber foam in order to reduce heat exchanges with the external

environment.


Figure 3.5 - Positioning of thermocouples for each cross section along the test section.

3.2.2 Visualization sections

Two visualization sections are installed in the refrigerant circuit with the aim of

verify flow pattern transitions along the test section during the experiments. The first

one is installed between the outlet of the pre-heater and the test section inlet while

the second is located just downstream the test section outlet. The visualization

sections are 140 and 210 mm length, respectively. They are made of bore silicate

with internal diameter of 16.4 mm and wall thickness of 1.8 mm. Figure 3.6 shows the

visualization section just downstream the test section outlet.

Figure 3.6 - Visualisation section at the test section outlet.

3.2.3 Pressure drop measurement instruments

For the measurement of pressure drop along the test section, three

differentials pressure transducers from Endress–Hauser, PMD-75 model were

installed in the test section as shown in Fig. 3.7. Their nominal ranges are equal to ±

3, 10 and 300 kPa with accuracy equal to 0.075% of the set span. It is adopted more

Thermocouples positions 2 and 4 are Lateral, 1 is Upper and 3 is Bottom


than one differential pressure transducer in order to reduce the relative error during

measurements since the experiments covers a wide pressure drop range. The

capiliarries tubes connecting the differential pressure transducers were heated up by

circulating hot water from a thermostatic bath through copper tubes

contacting the capillaries. The purpose of heating the capillary was preventing

formation of bubbles in the capillaries and to guarantee that the sensors are always

in contact with vapor at their both sides, otherwise they would provide erroneous

measurement.

Figure 3.7 - Illustration of fitting of differential pressure transducers.

3.2.4 Temperature measurements

Wall temperatures along the test section were measure with K-type

thermocouples of 120 m wire diameter with accuracy of 0.13oC. These

thermocouples were nested in longitudinal grooves 0.5 mm distant from the internal

surface, filled with high-conductive epoxy and distributed in four sections 460 mm

distant from each other. At each measuring cross section, the surface temperature

was read at four locations 90o spaced from the bottom to the top of the tube.

In the present study the thermocouples nested on the test section surface

were used for determining the heat transfer coefficient during diabatic tests and the

exchange of heat in the test section between the working fluid and the environment.


3.2.5 Pre-Heater Section

The pre-heater is used to control and adjust the thermodynamic state, and

consequently the vapor quality, at the test section inlet. It consists of a 12.7 mm ID

copper tube, wrapped with 20 electrical resistances that totalize 12 kW. The system

is thermally insulated with ceramic fiber and elastomeric foam in order to reduce the

heat exchange with the environment. The pre-heater possess two thermocouples

(0.120 mm wire diameter) fixed within its tube wall. Additionally, absolute pressure

transducers and thermocouples were installed in the pre-heater inlet and outlet. The

heating effect in the pre-heater is controlled through electrical resistances powered

by two variable autotransformers (Variac), with power ratings of 3 and 9 kW. The

electrical power supplied to the pre-heater is measured by active power transducers,

model 2285A of Yokogawa. Figure 3.8 shows a photograph of the pre-heater, without

the elastomeric insulation foam, illustrating part of the ceramic fibre insulation and the

upper portion of the coil with the electrical resistances installed on its surface.

Figure 3.8 - Photograph of the Pre-heater.

3.2.6 Flow Stabilization section

The flow stabilization section consists of a horizontal 1.4 m long tube of the

same inner and outer diameters and material of the test section. The stabilization

section is used to guarantee that the flow at the test section inlet is fully developed.

For the setup with 15.9 mm ID tube, this length corresponds to approximately 90

diameters, and for 12.7 mm ID tube, it corresponds to 110 diameters. Both values

are considered sufficient for the two-phase flow development. The stabilization

section and the pre-heater are contained in the same thermal-insulation device

separated by a wide layer of ceramic fiber.


3.2.7 Sub-Cooler

The sub-cooler is a tube-in-tube heat exchanger type with the test fluid flowing

in the internal tube. The sub-cooler is used to ensure that the fluid is sub-cooled at

the pre-heater inlet. Thus, the thermodynamic state of the fluid at the pre-heater inlet

is estimated based on the local temperature and pressure measurements. The

temperature of the refrigerant at the sub-cooler outlet and pre-heater inlet is

measured with a thermocouple (0.120 mm wire diameter), installed in a bulb

positioned in the center of the tube cross section. The inner tube has a nominal size

of ½ "(12.7 mm), and the outer 1 ½". The cooling effect in the sub-cooler is obtained

through the circulation of the anti-freezing solution from the ethylene-glycol circuit.

3.2.8 Condenser

The function of the condenser is to condense and subcool the working fluid

heated up in the test section and the pre-heater. It also allows controlling the

saturation temperature by adjusting the pressure in the system. It is a shell and tube

type heat exchanger and its cooling effect is obtained through the solution of

ethylene-glycol and water circulating inside the tubes. The flow rate of ethylene-

glycol and water solution through the condenser is controlled manually with the help

of a needle valve. The condenser is insulated with elastomeric foam manufactured by

Armaflex, with a thickness of 25 mm.

3.2.9 Reservoir

The refrigerant reservoir main objective is to adjust the refrigerant inventory

without adding any external refrigerant charge to the overall refrigerant circuit

(including the reservoir itself). It consists of a bottle of refrigerant wounded round with

a coil consisting of a copper tube inside which the solution of ethylene-glycol / water

from the chiller is circulated. The reservoir is insulated with elastomeric foam

(armaflex) of 25 mm thick and is suspended by a dynamometric balance (full scale

reading of 90 kg) for registering the amount of refrigerant in the main circuit. The

reservoir is connected to the refrigerant circuit through a ½ " copper tube. A ball valve

is installed in the connection line in order to isolate the reservoir from the refrigerant

circuit.


3.2.10 Micro Pump

A micro-pump gear type that works without lubricant, drives the test fluid

through the refrigerant circuit. The micro pump is of 223/56C model with nominal

displacement of 3.48 ml per rotation. Its gear is made from a material commercially

known as Ryton and the coupling between the drive shaft and gears is magnetic. The

motor speed is controlled through a frequency converter, Danfoss VLT-2800 model

with frequencies from 0 to 60 Hz and output of 0 to 10 V using the communication

and data acquisition system control.

3.2.11 Flow meter

The mass flow in the refrigerant circuit is measured through a Coriolis type

mass flow meter. The Coriolis type mass flow meter is a flowmeter of 2100 model

with calculated uncertainty of ± 0.276 kg / m² s and measuring range from 1 to

52,000 kg / h or 867 kg / min

3.3 Ethylene-Glycol/Water Solution Circuit

The ethylene-glycol / water circuit, not completely illustrated in Fig. 3.2, is an

auxiliary circuit responsible for the cooling effects of the test fluid in the refrigerant

circuit. The solution is composed of 60% ethylene glycol in water and its freezing

temperature is about -55 °C. This solution is driven through the circuit by a centrifugal

pump and flows from a tank of 60 litters, through the closed loop containing the

condenser and the sub-cooler, both in the refrigerant circuit, and the evaporator of

the chiller. Electrical heaters of 12 kW were installed inside the tank. The power

supplied by the electrical heater is controlled by a PID controller actuating on solid-

state relay based on the temperature of the solution in the tank measured by a PT-

100 sensor and the temperature imposed to the control by the operator. The

electrical heater works in order to compensate the variation of the cooling power and

keep a minimal thermal load in the refrigerant circuit. Then, the chiller rejects the heat

to the external environment through an evaporative cooling tower.

3.4 Control and Data Acquisition System

Monitoring, controlling and recording of experimental results were conducted

using a data acquisition system from National Instruments installed on a personal


computer of 3.0 GHz processor. The data acquisition system is comprised of 40

channels for voltage reading and 2 channels for output voltage; a chassis multiplexer

SCXI-1000, a board to communicate with the computer (NI PCI 6221); a SCXI 1302

terminal for acquisition and transmission of analog signals; SCXI 1303 terminal for

amplifying analog signals and SCXI 1112 terminal for amplifying the read enable

signal from the thermocouples and cold junction compensation.

A PI type controller is designed so that an analog signal is given by the data

acquisition system and acts on the variable-frequency drive base on the mass

velocity determine by the operator and the mass flow measurement provided by the

Coriolis flowmeter. Due to the fact that the absolute and differential pressure

transducers provide as an output signal of 4-20 mA, electrical resistors designed for

military application of 250 Ω were used with 0.1% error. The resistors were installed

in parallel with the terminals of the data acquisition system given voltage signals

between 1-5 V. These are precision resistors and present negligible variation in their

value with temperature.

Figure 3.9 shows schematically the components and the terminals of the

acquisition system.

Figure 3.9 - Schematic diagram of the acquisition system and terminals.

A LabVIEW version 8.2 from National Instruments was used to develop the

software for data acquisition and control of the apparatus. Calibration curves of the

sensors and transducers were also added to the program. Figure 3.10 shows the

interface of the LabVIEW software used to control and monitorate the test facility and

record the data.


Figure 3.10 - Image of the program implemented for data acquisition.

3.5 Twisted-tape inserts

The twisted-tape inserts are made from an aluminum foil of 1.0 mm thick and

2.0 meters long, and are manufactured as suggested by Lopina and Bergles (1969).

A weight of approximately 20 kg was hanged at the free edge of the tape, while its

upper end is clamped in a fixed structure. Then, the weight is slowly twisted until the

desired twist-ratio is obtained. Due to the fact that the test section plus the

visualizations and stabilization sections are longer than the aluminum foil, for each

twist-ratio two strips were prepared and welded together in order to obtain a twisted-

tape length covering from the stabilization section until the downstream visualization

section. Twisted-tapes with twist-ratios, y, of 3, 4, 9 and 14 were manufactured for

each diameter. Figure 3.11 presents an image of the twisted-tapes inserts for 12.7

and 15.9 mm ID tubes. The tapes were loosly positioned in the test section, in order

to allow the change between different tapes, and are unmovable by the flow, due to

friction with the wall and to the fact that they are fixed by the curve of the piping

downstream the last visualization section. The clearance in diameter between the

tape and the tube wall is equal to 0.6 mm in average for the 15.9 mm ID tube, and

equal to 0.5 mm for the 12.7 mm ID tube.


Twisted-tape inserts for 12.7 mm ID

Twisted-tape inserts for 15.9 mm ID

Figure 3.11 - Photograph of the twisted-tape inserts used during the experimental compaign.

y=3

y=3

y=4

y=4

y=9

y=9

y=14

y=14


3.6 Experimental procedure

3.6.1 Single-phase flow tests

During single-phase flow experiments, firstly the valve connecting the main

circuit and the refrigerant reservoir was open. So, all the main circuit was filled with

liquid refrigerant corresponding to the addition of 18 kg of refrigerant to the main

circuit compared to two-phase flow experiments. Single-phase pressure drop

experiments were carried out under adiabatic conditions.

Before starting the experiments and after turning on the data acquisition

system, all the transducers and sensors were evaluated to check for possible

inconsistencies of their signal, i.e. null values of pressure drop, mass velocity and

heat flux, and almost similar absolute pressures along the refrigerant circuit. Then,

single-phase flow was imposed to the circuit by turning on the micro-pump through

the data acquisition system. Then under adiabatic conditions the temperatures given

by the thermocouples along the test section and pre-heater are compared and the

temperatures indicated by the thermocouples are considered correct if their

measurements indicate temperature differences less than 0.3 °C. After the check of

the measurements, the thermostatic bath was turned on and its temperature was set

equal to 70 °C to heat the capillary tubes connecting the pressure differential

transducers to the test circuit. Then, the mass velocity was set by act on the variable

frequency drive through the data acquisition system and the mass flow measurement

provided by the Coriolis flowmeter. The ethylene-glycol/water circuit and the electrical

heating system are activated only after the mass velocity was set.

In addition to the procedure adopted for single-phase pressure drop

experiment, during single-phase heat transfer experiment and energy balance

validation test, the electrical resistance for the pre-heater and test section were also

activated. Then, the fluid temperature at the test section was adjusted by

manipulating a needle valve that determines the flow rate of ethylene-glycol/water

solution through the condenser.

The electrical power supplied to both sections was manually adjusted through

variable transformers and measured with electrical power transducers. It is

interesting to note that, the abscense of vapor bubbles during single-phase

experiment was assured by maintaining a minimum of 10 oC of the subcooling of the


test fluid at the test section outlet. The absence of the bubbles was also verified

through the visualization sections installed in the refrigerant circuit.

Steady state conditions were assumed when the variations of the

temperatures given by the thermocouples within the fluid at the inlet and outlet of the

test section were kept lower than twice the thermocouple uncertainty during a period

of at least 3 minutes. The recording system was initiated only after the establishment

of steady state conditions, and the experimental data were acquired during at least 1

minute with a recording rate of 25 Hz.

3.6.2 Two-phase flow test

Initially, the amount of refrigerant was adjusted by adding or draining

refrigerant from the main circuit to the refrigerant reservoir. The removal of refrigerant

from the main circuit was done by circulating the anti-freezing solution through the

coil in contact with the refrigerant reservoir, decreasing the refrigerant temperature

and consequently, its pressure. On the other hand, the addition of refrigerant was

implemented by circulating the anti-freezing solution through the condenser,

decreasing the temperature in the main circuit and consequently, its pressure. In the

container. So, the refrigerant was driven from the reservoir to the main circuit and

vice-versa by pressure gradient. Once the desired amount of refrigerant estimate

with the help of dynamometer was attained the ball valve connecting the reservoir

and the refrigerant circuit was closed. During the two-phase flow experiments, the

valve connecting the main circuit to the refrigerant tank was kept closed.

The procedures for the initiation of the experiments for two-phase flow are

similar to those adopted for the single-phase flow experiments. The consistency

among the different measurements of temperature and pressure were initially

observed. Subsequently, the mass velocity was set by act on the variable frequency

drive through the data acquisition system and the mass flow measurement provided

by the Coriolis flowmeter.

The ethylene-glycol/water circuit and the electrical heating system are

activated only after the mass velocity was set. The saturation temperature at the test

section was adjusted by manipulating a needle valve that determines the flow rate of

ethylene-glycol/water solution through the condenser. The vapor quality at the test

section inlet was obtained by imposing the appropriate heat flux to the pre-heater. By

varying the power supplied to the pre-heater, experimental results for distinct vapor


qualities at the test section inlet were obtained keeping the remaining parameters

constant.

During the experiment, a sharp decline in the system pressure was observed

with increasing the fluid flow rate under higher vapor qualities conditions and for the

lowest saturation temperature of 5 oC. This is related to the fact that there is increase

in specific volume of the fluid and hence lead to a higher pressure drop, which

subsequently beyond the capacity of experimental bench component.

Experimental data were gathered for mass velocities (referred to the plain

tubes cross sectional area) of 75, 100, 150 and 200 kg / m² s saturation temperatures

Tsat equal to 5 and 15 °C, and heat fluxes of 0, 5 and 10 kW / m². For adiabatic

experiments, the inlet vapor quality was varied from 5 to 95 %, with increments of 5

%, and for diabatic experiments the inlet vapor quality were varied from 5 %, with

increment of 5 % with the outlet vapor quality depending on the energy balance along

the test section. The system was automatically turned off when dryout conditions at

the test section outlet were achieved. Dryout conditions were characterized by a

drastic increase in the wall temperature indicated by the thermocouples.

As for single-phase tests, steady state conditions were also assumed when

the variations of the temperatures given by the thermocouples within the fluid at the

inlet and outlet of the test section were kept lower than twice the thermocouple

uncertainty during a period of at least 3 minutes. The recording system was initiated

only after the establishment of steady state conditions, and the experimental data

were acquired during at least 1 minute with a recording rate of 25 Hz.

3.7 Data reduction Procedures

In the present item, the data regression procedure used to obtain the heat

transfer coefficient and pressure drop data from the measured parameters are

described. In the present study, an experimental procedure was initially adopted

based on single-phase energy balances in order of estimating the heat exchanges

with environment which are taken into account during the data regression analysis.

Transport and thermodynamic properties were obtained from the commercial

software EES (Engineering Equation Solver,1992)

The heat flux was assumed uniform along the entire test section and is given as

follows:


Ld

E

i

TSTS

πφ = (3.1)

where ETS is the electrical power supplied to the test section minus the heat

exchanges with the external environment.

The mass velocity was defined as the ratio between the mass flow rate and

the cross sectional area for the tube without insert, as follows:

2

id

m4G

π

&= (3.2)

The vapor quality was determined based on the local thermodynamic state

given as follow:

( )

LV

L

i

izix

−= (3.3)

where Li is the enthalpy of the saturated liquid,

LVi is the latent heat of evaporation,

both estimated at the saturation temperature at the position z along the tube length.

In Eq. (3.3) ( )zi is the average local fluid enthalpy in a given cross section at position

z .

3.7.1 Pressure drop

The total pressure drop gradient is the sum of the frictional, accelerational, and

gravitational parcels given by Eq. (2.33).

Due to the fact that the test section is horizontal the gravitational parcel of the

pressure drop is null, therefore, the frictional pressure drop was assumed as equal to

the total pressure drop provided by the differential pressure transducer subtracted

the accelerational parcel. Consequently the frictional pressure drop is given by the

following relationship:

fric total acc

dp dp dp

dz dz dz

= −

(3.4)

It is important to highlight that Eq.(3.4) is related to the test section length of

2.0 m.


where total

dp

dz

is the pressure drop provided by the differential pressure transducers.

Adiabatic experiments were performed for obtaining the pressure drop data.

Consequently the vapor quality variation along the test section is mainly due to the

pressure reduction. Acceleration parcel was estimated based on the inlet and outlet

vapor qualities and superficial void fraction estimated according to Eq. (2.34) and Eq.

(2.26), respectively.

3.7.2 Heat Exchange with environment

Correlations were developed in order of estimating the heat exchanged with

the environment and taking its value into account when calculating the heat flux. For

this, single-phase flow experiments were performed and the heat exchanged with the

environment determined as the difference between the power supplied to the

electrical heater and the product between the mass flow rate and the variation of

enthalpy of the fluid along the pre-heater and test section length. The heat

exchanged with the environment is calculated as follows:

(3.5)

(3.6)

where , and , are the refrigerant enthalpies estimated from

the measurements of the temperature and pressure (P,T) at the test section and pre-

heater inlet and just downstream the test section and pre-heater respectively based

on and corresponds to electrical power supplied to the test section and pre-

heater, respectively, taken into account the heat exchanges with the external

environment. Then, empirical equations were obtained for the ratio between the heat

exchanged with the environment and the electrical power as a function of Grashof

number and tube average temperature as follows:

(3.7)

(3.8)


where is the Grashof number estimated for air properties at the film temperature

(mean value of wall and external temperature). In Eq. (3.7) refers to the wall

average temperature (2 thermocouples in the pre-heater), while corresponds to

the fluid average temperature between the inlet and outlet positions. In Eq. (3.8),

refers to the wall average temperature (16 thermocouples in test section

corresponds to the fluid average temperature between the inlet and outlet of the test

section. The coefficients and exponents of Eqs (3.7) and (3.8) were obtained from

the least square regression analysis of the single-phase pressure drop and heat

transfer coefficient experimental data realized during the validation of the test

section.

It is interesting to note that Eqs. (3.7) and (3.8) used to calculate the rate of

heat transfer exchanged with the environment for the pre-heater and the test section

for the 15.9 mm ID tube were also considered applicable for the 12.7mm ID tube,

because the same insulation configuration were used for both tubes. Thus, it is

expected that the thermal resistances are similar.

3.7.3 Heat transfer coefficient

The local heat transfer coefficient was calculated according to the Newton’s

cooling law as follows:

( )( )zTTh

satW

TS

−=

φ (3.9)

where WT is cross-sectional arithmetic average surface temperature of the inner tube

wall estimated according to the Fourier’s law assuming one-dimensional conduction

and based on the four wall temperature measurements at each cross section. The

internal average wall temperature is given as follows:

( )

Cu

ioi

i,TPW

k

rrlnrTT φ−= (3.10)

where iTPT , is the average temperature of the measurements by the thermocouple at

each cross section, is the internal radius of the section, is the distance between


the section centre and the thermocouples ( Tio rr δ+= and Tδ =0.5 mm) and Cu

k is the

thermal conductivity of the tube (copper or brass).

In Eq. (3.9), ( )zTsat is the local saturation temperature of the refrigerant

evaluated from the local saturation pressure assuming a constant pressure gradient

along the test section and based on the measurements of the absolute pressure

transducer at the test section inlet and differential pressure transducer.

3.8 Validation of the experimental bench and determination of the uncertainty

In the present study, procedures were performed to validate the experimental

data and evaluate the accuracy of their measurements through comparisons of

experimental results with consolidated methods available in the literature for single-

phase flows. The validation of the apparatus and experimental procedures involved

also checking the heat losses through energy balance along the pre-heater and test

section to assure the correct estimation of the heat flux and vapor quality.

3.8.1 Single-phase pressure drop experimental data validation

Single-phase frictional pressure drop experiments for plain tube without inserts

were performed in order to assure the accuracy of the pressure drop measurements.

Figure 3.12 presents the comparison between experimental Fanning friction factor, f

for single-phase adiabatic flow in tubes with 12.7 and 15.9 mm internal diameter, for

Reynolds number Re varying from 3200 to 35000, and estimatives according to

methods of Blasius (1913), Churchill (1977), and Colebrook (1939). As can be

observed from Fig. 3.12, the experimental results present good agreement with the

theoretical estimatives, with all data predicted within an error band less than ± 10 %.

3.8.2 Single-phase flow heat transfer experimental data validation

In order to evaluate the accuracy of the data and validate the flow boiling heat

transfer coefficient measurements, diabatic single-phase experiments were carried

out in plain tubes, for sub-cooling temperature at the test section inlet of 10 and 20

°C, Reynolds number varying from 4000 to 35000, and heat flux from 0.16 to 6.2 kW

/ m² for both diameters. Figures 3.13 and 3.14 present comparisons among the

experimental heat transfer coefficient data and predictions according to Gnielinski

(1976) and Dittus and Boelter (1930) correlations. As can be observed in Figs. 3.13


and 3.14, the experimental results agreed quiet well with the predictive methods for

the 12.7 mm ID tube, i.e., Dittus and Boelter (1930) and Gnielinski (1976) predicted

94.2 and 98.1 % of the experimental data within an error band of ±30 %. For the 15.9

mm ID tube, 98.4 % of the data was predicted within an error band of ±30 % by both

methods.

0.005 0.006 0.007 0.008 0.009 0.010 0.0110.005

0.006

0.007

0.008

0.009

0.010

0.011

fexperimental [-]

f est

imat

ed [

-]

+10 %

-10%

Blasius (1913)

Churchill (1977)

Colebrook (1939)

Figure 3.12 - Comparison between experimental friction factors and estimated friction factors, for single-phase flow in tubes with 12.7 mm ID (filled symbols) and 15.9 mm ID (empty symbols).

0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

hexperimental [kW/m2 oC]

hes

tim

ated

[k

W/m

2 oC

]

+30%

-30%

Figure 3.13 - Comparison of experimental and estimated heat transfer coefficient for liquid single-

phase flow, for 12.7 mm ID tube. Estimatives according to Dittus and Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols).


0.0 0.5 1.00.0

0.5

1.0

hexperimental [kW/m2 oC]

hes

tim

ated

[k

W/m

2 o

C]

+30%

-30%

Figure 3.14 - Comparison of experimental and estimated heat transfer coefficient for liquid single-

phase flow, for 15.9 mm ID tube. Estimatives according to Dittus and Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols).

The accuracy of the estimated vapor quality was ascertained from evaluation

of the effective rate of heat exchanges between pre-heater, test section and

environment during the single-phase experiments. The analyses of the parcel of

energy exchanged with environment relative to the total energy supplied can be

calculated for the pre-heater and the test section as follows,respectively:

(3.10)

(3.11)

Figures 3.15 and 3.16 present the variation of the ratio of along the test

section and pre-heater respectively with mass velocity. According to Figs. 3.15 and

3.16, the relative value of the heat exchanged with environment increases with

decreasing the mass velocity. Heat exchanges lower than 10 % were achieved for G

≥ 125 kg / m2 s and lower than 5 % for G ≥ 400 kg / m2 s. Also, in Figs. 3.15 and

3.16, reasonable heat losses were observed in the test section and pre-heater for G

≤ 100 kg / m2 s and G ≤ 275 kg / m2 s, respectively.

Based on the above analyses, it can be concluded that the experimental

facility is satisfactorily accurate for obtaining pressure drop and heat transfer

coefficient results during flow boiling inside tubes with and without twisted-tapes.


50 100 150 200 250 300 350 400 450

0.0

0.1

0.2

0.3

G [kg / m2 s]

∆∆ ∆∆E

/E [

-]

Figure 3.15 - Variation with mass velocity of the heat exchanged between the test section and the

surroundings.

100 150 200 250 300 350 400 450-0.05

0

0.05

0.1

0.15

0.2

G [kg / m2 s]

∆∆ ∆∆E

/E [

-]

Figure 3.16 - Variation with mass velocity of the heat exchanged between the pre-heater and the

surroundings.

3.9 Uncertainty analysis

An uncertainty analysis of the experimental results and their propagation was

performed for the pressure drop, heat transfer. The uncertainty of the measuring

instrument was evaluated using the methodology presented by Abernethy and

Thompson (1973) taken into account the technical specifications provided by the

manufacturer.

The evaluation of the uncertainty of the temperature measurement was also

performed using 5 calibration curves obtained from the thermocouples. Table 3.1


presents uncertainties associated with measured parameters and detailed in

Appendix A.

Table 3.1 - Uncertainty of the measured parameters

The method developed by Taylor and Kuyatt (1994) was used to estimate

the uncertainty propagation of the calculated parameters. The estimation was

performed with the aid of the EES. Software. Table 3.2 shows the uncertainty

associated with the estimated parameters.

Table 3.2 - Uncertainty of the calculated parameters

Parameters Uncertainty

Heat flux 3.0%

Heat transfer coefficient <10%

Mass velocity 0.276 kg / m2 s

Vapor quality 0.032

Parameters Uncertainty

TPH,inlet 0.1 °C

TPH,outlet 0.1 °C

TST,outlet 0.1 °C

m& 5.45.10-5 kg / s

Power 3.04 %

PPH,inlet 1.4 kPa

PPH,outlet 1.6 kPa

∆p 0.075 %

Experimental results 131

4 EXPERIMENTAL RESULTS

This chapter presents the flow boiling experimental results obtained in the

present study for pressure drop and heat transfer coefficient in tubes with and without

twisted-tape inserts. The results were obtained using two test sections with internal

diameters of 12.7 and 15.9 mm from the experimental apparatus located at the

Department of Mechanical Engineering of the School of Engineering of São Carlos

(EESC-USP), built for the previous study of Kanizawa (2011). In the study of

Kanizawa (2011) flow pattern and pressure drop results were obtained for the 15.9

mm ID test section for R134a and the same twist-ratios considered in the present

study. A parametric analysis and critical discussion of the effect of experimental

parameters is also presented. Moreover, the results obtained in the present study are

compared with the predictive methods available in the literature.

The experimental data were obtained for the conditions described in Tab. 4.1.

Results for wider ranges of conditions were not possible due to limitation of the

apparatus as a sharp decline in the system pressure was observed with increasing

the fluid flow rate under higher vapor qualities conditions and for the lower saturation

temperature considered in the present study. This is related to the fact that there is

increase in specific volume of the fluid and hence lead to a higher pressure drop,

which subsequently beyond the capacity of experimental bench component.

Table 4.1 - Experimental conditions covered in the present study.

Paramters Conditions

Mass velocity 75,100, 150 and 200 kg / m2 s

Saturation temperature 5 o and 15 oC

Internal diameter 12.7 and15.9 mm

Vapor quality 0.05 to 0.95

Twist ratios 3,4,9,14 and

Heat flux 5 and 10 kW / m2

Working fluid R134a

In the present study, the thermo-hydraulic performance of refrigerant R134a is

analyzed during convective boiling inside tubes containing twisted-tape inserts. The

refrigerant R134a (tetrafluoroethane) is a halogenated hydrocarbon developed to

132 Experimental results

replace CFCs (chlorofluorocarbons) in refrigeration system. It is a medium-to-high

pressure refrigerant and its impact on the ozone layer is null. Table 4.2 presents the

thermodynamic and transport properties of R134a.

Table 4.2 - Physical, chemical and thermodynamic properties of R134a

Properties Ranges

Molecular weight [g / mol] 102.03

Boiling point 1 atm [° C] -26.1

Critical Temperature [° C] 101.1

Critical pressure [kPa (abs)] 4060

Saturated liquid density 25 ° C [kg / m³] 1206

Saturated vapor density 25 ° C [kg / m³] 32.34

Specific heat of saturated liquid 25 ° C [kJ / kg • K] 1.44

Specific heat of vapor 25 ° C and 1 atm [kJ / kg • K] 0.85

Saturated liquid pressure 25 ° C [kPa (abs)] 666

Thermal conductivity of saturated liquid 25 ° C [W / m • K] 0.08325

Thermal conductivity of saturated vapor 25 ° C [W / m • K] 0.01456

Viscosity of saturated liquid 25 ° C [Pa • s] 1.944*10-4

Viscosity of saturated vapor 25 ° C [Pa • s] 1.197*10-5

Surface tension [N / m] 8.081*10-3

4.1 Pressure drop results

This item describes the results of adiabatic two-phase flow experiments

performed focusing on determination of frictional pressure drop in tubes with and

without twisted-tape inserts. Additionally, predictive methods available in the

literature and described in Chapter 2 are compared against these data.

4.1.1 Pressure drop for tubes without twisted-tape inserts

A total of 284 experimental pressure drop data were obtained in the present

study, being 129 for the 12.7mm ID tube and 155 for the 15.9 mm ID tube.

Figures 4.1 and 4.2 display experimental results illustrating the variation of

frictional pressure drop gradient with vapor quality. These results were obtained for

R134a and saturation temperatures of 5 and 15 °C in 12.7 and 15.9 mm ID tubes.

According to Figs. 4.1 and 4.2, the frictional pressure drop increases with increasing

the mass velocity and decreasing the tube diameter and saturation temperature. By

decreasing the saturation temperature from 15 to 5 °C, the vapor specific volume


varies from 0.0421 to 0.0584 m³/kg. This behavior implies higher two-phase flow

velocities for lower saturation temperature and, consequently, higher pressure drops.

The liquid viscosity also increases with decreasing saturation temperature

contributing to the pressure drop augmentation.

Figures 4.1 and 4.2 also show that the pressure drop increases with the vapor

quality for low and intermediary vapor quality values. Moreover, pressure drop peaks

at high vapor qualities are displayed in Figs. 4.1 and 4.2 which seems to move to

lower vapor qualities with increasing the mass velocity and decreasing tube diameter.

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

G = 75 kg / m² s

G = 100 kg / m² s

G = 150 kg / m² s

G = 200 kg / m² s

Figure 4.1 - Variation of frictional pressure drop gradient with vapor quality for adiabatic two-phase

flow in 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

G = 75 kg / m² s

G = 100 kg / m² s

G = 150 kg / m² s

G = 200 kg / m² s

Figure 4.2 - Variation of frictional pressure drop gradient with vapor quality for adiabatic two-phase

flow in 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).


4.1.2 Pressure drop for tubes with twisted-tape inserts

Figures 4.3 to 4.10 present experimental results of frictional pressure drop

during two-phase flow in tubes with twisted-tape inserts for saturation temperatures

of 5 and 15 °C, mass velocities from 75 to 200 kg / m² s, and twist-ratios equal to 3,

4, 9 and 14. In general as expected, the frictional pressure drop gradient increases

with decreasing twist-ratio, saturation temperature and tube diameter. Moreover, the

pressure drop increases with increasing the mass velocity. These trends are in

agreement with those observed by the study of Kanizawa and Ribatski (2012).

Figures. 4.3, 4.4 and 4.7 also display inflections in the trends of the pressure drop

gradient with increasing vapor quality for reduced mass velocities and twist-ratios.

The same behavior is not displayed in Figs. 4.9 and 4.10 for mass velocities of 150

and 200 kg / m² s. Kanizawa and Ribatski (2012) presented an analysis on the

influence of flow pattern on the pressure drop, concluding that these inflections are

related to the transition from stagnant flow to intermittent flow patterns. It is also

observed that the pressure drop gradient presents peaks for vapor qualities close to

0.73 and 0.87 for 12.7 and 15.9 mm ID tubes, respectively . The pressure drop

augmentation by the twisted-tape is related to the fact that, additionally to the

reduction of the cross sectional area, the insert induces turbulence and swirl effects

on the liquid film and vapor core.

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

y = 3

y = 4

y = 9

y = 14

Inflection

Figure 4.3 - Variation of frictional pressure drop gradient with vapor quality for R134a, 12.7 mm ID tube, G = 75 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

x [-]

∆∆ ∆∆p

fric

/ L

[kP

a / m

]

y = 4

y = 9y = 14

y=3

Inflection


0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

y = 3

y = 9

y = 14

y=4



0.0 0.2 0.4 0.6 0.8 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

y = 3

y = 4

y = 9

y = 14


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

y = 3

y = 4

y = 9

y = 14

Inflection



0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

y = 3

y = 4

y = 9

y = 14


0.0 0.2 0.4 0.6 0.8 1.00.0

1.0

2.0

3.0

4.0

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

y = 3

y = 4

y = 9

y = 14

Figure 4.9 - Variation of frictional pressure drop gradient with vapor quality fo R134a, 15.9 mm ID tube, G = 150 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).


0.0 0.2 0.4 0.6 0.8 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

x [-]

∆∆ ∆∆p

fric

/ L

[k

Pa

/ m

]

y = 3

y = 4y = 9

y = 14

Figure 4.10 - Variation of frictional pressure drop gradient with vapor quality for R134a 15.9 mm ID tube, G = 200 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).

4.1.3 Comparison between the experimental frictional pressure drop results

and the predictive methods

In this section, the experimental results of the two-phase flow frictional

pressure drop data obtained in the present study for plain tubes and tubes with

twisted-tape inserts are compared against estimatives according to predictive

methods available in the literature described in Chapter 2.

In Figs 4.11 and 4.12, the experimental pressure drop data for the 12.7 and

15.9 mm ID plain tubes, respectively, are compared against the predictive methods

of Friedel (1979), Grönnerud (1979), Müller-Steinhagen and Heck (1986) and

Moreno-Quibén and Thome (2007). According to these figures the method proposed

by Friedel (1979) and Moreno-Quibén and Thome (2007) presents higher deviation

from the experimental data. For higher mass velocity conditions, the predictive

methods of Friedel (1979), Grönnerud (1979), Müller-Steinhagen and Heck (1986)

perfomed better independent of the saturation temperature. On the other hand, the

predictive method of Moreno-Quibén and Thome (2007) underpridicts most of the

experimental data. Figure 4.13 displays comparisons of the behaviors of the pressure

drop data obtained in the present study with varying the vapor quality and the results

provided by the predictive methods. According to this figure, the methods of

Grönnerud (1979) and Müller-Steinhagen and Heck (1986) capture reasonable well

the pressure drop trends of the experimental data. Friedel (1979) over predicts most


of the experimental results, however captures reasonably the pressure drop peak

according to Fig. 4.13.

0.0 0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

2.0

2.5

(∆∆∆∆pfric / L)experimental [kPa / m]

( ∆∆ ∆∆p

fric

/ L

) est

imat

ed

[kP

a /

m]

Friedel (1979)Grönnerud (1979)Müller-Steinhagen and Heck (1986)

-30 %

+30 %

Moreno-Quibén and Thome (2007)

Figure 4.11 - Comparison between estimated and experimental frictional pressure drop, for 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6


( ∆∆ ∆∆p

fric

/ L

) est

imat

ed

[kP

a /

m] Friedel (1979)

Grönnerud (1979)Müller-Steinhagen and Heck (1986)

+30 %

-30 %


Figure 4.12 - Comparison between estimated and experimental frictional pressure drop, for 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).


0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

x [-]

( ∆∆ ∆∆p

fric

/ L

) [

kPa

/ m

] Friedel (1979)

Exprimental data

Grönnerud (1979)

Müller-Steinhagen and Heck (1986)


Figure 4.13- Comparison of the trends of the frictional pressure drop according to predictive methods and experimental data for plain tube without twisted-tape,for 15.9 mm ID plain tube, Tsat = 15 °C and G

= 100 kg / m² s.

Table 4.3 presents the results of the statistical analysis of the comparison

between experimental results and predictive methods for two-phase pressure drop in

plain tubes without twisted-tape. The results are given in terms of the parcel of

experimental data predicted within an error band of ±30 % and the mean absolute

error defined as follows:

( ) ( )( ) points data

of number

Lp

LpLp

points data of number erimentalexpfric

erimentalexpfricestimatedfric

∑−

=∆

∆∆η (4.1)

Based on the results provided in Tab. 4.3, it is concluded that the method of

Grönnerud (1979) provides the best prediction of the overall database with mean

absolute deviation of 13 % and predicting 88 % of experimental data within an error

band of ±30 %. Müller-Steinhagen and Heck (1986) provides also reasonable

predictions. The abovementioned behaviors and the results displayed in Tab. 4.3 are

in agreement with the observations of Kanizawa and Ribatski (2012).


Table 4.3 - Results of the statistical analysis of the comparison between experimental data and predictive methods for frictional pressure drop in plain tubes.

Authors ζ30 [%] η [%]

Friedel (1979) 33 56

Grönnerud (1979) 88 13

Müller-Steinhagen and Heck (1986) 72 24

Moreno-Quibén and Thome (2007) 32 42

In Figs 4.14 and 4.15 the experimental results of frictional pressure drop in

12.7 and 15.9 mm tubes with twisted-tape inserts are compared with the predictive

methods of Jensen et al. (1985), Agrawal et al. (1982), Akhavan-Behabadi et al.

(2009a) and Kanizawa and Ribatski (2012). The statistics of the comparison are

presented in Tab. 4.4. In general, the predictive methods of Jensen et al. (1985),

Agrawal et al. (1982) and Akhavan-Behabadi et al. (2009a) provide reasonable

predictions of the experimental data only for high mass velocities corresponding to

annular flows. Poor predictions of the present database by the methods from

literature were already expected, considering the relatively wide range of operational

conditions covered in the present study and the fact that some of these methods are

based on fluids different than R134a. It should also be highlighted that these

methods do not take into account the influence of twisted-tape on the transitions

among stagnant, stratified and intermittent flow patterns, and so are not suitable for

reduced mass flow conditions.

According to Tab. 4.4, the method of Kanizawa and Ribatski (2012) provides

accurate prediction of the data obtained in the present study, predicting 99 % of

experimental data within an error band of ±30 %, and providing mean absolute

deviation of 7 %. The good predictions provided by the method of Kanizawa and

Ribatski (2012) is related to the fact that the method was developed considering in

detail the influence of flow pattern transitions on the pressure drop capturing its

tendencies under low and high mass velocity conditions. It is important mentioning

that the method of Kanizawa and Ribatski (2012) is based on experimental data

different from the data obtained in the present study.


0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

(∆∆∆∆pfric / L)experimental [kPa/m]

( ∆∆ ∆∆p

fric

/ L

) est

imat

ed

[kP

a /

m]

+30 %

-30 %





Figure 4.14 - Comparison between estimated and experimental frictional pressure drop gradient, for 12.7 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3, 4, 9 and 14.

0.0 1.0 2.0 3.0 4.0 5.0 6.00.0

1.0

2.0

3.0

4.0

5.0

6.0


( ∆∆ ∆∆p

fric

/ L

) est

imat

ed

[kP

a /

m] +30 %

-30 %





Figure 4.15 - Comparison between estimated and experimental frictional pressure drop gradient, for 15.9 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3, 4, 9 and 14.


Table 4.4 – Results of the statistical analysis of the comparison between experimental and predicted pressure drop data during two-phase flow in tubes with twisted-tape inserts.

ζ30 [%] η [%] Authors

di = 12.7 mm di = 15.9 mm Overall di = 12.7 mm di = 15.9 mm Overall

Akhavan-Behabadi et al.(2009a) 62 66 64 25 26 26

Jensen et al. (1985) 64 69 66 25 24 24

Agrawal et al (1982) 63 57 60 25 28 26

Kanizawa and Ribatski (2012) 99 99 99 8 7 7.5

Figures 4.16 and 4.17 display comparisons of the behaviors of pressure drop

with varying the vapor quality for the experimental data obtained in the present study

and the predictive methods. According to Figs. 4.16a and 4.17a, for mass velocity of

75 kg / m2 s, the predictive methods of Jensen et al. (1985), Agrawal et al. (1982)

and Akhavan-Behabadi et al. (2009a) fails to capture the pressure drop trends of the

experimental data independent of the vapor quality conditions. These methods,

under predict and over predict the data for low vapor qualities and for vapor qualities

higher than 0.4.

For mass velocity of 150 kg / m2 s, it can be noted in Fig. 4.17b that the

predictive methods of Jensen et al. (1985) and Akhavan-Behabadi et al. (2009a)

capture reasonably well the pressure drop trends of the experimental data while

Agrawal et al. (1982) method under predicts the data for high vapor qualities.

Significant differences between the database obtained in the present study and the

experimental data used by these authors when developing their methods can

partially explain their unsatisfactory performance. Moreover, these methods do not

take into account the influence of twisted-tape on the flow pattern transitions among

stagnant, stratified and intermittent flow and so they cannot be considered suitable

for reduced mass flow conditions.

Contrary to the predictive methods of Jensen et al. (1985), Agrawal et al.

(1982) and Akhavan-Behabadi et al. (2009a), it can be noted in Figs. 4.16 and 4.17,

that the predictive method of Kanizawa and Ribatski (2012) captures well the

experimental pressure drop data and their trend with increasing vapor quality and

twist-ratio, independently of the mass velocity. It can be noticed that the method

obeys the inflection in the pressure drop for vapor qualities about 0.2 related to the

transition from the stagnant to intermittent flow pattern. The method predicts

accurately well also the data under conditions of high vapor quality and twist-ratios.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0

0.5

1.0

1.5

x [-]

∆∆ ∆∆p

fri

c /

L

[kP

a/m

]

Experimental

Kanizawa and Ribatski (2012)Akhavan-Behabadi et al. (2009a)

Jensen et al. (1985)Agrawal et al. (1982)

G=75 kg/m2s, y=3

(a)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.0

0.5

1.0

1.5

2.0

x [-]

∆∆ ∆∆p

fri

c /

L

[kP

a/m

]

Experimental


Agrawal et al. (1982)Akhavan-Behabadi et al. (2009a)Jensen et al. (1985)

G=150 kg/m2s, y=14

(b)

Figure 4.16 - Comparison of the trends of the frictional pressure drop according to predictive methods and experimental data for plain tube with twisted-tape, for 12.7 mm ID tube Tsat = 15 °C.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.5

1.0

1.5

x [-]

∆∆ ∆∆p

fri

c /

L

[kP

a/m

]

Experimental





G=75 kg/m2s, y=3

(a)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

1.0

2.0

3.0

4.0

x [-]

∆∆ ∆∆p

fric

/ L

[kP

a/m

]

Experimental





G=150 kg/m2s, y=14

(b)

Figure 4.17 - Comparison of the trends of the frictional pressure drop according to predictive methods and experimental data for plain tube with twisted-tape, for 15.9 mm, ID tube, Tsat = 15 °C.

4.1.4 Evaluation of the pressure drop penalty due to twisted-tape inserts

Figures 4.18 and 4.19 illustrate the variation of the pressure drop penalty with

the vapor quality for different mass velocities, saturation temperatures and twist-

ratios for tubes with internal diameters of 12.7 and 15.9 mm. The pressure drop

penalty illustrated in these figures is defined as the ratio between the experimental

frictional pressure drop for the tube with twisted-tape insert and its corresponding

value for the plain tubes without inserts, estimated according to the correlation of

Grönnerud (1979), keeping the same experimental conditions. The predictive method

of Grönnerud (1979) was used in this comparison because it provided the best

prediction of the pressure drop data for the tube without twisted-tape insert.


According to Figs. 4.18 and 4.19 and as observed by Salimpour and Yarmohammadi

(2012) and Kanizawa and Ribatski (2012), the pressure drop penalty increases with

decreasing mass velocity and twist-ratio. Moreover, the pressure drop penalty tends

to a similar value independently of the twist-ratio as the vapor quality approaches to

the unity.

From Figs. 4.18 and 4.19 pressure drop penalties values higher than 30 are

observed for both tubes diameter under conditions of reduced vapor qualities and

mass velocities. By comparing Figs. 4.18 and 4.19, it is also noted under similar

experimental conditions that the 15.9 mm ID tube presents higher pressure drop

penalties than the 12.7 mm ID tube. Moreover, the effect of saturation temperature

on the pressure drop penalty seems only marginal for the range of experimental

conditions evaluated in the present study.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

x [-]

∆∆ ∆∆p

fric

,TT /

∆∆ ∆∆p

fric

,Pla

in [

-]

y = 3

y = 4

y = 9

y = 14

G = 75 kg / m2 s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

5

10

15

20

25

30

x [-]

∆∆ ∆∆p

fric

,TT /

∆∆ ∆∆p

fric

,Pla

in [

-]

y=14

y=9

y=4

y=3G = 100 kg / m2 s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

x [-]

∆∆ ∆∆p

fric

,TT /

∆∆ ∆∆p

fric

,Pla

in [

-]

y=3

y=4

y=9

y=14

G = 150 kg / m2 s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

5

10

15

20

25

30

x [-]

∆∆ ∆∆p

fric

,TT /

∆∆ ∆∆p

fric

,Pla

in [

-] y = 3

y = 4

y = 9

y = 14

G = 200 kg / m2 s

Figure 4.18 – Illustration of the variation of pressure drop penalty with vapor quality, for ID = 12.7 mm and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols).


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

x [-]

∆∆ ∆∆p

fric

,TT /

∆∆ ∆∆p

fric

,Pla

in [

-]

y=14

y=9

y=4

y=3G =75 kg / m2 s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

5

10

15

20

25

30

35

x [-]∆∆ ∆∆

pfr

ic,T

T /

∆∆ ∆∆p

fric

,Pla

in [

-] y=3

y=4

y=9

y=14

G =100 kg / m2 s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

x [-]

∆∆ ∆∆p

fric

,TT /

∆∆ ∆∆p

fric

,Pla

in [

-]

y=14

y=9

y=4

y=3

G =150 kg / m2 s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

5

10

15

20

25

30

35

x [-]

∆∆ ∆∆p

fric

,TT /

∆∆ ∆∆p

fric

,Pla

in [

-]

y=3

y=4

y=9

y=14

G =200 kg / m2 s

Figure 4.19 - Illustration of the variation of pressure drop penalty with vapor quality for ID = 15.9 mm, and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols).

4.2 Heat transfer coefficient results

Initially, this section presents an analyses of the heat transfer coefficient results

for tubes without twisted-tapes. Then, a parametric discussion into the effect of the

experimental variables on the heat transfer coefficient for tubes with and without

twisted-tape inserts is presented. Additionally, the experimental data for tubes with

and without twisted-tapes are compared against the predictive methods available in

the literature described in Chapter 2.


4.2.1 Results for tubes without twisted-tape

Figures 4.20 and 4.21 illustrate the variation of the heat transfer coefficient

with vapor quality according to the experimental results. These data were obtained

during two-phase flows of R134a in tubes without twisted-tape inserts for saturation

temperatures of 5 and 15 °C, heat flux values of 5 and 10 kW / m² and mass

velocities from 75 to 200 kg / m² s. According to Figs. 4.20 and 4.21, the heat transfer

coefficient increases with increasing the mass velocity and decreasing the tube

diameter and saturation temperature. For mass velocities of 75 and 100 kg / m² s, the

heat transfer coefficient remains almost constant over a wide range of vapor quality.

This behavior is due to the occurrence of stratified flows for low mass velocities and

is related to the presence of a dry region on the tube upper part and a significant

layer of liquid on the bottom of the tube with occurrence of nucleate boiling in this

region. For intermediary and high mass velocities and prior to the surface dryout, the

heat transfer coefficient increases with increasing vapor quality. As illustrated in Fig.

4.20, this effect is more pronounced for the tube with smaller diameter compared to

the tube with larger diameter due to the higher vapor shear stress on the liquid film,

enhancing convective effects for the former. This behavior is typical of intermittent

and annular flow patterns as already pointed out by Saiz-Jabardo and Bandarra Filho

(2006), Wojtan et al. (2005) and Cheng et al. (2008).

According to Fig. 4.21, the heat transfer coefficient increases with increasing

the mass velocity and decreasing saturation temperature. For lower saturation

temperature, higher heat transfer coefficient is observed with increasing vapor quality

especially for intermediary and high mass velocities. Such behavior is related to the

fact that the vapor specific volume increases by decreasing the saturation

temperature, causing an increase in two-phase flow velocity.

According to Fig. 4.22, under high mass velocity conditions, the heat transfer

coefficient increases with increasing heat flux over the whole range of vapor quality.

Almost constant heat transfer coefficient is also observed in the lower vapor quality

region especially for mass velocities of 75 and 100 kg / m² s independent of the heat

flux effect, due to the predominance of nucleate boiling effects.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

x [-]

h

[kW

/ m

2 o C

] G = 200kg / m2 s

G = 150 kg / m2 s

G = 100 kg / m2 s

G = 75 kg / m2 s

Figure 4.20 – Variation of heat transfer coefficient with vapor quality during flow boiling in tube without

twisted-tape inserts, ϕ = 10 kW / m², Tsat = 5 °C, di = 12.7 mm (empty symbols) and di = 15.9 mm (filled symbols).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

x [-]

h

[kW

/ m

2 o C

] G = 200kg / m2 s

G = 150 kg / m2 s

G = 100 kg / m2 s

G = 75 kg / m2 s

Figure 4.21 - Variation of heat transfer coefficient with vapor quality during flow boiling in tube without

twisted-tape inserts, ϕ = 10 kW / m², di = 15.9 mm , Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

x [-]

h

[kW

/ m

2 o C

]G = 200 kg / m2 s

G = 150 kg / m2 s

G = 100 kg / m2 s

G = 75 kg / m2 s

Figure 4.22 - Variation of heat transfer coefficient with vapor quality during flow boiling in tube without

twisted-tape inserts, Tsat = 15 °C ,di = 15.9 mm ,ϕ = 10 kW / m² (empty symbols) and ϕ = 5 kW / m², (filled symbols).

4.2.2 Comparison between the experimental heat transfer coefficients results

for tubes without twisted-tape inserts and the predictive methods.

In this section, the experimental results of the two-phase flow heat transfer

coefficient data obtained in the present study for tubes without twisted-tape inserts

are compared against estimatives obtained using the predictive methods described in

Chapter 2.

In the present study, 420 and 342 experimental data for heat transfer

coefficient in 12.7 and 15.9 mm ID plain tubes without twisted-tape, respectively,

were obtained. Table 4.5 presents the results of statistical analysis of the

comparisons between experimental results and predictive methods for heat transfer

coefficient, namely Kandlikar (1990), Liu and Winterton (1991), Bandarra Filho (2002)

and Wojtan et al. (2005b). As can be observed in Tab. 4.5, Kandlikar (1990) presents

the best prediction of the experimental dataset for the plain tubes, predicting 64.6 %

of the experimental data within an error band of ±30 % and mean absolute deviation

of 25.9 %. Liu and Winterton (1991) and Wojtan et al. (2005b) also provide

predictions as accurate as Kandlikar (1990). However, considering only experimental

results for 12.7 mm ID tube, Kandlikar (1990) and Liu and Winterton (1991) methods


predicted respectively 82 and 71 % of the experimental data obtained in the present

study within an error band of ±30 %. This result suggested that these methods are

more appropriate to smaller diameter tubes. On the hand, Wojtan et al. (2005b)

predicts almost the same parcel of the data within an error band of ±30 % for larger

tube. Figure 4.23 shows a comparison of the experimental heat transfer coefficient

data and calculated values according to the predictive method of Kandlikar (1990).

Table 4.5 – Results of the statistical analysis of the comparison between experimental results for heat transfer coefficient during two-phase flow in plain tubes and predictive methods from literature.



Kandlikar (1990) 82 47 65 24 28 26

Liu and Winterton (1991) 71 58 64 23 29 26

Bandarra Filho (2002) 32 35 34 88 83 85

Wojtan et al. (2005b) 62 66 64 29 27 28

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

hexperimental [kW / m2 oC]

hes

tim

ated

[kW

/ m

2 oC

]

+30 %

-30 %

Figure 4.23- Comparison between estimated and experimental heat transfer coefficients for the12.7 mm ID tube without inserts according to Kandlikar (1990).

4.2.3 Results for tubes with twisted-tape inserts

4.2.3.1 Twisted-tape effect

The twisted-tape effect on the heat transfer coefficient is illustrated in Figs.

4.24 and 4.25 for the 12.7 mm ID tube, and in Figs. 4.26 and 4.27 for the 15.9 mm ID

tube for heat flux of 10 kW / m2 and saturation temperature of 5 oC. According to

these figures, inserting twisted-tape inside a plain tube increase significantly the heat


transfer coefficient compared to tube without the swirl flow device, independently of

the mass velocity. This behavior is due to the promotion by the tape of better fluid

mixing and higher flow velocity of fluid in the vicinity of the tube wall compared to that

of the tube without tape.

It can be observed in Figs. 4.24 and 4.26 for mass velocity of 75 kg / m2 s,

heat transfer coefficients almost constant over nearly the whole range of vapor

qualities for tubes with twist-ratios of 9 and 14. This effect is more pronounced for

larger diameter. This trend is in agreement with the observations posted by Akhavan-

Behabadi et al. (2009b).

Generally speaking, for mass velocity of 150 kg / m2 s the heat transfer

coefficient increases with increasing the vapor quality for the plain tube and the tube

with twisted-tape inserts as illustrated in Figs. 4.25 and 4.27. According to Fig. 4.25,

for the reduced twist-ratios of 3 and 4 in both tubes, the heat transfer coefficient

increases with vapor quality also for the low mass velocity of 75 kg / m2 s. This

behavior can be related to an earlier transition from stratified to intermittent and

annular flow patterns for low twist-ratios due to the presence of twisted-tapes.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

x [-]

h

[kW

/ m

2 o C

]

Plain tube

y=4

y=3

y=9

y=14

Figure 4.24 - Heat transfer coefficient variation with vapor quality during flow boiling in 12.7 mm ID,

G = 75 kg / m2 s, φ = 10 kW / m², Tsat = 5 oC.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

x [-]

h

[kW

/ m

2 o C

]

Plain tube

y=3

y=4

y=9

y=14

Figure 4.25 - Heat transfer coefficient variation with vapor quality during flow boiling in 12.7 mm ID, G

= 150 kg / m2 s, φ = 10 kW / m², Tsat =5 oC.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

x [-]

h

[kW

/ m

2 o C

]

Plain tube

y=3

y=4

y=14

y=9


= 75 kg / m2 s, φ = 10 kW / m², Tsat = 5 oC.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

x [-]

h

[kW

/ m

2 o C

]Plain tube

y=3

y=4

y=9

y=14


= 150 kg / m2 s,φ = 10 kW / m², Tsat = 5 oC.

4.2.3.2 Heat flux

Figures 4.28 and 4.29 display the effect of heat flux on the heat transfer

coefficient for 12.7 and 15.9 mm ID tubes, respectively, with and without twisted-tape

inserts for mass velocity of 150 kg / m2 s, twist-ratio of 3 and heat flux values of 5 and

10 kW / m2. According to Figs. 4.28 and 4.29, the heat transfer coefficient increases

with increasing the heat flux for tubes with twisted-tape and without twisted-tape

inserts. For tubes without twisted-tape inserts, the heat flux affects the heat transfer

coefficient at lower vapor quality conditions, indicating the occurrence of stratified

wavy flow pattern and predominance of nucleate boiling effects. Moreover, from Figs.

4.28 and 4.29, higher heat transfer coefficient is observed at lower vapor quality

region for the tube with twisted-tape inserts than the tube without inserts,

independent of the heat flux values. This may be due to intense swirl flow promoted

by the twisted-tape, improving convective effects even at lower vapor qualities.

These trends are in agreement with those observed in the study of Agrawal and

Varma (1990).


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

x [-]

h

[kW

/ m

2 o C

]

q = 10 kW / m2

q = 5 kW / m2

Figure 4.28 - Illustration of the effect of heat flux on heat transfer coefficient for plain tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 12.7 mm ID Tsat = 5 oC.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

x [-]

h

[kW

/ m

2 o C

]

q= 10 kW / m2

q= 5 kW / m2

Figure 4.29 - Illustration of the effect of heat flux on heat transfer coefficient for plain tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 15.9 mm ID Tsat = 5 oC.

4.2.3.3 Mass Velocity

Figure 4.30 displays the heat transfer results for the 15.9 mm ID tube for twist-

ratios of 3 and 14, saturation temperature of 15 oC, heat flux of 10 kW / m² and

diferent mass velocities. In general, the heat transfer coefficient increases with

increasing mass velocity and decreasing twist-ratio. According to this figure and as

observed by Akhavan-Behabadi et al. (2009b) for mass velocities of 75 and 100 kg /


m² s and twist-ratio of 14, the heat transfer coefficient remains almost constant over a

wide range of vapor quality. This behavior is due to the occurrence of stratified flow

for low mass velocities. For mass velocities of 150 and 200 kg / m² s, the heat

transfer coefficient increases with increasing vapor quality. This behavior is typical of

annular flow patterns and is more pronounced for the lowest twist-ratio of 3.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

x [-]

h [

kW /

m2 o

C]

G =200 kg / m2 s

G =150 kg / m2 s

G =100 kg / m2 s

G =75 kg / m2 s

Figure 4.30 - Heat transfer coefficient variation with vapor quality during flow boiling in 15.9 mm ID, φ = 10 kW / m², Tsat = 15 oC; y = 14 (filled symbol) and y = 3 (empty symbol).

4.2.3.4 Tube diameter

Figure 4.31 shows for both tube diameters, the variation of the heat transfer

coefficient with vapor quality, for heat flux of 10 kW / m2, mass velocity of 100 kg / m2

s, saturation temperature of 15 °C and twist-ratios of 3 and 14. According to this

figure, in general, the heat transfer coefficient increases with decreasing tube

diameter. This effect is more pronounced for lower twist-ratios. These behavior may

be attributed to the higher vapor shear stress in 12.7 mm ID tube and lower twist-

ratio. The insertion of twisted-tape inside the 12.7 mm ID tube is more effective in

order of promoting an earlier transition of flow pattern from stratified-wavy to annular

flow. This behavior is clearly indicated by the sudden increase of the heat transfer

coefficient at vapor quality of approximately 0.32 and 0.16 according to the data of

12.7 mm ID tube and twist-ratio of 14 and 3, respectively. The augmentation of heat

transfer coefficient inside tubes with twisted-tape is related to the fact that,

additionally to the reduction of the cross sectional area, the insert induces swirl


effects on the liquid film and vapor core, increasing the total wetted perimeter and

improving the heat transfer coefficient of the tube with smaller diameter compared to

the tube with larger diameter.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

x [-]

h

[kW

/ m

2 o

C]

y=3, di=12.7 mm

y=3, di=15.9 mm

y=14, di=12.7 mm

y=14, di=15.9 mm

Figure 4.31 – Illustration of the effect of tube diameter on the heat transfer coefficient with vapor

quality inside tubes with twisted-tape inserts, G = 100 kg / m2 s, φ = 10 kW / m², Tsat = 15 oC.

4.2.3.5 Saturation temperature

Figures 4.32 and 4.33 illustrate the effects of the saturation temperature on the

heat transfer coefficient during flow boiling in tubes with twisted-tape inserts for mass

velocities of 75 and 150 kg / m2 s, heat flux of 10 kW / m2 and saturation

temperatures of 5 and 15 oC. From these figures, it can be noted that the heat

transfer coefficient increases with increasing vapor quality independent of saturation

temperatures. This behavior is more pronounced for the twist-ratio of 4. For lower

saturation temperature, higher heat transfer coefficient is observed with increasing

vapor quality. Such behaviour is related to the fact that the vapor specific volume

increases by decreasing the saturation temperature, causing an increase in the flow

velocity, and consequently in its longitudinal and centrifugal effects responsible for

increasing convective effects.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

x [-]

h

[kW

/ m

2 o C

]

Tsat=5 o C

Tsat=15 o C

Figure 4.32 - Effect of the saturation temperature on the heat transfer coefficient during flow boiling in 15.9 mm ID, G = 75 kg / m2 s, φ = 10 kW / m², y = 14 (filled symbol) and y = 4 (empty symbol).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

x [-]

h

[kW

/ m

2 o C

]

Tsat=5 o C

Tsat=15 o C

Figure 4.33 - Effect of the saturation temperature on the heat transfer coefficient for during flow boiling in 15.9 mm ID, G = 150 kg / m2 s, φ = 10 kW / m², y = 14 (filled symbol) and y = 4 (empty symbol).

4.2.4 Comparison between the experimental heat transfer coefficient results for

tubes with twisted-tape inserts and the predictive methods.

In this section, the experimental flow boiling results for the heat transfer

coefficient obtained in the present study for tubes with twisted-tape inserts are


compared against estimatives provided by the predictive methods available in the

literature.

In the present study, 1263 and 1098 heat transfer coefficient data were

obtained for 12.7 and 15.9 mm ID tubes, respectively for tubes with twisted-tape

inserts. Table 4.6 presents the results of the statistical analysis of the comparisons

between experimental and predicted data for tubes with twisted-tape inserts. This

analyses includes predictive methods of Akhavan-Behabadi et al. (2009b), Jensen

and Bensler (1986) and Agrawal et al. (1986). According to this table, it can be

concluded that Akhavan-Behabadi et al. (2009b) presents the best prediction of the

present experimental database. This can be related to the fact that their correlation

was developed based on database obtained for R134a, mass velocities between 54

and 136 kg / m² s and saturation temperature between -19 and -3 °C. Considering

only experimental results for 12.7 mm ID tube, Akhavan-Behabadi et al. (2009b),

methods predicted 79 % of the experimental data obtained in the present study within

an error band of ±30 %, indicating that this method is also more appropriate to

smaller diameter tubes. This can be related to the fact that, these authors have

performed experiments for 7.5 mm ID tube which value is closer to 12.7 than 15.9

mm. Figure 4.34 shows a comparison of the experimental heat transfer coefficient

data and the calculated values according to the predictive method of Akhavan-

Behabadi et al. (2009b).

The predictive methods proposed by Jensen and Bensler (1986) and Agrawal

et al. (1986) under predicts the experimental results obtained in the present study for

the entire database. Such a result was expected, given significant differences of

experimental conditions between the present study and the experimental data

obtained in their studies.

Figures 4.35 and 4.36 illustrate comparisons of the behaviors of the heat

transfer coefficient according to the experimental data and the counterparts results

provided by the predictive methods of Akhavan-Behabadi et al. (2009b), Jensen and

Bensler (1986) and Agrawal et al. (1986). It can be noted in Figs 4.35 and 4.36 that

the predictive methods of Akhavan-Behabadi et al. (2009b) and Agrawal et al. (1986)

provide an unexpected behavior corresponding to heat transfer coefficient reduction

with increasing vapor quality. This behavior is more pronounced for the 15.9 mm ID

tube. According to Fig. 4.35a, Akhavan-Behabadi et al. (2009b) captures reasonably

the main trend of the experimental data. The fact that the method of Akhavan-


Behabadi et al. (2009b) provided worst predictions of the trend of the heat transfer

coefficient with vapor quality for y=3 as shown in Fig. 4.35b can be also related to the

limitations of their database which minimum evaluated twist-ratio was 6.

As can be observed in Figs. 4.35 and 4.36, Jensen and Bensler (1986) under

predicts most of the heat transfer coefficient data independently of the mass velocity

and twist-ratio. However, under high mass velocity conditions and low twist-ratios, it

seems that the method of Jensen and Bensler (1986) captures reasonably well the

heat transfer coefficient trends with increasing vapor quality as shown in Figs. 4.35b,

4.36a and 4.36b. This result can be related to the fact that Jensen and Bensler

(1986) based their method on data for upwards flow in a vertical tube when the

effects of gravitational forces on the flow stratification are absent. For horizontal

tubes, two-phase flow stratification effects are reduced relatively to inertial forces with

increasing mass velocity.

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0


hes

tim

ated

[kW

/ m

2 o

C] y=9

+30%

-30%

y=4

y=3

y=14

Figure 4.34 - Comparison between estimatives according to Akhavan-Behabadi et al. (2009b) and experimental heat transfer coefficients.

Table 4.6 - Results of the statistical analysis of the comparison between experimental results and predictive methods for heat transfer coefficient in tubes with twisted tape inserts.



Akhavan-Behabadi et al.(2009b) 79 62 71 20 34 26

Jensen and Bensler (1986) 8 30 18 54 36 46

Agrawal et al. (1986) 31 24 28 54 78 65


0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

x [-]

h

[kW

/ m

2 o C

]

ExperimentalAkhavan-Behabadi et al. (2009b)Jensen and Bensler (1986)Agrawal et al. (1986)

G=75 kg/m2s, y=14

(a)

0.0 0.1 0.2 0.3

0.0

3.0

6.0

9.0

x [-]

h

[kW

/ m

2 o C

]

ExperimentalAkhavan-Behabadi et al. (2009b)Jensen and Bensler (1986)Agrawal et al. (1986)

G=150 kg/m2s, y=3

(b)

Figure 4.35 - Comparison of the trends of the heat transfer coefficient according to predictive methods and experimental data for plain tube with twisted-tape, for 12.7 mm ID tube, Tsat = 5 °C, φ = 10 kW/m².

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

x [-]

h

[kW

/ m

2 o C

]

Experimental




G=75 kg/m2s, y=3

(a)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

x [-]

h

[kW

/ m

2 o C

]

Experimental




G=150 kg/m2s, y=14

(b)

Figure 4.36 - Comparison of the trends of the heat transfer coefficient according to predictive methods and experimental data for plain tube with twisted-tape, for 15.9 mm ID tube, Tsat= 5 °C, φ = 10 kW/m².

4.2.5 Overall Performance of the heat transfer enhancement technique

In order to determine the working conditions under which the use of twisted-

tape would present advantage over plain tube, parameters providing an overall view

of the performance enhancement are necessary. These parameters must include

pressure drop and heat transfer characteristics, keeping similar operational

constraints. Agarwal and Raja Rao (1996) have analyzed the enhancement

performance for single-phase flows inside tubes containing twisted-tape inserts

based on the heat transfer coefficient per unit of pumping power keeping fixed the

Reynolds number. Webb (1981) has presented a broad discussion on different

approaches to evaluate the heat transfer enhancement for heat exchangers


operating under single-phase flow conditions. His analysis takes into account the

heat exchanger characteristics by fixing different design constrains. For each group

of design constraints, he has imposed additional restrictions by keeping fixed

parameter as the pumping power, heat transfer capacity, mass flow rate and

temperature difference between the fluids given in terms of the logarithmic mean

temperature difference. For two-phase flows, Webb (1981) also argued that the

hypothesis of fixing the logarithmic mean temperature difference is not suitable due

to the reduced variation of fluid temperature. Shah (1978) has also analyzed the

different parameters of enhancement performance and from his study he has

suggested a thermodynamic analysis based on the minimum entropy generation for

evaluation of heat transfer enhancement technique.

In the present study, the overall performance enhancement technique was

evaluated according to the following parameters: the ratio between the heat transfer

coefficients per unit of pumping power of the tube with and without twisted-tape; and

the ratio of heat transfer coefficients of the tube with and without twisted-tape for the

same pumping power. These parameters are given, respectively, as follows:

dimensionless (4.2)

dimensionless (4.3)

In the equations above, the sub indexes TT and Plain correspond to tubes with

and without twisted-tape inserts, respectively. The subscripts of the terms between

parentheses represent the conditions adopted as reference and, so, kept fixed for

evaluation of the twisted-tape performance. In Eqs. (4.2) and (4.3), hTT is the heat

transfer coefficient for the tube with twisted-tape based on the experimental results.

The pumping power in Eq. (4.2) was estimated as the product between the

experimental frictional pressure drop, ,over the test section defined by Eq.

(3.2) and the volumetric flow rate of the liquid at its saturation temperature.

In Eq. (4.3) the mass flow rate for the plain tube was estimated based on the

pumping power based on the experimental results for the tubes with twisted-tape


inserts. For the estimation of both performance parameters ( and ), plain tube

heat transfer coefficient, hPT, and frictional pressure drop, ∆pPT, were evaluated

according to Kandlikar (1990) and Grönnerud (1979) methodologies, respectively.

Frictional pressure drop for tube with twisted-tape insert ∆pTT was estimated

according to Kanizawa and Ribatski (2012) correlation. These predictive methods

were chosen based on the fact that they have provided the best predictions of the

experimental data obtained in the present study.

The enhancement parameters and were chosen with the aim of

analyzing the gain in heat transfer for a given heat exchanger with fixed geometry

due to the installation of twisted-tape inserts, keeping the same pumping power or

per unit of pumping power. These approaches were considered since they are based

on characteristics directly applied by system designers such as pumping power,

temperature differences and heat exchanger size.

Figure 4.37 illustrates the behavior of the performance factor based on heat

transfer coefficient per unit of pumping power, 1ε , with increasing vapor quality for G

= 75 kg/m²s. As can be observed in this figure, 1ε increases with increasing vapor

quality and twist-ratio. Moreover, it is also noted that 1ε decreases with decreasing

saturation temperature and the tube diameter from 12.7 to 15.9 mm. Analyses of the

experimental results for other conditions (not shown in Fig. 4.37) revealed that 1ε

increases with increasing mass velocity and that the effect of augmenting the heat

flux from 5 to 10 kW / m² is only marginal on 1ε .

Figures 4.38 and 4.39 display the variation of the performance factor 2ε with

vapor quality for 12.7 and 15.9 mm ID tubes, respectively. According to these figures,

performance enhancements based on 2ε factor up to 45 % can be obtained keeping

the same pumping power through the use of twisted-tape inserts. Generally

speaking, Figs. 4.38 and 4.39 display that the performance factor 2ε increases with

increasing mass velocity and decreasing tube diameter. Moreover, initially the

performance factor 2ε increases with increasing vapor quality then passes through a

peak under intermediary to moderate-high vapor qualities. After the peak, 2ε

decreases drastically with further vapor quality augmentation. Although not shown for

all experimental conditions displayed in Figs. 4.38 and 4.39, the peak is an expected

behavior due to the fact that twisted-tapes promote earlier transitions to dryout


compared with tubes without twisted-tapes as displayed in Figs. 4.20 and 4.21. This

behavior moves the drastic reduction of the heat transfer coefficient to lower vapor

qualities. For reduced vapor quality values, it can be also noticed that the

enhancement factor is lower than unity for majority of conditions. This behavior is due

to high pressure drop penalty that the insert causes in the system. Based on section

4.1.4, pressure drop penalty values higher than 30 were obtained for reduced twist-

ratios and low vapor quality, while the heat transfer coefficient increment is about one

order of magnitude lower.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.2

0.4

0.6

0.8

1.0

x [-]

εε εε1

[-]

y = 3, di = 12.7 mm

y = 9, di = 12.7 mm

y = 3, di = 15.9 mm

y = 9, di = 15.9 mm

Figure 4.37 - Variation of enhancement factor 1ε for unit pumping power, for G = 75 kg/m²s, ϕ = 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).

In general, the performance factor 2ε increases with increasing saturation

temperature from 5 to 15 °C. This behavior can be attributed to the fact that at high

saturation temperature conditions, the volumetric flow rate is lower than at low

saturation temperature conditions. This pose little effect on the system pumping

power resulting in increasing the overall performance factor.

Finally, based on Figs. 4.38 and 4.39, it can be concluded that higher twist-

tape-ratios are recommendable for high mass velocities and low vapor quality

conditions while lower twist-tape ratios are recommendable for high mass velocities

and intermediary vapor qualities prior the dryout. On the other hand, under low mass

velocity conditions, lower twist-ratios are recommendable for intermediary vapor


qualities. This is related to the fact that for reduced mass velocities, the twisted-tape

promotes the transition from stratified to annular flow what is absent for the tube

without swirl promoter devices. Annular flows are characterized by higher heat

transfer coefficients than stratified flows.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.5

1.0

1.5

2.0

x [-]

εε εε2

[-]

y = 3, di = 12.7 mmy = 4, di = 12.7 mmy = 14, di = 12.7 mmy = 3, di = 15.9 mmy = 4, di = 15.9 mmy = 14, di = 15.9 mm

Figure 4.38 – Variation of enhancement factor 2ε for the same pumping power, for G = 75 kg/m²s, ϕ

= 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.5

1.0

1.5

2.0

2.5

x [-]

εε εε2

[-]

y = 4

y = 14

y = 3

Figure 4.39 – Variation of enhancement factor 2ε for the same pumping power, for G = 200 kg/m²s, ϕ

= 10 kW/m², Tsat = 15 °C, d = 12.7 mm (empty symbols) and di = 15.9 mm (filled symbols).

166 Heat transfer predictive method

5 PREDICTIVE METHOD FOR HEAT TRANSFER

COEFFICIENT DURING FLOW BOILING INSIDE

TUBES CONTAINING TWISTED-TAPE INSERTS

This chapter deals with the development of a new method for predicting heat

transfer coefficient during flow boiling inside tubes containing twisted-tape inserts.

The proposed method takes into account the swirl flow effects of the twisted-tape

inserts on the enhancement of convective effects and nucleate boiling suppression.

The new method was developed based on the following suggestions posted

by Shatto and Peterson (1996): (1) Obtain a reasonable prediction of experimental

data for plain tube without twisted-tape using well-established correlation from the

literature; (2) modify this correlation to predict the twisted-tape heat transfer data.

Taken into accounts the suggestion (1) of Shatto and Peterson (1996), the

new predictive method was developed based on the Liu and Winterton (1991)

method. This method was chosen because it predicted the data for tubes without

twisted-tape inserts gathered in the present study satisfactorily well. Moreover, the

method of Liu and Winterton (1991) was developed based on a wide range of

saturated and subcooled flow boiling data collected from 30 different literature

sources involving various types of fluids. Additionally, instead of the method of

Kandlikar (1990) that has provided also a reasonable prediction of the data obtained

in the present study, but is purely empirical, the method of Liu and Winterton (1991)

is based on the superposition of convective and nucleate boiling effects. So, following

the same approach of Liu and Winterton (1991) the effects of swirl flow on nucleate

boiling suppression and convection enhancement can be taken into account.

Based on the second suggestion of Shatto and Peterson (1996), the method

of Liu and Winterton (1991) was modified based on the data obtained in the present

study for flow boiling inside horizontal tubes containing twisted-tape inserts.

The following paragraphs describe the predictive method developed in the

present study to estimate the heat transfer coefficient during flow boiling inside tubes

containing twisted-tape inserts.

Heat transfer predictive method 167

Dryout inception and completion

As revealed in Figs. 4.24 and 4.25 and already discussed in Chapter 4, the

dryout inception for tubes with twisted-tape inserts occurs under lower vapor qualities

than for plain tubes without twisted-tapes. So, the prediction of dryout inception is

more relevant for tubes with twisted-tape inserts than for empty tubes and should be

taken into account in a predictive method for the heat transfer coefficient during flow

boiling inside tubes containing twisted-tape.

Based on the abovementioned, the method developed in the present study

considers the following three heat transfer regions: (i) Flow boiling region,

characterized by vapor qualities lower than dryout inception; (ii) Dryout region

covering vapor qualities between dryout inception and dryout completion; and (iii)

Mist flow region that occurs for vapor qualities higher than the vapor quality

corresponding to the dryout completion. The earlier dryout under swirl flow conditions

is due to centrifugal acceleration that detach the liquid droplets from the liquid film as

the vapor quality and two-phase flow velocity increase. Figure 5.1 presents a

comparison between the predictive method of Wojtan et al. (2005) for dryout

inception vapor quality given by Eq. (2.28) and the experimental dryout inception

data for plain tubes obtained in the present study. According to this figure, the

method of Wojtan et al. (2005) provides accurate prediction of the present study

experimental data. So, in the present study, a new predictive method for dryout

inception inside tubes with twisted-tape inserts was proposed based on the previous

method of Wojtan et al. (2005). In the new method, the dryout inception vapor quality

is given as follows:

(5.1)

where 1Π is a dimensionless parameter that takes into account the effects of twist-

ratio, heat flux, tube diameter and fluid properties on the dryout inception. The

parameter 1Π was correlated based on the regression analysis of the vapor quality


data for the onset of dryout obtained in the present study. The parameter 1Π is given

by the following correlation:

(5.2)

where 2Π is defined as the ratio between the internal tube diameter and the

maximum tube diameter evaluated in the present study (15.9 mm) as follows:

)Max(i

i

2d

d=Π (5.3)

50 75 100 125 1500.5

0.6

0.7

0.8

0.9

1.0

G [kg / m2 s]

x di [

-]

Experimental , di=12.7 mm

Wojtan et al. (2005) Eq. (2.28)

Experimental , di=15.9 mm

Figure 5.1 - Comparison of the experimental vapor quality data for the dryout inception in plain tubes and the predictions according to the method of Wojtan et al. (2005), Tsat = 15 oC and φ = 10 kW / m2 .

It can be expected that the augmentation by the twisted-tape of the shear

effects on the film due to the increase of vapor velocity near the interface gas-liquid

affects equally the vapor qualities for dryout inception and completion. So, it seems

logical to propose the following correlation for the dryout completion vapor quality:

(5.4)

Flow boiling region


Prior to the dryout inception and as above mentioned, the predictive method

proposed in the present study for the heat transfer coefficient during flow boiling

inside tubes containing twisted-tapes is based on the superposition of convective and

nucleate boiling effects. Analogous to Liu and Winterton (1991), an asymptotic

exponent of 2 is assumed and the flow boiling heat transfer coefficient is given


(5.5)

where the sub index refers to tubes with twisted-tape.

On contrary to Liu and Winterton (1991) that have correlated the single-phase

heat transfer coefficient in Eq. (5.5) according to Dittus and Boelter (1930) method, in

the present study the predictive method of Lopina and Bergles (1969), Eq. (2.130),

for single-phase flow inside tubes with twisted-tape inserts was adopted. The Lopina

and Bergles (1969) method is described in Chapter 2 and was selected because as

shown in Fig. 5.2 provided the best predictions of the single-phase heat transfer

coefficient data for swirl flow gathered in the present study. The method of Lopina

and Bergles (1969) is adopted considering the Reynolds number of the two-phase

mixture as liquid and using the internal diameter instead of hydraulic diameter as

follows:

( )i

L4.0

L

8.0

0LTT,Ld

kPrReFe023.0h α= (5.6)

where:

1.10Fe = (5.7)

Instead of the method of Cooper (1984) used by Liu and Winterton (1991) to

predict the pool boiling heat transfer coefficient in Eq. (5.5), in the present study the

method of Ribatski and Saiz-Jarbado (2003) was adopted because this method is

based on a broad database only for halocarbon refrigerants and, so, can be

considered more adequate to predict the present database for R134a. The method

proposed by Ribatski and Saiz-Jarbado (2003) is given as follows:

( )[ ]( )5.02.08.0

r

45.0

rW

m

nb MRaplogpfh−−

−= φ (5.8)


where:

0.2r0.9 0.3m p= − (5.9)

and Wf is the surface material parameter and presents the following values for

copper, brass and stainless steel 100, 110 and 85, respectively.

1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

4000

Sw [-]

Nu

[-]


Naphon (2006)



Experimental y=9

2000 4000 6000 8000 10000 12000 140000

1000

2000

3000

4000

5000

6000

7000

Sw [-]

Nu

[-]



Naphon (2006)


Experimental y=3

Figure 5.2 - Comparison between the experimental and predicted values of the heat transfer coefficient during single-phase flows inside tube with twisted-tape insert, ID =12.7 mm.

New correlations were adjusted for convective enhancement and nucleate

boiling suppression factors based on the database obtained in the present study.


New coefficients and exponents were obtained based on a least square regression

analyses keeping the same dimensionless numbers as proposed by Liu and

Winterton (1991). The new convective enhancement and nucleate boiling

suppression factors are given as follows:

37.0

V

L75.0

TT 1Prx1F

−+=

ρ

ρ (5.10)

( ) 116.0

0L

1.0

TTTT ReF055.01S−

+= (5.11)

Figures 5.3 and 5.4 present flow images and the schematic diagram

corresponding to the flow pattern observed in the present study. Both stratified and

stratified wavy flows were observed only under conditions of high twist-ratios and

reduced flow velocities, indicating the predominance of gravitational effects on the

two-phase distribution. Annular flow is observed for high vapor qualities and

becomes predominant under conditions of high mass velocities and reduced twist-

ratios. As mentioned in Chapter 4, the twisted-tapes promote transition from stratified

to annular flow pattern under lower mass velocities when compared to the plain tube

without twisted-tape. These effects are intensified with decreasing the tube diameter.

It is well known in the literature that the two-phase topology and heat transfer

coefficient are intrinsically related.

So, new correlations were adjusted for the parameters Se and Fe

which took

into account the stratification effects for empty tube in the method proposed by Liu

and Winterton (1991). The correlations for the parameters TTSe , and TTFe , were

obtained based on the present study database. If the tube is horizontal for

, then and in

Eq. (5.5) should be multiplied by TTSe , and TTFe , respectively.

The TTSe , and TTFe , , are given as follows:

( ) ( )( )( )Bo6.51x611.0

TT,S2ee

Π−−= (5.12)

( ) 44.0

r

6.3x15.1

TT,F pe468.0e−−= α (5.13)


where 2Π is the dimensionless number given in Eq. (5.3) and Bo is the Boiling

number calculated according to Eq. (2.84).

The parameter α defined by Eq. (2.132), takes into account the swirl velocity effect.

Figure 5.3 - Flow images. (a) Stratified flow (y = 14, G = 75 kg / m2 s, x = 0.25, Tsat = 5 oC); (b) stratified wavy flow (y =14,G = 100 kg / m2 s, x = 0.20, Tsat = 5 oC); (c) Anular flow ( y = 3, G = 150 kg /

m2 s, x = 0.35, Tsat = 5 oC); (d) Dryout (y = 3, G = 200 kg / m2 s, x = 0.45, Tsat = 5 oC).

(a)

(b)

(c)

(d)


Figure 5.4 - Flow pattern Schematic diagram

Mist flow region

For vapor qualities higher than the dryout completion, mist flow is assumed. In

the present study, the heat transfer coefficient in the mist flow region is obtained

using a modified version of Groeneveld (1973) correlation for mist flow heat transfer

coefficient used by Wojtan et al. (2005) for plain tubes without twisted-tapes. In the

modified version the fin effect generated by the twisted-tape inserts is taken into

account. The homogenous Reynold number considered by Wojtan et al. (2005)

method is also modified in order of taking into consideration the twisted-tape swirl

velocity effect. A modified version of Wojtan et al. (2005) method was adopted since

no data was obtained for mist flow region in the present study. This method seems

the most accurate for this flow pattern according to literature in case of empty tubes.

The heat transfer coefficient during mist flow for tubes with twisted-tape inserts is

given as follows:

Fed

kPrRe0117.0h

i

V83.1

3

06.1

V

79.0

TT,HTT,mist

−= Π (5.14)

where

( ) αρ

ρ

µ

−+= x1x

GdRe

L

V

V

i

TT,H (5.15)

(a

(b

(c)

(d


( )0.4

3 1 0.1 1 1L

V

xρ

ρ

Π = − − −

(5.16)

Fe and α are estimated by Eq. (5.7) and Eq. (2.132) respectively.

Dryout flow region

The heat transfer coefficient in the dryout region is obtained using the same

approach used by Wojtan et al. (2005) for plain tubes without twisted-tapes. The heat

transfer coefficient is calculated from the following interpolating equation:

( ) ( ) ( )[ ]TT,deTT,mistdiTTTT,2

TT,diTT,de

TT,di

diTTTT,2TT,dryout xhxhxx

xxxhh −

−

−−= ΦΦ (5.17)

where ( )diTTTT xh ,2Φ is the two-phase flows heat transfer coefficient calculated from Eq.

(5.5) at the dryout inception vapor quality TTdix , and ( )TTdeTTmist xh ,, is the mist flow heat

transfer coefficient calculated from Eq. (5.14) at the dryout completion vapor quality

TTdex , . If the dryout completion vapor quality given by Eq. (5.4) is higher than 1, it

should be assumed that 999.0=dex as proposed by Wojtan et al. (2005).

Comparison of the proposed predictive method with experimental results

Figure 5.4 shows a comparison between the heat transfer data obtained in the

present study and the predictions given by Eq. (5.5). According to this figure, the

method seems accurate, predicting most of the data within an error band of ±30 %.

Table 5.1 presents the results of the statistical analyses of the comparison between

experimental and predicted results according to the proposed method. According to

Tab. 5.1, the new method predicted 89.1 % of the database obtained in the present


study within an error band of ±30 %, and absolute mean deviation of 15.7 %. It

should be highlighted that the best predictive method from the literature predicted

only 70.9 % of the same database within an error band of ±30 % and absolute mean

deviation of 26.4 % as shown in Chapter 4. This scenario is reinforced by Fig. 5.5,

that illustrates the parcels of the database predicted by the new method within an

error band of ±30 % and the respective absolute mean deviation according to

different experimental parameters. According to this figure, it can be noticed that the

proposed method is well weighed predicting the experimental data for different

conditions with approximately similar error margins.

0.0 1.0 2.0 3.0 4.0 5.0 6.00.0

1.0

2.0

3.0

4.0

5.0

6.0


hes

tim

ated

[kW

/ m

2 o

C]

-30%

+30%

Figure 5.5 - Comparison between the method proposed in the present study and the experimental heat transfer results for tubes with twisted-tape inserts.

Table 5.1 - Results of the statistical analysis of the comparison between the proposed method and the heat transfer experimental results, G = 75-200 kg / m² s, Tsat = 5 and 15 °C, φ = 5 and 10 kW / m².



Present study (2013) 92 87 89 16 16 16


Figure 5.6 - Results of the statistical analyses of the comparison between experimental and predicted results according to the present method for different experimental conditions, G = 75-200 kg / m² s,

y=3-14, Tsat = 5 and 15°C, φ = 5 and 10 kW / m².

Considering the fact that a good predictive method should not only be

statistically accurate, but also be able of capturing the main trends of the

experimental results, Figs. 5.6 to 5.13 display comparisons of the evolution of the

heat transfer coefficient with vapor quality according to the experimental results and

Kg/m2 s

η, ζ

30 [%

] η, ζ

30 [%

] η, ζ

30 [%

] η, ζ

30 [%

]


estimatives by the predictive method proposed in the present study. From this

figures, it can be noted that the proposed method captures the main trend of the

experimental data predicting the increase of the heat transfer coefficient with

increasing vapor quality, decreasing tube diameter and twist-ratios, independently of

the mass velocity. By analysing Figs. 5.6 and 5.7 for G = 75 kg / m2 s, it can be

noticed that the method also captures reasonably well the typical behaviour of

stratified flows corresponding to an almost constant heat transfer coefficient with

varying the vapor quality until the onset of dryout. According to these figures, the

effect of twist-ratio on heat transfer coefficient and the onset of dryout are also well

predicted. The same behavior are also captured for a mass velocity of 100 kg / m2 s

as shown in Figs. 5.8 and 5.9.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

[x]

h [

kW /

m2 o

C]

y=3y=3y=4y=4y=9y=9

y=14y=14

Figure 5.7 - Evolution of the heat transfer coefficient with vapor quality according to the experimental

results (symbols) and predictions according to the proposed method (lines), ϕ = 10 kW / m², Tsat= 5 °C, G = 75 kg / m2 s and ID = 12.7 mm.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

[x]

h [

kW /

m2

oC

]y=3y=3y=4y=4y=9

y=14 y=14y=9

Figure 5.8 – Evolution of the heat transfer coefficient with vapor quality according to the experimental

results (symbols) and predictions according to the proposed method (lines) , ϕ= 10 kW/m², Tsat= 15 °C, G = 75 kg / m2 s and ID = 15.9 mm.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

[x]

h [

kW /

m2

oC

]

y=3y=3y=4y=4y=9y=9

y=14y=14


results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat= 5 °C, G = 100 kg / m2 s and ID = 12.7 mm.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

[x]

h [

kW /

m2

oC

]

y=3y=3y=4y=4y=9y=9

y=14y=14


results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat= 15 °C, G = 100 kg / m2 s and ID = 15.9 mm.

Figures 5.10 to 5.13 present comparisons between predictions and

experimental data for mass velocities of 150 and 200 kg / m2 s corresponding to

annular flows. Again, the method proposed in the present study captures

satisfactorily the experimental trends corresponding to the heat transfer coefficient

augmentation with increasing vapor quality. Moreover, the method also captures the

facts that the vapor quality for the onset of dryout decreases with increasing the

mass velocity and decreasing the twist-ratio.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

[x]

h [

kW /

m2 o

C]

y=3y=3y=4y=4y=9y=9

y=14y=14

Figure 5.11– Evolution of the heat transfer coefficient with vapor quality according to the experimental

results (symbols) and predictions according to the proposed method (lines), ϕ = 10 kW / m²,Tsat = 5 °C, G = 150 kg / m2 s and ID = 12.7 mm.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

[x]

h [

kW /

m2 o

C]

y=3y=3y=4y=4y=9y=9

y=14y=14


results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat =15 °C, G = 150 kg / m2 s and ID = 15.9 mm.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

[x]

h [

kW /

m2 o

C]

y=4y=4y=3 y=3

y=9y=9

y=14y=14


results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat = 5 °C, G = 200 kg / m2 s and ID = 12.7 mm.


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

1.0

2.0

3.0

4.0

5.0

6.0

[x]

h [

kW /

m2

oC

]

y=3y=3y=4y=4y=9y=9

y=14y=14


results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat = 15 °C, G = 200 kg / m2 s and ID = 15.9 mm.

The performance of the proposed method has also been evaluated through

comparisons with experimental results of Agrawal et al. (1986) and Akhavan-

Behabadi et al. (2009b). According to Fig. 5.14, the proposed method provides in

average reasonable predictions of the data from Agrawal et al. (1986) despite the

fact that the method is based on data for R12 while the method developed in the

present study considers only results for R134a. However, it should be highlighted

that the data of Agrawal et al. (1986) provides an unexpected behavior,

corresponding to heat transfer coefficient reduction with increasing vapor quality as

revealed in Figs. 2.17 to 2.20 and already discussed in Chapter 2

Data from Akhavan-Behabadi et al. (2009b) for R134a, the same refrigerant of

the present study, have also been considered for comparison. Figure 5.15 shows the

comparison between the estimated versus the experimental heat transfer coefficient

data. According to this figure, the method proposed in present study satisfactorily

predicted the database of Akhavan-Behabadi et al. (2009b) predicting 79 % of the

data points within an error band of ±30 % and absolute mean deviation of 23 %.

However, Akhavan-Behabadi et al. (2009b) have obtained averaged heat transfer

coefficient over the test section while in the present study local heat transfer


coefficient results were obtained. This difference between data regression

procedures can be related to the disagreements between the experimental data of

these authors and the predictive method developed in the present study. It should be

highlighted that average heat transfer coefficients are typical of the experimental

conditions and test section characteristics as the tube length and, so, are not the best

approach to be considered for the development of design tools for heat exchangers.

0.0 1.0 2.0 3.0 4.0 5.0 6.00.0

1.0

2.0

3.0

4.0

5.0

6.0


Pro

po

sed

met

ho

d [

kW/

m2 o

C]

+30%

-30%

y=10.15

y=7.37

y=5.58

y=3.76

Agrawal et al. (1986) (ζζζζ30=67%)

Figure 5.15 - Comparism between experimental heat transfer data from Agrawal et al. (1986) and the prediction by the present study proposed model.

0.0 1.0 2.0 3.0 4.0 5.00.0

1.0

2.0

3.0

4.0

5.0


Pro

po

sed

met

ho

d [

kW/

m2 o

C]

+30%

-30%

y=9

y=12

y=15

y=6

Akhavan-Behabadi et al. (2009) (ζζζζ30=79%)

Figure 5.16 - Comparism between experimental heat transfer data from Akhavan-Behabadi et al. (2009b) and the prediction by the present study proposed model.

Conclusions and recommendations 183

6 CONCLUSIONS AND RECOMMENDATIONS

6.1 Conclusions

In the present study, flow boiling inside tubes (12.7 and 15.9 mm) containing

twisted-tape inserts was investigated. A broad literature review was performed. Heat

transfer and pressure drop data were collected for tubes without and with twisted-

tape inserts for four twist-ratios. Based on these experimental results, a new model

for predicting flow boiling heat transfer inside tubes containing twisted-tape has been

developed. From the present study, the following main conclusions can be draw:

• Based on the analyses of experimental results obtained in the present study, it

was observed that the frictional pressure drop increases for tubes with and

without twisted-tape inserts with increasing the mass velocity, vapor quality

and decreasing the tube diameter, saturation temperature and twist-ratio.

Pressure drop peaks were also observed at high vapor qualities

corresponding to conditions close to the flow pattern transition from annular to

mist flow. Additionally, a significant influence of flow pattern on pressure drop

was also observed. The transition from stratified flow to annular flow in tubes

with twisted-tape inserts occurs for lower vapor qualities and mass velocities

when compared with the plain tube counterparts independent of the tube

diameter;

• Experimental pressure drop data were compared against predictive methods

available in the literature. From this analyses it was concluded that Kanizawa

and Ribatski (2012) and Grönnerud (1979) methods provide the best results,

predicting 99.6 and 88.0 % of experimental data within an error band of ±30

%, for tubes with and without twisted-tape inserts, respectively;

• Based on the analyses of experimental results obtained in the present study, it

was observed that the heat transfer coefficient increases with increasing the

mass velocity and decreasing the tube diameter and saturation temperature

for tubes with and without twisted-tape inserts. Significant influence of flow

pattern on the heat transfer coefficient were also observed. The heat transfer

coefficient was almost constant for stratified flow pattern while its value

increases significantly with vapor quality under annular flow conditions.

184 Conclusions and recommendations

Moreover, a sharply decrease of the heat transfer coefficient with increasing

vapor quality was observed under high vapor qualities corresponding to the

onset of dryout. These behaviors are more pronounced by decreasing twist-

ratio and tube diameter;

• The heat transfer experimental results were compared against predictive

methods from literature. It was concluded from these comparisons that the

methods of Kandlikar (1990) and Akhavan-Behabadi et al. (2009b) provide the

best predictions of the experimental results for plain tubes and tubes with

twisted-tape inserts, respectively, predicting 64.6 and 70.9 % of the

experimental data gathered in the present study within an error band of ±30 %,

respectively;

• Pressure drop penalties of about 35 % were observed for low mass velocities

and twist-ratios. The pressure drop penalty is found to decrease sharply with

increasing vapor quality;

• Analysis of the enhancement factor was carried out in order to identify

operational conditions under which the use of twisted tape-inserts would be

advantageous. Heat transfer coefficient increments up to 45 % keeping the

same pumping power were obtained by using twisted-tape relative to tubes

without inserts. Additionally, according to the parameter defined by Eq.

(4.3), the use of twisted-tape insert is advantageous for most of the

operational conditions evaluated in the present study;

• The results from Tab. (4.4) revealed that both predictive method of Jensen

and Bensler (1986) and Agrawal et al. (1986) fail to predict the trends of the

data obtained in the present study. However, it is worth noting that the method

of Akhavan-Behabadi et al. (2009b) present satisfactory results but was

unable to capture well the data obtained for reduce twist-ratios. In this way, a

new predictive method for heat transfer coefficient inside tubes containing

twisted-tape inserts has been developed. The predictive method of Liu and

Winterton (1991) was modified in order of taking into account the effects of the

swirl flow induced by the twisted-tape on the heat transfer coefficient. The new

method includes the prediction of the dryout inception observed to be

dependent on the tubes diameter and twist-ratios. Moreover, the method is

flow pattern based and predicts the heat transfer coefficient under dryout and

mist flow conditions. The proposed method predicts satisfactorily well the data

Conclusions and recommendations 185

obtained in the present study, predicting 89.1 % of the experimental data

within an error band of ±30 % and absolute mean deviation of 15.7 %. It

should be highlighted that the dryout inception displayed by the experimental

data is also well captured by the method proposed in the present study.

6.2 Recommendations for future studies

The present study concerns a broad evaluation of the effect of twisted-tape

inserts on augmentation of heat transfer coefficient and pressure drop during flow

boiling of R134a inside horizontal tubes. However, several additional aspects were

not explored in the present study which are recommended for future studies:

• Conduct experimental test with low pressure refrigerants as R245fa. Usually,

these refrigerants present higher vapor specific volume and the two-phase

velocity increases with increasing this property. So, it is expected that this

effect combined with the twisted-tape improves the swirl effects affecting,

consequently, the nucleate boiling suppression and convective enhancement.

These data would be useful in order to extend the predictive method proposed

in the present study to broader conditions;

• Perform experimental tests for refrigerant/lubricant oil mixtures with the

objective of evaluating the effect of oil lubricant on pressure drop and heat

transfer coefficient during flow boiling inside tubes containing twisted-tape

inserts. It is expected that the twisted-tape improves the mixing effect due to

swirl flow. Thus, it can avoid the formation of a layer of liquid richer of lubricant

on the wall, favouring nucleate boiling under low vapor quality conditions and

reducing the thermal resistance across the liquid film during annular flow. For

both cases, a heat transfer coefficient enhancement is expected with the use

of twisted-tape due to the improvement of mixing. The same effect is expected

for the case of zeotropic mixtures as R407C;

• Conduct experimental test with natural refrigerants as ammonia, cabon dioxide

and hydrocarbons. These refrigerants are candidates to replace R134a in

some applications since this refrigerant although is not harmful to the ozone

layer but presents a high global warming potential (GWP). The like of natural

fluid as carbon dioxide and hydrocarbons are found to present low global

186 Conclusions and recommendations

warming potential. Additionally, the impact of ammonia on ozone layer (ODP)

and global warming potential (GWP) is null;

• Perform experimental test for mist flow data, since no data was obtained for

this flow pattern in the present study. In the actual configuration of the test

facility, the heating effect is obtained by imposing the heat flux through

electrical heaters. So, reaching post dryout conditions means damaging the

test section. Thus, a new experimental bench should be designed and

constructed using hot water as heating source and having the wall

temperature as boundary condition instead of heat flux. In this case, heat

transfer and pressure drop measurements can be made under safety

conditions. Moreover, the dryout phenomena can also be studied. This new

facility would be able also of running condensation test by using the water as

cooling medium instead of heating source;

• Perform pressure drop and heat transfer coefficient experimental tests during

condensation inside tubes containing twisted-tape inserts. Results from the

present study revealed that for higher saturation temperature, higher heat

transfer enhancement than pressure drop penalties can be obtained. It is

expected that pressure drop penalties inside tubes containing twisted-tape

inserts during condensation process will be lower compare to that in

evaporation process due to low vapor specific volume for high saturation

temperature conditions. It is also knows that pressure drop in the evaporator

are more detrimental to the system performance than in the condenser. This

corroborate the fact that the use of twisted-tape is more profitable to be use in

the condenser.

References 187

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Appendix A 195

Appendix A – Calibration of the Experimental

measuring equipments

This section describes the methods and results related to the verification steps

and calibration of the components of the experimental apparatus.

A.1 Uncertainty analysis

Estimation of the experimental apparatus uncertainties as mentioned in

section 3.9 are given in detail as follow:

Measurement of uncertainty is given by:

( )StBU 95+±= (Appendix A.1)

The parameter B corresponds to the instrument uncertainty (or accuracy)

reference for measurement, 95t is the 95th point for the Student t -distribution with two

tails (two-tailed), which depends on the number of degrees of freedom of the

measured quantity. The term S corresponds to the precision obtained through

experimental tests, according to the following equation:

2

1

k

j

j

S

Sk

== ±

∑ (Appendix A.2)

where k is the number of the experimental points obtained from the curve and it

depends on the increment between the consecutive measurements and jS

is the

mean standard deviation for each point considered, given as follows:

( )2

1

1

N

ij ij

ij

x x

SN

=

−

=−

∑ (Appendix A.3)

N is equal to the number of curve plotted, ijx is the estimated value for each

curve i for the point j, and ijx is the average of the ijx . Each curve i obtained

196 Appendix A

experimentally corresponds to the lines that provide the estimated value of point j,

considering the actual reading, given by:

ij i j ix a x b= + (Appendix A.4)

where ia and ib are the coefficients of the line and jx is the real value of the reading

given by the calibrated instrument.

The degree of freedom of the parameter S depends on the type of magnitude

considered for pressure and temperature; the number of degrees of freedom is given

by:

( )1NKdfTS −= (Appendix A.5)

In the following subsections the calculated uncertainties for each type of

transduser is presented.

A.2 Absolute pressure transducers

The absolute pressure transducers are AKS-33 model manufactured by

Danfoss, with output 4-20 mA. The transduser is of nominal pressure measurement

from 0 to 11bar. The measurement was performed using a column manometer of

mercury, with approximately 1.4 meters high and 2.0 mm wide in conjunction with a

mercury column barometer for verification of atmospheric pressure. The maximum

height of the mercury column results in strain gauge pressure of 185 kPa, making it

impossible to cover the entire measurement range of the transducer.

During the calibration step, the transducers were connected to the data

aquisition system, by the use of precision resistors of 250 ohms. And the pipe

connected to one end of the column manometer, the calibration of the three

transdusers were perfomed simultaneously.

Table A.1 shows the coefficient and uncertainties obtained by the method

described in Section A.1:

Appendix A 197

Table A.1 - Coefficients of the equation for the pressure transducers and uncertainty

Parameters Pre-heater inlet Pre-heater outlet Test section inlet

[ ]a kPa V 326.7 326.0 326.2

[ ]b kPa -326.7 -326.5 -324.2

[ ]U kPa± 1.4 1.5 1.6

with the pressure given by the following equation:

p aV b= + (Appendix A.6)

A.3 Flowmeter

The main characteristics of the flowmeter are:

Flow meter type Coriolis FLOWMETER Model 2100 analyzer with signal MASSFLO

3000 Danfoss;

• Output current of 4 to 20 mA;

• Measure up to 52000 kg / h;

• Nominal connection of ½ inches.

The measurement was performed using water supplied by a reservoir of large

volume, balance and stopwatch. The scales used for the measurement is from the

manufacturer Toledo with 0.1 grams., and the container used for each measurement

has a maximum nominal volume of 12 liters. For the tests, a registry downstream of

the flowmeter was adjusted in order to obtain flow near the objective value. After

obtaining the steady-state condition, the output of the flowmeter was directed to the

container and the timer was activated with consequent measurement of the mass of

water.

The uncertainty analysis of the flow transductor after the tests was however

estimated using the methodology presented in section A.1. As a result, calculated

uncertainty of ± 0.276 kg / m² s was obtained considering the area for a nominal

diameter of the tube.

A.4 Calibration of thermocouples channels

Thermocouples channels calibration was performed between -4 and 52 °C

with increments of 4 °C. The calibration of the channels occurred with the use of a

198 Appendix A

thermostatic bath brand HAAKE, Model F6-C35 shown in Figure A. 01, together with

NIST (National Institute of Standards and Technology) and traceable thermometers.

The characteristics of the traceable thermometers are shown in Table A.2.

Table A.2 - Features of the thermometers used during calibration of the acquisition system channel for temperature.

Model Measuring range Resolution

3543Y -35 to 25 oC 0.1 oC

3570Y 20 to 60 oC 0.1 oC

Table A.3 - Coefficients for the reading temperature and estimated uncertainties for the thermocouples channels

Channel [ ]oa C V [ ]ob C [ ]oU C±

0 0.99 -0.20 0.10

1 0.99 -0.01 0.09

2 0.99 -0.14 0.09

13 0.99 -1.22 0.13

14 0.99 -1.25 0.12

15 0.99 -1.09 0.12

16 0.99 -1.14 0.12

17 0.99 -0.97 0.12

18 0.99 -1.10 0.12

19 0.99 -1.08 0.13

20 0.99 -1.14 0.13

21 0.99 -0.99 0.13

22 0.99 -1.07 0.12

23 0.99 -0.86 0.13

24 0.99 -0.68 0.12

25 0.99 -0.49 0.11

26 0.99 -0.73 0.12

27 0.99 -0.53 0.12

28 0.99 -0.74 0.11

Appendix A 199

Figure A.1 - Thermostatic bath used to calibrate the system thermocouple channels

To perform the calibration measurement, the temperature of the thermostatic

bath was set and after stabilization, the voltage at the terminals was recorded for

minimum of one minute, in conjunction with the direct reading of the temperature

values via thermometers.

From the data obtained experimentally, the temperature uncertainty was

estimated , according to the methodology presented in section A.1, resulting to the

values shown in Tab A.3, together with the coefficients for reading temperature


real measuredT aT b= + (Appendix A. 7)

A.5 Calibration of the active power transducers

Calibration of the active power transducers, for reading the electrical power

added to the system, was carried out while the refrigerant circuit micro pump with

frequency of 60Hz and the antifreeze solution circuit were activated.

The main characteristics of the active power transducers are given as follows:

• Transducer Yokogawa, model 2285A;

• output current of 4 to 20 Ma;

• Two transducers with full scale of 3 and 9 kW

200 Appendix A

The calibration was performed with the use of digital multimeters, linked to

output terminals of the electrical resistance (VARIACS). The power transducers were

connected to the acquisition system, using 250 ohm resistors. Characteristics of the

multimeters used during the calibration are shown in Table A.4

Table A.4 - Characteristics of the multimeters used during the calibration of power transducers

Model Voltage accuracy/range Current accuracy/range

Minipa ET-2042C ±0.8% / 200V ±2.0% / 20A

Minipa ET-3200 ±1.2% / 200V ±3.0% / 20A

Fluke 8050A ±0.5% / 200V

Due to the fact that the output current of the electrical resistance (VARIACS)

with nominal output of 9 kW surpass the maximum allowable current for the

multimeters, corresponding to 20A, the calibration of the entire measurement range

of this was not possible.

The electrical power of the instruments calibrated is given by the product of

voltage and current.

VIPower = (Appendix A.8)

Analysis was performed to estimate the uncertainty of the measured electrical

power based on the data obtained experimentally according to the methodology

presented in section A.1. The calculated uncertainties are shown in Table A.5,

together with the coefficients from the equation given as follows:

bmVPower += (Appendix A. 9)

Table A.5 - Coefficients and calculated uncertainty results of the active power transducers

Transducer Pre-heater

9 kW

Pre-heater

3 kW Test section

maq [W/V] 2180.1 914.9 971.0

baq [W] -2191.9 -915.0 -968.0

ST [±W] 5.1 6.5 0.9

t95.ST [±W] 10.1 13.0 1.7

B1/VI*100 (%) 3.0 3.0 3.0

Appendix A 201

A.6 Characteristics of differential pressure transducers

The differential pressure transducers used in the experimental setup are

manufactured by Endress-Hauser with PMD75 model.

The main characteristics of the differential pressure transducers are as listed

below:

• Transducers Endress-Hauser, PMD75 model;

• Measuring ranges up to 3, 10 and 300 kPa;

• Precision of 0.075 % of full scale, according to the manufacturer;

• Output with current, 4-20 mA;

Calibration of transducers was not carried due to the fact that, the transducers

are new, and indicated the same value of pressure loss during preliminary tests, with

the curve considered by the manufacturer.

202 Appendix B

Appendix B – Experimental Data

In this section raw experimental results obtained for the flow boiling pressure

drop and heat transfer coefficient for both tubes with and without twisted-tape inserts

during the experimental campain of this study are presented

Table B.1 – Flow boiling pressure drop experimental results for Tsat = 5oC under adiabatic conditions inside 12.7 mm internal diameter tube

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 5.0 5.2 Plain tube 74.6 0.052 0.041

0.0127 4.8 5.1 Plain tube 75.2 0.102 0.047

0.0127 5.0 5.3 Plain tube 75.3 0.151 0.050

0.0127 4.8 5.1 Plain tube 74.9 0.209 0.061

0.0127 4.8 5.1 Plain tube 75.5 0.251 0.072

0.0127 5.0 5.2 Plain tube 75.8 0.299 0.080

0.0127 4.8 5.0 Plain tube 74.7 0.360 0.113

0.0127 4.9 5.1 Plain tube 74.9 0.406 0.131

0.0127 5.0 5.2 Plain tube 75.3 0.458 0.154

0.0127 5.0 5.1 Plain tube 75.0 0.506 0.175

0.0127 4.8 4.9 Plain tube 75.3 0.556 0.202

0.0127 5.1 5.2 Plain tube 75.0 0.612 0.214

0.0127 4.9 5.0 Plain tube 74.7 0.661 0.235

0.0127 5.0 5.0 Plain tube 74.7 0.706 0.250

0.0127 5.1 5.1 Plain tube 75.3 0.761 0.271

0.0127 5.2 5.2 Plain tube 76.1 0.800 0.276

0.0127 5.1 5.1 Plain tube 75.9 0.864 0.299

0.0127 5.2 5.2 Plain tube 75.6 0.910 0.233

0.0127 5.0 5.2 Plain tube 100.1 0.051 0.052

0.0127 4.8 5.1 Plain tube 100.2 0.103 0.072

0.0127 5.1 5.2 Plain tube 100.3 0.155 0.075

0.0127 4.8 5.0 Plain tube 100.7 0.201 0.106

0.0127 5.0 5.2 Plain tube 99.5 0.254 0.128

0.0127 4.9 5.0 Plain tube 99.9 0.306 0.167

0.0127 4.9 5.0 Plain tube 100.3 0.356 0.210

0.0127 4.9 5.0 Plain tube 99.5 0.413 0.245

0.0127 5.0 5.0 Plain tube 99.2 0.459 0.275

0.0127 5.0 5.0 Plain tube 99.3 0.513 0.317

0.0127 5.1 5.1 Plain tube 99.9 0.558 0.346

0.0127 5.1 5.1 Plain tube 99.7 0.616 0.391

0.0127 5.1 5.1 Plain tube 100.5 0.653 0.427

0.0127 5.2 5.2 Plain tube 101.1 0.712 0.477

Appendix B 203

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 5.0 5.2 Plain tube 149.8 0.053 0.105

0.0127 5.1 5.3 Plain tube 150.1 0.104 0.130

0.0127 5.1 5.2 Plain tube 150.7 0.151 0.161

0.0127 4.9 5.0 Plain tube 150.0 0.209 0.262

0.0127 5.0 5.1 Plain tube 150.5 0.253 0.297

0.0127 4.9 4.9 Plain tube 149.4 0.309 0.404

0.0127 5.1 5.0 Plain tube 149.5 0.356 0.445

0.0127 5.1 5.0 Plain tube 149.6 0.410 0.549

0.0127 5.3 5.1 Plain tube 150.2 0.460 0.658

0.0127 5.0 4.8 Plain tube 149.6 0.513 0.767

0.0127 5.2 5.0 Plain tube 151.2 0.555 0.864

0.0127 5.1 4.9 Plain tube 150.7 0.609 1.010

0.0127 5.3 5.0 Plain tube 149.5 0.667 1.122

0.0127 5.3 4.9 Plain tube 148.9 0.725 1.275

0.0127 5.2 4.8 Plain tube 151.1 0.758 1.345

0.0127 5.4 5.0 Plain tube 148.5 0.825 1.401

0.0127 4.9 5.1 Plain tube 200.6 0.052 0.158

0.0127 5.1 5.2 Plain tube 200.1 0.103 0.210

0.0127 4.8 4.9 Plain tube 200.0 0.151 0.325

0.0127 4.9 4.9 Plain tube 200.6 0.202 0.439

0.0127 5.1 5.0 Plain tube 199.7 0.253 0.552

0.0127 5.1 4.9 Plain tube 199.3 0.309 0.715

0.0127 5.1 4.8 Plain tube 200.1 0.353 0.908

0.0127 5.2 4.8 Plain tube 200.3 0.409 1.109

0.0127 5.3 4.9 Plain tube 201.2 0.450 1.300

0.0127 5.4 4.8 Plain tube 200.0 0.511 1.529

0.0127 5.5 4.9 Plain tube 198.8 0.567 1.822

0.0127 5.3 4.5 Plain tube 202.1 0.604 2.047

0.0127 5.4 4.6 Plain tube 203.9 0.637 2.109

0.0127 5.7 4.8 Plain tube 197.6 0.727 2.386

0.0127 5.0 5.2 14 75.3 0.053 0.178

0.0127 5.0 5.1 14 75.0 0.102 0.193

0.0127 5.0 5.1 14 75.4 0.151 0.217

0.0127 5.0 5.1 14 75.4 0.205 0.239

0.0127 5.0 5.1 14 75.3 0.252 0.255

0.0127 5.1 5.2 14 74.9 0.308 0.281

0.0127 5.1 5.2 14 75.7 0.350 0.321

0.0127 5.1 5.1 14 75.2 0.404 0.367

0.0127 5.2 5.2 14 75.3 0.453 0.409

0.0127 5.1 5.1 14 74.6 0.511 0.468

0.0127 5.0 4.9 14 75.1 0.567 0.505

0.0127 5.2 5.2 14 75.2 0.610 0.537

0.0127 5.2 5.1 14 74.5 0.660 0.565

204 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 5.0 4.9 14 75.8 0.706 0.659

0.0127 5.1 4.9 14 74.5 0.774 0.640

0.0127 5.0 5.1 14 100.5 0.053 0.237

0.0127 5.1 5.2 14 100.1 0.102 0.276

0.0127 5.0 5.1 14 100.9 0.151 0.323

0.0127 4.9 5.0 14 99.3 0.208 0.407

0.0127 5.1 5.1 14 100.7 0.254 0.443

0.0127 5.1 5.1 14 100.8 0.303 0.498

0.0127 5.0 4.9 14 100.3 0.356 0.605

0.0127 5.1 5.1 14 100.3 0.406 0.677

0.0127 5.2 5.1 14 100.5 0.453 0.759

0.0127 4.9 4.7 14 99.6 0.520 0.893

0.0127 5.2 5.0 14 100.5 0.554 0.970

0.0127 5.0 4.8 14 101.0 0.606 1.054

0.0127 5.1 4.9 14 99.4 0.662 1.058

0.0127 5.0 5.1 14 150.4 0.052 0.329

0.0127 5.2 5.2 14 150.3 0.104 0.463

0.0127 5.2 5.1 14 150.9 0.153 0.609

0.0127 5.0 4.8 14 150.4 0.207 0.852

0.0127 5.1 4.9 14 150.0 0.255 0.993

0.0127 5.1 4.8 14 151.6 0.298 1.191

0.0127 5.3 5.0 14 152.6 0.343 1.357

0.0127 5.1 5.2 14 200.4 0.054 0.492

0.0127 5.0 5.0 14 199.9 0.104 0.807

0.0127 5.1 4.9 14 200.6 0.155 1.149

0.0127 5.2 4.8 14 199.4 0.211 1.558

0.0127 5.2 4.7 14 200.5 0.254 1.948

0.0127 5.3 4.6 14 200.4 0.306 2.452

0.0127 5.6 4.7 14 199.5 0.357 2.972

0.0127 5.6 4.5 14 200.0 0.410 3.529

0.0127 5.8 4.5 14 200.5 0.456 4.025

0.0127 5.6 4.1 14 199.7 0.523 4.680

0.0127 6.0 4.3 14 196.6 0.576 5.010

0.0127 5.8 3.9 14 197.5 0.629 5.265

0.0127 6.0 4.1 14 194.6 0.680 5.094

0.0127 5.1 5.2 9 75.1 0.054 0.189

0.0127 4.8 4.9 9 75.1 0.105 0.224

0.0127 5.1 5.2 9 75.3 0.152 0.267

0.0127 5.1 5.2 9 74.3 0.205 0.262

0.0127 5.2 5.2 9 75.1 0.256 0.278

0.0127 4.8 4.8 9 75.0 0.307 0.289

0.0127 4.9 4.9 9 75.1 0.360 0.330

0.0127 5.3 5.3 9 75.1 0.402 0.387

Appendix B 205

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 5.3 5.3 9 75.0 0.464 0.434

0.0127 5.1 5.0 9 75.1 0.509 0.476

0.0127 5.0 4.9 9 74.9 0.555 0.531

0.0127 5.1 5.0 9 75.0 0.610 0.562

0.0127 5.1 5.0 9 75.1 0.659 0.615

0.0127 5.2 5.0 9 75.7 0.707 0.614

0.0127 4.9 5.0 9 100.6 0.054 0.257

0.0127 4.9 5.0 9 100.7 0.102 0.299

0.0127 4.9 5.0 9 101.1 0.151 0.349

0.0127 5.1 5.2 9 100.4 0.206 0.418

0.0127 4.9 4.9 9 100.2 0.254 0.464

0.0127 5.1 5.1 9 100.5 0.302 0.518

0.0127 5.0 4.9 9 100.8 0.358 0.598

0.0127 5.1 4.9 9 101.2 0.407 0.711

0.0127 5.2 5.0 9 99.8 0.456 0.826

0.0127 4.9 4.7 9 100.2 0.506 0.924

0.0127 5.1 4.8 9 99.3 0.567 0.988

0.0127 5.2 4.9 9 99.0 0.618 1.079

0.0127 5.0 5.0 9 149.6 0.053 0.431

0.0127 5.1 5.1 9 148.7 0.107 0.554

0.0127 5.0 4.9 9 150.7 0.154 0.681

0.0127 5.1 5.0 9 149.6 0.205 0.867

0.0127 5.2 4.9 9 150.9 0.254 1.095

0.0127 5.0 4.7 9 150.0 0.357 1.294

0.0127 5.2 4.7 9 149.7 0.431 1.405

0.0127 5.0 4.6 9 152.5 0.495 1.468

0.0127 5.2 5.2 9 200.1 0.052 0.564

0.0127 5.2 5.2 9 200.3 0.101 0.842

0.0127 5.0 4.7 9 200.5 0.155 1.288

0.0127 5.3 4.8 9 200.1 0.208 1.664

0.0127 5.5 4.9 9 200.4 0.256 2.099

0.0127 5.5 4.7 9 200.3 0.312 2.727

0.0127 5.4 4.5 9 200.1 0.355 3.162

0.0127 5.6 4.4 9 200.3 0.409 3.802

0.0127 5.6 4.2 9 199.8 0.461 4.387

0.0127 5.6 4.1 9 200.5 0.517 4.569

0.0127 6.0 4.4 9 201.8 0.551 4.850

0.0127 6.3 4.4 9 196.5 0.637 5.053

0.0127 5.0 5.0 4 75.2 0.052 0.406

0.0127 5.0 5.0 4 75.4 0.106 0.425

0.0127 5.2 5.2 4 75.5 0.149 0.448

0.0127 5.2 5.2 4 74.4 0.210 0.468

0.0127 4.9 4.9 4 74.9 0.258 0.483

206 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 4.8 4.8 4 76.1 0.300 0.489

0.0127 5.2 5.1 4 75.2 0.359 0.548

0.0127 5.2 5.1 4 74.9 0.412 0.594

0.0127 5.1 4.9 4 75.1 0.456 0.663

0.0127 5.2 5.1 4 74.0 0.512 0.694

0.0127 4.9 4.7 4 74.7 0.555 0.770

0.0127 4.9 4.8 4 74.6 0.614 0.831

0.0127 5.3 5.2 4 75.6 0.659 0.863

0.0127 5.3 5.1 4 75.8 0.726 0.996

0.0127 5.1 5.1 4 100.3 0.053 0.499

0.0127 4.9 4.9 4 100.4 0.105 0.542

0.0127 5.0 4.9 4 100.4 0.153 0.619

0.0127 5.2 5.2 4 100.4 0.202 0.656

0.0127 5.2 5.1 4 100.2 0.253 0.745

0.0127 5.2 5.1 4 99.8 0.311 0.891

0.0127 5.1 4.9 4 100.5 0.354 0.980

0.0127 5.1 4.8 4 100.4 0.403 1.082

0.0127 5.2 4.9 4 100.4 0.451 1.193

0.0127 5.1 4.8 4 100.5 0.508 1.354

0.0127 5.1 4.7 4 99.7 0.558 1.458

0.0127 5.1 5.1 4 150.4 0.052 0.705

0.0127 5.1 5.0 4 150.0 0.101 0.831

0.0127 5.3 5.1 4 150.2 0.153 1.078

0.0127 5.1 4.8 4 150.4 0.203 1.271

0.0127 5.3 4.9 4 150.3 0.255 1.632

0.0127 5.3 4.7 4 150.6 0.305 1.932

0.0127 5.2 4.7 4 150.6 0.354 2.174

0.0127 5.3 4.6 4 150.2 0.413 2.546

0.0127 5.5 4.6 4 149.9 0.466 2.960

0.0127 5.3 5.2 4 199.7 0.076 0.847

0.0127 5.1 4.9 4 201.0 0.102 1.312

0.0127 5.1 4.7 4 200.7 0.153 1.821

0.0127 5.4 4.8 4 200.8 0.208 2.416

0.0127 5.6 4.7 4 200.6 0.254 2.924

0.0127 5.5 4.3 4 200.0 0.315 3.876

0.0127 5.7 4.3 4 200.0 0.362 4.384

0.0127 5.8 4.3 4 199.9 0.408 4.872

0.0127 5.9 4.1 4 199.9 0.461 5.704

0.0127 6.2 4.2 4 200.4 0.510 6.178

0.0127 5.1 5.2 3 75.1 0.053 0.362

0.0127 5.0 5.0 3 75.7 0.104 0.476

0.0127 5.1 5.1 3 75.7 0.154 0.547

0.0127 4.9 4.9 3 75.2 0.210 0.612

Appendix B 207

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 5.2 5.2 3 74.5 0.256 0.636

0.0127 5.0 5.0 3 75.0 0.305 0.655

0.0127 4.9 4.9 3 75.0 0.355 0.679

0.0127 5.0 4.9 3 75.1 0.401 0.737

0.0127 5.0 4.8 3 75.1 0.458 0.807

0.0127 5.0 4.9 3 75.5 0.519 0.849

0.0127 5.0 4.8 3 75.7 0.552 0.932

0.0127 5.1 4.9 3 75.2 0.614 0.981

0.0127 5.1 4.8 3 75.1 0.680 1.008

0.0127 4.9 4.9 3 100.1 0.053 0.519

0.0127 5.1 5.1 3 99.8 0.104 0.628

0.0127 5.0 4.9 3 100.0 0.154 0.732

0.0127 5.1 5.0 3 100.0 0.204 0.774

0.0127 5.2 5.1 3 100.2 0.258 0.914

0.0127 5.2 5.0 3 100.3 0.308 1.043

0.0127 5.2 5.0 3 100.8 0.354 1.200

0.0127 5.0 4.8 3 100.4 0.401 1.224

0.0127 5.1 4.8 3 100.8 0.468 1.393

0.0127 5.3 4.9 3 100.6 0.504 1.435

0.0127 5.1 5.0 3 150.4 0.054 0.844

0.0127 5.1 4.9 3 149.2 0.103 0.986

0.0127 5.1 4.8 3 150.1 0.154 1.382

0.0127 5.1 4.8 3 150.6 0.203 1.660

0.0127 5.0 4.6 3 150.9 0.255 1.861

0.0127 5.4 4.8 3 150.7 0.310 2.216

0.0127 5.4 4.7 3 149.0 0.355 2.460

0.0127 5.0 4.8 3 200.7 0.052 1.133

0.0127 5.3 4.9 3 199.8 0.104 1.609

0.0127 5.2 4.7 3 200.5 0.153 2.133

0.0127 5.5 4.7 3 200.1 0.208 2.736

0.0127 5.4 4.4 3 200.5 0.255 3.470

0.0127 5.6 4.3 3 200.1 0.313 4.400

0.0127 5.9 4.4 3 200.1 0.360 4.906

0.0127 6.0 4.2 3 200.3 0.408 5.511

0.0127 6.0 4.1 3 200.3 0.459 6.010

0.0127 6.1 3.7 3 196.7 0.525 6.704

Table B.2 - Flow boiling pressure drop experimental results for Tsat = 15oC under adiabatic conditions inside 12.7 mm internal diameter tube

D [m]

TTS,in

[oC] TTS,out

[oC] y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 15.1 15.2 Plain tube 74.7 0.053 0.039

0.0127 14.8 15.0 Plain tube 75.5 0.105 0.044

0.0127 15.1 15.2 Plain tube 75.9 0.153 0.044

208 Appendix B

0.0127 14.8 14.9 Plain tube 75.3 0.204 0.051

0.0127 14.9 15.0 Plain tube 76.2 0.249 0.056

0.0127 15.1 15.2 Plain tube 75.6 0.304 0.061

0.0127 14.9 15.0 Plain tube 74.7 0.355 0.081

0.0127 15.1 15.2 Plain tube 75.0 0.398 0.083

0.0127 15.0 15.1 Plain tube 75.1 0.456 0.104

0.0127 15.0 15.1 Plain tube 74.6 0.511 0.129

0.0127 15.1 15.2 Plain tube 75.1 0.549 0.139

0.0127 15.1 15.2 Plain tube 74.9 0.613 0.153

0.0127 15.2 15.3 Plain tube 75.1 0.651 0.168

0.0127 15.0 15.0 Plain tube 74.9 0.716 0.187

0.0127 15.0 15.0 Plain tube 75.3 0.757 0.196

0.0127 15.0 15.0 Plain tube 74.5 0.832 0.186

0.0127 15.0 15.1 Plain tube 76.2 0.840 0.210

0.0127 15.3 15.1 Plain tube 75.4 0.905 0.168

0.0127 14.9 15.1 Plain tube 100.3 0.050 0.049

0.0127 15.1 15.2 Plain tube 100.9 0.102 0.052

0.0127 15.0 15.1 Plain tube 100.8 0.150 0.060

0.0127 14.9 15.1 Plain tube 100.5 0.206 0.074

0.0127 14.9 15.1 Plain tube 100.9 0.255 0.094

0.0127 14.9 15.0 Plain tube 99.9 0.308 0.120

0.0127 15.1 15.2 Plain tube 99.9 0.353 0.132

0.0127 15.2 15.2 Plain tube 100.0 0.407 0.165

0.0127 15.1 15.2 Plain tube 100.4 0.454 0.190

0.0127 15.0 15.0 Plain tube 100.3 0.507 0.228

0.0127 15.0 15.1 Plain tube 100.3 0.551 0.248

0.0127 15.1 15.1 Plain tube 100.0 0.604 0.267

0.0127 15.2 15.2 Plain tube 100.0 0.659 0.292

0.0127 14.9 14.9 Plain tube 99.5 0.712 0.320

0.0127 15.0 15.0 Plain tube 100.1 0.764 0.345

0.0127 15.1 15.1 Plain tube 99.9 0.820 0.364

0.0127 15.0 15.0 Plain tube 101.5 0.840 0.392

0.0127 15.0 15.0 Plain tube 103.1 0.865 0.363

0.0127 15.1 15.3 Plain tube 150.6 0.053 0.072

0.0127 15.1 15.3 Plain tube 150.6 0.102 0.105

0.0127 15.1 15.2 Plain tube 149.5 0.152 0.130

0.0127 14.9 15.0 Plain tube 149.5 0.201 0.171

0.0127 15.1 15.2 Plain tube 150.2 0.251 0.209

0.0127 14.9 15.0 Plain tube 149.8 0.304 0.284

0.0127 15.0 15.1 Plain tube 149.8 0.353 0.309

0.0127 15.0 15.0 Plain tube 150.3 0.404 0.372

0.0127 15.1 15.1 Plain tube 150.8 0.454 0.420

0.0127 15.2 15.2 Plain tube 151.2 0.507 0.485

0.0127 15.2 15.2 Plain tube 150.5 0.555 0.553

0.0127 15.1 15.0 Plain tube 150.8 0.607 0.653

Appendix B 209

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 15.2 15.1 Plain tube 151.1 0.646 0.682

0.0127 15.2 15.1 Plain tube 149.6 0.705 0.771

0.0127 15.2 15.1 Plain tube 149.3 0.768 0.832

0.0127 15.1 15.2 Plain tube 200.5 0.051 0.104

0.0127 15.0 15.1 Plain tube 200.3 0.101 0.163

0.0127 15.1 15.2 Plain tube 200.7 0.151 0.220

0.0127 14.9 14.9 Plain tube 200.4 0.202 0.325

0.0127 15.1 15.1 Plain tube 200.4 0.251 0.373

0.0127 15.0 15.0 Plain tube 199.7 0.306 0.486

0.0127 15.0 14.9 Plain tube 199.7 0.354 0.563

0.0127 15.1 15.0 Plain tube 199.8 0.408 0.693

0.0127 15.2 15.1 Plain tube 200.2 0.451 0.783

0.0127 15.1 14.9 Plain tube 200.0 0.502 0.953

0.0127 15.2 15.0 Plain tube 199.3 0.553 1.108

0.0127 15.2 14.9 Plain tube 200.0 0.608 1.320

0.0127 15.1 14.7 Plain tube 200.5 0.653 1.477

0.0127 15.4 15.0 Plain tube 199.9 0.704 1.554

0.0127 15.2 14.8 Plain tube 201.4 0.754 1.784

0.0127 15.2 14.8 Plain tube 202.0 0.796 1.826

0.0127 14.9 15.0 14 74.9 0.051 0.155

0.0127 14.8 14.9 14 75.3 0.106 0.174

0.0127 14.9 15.0 14 75.2 0.152 0.186

0.0127 15.2 15.3 14 74.9 0.207 0.188

0.0127 14.9 15.0 14 75.1 0.251 0.204

0.0127 15.0 15.1 14 75.6 0.304 0.227

0.0127 15.1 15.2 14 74.3 0.358 0.238

0.0127 15.1 15.1 14 74.9 0.405 0.268

0.0127 15.0 15.0 14 75.0 0.455 0.302

0.0127 15.1 15.1 14 75.1 0.500 0.323

0.0127 15.0 15.0 14 75.2 0.557 0.358

0.0127 15.1 15.1 14 75.0 0.611 0.400

0.0127 15.0 15.0 14 75.3 0.654 0.423

0.0127 15.1 15.1 14 75.6 0.708 0.445

0.0127 15.0 15.0 14 75.7 0.750 0.450

0.0127 15.2 15.2 14 75.5 0.795 0.491

0.0127 15.1 15.1 14 75.2 0.891 0.430

0.0127 15.0 15.1 14 100.8 0.051 0.192

0.0127 15.0 15.1 14 100.6 0.102 0.215

0.0127 15.0 15.1 14 100.9 0.149 0.255

0.0127 14.8 14.9 14 100.9 0.205 0.290

0.0127 15.0 15.1 14 100.9 0.244 0.320

0.0127 14.8 14.8 14 100.9 0.301 0.333

0.0127 15.1 15.1 14 100.7 0.351 0.467

210 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 15.0 15.0 14 100.1 0.406 0.491

0.0127 15.1 15.1 14 101.1 0.446 0.534

0.0127 15.0 14.9 14 100.3 0.508 0.599

0.0127 15.1 15.0 14 100.7 0.551 0.628

0.0127 14.9 14.8 14 100.7 0.612 0.765

0.0127 15.0 15.0 14 150.5 0.050 0.277

0.0127 15.1 15.1 14 150.5 0.102 0.338

0.0127 15.2 15.2 14 150.4 0.151 0.436

0.0127 15.1 15.1 14 150.5 0.201 0.551

0.0127 15.1 15.0 14 150.9 0.251 0.724

0.0127 15.0 14.9 14 150.1 0.302 0.778

0.0127 14.9 14.8 14 148.3 0.373 1.032

0.0127 14.9 14.9 14 199.6 0.052 0.402

0.0127 15.0 15.0 14 199.9 0.101 0.568

0.0127 14.8 14.8 14 200.3 0.153 0.849

0.0127 14.9 14.7 14 199.7 0.203 1.105

0.0127 15.3 15.0 14 199.9 0.253 1.327

0.0127 15.0 14.6 14 200.2 0.306 1.655

0.0127 15.2 14.8 14 199.8 0.355 1.952

0.0127 15.3 14.7 14 199.3 0.405 2.328

0.0127 15.4 14.8 14 199.5 0.456 2.742

0.0127 15.5 14.7 14 199.1 0.504 3.200

0.0127 15.6 14.6 14 199.4 0.569 3.796

0.0127 14.9 15.1 9 74.9 0.051 0.181

0.0127 14.9 15.0 9 75.0 0.104 0.195

0.0127 15.1 15.2 9 74.9 0.150 0.204

0.0127 15.1 15.2 9 75.1 0.200 0.207

0.0127 15.0 15.0 9 75.2 0.252 0.230

0.0127 15.2 15.3 9 75.2 0.310 0.239

0.0127 15.1 15.1 9 75.1 0.348 0.263

0.0127 15.1 15.1 9 75.1 0.401 0.283

0.0127 15.3 15.3 9 75.0 0.450 0.295

0.0127 15.0 15.0 9 74.6 0.514 0.344

0.0127 15.1 15.1 9 75.2 0.557 0.378

0.0127 15.2 15.1 9 75.2 0.605 0.402

0.0127 14.9 14.9 9 75.5 0.648 0.423

0.0127 15.2 15.1 9 75.1 0.712 0.437

0.0127 15.1 15.1 9 76.2 0.746 0.481

0.0127 15.2 15.1 9 75.5 0.802 0.532

0.0127 15.1 15.0 9 74.8 0.865 0.496

0.0127 14.9 14.8 9 75.4 0.891 0.472

0.0127 15.2 15.3 9 100.6 0.052 0.218

0.0127 14.9 14.9 9 100.9 0.101 0.256

Appendix B 211

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 15.1 15.1 9 101.0 0.150 0.276

0.0127 15.2 15.3 9 100.6 0.202 0.305

0.0127 15.0 15.0 9 100.7 0.245 0.366

0.0127 15.2 15.2 9 100.8 0.308 0.382

0.0127 15.0 15.0 9 100.6 0.351 0.420

0.0127 14.9 14.9 9 100.4 0.401 0.513

0.0127 15.0 14.9 9 101.0 0.452 0.569

0.0127 15.1 15.0 9 100.3 0.504 0.631

0.0127 15.3 15.1 9 100.8 0.550 0.663

0.0127 14.9 14.8 9 101.4 0.610 0.706

0.0127 15.0 15.1 9 150.5 0.051 0.302

0.0127 14.8 14.9 9 149.9 0.106 0.425

0.0127 15.0 15.0 9 149.7 0.153 0.526

0.0127 14.9 14.8 9 150.7 0.206 0.653

0.0127 15.2 15.1 9 151.1 0.249 0.748

0.0127 15.0 14.8 9 151.5 0.309 0.897

0.0127 15.1 14.9 9 150.7 0.354 0.939

0.0127 15.0 14.8 9 152.1 0.404 1.019

0.0127 15.0 15.0 9 200.5 0.052 0.495

0.0127 15.2 15.2 9 200.8 0.101 0.632

0.0127 14.9 14.8 9 200.1 0.152 0.887

0.0127 15.2 15.0 9 200.1 0.205 1.121

0.0127 15.2 14.9 9 200.3 0.253 1.450

0.0127 15.2 14.8 9 200.0 0.302 1.763

0.0127 15.2 14.7 9 200.3 0.353 2.140

0.0127 15.4 14.8 9 200.3 0.407 2.555

0.0127 15.5 14.8 9 200.9 0.454 2.928

0.0127 15.5 14.7 9 200.1 0.512 3.356

0.0127 15.6 14.6 9 200.0 0.561 3.698

0.0127 15.6 14.5 9 200.8 0.605 3.904

0.0127 15.5 14.4 9 200.6 0.663 4.092

0.0127 15.0 15.1 4 75.0 0.053 0.408

0.0127 15.1 15.2 4 75.6 0.107 0.429

0.0127 14.9 15.0 4 75.4 0.158 0.444

0.0127 15.0 15.0 4 74.7 0.205 0.457

0.0127 15.2 15.2 4 75.2 0.255 0.440

0.0127 14.9 14.9 4 74.8 0.309 0.457

0.0127 14.9 14.9 4 73.9 0.363 0.454

0.0127 14.9 14.9 4 75.3 0.405 0.467

0.0127 15.1 15.1 4 75.2 0.452 0.517

0.0127 15.0 15.0 4 74.7 0.519 0.534

0.0127 14.9 14.9 4 74.8 0.557 0.576

0.0127 15.2 15.2 4 100.2 0.052 0.466

212 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 15.0 15.0 4 100.5 0.109 0.504

0.0127 15.0 15.0 4 100.3 0.149 0.529

0.0127 15.0 15.0 4 100.2 0.204 0.563

0.0127 15.1 15.1 4 101.6 0.248 0.568

0.0127 15.2 15.2 4 100.0 0.309 0.615

0.0127 15.0 15.0 4 100.2 0.357 0.712

0.0127 14.9 14.9 4 100.9 0.400 0.794

0.0127 15.1 15.0 4 100.2 0.454 0.897

0.0127 15.2 15.0 4 99.2 0.512 0.927

0.0127 15.0 14.9 4 99.6 0.564 0.897

0.0127 15.0 15.0 4 149.5 0.052 0.564

0.0127 14.9 14.9 4 150.2 0.100 0.648

0.0127 15.3 15.2 4 150.3 0.153 0.861

0.0127 15.2 15.1 4 149.5 0.205 1.000

0.0127 15.2 15.0 4 150.6 0.250 1.156

0.0127 15.0 14.8 4 150.7 0.304 1.439

0.0127 15.2 14.8 4 151.5 0.353 1.912

0.0127 15.3 14.9 4 148.9 0.409 1.983

0.0127 15.3 15.3 4 201.0 0.051 0.645

0.0127 15.1 15.0 4 201.0 0.100 0.906

0.0127 15.1 14.9 4 200.0 0.153 1.364

0.0127 15.2 14.9 4 200.6 0.201 1.659

0.0127 15.3 14.8 4 200.5 0.253 2.212

0.0127 15.4 14.9 4 199.4 0.306 2.428

0.0127 15.3 14.8 4 198.5 0.350 2.731

0.0127 15.0 15.0 3 75.0 0.051 0.401

0.0127 14.8 14.9 3 74.9 0.107 0.452

0.0127 14.9 15.0 3 75.2 0.151 0.466

0.0127 15.1 15.1 3 75.3 0.201 0.492

0.0127 14.9 14.9 3 75.2 0.265 0.478

0.0127 14.8 14.8 3 75.2 0.306 0.511

0.0127 15.2 15.2 3 76.0 0.352 0.553

0.0127 14.9 14.9 3 74.9 0.402 0.588

0.0127 15.0 15.0 3 75.0 0.451 0.597

0.0127 15.3 15.2 3 75.3 0.501 0.613

0.0127 15.1 15.1 3 75.7 0.556 0.631

0.0127 15.0 15.0 3 75.7 0.602 0.646

0.0127 15.2 15.2 3 75.8 0.658 0.677

0.0127 14.9 14.9 3 100.3 0.052 0.457

0.0127 15.0 15.0 3 100.4 0.104 0.573

0.0127 15.1 15.1 3 99.9 0.151 0.644

0.0127 15.0 15.0 3 100.9 0.198 0.705

0.0127 14.8 14.8 3 100.1 0.254 0.772

Appendix B 213

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0127 15.0 14.9 3 99.6 0.336 0.918

0.0127 15.2 15.2 3 150.1 0.051 0.628

0.0127 15.2 15.1 3 150.1 0.104 0.853

0.0127 15.2 15.1 3 150.2 0.152 1.044

0.0127 15.3 15.1 3 150.4 0.203 1.259

0.0127 15.2 14.9 3 150.4 0.251 1.517

0.0127 15.1 14.8 3 149.0 0.316 1.714

0.0127 15.5 15.1 3 150.0 0.356 1.886

0.0127 15.1 15.0 3 199.8 0.051 0.948

0.0127 15.0 14.8 3 199.8 0.102 1.342

0.0127 15.1 14.9 3 200.4 0.152 1.618

0.0127 15.3 14.9 3 200.5 0.203 2.090

0.0127 15.4 14.9 3 200.2 0.253 2.605

0.0127 15.5 14.8 3 199.7 0.313 3.084

0.0127 15.2 14.4 3 201.7 0.338 3.452

0.0127 15.5 14.5 3 193.3 0.433 3.752

Table B.3 - Flow boiling pressure drop experimental results for Tsat = 5oC under adiabatic conditions inside 15.9 mm internal diameter tube

D

[m]

TTS,in

[oC]

TTS,out

[oC]

y

[-]

G

[kg/m2 s]

x

[-]

∆p

[kPa/m]

0.0159 5.2 4.7 Plain tube 75.1 0.053 0.043

0.0159 5.5 5.0 Plain tube 75.2 0.108 0.046

0.0159 5.3 4.8 Plain tube 76.4 0.150 0.047

0.0159 5.2 4.6 Plain tube 74.6 0.208 0.049

0.0159 5.1 4.6 Plain tube 75.1 0.253 0.056

0.0159 5.2 4.6 Plain tube 75.3 0.304 0.066

0.0159 5.2 4.7 Plain tube 75.0 0.352 0.079

0.0159 5.4 5.0 Plain tube 74.9 0.409 0.094

0.0159 5.3 4.9 Plain tube 75.2 0.457 0.116

0.0159 5.3 4.9 Plain tube 75.0 0.506 0.130

0.0159 5.4 5.0 Plain tube 75.0 0.553 0.149

0.0159 5.1 4.7 Plain tube 74.5 0.612 0.170

0.0159 5.2 4.7 Plain tube 74.8 0.654 0.186

0.0159 5.2 4.7 Plain tube 74.8 0.707 0.203

0.0159 5.4 4.8 Plain tube 74.8 0.756 0.216

0.0159 5.3 4.8 Plain tube 74.8 0.808 0.233

0.0159 5.5 4.9 Plain tube 74.8 0.859 0.244

0.0159 5.5 5.0 Plain tube 74.8 0.908 0.248

0.0159 5.4 4.9 Plain tube 74.9 0.960 0.238

0.0159 5.2 4.7 Plain tube 99.8 0.053 0.051

0.0159 5.3 4.8 Plain tube 100.5 0.104 0.052

0.0159 5.1 4.6 Plain tube 100.0 0.153 0.062

214 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 5.3 4.8 Plain tube 99.8 0.208 0.079

0.0159 5.1 4.6 Plain tube 100.3 0.254 0.098

0.0159 5.3 4.8 Plain tube 100.3 0.304 0.118

0.0159 5.2 4.8 Plain tube 100.0 0.353 0.148

0.0159 5.3 4.8 Plain tube 99.8 0.405 0.173

0.0159 5.3 4.8 Plain tube 100.4 0.455 0.202

0.0159 5.1 4.7 Plain tube 100.3 0.504 0.232

0.0159 5.5 5.0 Plain tube 100.5 0.553 0.259

0.0159 5.4 4.8 Plain tube 100.4 0.606 0.296

0.0159 5.5 5.0 Plain tube 100.1 0.653 0.320

0.0159 5.5 4.9 Plain tube 100.2 0.708 0.358

0.0159 5.3 4.7 Plain tube 99.7 0.755 0.393

0.0159 5.5 4.9 Plain tube 99.6 0.807 0.421

0.0159 5.5 4.9 Plain tube 100.4 0.856 0.457

0.0159 5.4 4.8 Plain tube 99.7 0.910 0.464

0.0159 5.5 4.9 Plain tube 99.8 0.952 0.454

0.0159 5.5 4.9 Plain tube 149.5 0.053 0.084

0.0159 5.3 4.7 Plain tube 150.6 0.103 0.098

0.0159 5.1 4.5 Plain tube 149.9 0.155 0.138

0.0159 5.3 4.7 Plain tube 149.7 0.207 0.178

0.0159 5.2 4.7 Plain tube 150.6 0.253 0.217

0.0159 5.1 4.5 Plain tube 150.4 0.307 0.278

0.0159 5.4 4.8 Plain tube 149.8 0.354 0.320

0.0159 5.4 4.8 Plain tube 149.7 0.404 0.378

0.0159 5.4 4.8 Plain tube 149.8 0.456 0.452

0.0159 5.6 4.9 Plain tube 149.1 0.511 0.522

0.0159 5.5 4.8 Plain tube 149.7 0.554 0.609

0.0159 5.6 4.9 Plain tube 149.4 0.605 0.699

0.0159 5.6 4.8 Plain tube 150.0 0.653 0.808

0.0159 5.4 4.6 Plain tube 149.3 0.709 0.940

0.0159 5.6 4.7 Plain tube 149.1 0.757 1.036

0.0159 5.3 4.4 Plain tube 150.0 0.807 1.181

0.0159 5.6 4.7 Plain tube 149.3 0.854 1.235

0.0159 5.5 4.6 Plain tube 150.6 0.900 1.281

0.0159 5.8 4.8 Plain tube 149.7 0.953 1.309

0.0159 5.4 4.9 Plain tube 199.9 0.053 0.117

0.0159 5.2 4.6 Plain tube 200.9 0.104 0.162

0.0159 5.4 4.8 Plain tube 199.9 0.153 0.233

0.0159 5.4 4.8 Plain tube 199.5 0.204 0.305

0.0159 5.3 4.7 Plain tube 200.0 0.256 0.394

0.0159 5.1 4.4 Plain tube 200.1 0.309 0.505

0.0159 5.5 4.8 Plain tube 200.0 0.353 0.596

Appendix B 215

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 5.5 4.8 Plain tube 200.0 0.407 0.749

0.0159 5.4 4.7 Plain tube 200.1 0.451 0.890

0.0159 5.3 4.5 Plain tube 200.8 0.501 1.084

0.0159 5.5 4.6 Plain tube 200.0 0.557 1.255

0.0159 5.6 4.7 Plain tube 200.0 0.607 1.405

0.0159 5.5 4.9 14 75.3 0.053 0.139

0.0159 5.4 4.8 14 74.9 0.105 0.154

0.0159 5.4 4.9 14 75.4 0.155 0.163

0.0159 5.4 4.9 14 75.5 0.211 0.185

0.0159 5.4 4.9 14 75.1 0.254 0.199

0.0159 5.5 4.9 14 75.4 0.307 0.216

0.0159 5.5 4.9 14 75.2 0.356 0.247

0.0159 5.2 4.7 14 75.4 0.409 0.275

0.0159 5.5 4.9 14 75.7 0.455 0.304

0.0159 5.5 4.9 14 75.5 0.513 0.342

0.0159 5.3 4.7 14 75.1 0.556 0.381

0.0159 5.5 4.9 14 75.5 0.605 0.410

0.0159 5.3 4.7 14 75.4 0.657 0.452

0.0159 5.5 4.9 14 75.0 0.712 0.483

0.0159 5.6 4.9 14 74.9 0.758 0.511

0.0159 5.6 4.9 14 74.7 0.814 0.539

0.0159 5.4 4.8 14 74.8 0.859 0.555

0.0159 5.4 4.8 14 74.9 0.914 0.558

0.0159 5.4 4.8 14 75.0 0.961 0.547

0.0159 5.5 4.9 14 100.4 0.053 0.175

0.0159 5.1 4.6 14 100.4 0.104 0.208

0.0159 5.3 4.7 14 100.6 0.153 0.232

0.0159 5.5 4.9 14 100.3 0.204 0.251

0.0159 5.4 4.8 14 99.9 0.255 0.309

0.0159 5.5 4.9 14 99.9 0.309 0.334

0.0159 5.5 4.9 14 101.3 0.351 0.407

0.0159 5.3 4.7 14 100.0 0.405 0.472

0.0159 5.5 4.9 14 101.1 0.453 0.520

0.0159 5.5 4.9 14 100.8 0.508 0.609

0.0159 5.5 4.9 14 100.4 0.553 0.683

0.0159 5.6 4.9 14 99.9 0.613 0.770

0.0159 5.6 4.9 14 100.0 0.657 0.846

0.0159 5.6 4.9 14 99.4 0.706 0.910

0.0159 5.5 4.8 14 99.3 0.756 0.989

0.0159 5.6 4.9 14 99.3 0.808 1.045

0.0159 5.5 4.7 14 100.3 0.854 1.113

0.0159 5.2 4.4 14 100.2 0.911 1.135

216 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 5.6 4.8 14 99.7 0.963 1.123

0.0159 5.3 4.7 14 149.9 0.053 0.275

0.0159 5.2 4.6 14 150.0 0.104 0.357

0.0159 5.4 4.8 14 151.3 0.152 0.394

0.0159 5.5 4.8 14 150.7 0.205 0.542

0.0159 5.6 4.9 14 150.6 0.254 0.675

0.0159 5.5 4.8 14 150.5 0.308 0.865

0.0159 5.7 4.9 14 150.3 0.357 1.025

0.0159 5.7 4.8 14 149.6 0.408 1.191

0.0159 5.6 4.7 14 150.3 0.453 1.435

0.0159 5.7 4.7 14 149.5 0.510 1.650

0.0159 5.7 4.6 14 149.8 0.557 1.899

0.0159 5.8 4.7 14 149.4 0.607 2.092

0.0159 5.6 4.4 14 149.6 0.658 2.364

0.0159 5.8 4.6 14 150.4 0.708 2.539

0.0159 5.6 4.3 14 149.8 0.762 2.729

0.0159 5.9 4.6 14 150.3 0.803 2.791

0.0159 5.9 4.5 14 150.9 0.853 2.924

0.0159 5.9 4.4 14 149.5 0.909 2.884

0.0159 5.5 4.8 14 201.5 0.053 0.367

0.0159 5.4 4.7 14 200.7 0.105 0.560

0.0159 5.4 4.7 14 200.6 0.154 0.744

0.0159 5.6 4.8 14 199.5 0.208 0.982

0.0159 5.5 4.6 14 200.6 0.255 1.320

0.0159 5.7 4.8 14 200.2 0.308 1.608

0.0159 5.6 4.5 14 199.9 0.356 2.034

0.0159 5.8 4.6 14 199.9 0.412 2.449

0.0159 5.8 4.4 14 200.3 0.454 2.913

0.0159 5.7 4.2 14 200.3 0.510 3.370

0.0159 5.3 4.8 9 75.0 0.053 0.165

0.0159 5.3 4.7 9 74.9 0.105 0.180

0.0159 5.5 5.0 9 74.8 0.154 0.206

0.0159 5.3 4.8 9 74.7 0.207 0.226

0.0159 5.3 4.7 9 75.0 0.256 0.239

0.0159 5.5 4.9 9 75.1 0.310 0.255

0.0159 5.4 4.8 9 74.9 0.356 0.280

0.0159 5.0 4.5 9 75.5 0.412 0.312

0.0159 5.4 4.8 9 75.5 0.411 0.307

0.0159 5.5 4.9 9 75.3 0.456 0.338

0.0159 5.4 4.8 9 75.0 0.509 0.371

0.0159 5.2 4.5 9 75.3 0.557 0.410

0.0159 5.2 4.5 9 74.8 0.611 0.441

Appendix B 217

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 5.4 4.7 9 75.4 0.657 0.472

0.0159 5.4 4.8 9 74.9 0.709 0.500

0.0159 5.5 4.8 9 75.2 0.756 0.535

0.0159 5.3 4.6 9 75.1 0.815 0.568

0.0159 5.6 4.9 9 74.9 0.859 0.583

0.0159 5.5 4.8 9 74.7 0.917 0.588

0.0159 5.4 4.9 9 100.2 0.053 0.200

0.0159 5.5 4.9 9 100.3 0.102 0.239

0.0159 5.3 4.7 9 101.0 0.153 0.289

0.0159 5.4 4.8 9 101.0 0.208 0.317

0.0159 5.1 4.5 9 100.7 0.253 0.356

0.0159 5.5 4.8 9 101.0 0.309 0.422

0.0159 5.5 4.8 9 101.0 0.355 0.462

0.0159 5.5 4.9 9 100.2 0.405 0.510

0.0159 5.5 4.8 9 100.5 0.455 0.591

0.0159 5.5 4.8 9 100.6 0.505 0.686

0.0159 5.6 4.8 9 100.0 0.604 0.828

0.0159 5.2 4.4 9 101.3 0.655 0.990

0.0159 5.7 4.9 9 99.9 0.713 1.020

0.0159 5.6 4.7 9 99.7 0.754 1.085

0.0159 5.7 4.9 9 100.0 0.804 1.146

0.0159 5.2 4.3 9 99.9 0.855 1.212

0.0159 5.5 4.7 9 99.7 0.911 1.188

0.0159 5.6 4.8 9 99.8 0.959 1.164

0.0159 5.6 4.9 9 150.1 0.053 0.327

0.0159 5.5 4.9 9 150.5 0.103 0.420

0.0159 5.6 4.9 9 150.4 0.154 0.508

0.0159 5.5 4.8 9 150.8 0.208 0.611

0.0159 5.2 4.5 9 150.4 0.254 0.797

0.0159 5.6 4.8 9 149.4 0.312 0.941

0.0159 5.6 4.7 9 150.5 0.354 1.145

0.0159 5.4 4.5 9 149.9 0.407 1.410

0.0159 5.6 4.6 9 150.7 0.452 1.621

0.0159 5.4 4.4 9 149.7 0.510 1.891

0.0159 5.6 4.5 9 149.8 0.559 2.113

0.0159 5.7 4.5 9 149.2 0.613 2.337

0.0159 5.7 4.4 9 150.7 0.656 2.593

0.0159 5.8 4.5 9 149.0 0.714 2.730

0.0159 5.9 4.5 9 150.4 0.754 2.911

0.0159 5.8 4.4 9 150.7 0.804 3.062

0.0159 5.7 4.2 9 150.7 0.854 3.133

0.0159 5.8 4.2 9 148.3 0.903 3.044

218 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 5.5 4.9 9 200.2 0.054 0.455

0.0159 5.4 4.6 9 199.4 0.106 0.651

0.0159 5.5 4.7 9 200.5 0.154 0.863

0.0159 5.5 4.7 9 199.7 0.211 1.169

0.0159 5.4 4.4 9 200.8 0.255 1.526

0.0159 5.6 4.5 9 200.1 0.306 1.899

0.0159 5.6 4.4 9 199.2 0.356 2.295

0.0159 5.8 4.5 9 199.7 0.410 2.763

0.0159 5.9 4.4 9 200.1 0.455 3.195

0.0159 5.8 4.2 9 200.0 0.507 3.515

0.0159 5.9 4.2 9 200.6 0.556 4.057

0.0159 5.4 4.9 4 75.3 0.052 0.310

0.0159 5.4 4.9 4 75.7 0.106 0.312

0.0159 5.4 4.8 4 74.9 0.156 0.353

0.0159 5.3 4.7 4 75.6 0.206 0.384

0.0159 5.3 4.7 4 75.4 0.256 0.402

0.0159 5.4 4.8 4 75.3 0.311 0.405

0.0159 5.2 4.6 4 75.3 0.360 0.412

0.0159 5.4 4.8 4 74.7 0.413 0.437

0.0159 5.2 4.6 4 75.1 0.457 0.480

0.0159 5.4 4.8 4 74.8 0.507 0.518

0.0159 5.5 4.8 4 75.2 0.557 0.568

0.0159 5.6 4.9 4 75.1 0.611 0.608

0.0159 5.6 4.9 4 75.1 0.663 0.655

0.0159 5.3 4.6 4 75.3 0.714 0.711

0.0159 5.5 4.8 4 75.3 0.754 0.739

0.0159 5.6 4.8 4 74.8 0.815 0.761

0.0159 5.5 4.8 4 75.2 0.889 0.769

0.0159 5.3 4.7 4 100.5 0.055 0.376

0.0159 5.4 4.8 4 99.9 0.112 0.434

0.0159 5.6 4.9 4 100.4 0.153 0.478

0.0159 5.2 4.5 4 100.8 0.204 0.511

0.0159 5.5 4.8 4 100.0 0.258 0.554

0.0159 5.5 4.8 4 101.0 0.305 0.588

0.0159 5.6 4.9 4 100.3 0.358 0.699

0.0159 5.4 4.7 4 99.9 0.414 0.799

0.0159 5.4 4.6 4 100.0 0.459 0.903

0.0159 5.5 4.6 4 99.5 0.512 0.993

0.0159 5.6 4.7 4 100.9 0.558 1.097

0.0159 5.5 4.6 4 100.4 0.607 1.214

0.0159 5.5 4.6 4 100.8 0.656 1.333

0.0159 5.7 4.8 4 100.0 0.711 1.401

Appendix B 219

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 5.7 4.7 4 99.9 0.758 1.460

0.0159 5.5 4.5 4 99.7 0.814 1.518

0.0159 5.6 4.6 4 100.6 0.857 1.567

0.0159 5.6 4.6 4 101.6 0.895 1.499

0.0159 5.7 4.7 4 101.4 0.949 1.440

0.0159 5.3 4.7 4 150.6 0.053 0.541

0.0159 5.6 4.9 4 149.6 0.104 0.634

0.0159 5.6 4.8 4 150.5 0.154 0.766

0.0159 5.6 4.8 4 150.8 0.206 0.952

0.0159 5.4 4.5 4 149.9 0.257 1.202

0.0159 5.7 4.7 4 150.2 0.305 1.400

0.0159 5.6 4.7 4 150.0 0.355 1.645

0.0159 5.6 4.6 4 150.1 0.408 1.958

0.0159 5.7 4.5 4 149.7 0.460 2.282

0.0159 5.7 4.4 4 150.3 0.516 2.659

0.0159 5.6 4.2 4 150.8 0.558 2.915

0.0159 5.6 4.2 4 149.9 0.610 3.119

0.0159 6.0 4.5 4 149.5 0.659 3.251

0.0159 6.0 4.4 4 150.6 0.715 3.497

0.0159 5.9 4.2 4 149.8 0.758 3.633

0.0159 6.0 4.3 4 150.6 0.804 3.718

0.0159 5.9 4.3 4 149.4 0.859 3.721

0.0159 5.6 4.8 4 199.7 0.054 0.704

0.0159 5.5 4.7 4 199.2 0.105 0.968

0.0159 5.5 4.6 4 200.4 0.156 1.309

0.0159 5.5 4.4 4 200.7 0.214 1.840

0.0159 5.7 4.6 4 199.9 0.256 2.165

0.0159 5.7 4.4 4 200.8 0.306 2.718

0.0159 6.0 4.6 4 200.0 0.355 3.174

0.0159 5.3 4.8 3 75.5 0.054 0.380

0.0159 5.4 4.8 3 75.0 0.107 0.409

0.0159 5.5 4.9 3 75.2 0.155 0.437

0.0159 5.3 4.6 3 74.8 0.212 0.485

0.0159 5.2 4.5 3 74.9 0.258 0.483

0.0159 5.3 4.7 3 75.1 0.308 0.490

0.0159 5.5 4.9 3 74.8 0.358 0.501

0.0159 5.2 4.6 3 75.1 0.414 0.552

0.0159 5.6 5.0 3 75.6 0.454 0.570

0.0159 5.3 4.7 3 75.2 0.513 0.641

0.0159 5.5 4.9 3 75.1 0.558 0.674

0.0159 5.3 4.6 3 74.8 0.612 0.739

0.0159 5.4 4.7 3 75.1 0.657 0.780

220 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 5.3 4.6 3 74.9 0.711 0.848

0.0159 5.5 4.8 3 75.1 0.759 0.878

0.0159 5.3 4.6 3 75.3 0.810 0.904

0.0159 5.5 4.8 3 75.0 0.859 0.892

0.0159 5.5 4.8 3 75.4 0.910 0.849

0.0159 5.6 4.9 3 75.5 0.970 0.730

0.0159 5.4 4.8 3 100.5 0.054 0.427

0.0159 5.4 4.8 3 99.9 0.106 0.495

0.0159 5.3 4.6 3 99.7 0.153 0.575

0.0159 5.2 4.5 3 100.0 0.209 0.618

0.0159 5.5 4.8 3 100.1 0.257 0.649

0.0159 5.3 4.6 3 100.2 0.306 0.752

0.0159 5.5 4.7 3 99.9 0.355 0.833

0.0159 5.6 4.8 3 99.9 0.408 0.940

0.0159 5.4 4.6 3 100.0 0.457 1.059

0.0159 5.7 4.8 3 100.0 0.509 1.156

0.0159 5.5 4.6 3 100.0 0.557 1.315

0.0159 5.7 4.7 3 99.9 0.609 1.437

0.0159 5.7 4.7 3 100.2 0.657 1.555

0.0159 5.8 4.8 3 100.2 0.708 1.645

0.0159 5.5 4.5 3 100.4 0.754 1.723

0.0159 5.6 4.6 3 100.6 0.808 1.762

0.0159 5.8 4.7 3 100.6 0.855 1.746

0.0159 5.3 4.6 3 150.9 0.054 0.658

0.0159 5.6 4.9 3 150.6 0.102 0.767

0.0159 5.5 4.7 3 150.5 0.154 0.943

0.0159 5.6 4.8 3 151.0 0.202 1.157

0.0159 5.5 4.6 3 150.0 0.255 1.418

0.0159 5.7 4.7 3 150.1 0.306 1.696

0.0159 5.6 4.5 3 150.1 0.356 2.023

0.0159 5.7 4.5 3 150.6 0.410 2.413

0.0159 5.6 4.3 3 150.3 0.454 2.694

0.0159 5.7 4.3 3 149.0 0.515 3.059

0.0159 5.9 4.4 3 151.5 0.571 3.232

0.0159 5.4 4.6 3 200.2 0.054 0.871

0.0159 5.5 4.6 3 200.4 0.104 1.157

0.0159 5.7 4.7 3 200.2 0.155 1.553

0.0159 5.5 4.4 3 200.2 0.205 2.017

0.0159 5.9 4.6 3 199.7 0.255 2.502

0.0159 5.8 4.3 3 200.3 0.309 3.098

0.0159 6.0 4.5 3 200.8 0.357 3.600

Appendix B 221

Table B.4 - Flow boiling pressure drop experimental results for Tsat =15 oC under adiabatic conditions inside 15.9 mm internal diameter tube

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.4 14.9 Plain tube 75.1 0.051 0.049

0.0159 15.3 14.9 Plain tube 75.2 0.101 0.043

0.0159 15.4 14.9 Plain tube 74.9 0.152 0.041

0.0159 15.4 14.9 Plain tube 75.1 0.203 0.042

0.0159 15.3 14.9 Plain tube 75.2 0.251 0.046

0.0159 15.4 14.9 Plain tube 75.0 0.306 0.053

0.0159 15.4 15.0 Plain tube 74.9 0.350 0.059

0.0159 15.2 14.8 Plain tube 75.6 0.399 0.069

0.0159 15.3 14.8 Plain tube 74.7 0.457 0.081

0.0159 15.1 14.7 Plain tube 75.0 0.497 0.089

0.0159 15.4 15.0 Plain tube 75.4 0.553 0.103

0.0159 15.3 14.9 Plain tube 74.9 0.597 0.118

0.0159 15.4 14.9 Plain tube 75.8 0.650 0.135

0.0159 15.1 14.7 Plain tube 75.7 0.704 0.148

0.0159 15.1 14.7 Plain tube 74.5 0.753 0.156

0.0159 15.2 14.8 Plain tube 75.2 0.797 0.167

0.0159 15.2 14.7 Plain tube 74.8 0.858 0.174

0.0159 15.3 14.9 Plain tube 75.1 0.897 0.179

0.0159 15.0 14.6 Plain tube 75.1 0.954 0.175

0.0159 15.1 14.7 Plain tube 99.8 0.054 0.049

0.0159 15.1 14.7 Plain tube 100.2 0.107 0.051

0.0159 15.4 15.0 Plain tube 100.1 0.151 0.052

0.0159 15.4 15.0 Plain tube 100.2 0.204 0.055

0.0159 15.3 14.9 Plain tube 100.7 0.251 0.071

0.0159 15.2 14.8 Plain tube 100.7 0.304 0.089

0.0159 15.0 14.6 Plain tube 100.3 0.352 0.108

0.0159 15.3 14.9 Plain tube 100.4 0.404 0.123

0.0159 15.2 14.8 Plain tube 99.7 0.455 0.150

0.0159 15.0 14.6 Plain tube 99.8 0.508 0.171

0.0159 15.2 14.7 Plain tube 99.7 0.552 0.193

0.0159 15.4 15.0 Plain tube 100.9 0.600 0.208

0.0159 15.4 14.9 Plain tube 99.9 0.652 0.232

0.0159 15.5 15.0 Plain tube 100.5 0.703 0.254

0.0159 15.3 14.8 Plain tube 100.4 0.755 0.279

0.0159 15.1 14.6 Plain tube 100.4 0.811 0.305

0.0159 15.3 14.8 Plain tube 100.3 0.855 0.320

0.0159 15.3 14.8 Plain tube 100.6 0.898 0.336

0.0159 15.3 14.8 Plain tube 100.0 0.950 0.332

0.0159 15.6 15.1 Plain tube 100.5 0.982 0.326

0.0159 15.2 14.7 Plain tube 150.7 0.052 0.062

0.0159 15.3 14.8 Plain tube 150.2 0.104 0.077

222 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.3 14.9 Plain tube 150.2 0.152 0.095

0.0159 15.1 14.6 Plain tube 149.9 0.206 0.131

0.0159 15.4 14.9 Plain tube 150.0 0.250 0.156

0.0159 15.3 14.8 Plain tube 150.7 0.305 0.195

0.0159 15.3 14.8 Plain tube 150.3 0.350 0.227

0.0159 15.4 14.9 Plain tube 148.7 0.406 0.271

0.0159 15.4 14.9 Plain tube 149.8 0.450 0.307

0.0159 15.4 14.9 Plain tube 150.2 0.501 0.355

0.0159 15.2 14.6 Plain tube 149.7 0.552 0.408

0.0159 15.1 14.5 Plain tube 150.1 0.604 0.468

0.0159 15.3 14.7 Plain tube 149.7 0.653 0.525

0.0159 15.4 14.9 Plain tube 150.2 0.703 0.588

0.0159 15.3 14.7 Plain tube 150.3 0.753 0.670

0.0159 15.3 14.7 Plain tube 149.4 0.807 0.742

0.0159 15.5 14.8 Plain tube 149.9 0.852 0.807

0.0159 15.5 14.8 Plain tube 149.9 0.905 0.868

0.0159 15.2 14.5 Plain tube 149.2 0.954 0.887

0.0159 15.2 14.7 Plain tube 199.9 0.052 0.099

0.0159 15.1 14.6 Plain tube 199.4 0.105 0.130

0.0159 15.3 14.8 Plain tube 200.5 0.152 0.171

0.0159 15.2 14.7 Plain tube 200.9 0.203 0.234

0.0159 15.3 14.8 Plain tube 199.4 0.254 0.286

0.0159 15.4 14.9 Plain tube 201.5 0.301 0.343

0.0159 15.3 14.7 Plain tube 200.3 0.354 0.418

0.0159 15.4 14.8 Plain tube 199.1 0.415 0.497

0.0159 15.1 14.5 Plain tube 201.5 0.453 0.608

0.0159 15.5 14.9 Plain tube 200.7 0.501 0.682

0.0159 15.3 14.6 Plain tube 200.2 0.561 0.825

0.0159 15.6 14.9 Plain tube 198.8 0.610 0.925

0.0159 15.2 14.5 Plain tube 200.5 0.651 1.094

0.0159 15.2 14.3 Plain tube 200.5 0.708 1.255

0.0159 15.5 14.7 Plain tube 199.0 0.759 1.353

0.0159 15.6 14.8 Plain tube 199.5 0.809 1.456

0.0159 15.4 14.5 Plain tube 199.7 0.854 1.603

0.0159 15.6 14.7 Plain tube 199.7 0.910 1.654

0.0159 15.7 14.7 Plain tube 199.9 0.952 1.679

0.0159 15.3 14.8 14 75.8 0.056 0.135

0.0159 15.3 14.8 14 75.5 0.110 0.139

0.0159 15.3 14.8 14 75.2 0.153 0.148

0.0159 15.2 14.7 14 75.1 0.203 0.161

0.0159 15.1 14.7 14 74.8 0.253 0.173

0.0159 15.4 14.9 14 75.1 0.304 0.177

0.0159 15.5 15.0 14 74.9 0.352 0.199

Appendix B 223

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.2 14.7 14 75.3 0.407 0.216

0.0159 15.4 14.9 14 74.6 0.454 0.234

0.0159 15.4 14.9 14 75.2 0.503 0.242

0.0159 15.5 15.0 14 74.6 0.556 0.276

0.0159 15.1 14.6 14 76.0 0.602 0.320

0.0159 15.6 15.0 14 77.0 0.641 0.327

0.0159 15.0 14.6 14 74.6 0.716 0.350

0.0159 15.4 14.8 14 75.9 0.753 0.374

0.0159 15.6 15.0 14 76.2 0.813 0.389

0.0159 15.1 14.6 14 75.5 0.854 0.421

0.0159 15.1 14.6 14 75.2 0.906 0.413

0.0159 15.0 14.7 14 74.9 0.957 0.398

0.0159 15.4 15.0 14 100.1 0.052 0.170

0.0159 15.1 14.7 14 100.6 0.104 0.182

0.0159 15.3 14.8 14 100.2 0.153 0.204

0.0159 15.3 14.9 14 100.6 0.206 0.211

0.0159 15.2 14.7 14 100.6 0.252 0.245

0.0159 15.5 15.0 14 99.8 0.304 0.254

0.0159 15.4 14.9 14 100.2 0.353 0.309

0.0159 15.3 14.8 14 101.0 0.404 0.346

0.0159 15.1 14.6 14 100.0 0.451 0.404

0.0159 15.4 14.9 14 100.9 0.504 0.420

0.0159 15.5 15.0 14 100.5 0.552 0.480

0.0159 15.4 14.9 14 100.7 0.604 0.504

0.0159 15.3 14.8 14 100.9 0.653 0.594

0.0159 15.5 14.9 14 100.3 0.705 0.651

0.0159 15.4 14.8 14 99.9 0.752 0.663

0.0159 15.1 14.5 14 99.9 0.806 0.702

0.0159 15.4 14.8 14 100.0 0.853 0.705

0.0159 15.5 14.9 14 100.0 0.906 0.685

0.0159 15.5 14.9 14 100.2 0.954 0.649

0.0159 15.4 14.9 14 150.5 0.054 0.229

0.0159 15.5 15.0 14 149.8 0.104 0.276

0.0159 15.4 14.9 14 150.2 0.152 0.330

0.0159 15.3 14.8 14 149.9 0.204 0.378

0.0159 15.4 14.9 14 150.7 0.252 0.480

0.0159 15.3 14.8 14 150.3 0.304 0.596

0.0159 15.5 14.9 14 150.4 0.353 0.708

0.0159 15.5 14.9 14 150.7 0.408 0.825

0.0159 15.5 14.8 14 150.2 0.452 0.964

0.0159 15.5 14.8 14 150.3 0.506 1.097

0.0159 15.4 14.7 14 150.6 0.555 1.294

0.0159 15.5 14.8 14 149.9 0.613 1.441

224 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.3 14.5 14 150.3 0.656 1.563

0.0159 15.6 14.8 14 149.1 0.708 1.670

0.0159 15.4 14.5 14 150.6 0.758 1.890

0.0159 15.4 14.5 14 149.7 0.809 1.975

0.0159 15.5 14.6 14 150.1 0.857 2.055

0.0159 15.7 14.8 14 148.8 0.909 2.021

0.0159 15.5 14.6 14 149.6 0.957 1.956

0.0159 15.4 14.9 14 200.7 0.053 0.302

0.0159 15.5 14.9 14 199.9 0.103 0.411

0.0159 15.5 15.0 14 200.7 0.153 0.538

0.0159 15.5 15.0 14 201.8 0.203 0.701

0.0159 15.3 14.7 14 200.3 0.254 0.933

0.0159 15.6 14.9 14 200.3 0.308 1.100

0.0159 15.5 14.7 14 200.3 0.353 1.358

0.0159 15.5 14.7 14 200.5 0.407 1.631

0.0159 15.6 14.7 14 200.1 0.461 1.964

0.0159 15.5 14.5 14 201.1 0.508 2.290

0.0159 15.7 14.7 14 200.2 0.557 2.515

0.0159 15.6 14.5 14 200.1 0.606 2.760

0.0159 15.6 14.4 14 198.4 0.692 3.151

0.0159 15.7 14.4 14 197.1 0.754 3.384

0.0159 15.5 14.2 14 200.2 0.754 3.582

0.0159 15.9 14.6 14 199.1 0.810 3.655

0.0159 15.5 14.1 14 200.8 0.852 3.771

0.0159 15.9 14.5 14 199.7 0.907 3.711

0.0159 15.9 14.6 14 198.4 0.973 3.459

0.0159 15.5 14.9 9 75.1 0.053 0.175

0.0159 15.4 14.8 9 75.5 0.101 0.180

0.0159 15.3 14.7 9 75.1 0.154 0.188

0.0159 15.3 14.7 9 74.9 0.207 0.200

0.0159 15.5 14.9 9 75.8 0.253 0.210

0.0159 15.5 14.9 9 74.6 0.309 0.225

0.0159 15.2 14.7 9 75.5 0.357 0.235

0.0159 15.3 14.8 9 75.0 0.412 0.248

0.0159 15.3 14.8 9 75.4 0.450 0.255

0.0159 15.5 15.0 9 74.7 0.507 0.280

0.0159 15.3 14.8 9 75.4 0.553 0.293

0.0159 15.6 15.0 9 74.8 0.605 0.318

0.0159 15.1 14.6 9 75.2 0.654 0.341

0.0159 15.2 14.6 9 75.5 0.701 0.368

0.0159 15.3 14.7 9 74.8 0.753 0.373

0.0159 15.2 14.6 9 74.8 0.813 0.404

0.0159 15.4 14.8 9 76.1 0.849 0.418

Appendix B 225

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.4 14.8 9 74.8 0.904 0.417

0.0159 15.3 14.7 9 75.4 0.947 0.417

0.0159 15.4 14.9 9 100.1 0.053 0.207

0.0159 15.3 14.8 9 100.3 0.105 0.225

0.0159 15.3 14.9 9 100.3 0.151 0.235

0.0159 15.5 15.0 9 100.4 0.209 0.255

0.0159 15.4 14.9 9 100.2 0.254 0.293

0.0159 15.3 14.8 9 100.2 0.305 0.313

0.0159 15.5 14.9 9 101.0 0.354 0.348

0.0159 15.5 15.0 9 100.9 0.405 0.395

0.0159 15.5 14.9 9 100.2 0.455 0.437

0.0159 15.3 14.8 9 100.9 0.502 0.460

0.0159 15.4 14.8 9 100.4 0.552 0.523

0.0159 15.5 14.9 9 99.6 0.608 0.588

0.0159 15.4 14.9 9 100.9 0.650 0.608

0.0159 15.3 14.7 9 100.5 0.701 0.670

0.0159 15.4 14.8 9 100.7 0.754 0.745

0.0159 15.5 14.8 9 100.8 0.803 0.798

0.0159 15.5 14.9 9 100.6 0.854 0.815

0.0159 15.1 14.5 9 100.2 0.905 0.844

0.0159 15.3 14.7 9 100.1 0.963 0.824

0.0159 15.3 14.8 9 149.8 0.053 0.285

0.0159 15.3 14.7 9 150.2 0.102 0.347

0.0159 15.4 14.8 9 150.8 0.152 0.399

0.0159 15.1 14.6 9 150.4 0.204 0.469

0.0159 15.1 14.5 9 150.4 0.253 0.583

0.0159 15.5 14.9 9 149.7 0.315 0.693

0.0159 15.2 14.6 9 150.5 0.355 0.827

0.0159 15.4 14.8 9 150.4 0.402 0.927

0.0159 15.4 14.7 9 150.9 0.447 1.089

0.0159 15.2 14.5 9 149.7 0.505 1.271

0.0159 15.3 14.5 9 150.1 0.547 1.370

0.0159 15.5 14.7 9 150.0 0.601 1.546

0.0159 15.7 14.9 9 151.5 0.652 1.731

0.0159 15.3 14.3 9 150.6 0.708 1.940

0.0159 15.7 14.7 9 149.1 0.756 1.955

0.0159 15.4 14.4 9 151.2 0.801 2.186

0.0159 15.8 14.8 9 150.4 0.850 2.192

0.0159 15.2 14.2 9 149.3 0.911 2.225

0.0159 15.8 14.7 9 150.1 0.955 2.164

0.0159 15.4 14.8 9 200.7 0.053 0.389

0.0159 15.5 14.9 9 199.8 0.106 0.505

0.0159 15.3 14.7 9 200.4 0.154 0.647

226 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.5 14.9 9 199.4 0.209 0.802

0.0159 15.4 14.7 9 201.5 0.251 1.023

0.0159 15.3 14.5 9 200.4 0.312 1.355

0.0159 15.3 14.5 9 202.0 0.352 1.610

0.0159 15.2 14.3 9 201.1 0.411 1.964

0.0159 15.5 14.5 9 201.0 0.454 2.172

0.0159 15.7 14.7 9 199.7 0.513 2.456

0.0159 15.8 14.6 9 199.6 0.559 2.773

0.0159 15.7 14.5 9 199.2 0.616 3.101

0.0159 15.5 14.2 9 200.1 0.656 3.344

0.0159 15.8 14.4 9 201.1 0.707 3.684

0.0159 15.9 14.5 9 199.5 0.756 3.771

0.0159 15.8 14.3 9 199.6 0.818 4.011

0.0159 15.8 14.3 9 199.4 0.856 4.102

0.0159 15.6 14.1 9 200.1 0.906 4.083

0.0159 15.8 14.3 9 198.9 0.951 4.034

0.0159 15.3 14.8 4 75.1 0.053 0.272

0.0159 15.4 14.9 4 76.2 0.102 0.299

0.0159 15.2 14.7 4 75.7 0.152 0.328

0.0159 15.4 14.9 4 75.3 0.204 0.345

0.0159 15.5 14.9 4 74.6 0.254 0.366

0.0159 15.5 15.0 4 75.1 0.306 0.371

0.0159 15.4 14.9 4 74.7 0.370 0.370

0.0159 15.2 14.7 4 74.8 0.401 0.364

0.0159 15.4 14.9 4 74.9 0.455 0.363

0.0159 15.5 15.0 4 74.6 0.510 0.372

0.0159 15.3 14.7 4 75.4 0.557 0.430

0.0159 15.4 14.9 4 75.4 0.605 0.441

0.0159 15.5 14.9 4 75.3 0.659 0.474

0.0159 15.4 14.8 4 75.0 0.703 0.474

0.0159 15.1 14.5 4 74.8 0.750 0.523

0.0159 15.6 15.0 4 74.7 0.807 0.543

0.0159 15.4 14.8 4 74.5 0.864 0.519

0.0159 15.4 14.8 4 74.6 0.911 0.526

0.0159 15.3 14.8 4 100.8 0.052 0.362

0.0159 15.4 14.8 4 100.4 0.104 0.379

0.0159 15.3 14.8 4 100.4 0.153 0.427

0.0159 15.5 14.9 4 100.6 0.204 0.456

0.0159 15.2 14.7 4 101.0 0.253 0.462

0.0159 15.4 14.8 4 99.7 0.305 0.484

0.0159 15.4 14.9 4 100.1 0.353 0.521

0.0159 15.5 14.9 4 100.4 0.407 0.587

0.0159 15.3 14.7 4 100.5 0.451 0.639

Appendix B 227

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.4 14.8 4 99.5 0.505 0.708

0.0159 15.4 14.8 4 100.7 0.554 0.766

0.0159 15.4 14.8 4 100.2 0.607 0.849

0.0159 15.4 14.7 4 99.8 0.658 0.913

0.0159 15.5 14.8 4 100.9 0.702 0.968

0.0159 15.6 14.9 4 100.4 0.757 1.032

0.0159 15.5 14.8 4 100.3 0.804 1.074

0.0159 15.3 14.6 4 100.1 0.855 1.117

0.0159 15.5 14.8 4 99.9 0.905 1.080

0.0159 15.6 14.9 4 100.0 0.955 1.038

0.0159 15.4 14.8 4 150.4 0.054 0.509

0.0159 15.5 14.8 4 150.0 0.105 0.555

0.0159 15.4 14.7 4 150.8 0.153 0.631

0.0159 15.4 14.8 4 149.5 0.210 0.739

0.0159 15.5 14.8 4 150.8 0.253 0.863

0.0159 15.4 14.7 4 150.5 0.305 1.037

0.0159 15.5 14.8 4 151.5 0.352 1.205

0.0159 15.4 14.6 4 150.7 0.409 1.440

0.0159 15.4 14.5 4 150.5 0.455 1.593

0.0159 15.4 14.4 4 150.6 0.506 1.799

0.0159 15.6 14.6 4 150.3 0.556 2.005

0.0159 15.4 14.4 4 151.4 0.609 2.295

0.0159 15.7 14.7 4 150.5 0.654 2.375

0.0159 15.6 14.5 4 150.2 0.707 2.531

0.0159 15.4 14.2 4 150.5 0.756 2.684

0.0159 15.4 14.3 4 149.9 0.808 2.744

0.0159 15.5 14.3 4 150.6 0.856 2.792

0.0159 15.6 14.4 4 149.8 0.905 2.742

0.0159 15.7 14.6 4 150.0 0.957 2.522

0.0159 15.4 14.7 4 200.0 0.054 0.620

0.0159 15.4 14.7 4 201.4 0.105 0.757

0.0159 15.5 14.8 4 200.9 0.153 0.954

0.0159 15.3 14.5 4 199.6 0.205 1.315

0.0159 15.6 14.8 4 200.3 0.254 1.572

0.0159 15.5 14.6 4 200.3 0.308 1.916

0.0159 15.6 14.6 4 200.1 0.356 2.322

0.0159 15.6 14.5 4 199.8 0.406 2.692

0.0159 15.6 14.4 4 201.0 0.456 3.136

0.0159 15.8 14.5 4 199.6 0.508 3.420

0.0159 15.7 14.3 4 200.3 0.556 3.773

0.0159 15.7 14.2 4 199.5 0.607 3.942

0.0159 15.7 14.1 4 200.0 0.656 4.330

0.0159 15.8 14.2 4 199.7 0.704 4.535

228 Appendix B

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 16.0 14.4 4 200.0 0.755 4.721

0.0159 15.9 14.2 4 199.5 0.806 4.843

0.0159 15.9 14.2 4 200.0 0.855 4.797

0.0159 15.9 14.2 4 199.4 0.912 4.585

0.0159 15.3 14.8 3 74.5 0.053 0.468

0.0159 15.3 14.8 3 75.3 0.104 0.375

0.0159 15.4 14.9 3 74.8 0.154 0.396

0.0159 15.4 14.8 3 75.5 0.202 0.422

0.0159 15.4 14.9 3 74.9 0.254 0.438

0.0159 15.4 14.9 3 74.3 0.313 0.435

0.0159 15.4 14.9 3 75.6 0.352 0.436

0.0159 15.4 14.9 3 75.8 0.401 0.433

0.0159 15.4 14.9 3 75.2 0.453 0.430

0.0159 15.5 14.9 3 74.7 0.507 0.476

0.0159 15.3 14.8 3 75.4 0.555 0.500

0.0159 15.4 14.8 3 75.4 0.605 0.531

0.0159 15.3 14.8 3 75.1 0.659 0.563

0.0159 15.5 14.9 3 74.7 0.703 0.578

0.0159 15.4 14.8 3 75.0 0.755 0.618

0.0159 15.5 14.9 3 75.2 0.815 0.638

0.0159 15.2 14.6 3 75.3 0.855 0.656

0.0159 15.1 14.6 3 75.7 0.900 0.656

0.0159 15.4 14.9 3 75.5 0.956 0.571

0.0159 15.3 14.8 3 99.9 0.053 0.431

0.0159 15.2 14.7 3 100.4 0.106 0.465

0.0159 15.3 14.8 3 100.6 0.153 0.506

0.0159 15.4 14.9 3 99.6 0.203 0.527

0.0159 15.3 14.8 3 100.6 0.251 0.542

0.0159 15.2 14.6 3 100.0 0.305 0.577

0.0159 15.2 14.6 3 100.4 0.351 0.627

0.0159 15.4 14.8 3 100.3 0.405 0.661

0.0159 15.5 14.9 3 100.2 0.451 0.726

0.0159 15.2 14.6 3 100.2 0.504 0.831

0.0159 15.5 14.8 3 100.7 0.553 0.894

0.0159 15.4 14.7 3 99.5 0.607 0.976

0.0159 15.4 14.7 3 100.6 0.651 1.071

0.0159 15.4 14.7 3 100.1 0.707 1.155

0.0159 15.4 14.7 3 100.1 0.754 1.238

0.0159 15.4 14.6 3 100.6 0.808 1.284

0.0159 15.5 14.8 3 100.4 0.851 1.285

0.0159 15.3 14.6 3 100.3 0.907 1.240

0.0159 15.5 14.8 3 100.2 0.956 1.080

0.0159 15.4 14.8 3 150.4 0.053 0.572

Appendix B 229

D [m]

TTS,in

[oC] TTS,out

[oC] Y [-]

G [kg/m2 s]

x [-]

∆p [kPa/m]

0.0159 15.3 14.6 3 150.4 0.109 0.678

0.0159 15.5 14.9 3 149.8 0.153 0.751

0.0159 15.6 14.9 3 150.3 0.203 0.876

0.0159 15.5 14.9 3 150.6 0.252 1.031

0.0159 15.5 14.7 3 150.0 0.308 1.281

0.0159 15.5 14.7 3 150.5 0.353 1.431

0.0159 15.6 14.8 3 150.0 0.407 1.691

0.0159 15.4 14.5 3 150.3 0.456 1.976

0.0159 15.6 14.6 3 149.6 0.514 2.182

0.0159 15.7 14.7 3 150.1 0.554 2.392

0.0159 15.6 14.6 3 149.9 0.612 2.588

0.0159 15.6 14.5 3 150.4 0.653 2.740

0.0159 15.7 14.5 3 150.1 0.707 2.850

0.0159 15.6 14.4 3 150.4 0.754 2.974

0.0159 15.8 14.6 3 150.6 0.803 2.980

0.0159 15.6 14.4 3 150.1 0.855 3.010

0.0159 15.8 14.6 3 150.9 0.908 2.886

0.0159 15.6 14.5 3 149.7 0.969 2.468

0.0159 15.4 14.8 3 199.5 0.053 0.704

0.0159 15.5 14.8 3 199.9 0.107 0.956

0.0159 15.4 14.7 3 200.5 0.153 1.208

0.0159 15.6 14.8 3 199.7 0.208 1.519

0.0159 15.7 14.8 3 200.3 0.254 1.859

0.0159 15.7 14.7 3 200.2 0.307 2.288

0.0159 15.7 14.7 3 200.1 0.354 2.623

0.0159 15.7 14.5 3 200.8 0.404 3.055

0.0159 15.7 14.4 3 200.2 0.454 3.443

0.0159 15.8 14.4 3 200.6 0.508 3.875

0.0159 15.9 14.4 3 200.5 0.554 4.223

0.0159 16.0 14.4 3 200.5 0.609 4.584

0.0159 16.1 14.5 3 199.4 0.643 4.720

230

Appendix B

Table B.5 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 5 oC measured at each section of the of the test section inside 12.7 mm internal diameter tube

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 Plain tube 4.96 75.1 9.7 9.3 9.0 9.7 4.8 4.8 4.8 4.8 0.10 0.15 0.20 0.25 1.02 1.11 1.18 1.01

0.0127 Plain tube 4.99 74.9 9.8 9.6 9.2 9.8 5.0 5.0 5.0 5.0 0.15 0.20 0.25 0.30 1.03 1.08 1.19 1.03

0.0127 Plain tube 4.96 75.2 9.7 9.2 8.9 9.5 4.8 4.8 4.8 4.8 0.20 0.25 0.30 0.35 1.01 1.12 1.20 1.04

0.0127 Plain tube 4.95 74.6 9.7 9.3 9.0 9.8 4.9 4.9 4.9 4.8 0.25 0.30 0.35 0.40 1.03 1.11 1.20 1.00

0.0127 Plain tube 5.02 75.7 9.8 9.4 9.1 9.9 5.0 5.0 5.0 5.0 0.30 0.35 0.40 0.45 1.04 1.13 1.22 1.02

0.0127 Plain tube 4.98 75.5 9.8 9.4 9.1 10.0 4.9 4.9 4.9 4.9 0.36 0.41 0.45 0.50 1.03 1.11 1.21 0.99

0.0127 Plain tube 4.96 75.2 9.8 9.5 9.2 10.1 4.9 4.9 4.9 4.9 0.41 0.46 0.51 0.56 1.02 1.09 1.16 0.96

0.0127 Plain tube 4.96 75.3 10.0 9.7 9.4 10.3 5.1 5.1 5.1 5.0 0.45 0.50 0.55 0.60 1.02 1.08 1.14 0.95

0.0127 Plain tube 4.99 74.9 9.8 9.6 9.3 10.2 5.0 5.0 5.0 5.0 0.50 0.55 0.60 0.65 1.04 1.09 1.15 0.96

0.0127 Plain tube 5.01 75.8 10.0 9.7 9.4 10.3 5.0 5.0 5.0 5.0 0.55 0.60 0.65 0.70 1.02 1.07 1.14 0.94

0.0127 Plain tube 4.95 75.6 9.9 9.7 9.4 10.3 5.0 5.0 5.0 4.9 0.61 0.66 0.71 0.75 1.01 1.06 1.12 0.93

0.0127 Plain tube 4.96 74.6 9.9 9.7 9.4 10.3 4.9 4.9 4.8 4.8 0.67 0.72 0.77 0.82 1.00 1.04 1.09 0.91

0.0127 Plain tube 4.94 75.0 9.9 9.8 9.9 10.5 5.1 5.1 5.0 5.0 0.72 0.77 0.82 0.86 1.03 1.04 1.02 0.91

0.0127 Plain tube 4.95 75.1 9.9 9.9 10.0 10.6 5.0 5.0 5.0 5.0 0.77 0.82 0.87 0.92 1.02 1.02 0.99 0.88

0.0127 Plain tube 5.00 100.3 9.6 9.3 8.9 9.2 4.8 4.8 4.8 4.8 0.09 0.13 0.16 0.20 1.06 1.13 1.23 1.15

0.0127 Plain tube 4.94 101.8 9.5 9.1 8.6 9.1 4.8 4.8 4.8 4.8 0.14 0.18 0.21 0.25 1.06 1.16 1.32 1.15

0.0127 Plain tube 4.96 100.0 9.6 9.1 8.6 9.3 5.0 5.0 5.0 5.0 0.19 0.23 0.26 0.30 1.09 1.21 1.39 1.16

0.0127 Plain tube 5.00 100.4 9.5 9.1 8.6 9.5 5.1 5.1 5.1 5.1 0.24 0.28 0.32 0.36 1.13 1.24 1.42 1.13

0.0127 Plain tube 5.00 100.1 9.2 8.9 8.5 9.4 5.0 5.0 5.0 5.0 0.29 0.33 0.37 0.41 1.18 1.27 1.43 1.12

0.0127 Plain tube 5.01 100.7 9.3 9.0 8.5 9.5 5.0 5.0 5.0 5.0 0.34 0.38 0.42 0.45 1.19 1.28 1.43 1.13

0.0127 Plain tube 4.97 100.1 9.3 9.0 8.6 9.5 5.1 5.1 5.0 5.0 0.39 0.43 0.47 0.50 1.19 1.26 1.40 1.11

0.0127 Plain tube 5.00 101.1 9.3 9.1 8.7 9.6 5.1 5.1 5.1 5.0 0.44 0.48 0.51 0.55 1.18 1.25 1.39 1.10

0.0127 Plain tube 5.02 100.9 9.2 9.0 8.6 9.4 5.0 5.0 5.0 5.0 0.49 0.53 0.57 0.60 1.20 1.27 1.42 1.13

0.0127 Plain tube 4.99 100.2 9.2 9.0 8.6 9.4 5.0 5.0 5.0 4.9 0.54 0.58 0.62 0.65 1.20 1.26 1.40 1.13

0.0127 Plain tube 4.99 99.6 9.2 9.0 8.6 9.4 5.1 5.1 5.1 5.1 0.60 0.64 0.68 0.71 1.23 1.28 1.43 1.15

0.0127 Plain tube 4.99 101.0 9.2 9.0 8.6 9.4 5.1 5.1 5.1 5.1 0.64 0.67 0.71 0.75 1.24 1.29 1.44 1.16

A

ppendix B

231

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 Plain tube 5.00 100.2 9.1 9.0 8.6 9.3 5.0 5.0 5.0 5.0 0.70 0.74 0.78 0.81 1.24 1.28 1.41 1.17

0.0127 Plain tube 5.01 99.7 9.3 9.1 8.7 9.3 5.2 5.2 5.2 5.2 0.75 0.79 0.83 0.86 1.25 1.30 1.45 1.21

0.0127 Plain tube 4.96 150.2 9.0 8.7 8.5 8.9 5.0 5.0 5.0 5.0 0.08 0.10 0.13 0.15 1.24 1.35 1.43 1.27

0.0127 Plain tube 5.02 150 9.1 8.7 8.5 8.9 5.0 4.9 4.9 4.9 0.13 0.16 0.18 0.21 1.23 1.36 1.42 1.27

0.0127 Plain tube 5.01 150 8.8 8.5 8.4 8.8 5.0 5.0 5.0 5.0 0.18 0.20 0.23 0.25 1.31 1.42 1.48 1.30

0.0127 Plain tube 4.98 149.5 8.8 8.6 8.5 8.9 5.0 5.0 4.9 4.9 0.23 0.26 0.28 0.31 1.32 1.39 1.43 1.26

0.0127 Plain tube 4.94 150.4 8.8 8.5 8.4 8.8 5.0 5.0 4.9 4.9 0.28 0.30 0.33 0.35 1.31 1.39 1.45 1.27

0.0127 Plain tube 5.02 150.2 8.8 8.6 8.4 8.8 5.0 5.0 5.0 4.9 0.33 0.36 0.38 0.41 1.33 1.41 1.45 1.31

0.0127 Plain tube 5.01 150.4 8.9 8.6 8.4 8.8 5.2 5.2 5.2 5.1 0.38 0.41 0.43 0.46 1.38 1.47 1.57 1.37

0.0127 Plain tube 4.98 149.8 8.6 8.4 8.2 8.6 5.1 5.1 5.1 5.1 0.43 0.46 0.48 0.50 1.45 1.52 1.63 1.42

0.0127 Plain tube 4.94 150.1 8.3 8.2 7.9 8.4 5.1 5.1 5.1 5.0 0.48 0.50 0.53 0.55 1.57 1.61 1.77 1.50

0.0127 Plain tube 5.01 150.7 7.9 7.8 7.5 8.0 5.0 5.0 4.9 4.9 0.53 0.55 0.58 0.60 1.76 1.79 2.00 1.64

0.0127 Plain tube 4.97 150.1 7.6 7.6 7.2 7.6 5.1 5.1 5.0 5.0 0.58 0.60 0.63 0.65 1.97 2.00 2.28 1.90

0.0127 Plain tube 4.94 148.8 7.1 6.9 6.5 7.1 5.1 5.1 5.0 5.0 0.64 0.66 0.69 0.71 2.50 2.80 3.32 2.34

0.0127 Plain tube 4.94 150.1 6.7 6.7 6.5 7.1 5.2 5.2 5.1 5.1 0.68 0.70 0.73 0.75 3.46 3.29 3.57 2.42

0.0127 Plain tube 4.96 150.3 6.7 6.8 6.6 7.1 5.3 5.2 5.2 5.1 0.73 0.75 0.78 0.80 3.58 3.32 3.66 2.50

0.0127 Plain tube 4.99 150.1 6.6 6.6 6.4 7.0 5.3 5.2 5.2 5.1 0.78 0.81 0.83 0.86 3.78 3.57 3.97 2.62

0.0127 Plain tube 5.00 151.2 6.4 6.5 6.4 7.3 5.1 5.1 5.0 5.0 0.84 0.87 0.89 0.92 3.94 3.62 3.59 2.15

0.0127 Plain tube 4.93 199.9 8.6 8.6 8.4 8.6 4.9 4.9 4.9 4.9 0.07 0.09 0.11 0.12 1.35 1.35 1.43 1.34

0.0127 Plain tube 4.97 199.6 8.3 8.4 8.1 8.4 4.9 4.9 4.9 4.9 0.12 0.14 0.16 0.18 1.51 1.44 1.57 1.42

0.0127 Plain tube 4.98 199.7 8.4 8.4 8.2 8.4 5.1 5.1 5.1 5.0 0.17 0.19 0.21 0.23 1.53 1.49 1.60 1.50

0.0127 Plain tube 5.01 200.3 8.1 8.2 7.9 8.1 5.0 4.9 4.9 4.9 0.22 0.24 0.26 0.28 1.58 1.52 1.71 1.56

0.0127 Plain tube 4.98 199.5 8.0 8.1 7.6 7.9 5.0 5.0 4.9 4.9 0.27 0.29 0.31 0.33 1.65 1.61 1.91 1.69

0.0127 Plain tube 4.97 199.9 7.8 7.8 7.4 7.8 5.3 5.2 5.2 5.2 0.32 0.34 0.36 0.38 1.98 1.97 2.25 1.88

0.0127 Plain tube 4.94 200.1 7.2 7.4 7.0 7.4 5.3 5.2 5.2 5.1 0.37 0.39 0.41 0.43 2.52 2.24 2.73 2.21

0.0127 Plain tube 4.96 200.2 6.8 6.9 6.8 7.2 5.3 5.2 5.2 5.1 0.42 0.44 0.46 0.48 3.21 2.92 3.08 2.34

0.0127 Plain tube 5.01 201 6.8 6.9 6.7 7.1 5.3 5.2 5.1 5.1 0.47 0.49 0.51 0.53 3.23 2.93 3.17 2.45

0.0127 Plain tube 4.99 200.3 6.7 6.8 6.6 7.0 5.3 5.2 5.1 5.1 0.53 0.54 0.56 0.58 3.50 3.14 3.38 2.64

232

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 Plain tube 4.97 200.6 6.7 6.7 6.5 6.9 5.3 5.2 5.2 5.1 0.57 0.59 0.61 0.63 3.79 3.42 3.70 2.82

0.0127 Plain tube 4.97 200.3 6.7 6.8 6.6 6.9 5.5 5.4 5.3 5.3 0.62 0.64 0.66 0.68 4.15 3.72 4.02 3.00

0.0127 Plain tube 9.95 75.5 10.7 10.5 10.4 11.2 4.9 4.9 4.9 4.9 0.16 0.25 0.35 0.45 1.75 1.80 1.83 1.59

0.0127 Plain tube 9.94 75.9 10.9 10.7 10.6 11.4 5.1 5.1 5.1 5.1 0.20 0.30 0.40 0.49 1.72 1.79 1.83 1.59

0.0127 Plain tube 9.98 74.3 10.6 10.4 10.2 11.1 5.0 5.0 5.0 5.0 0.26 0.36 0.46 0.56 1.81 1.88 1.94 1.66

0.0127 Plain tube 9.89 75.6 10.9 10.6 10.5 11.2 5.0 5.0 5.0 5.0 0.31 0.40 0.50 0.60 1.70 1.79 1.82 1.61

0.0127 Plain tube 9.99 75.5 10.9 10.6 10.6 11.2 5.1 5.1 5.1 5.1 0.36 0.46 0.56 0.65 1.74 1.82 1.84 1.64

0.0127 Plain tube 9.89 76.2 11.0 10.8 10.8 11.4 5.0 5.0 5.0 5.0 0.42 0.52 0.61 0.71 1.66 1.71 1.72 1.57

0.0127 Plain tube 9.90 75.2 10.9 10.7 10.7 11.2 4.9 4.9 4.8 4.8 0.46 0.56 0.66 0.76 1.65 1.70 1.71 1.55

0.0127 Plain tube 9.97 76.4 11.2 11.0 11.0 11.8 5.1 5.0 5.0 5.0 0.51 0.60 0.70 0.80 1.64 1.67 1.68 1.48

0.0127 Plain tube 9.91 74.3 11.2 10.9 10.9 12.1 5.1 5.1 5.1 5.0 0.58 0.68 0.77 0.87 1.64 1.70 1.72 1.42

0.0127 Plain tube 9.93 74.6 11.1 10.9 10.9 12.6 4.9 4.9 4.9 4.9 0.57 0.67 0.77 0.87 1.62 1.68 1.67 1.29

0.0127 Plain tube 9.97 100.2 10.3 10.0 9.8 10.4 4.9 4.8 4.8 4.8 0.13 0.20 0.28 0.35 1.86 1.97 2.04 1.80

0.0127 Plain tube 9.97 102.0 10.5 10.3 10.1 10.8 5.0 5.0 5.0 5.0 0.17 0.25 0.32 0.39 1.83 1.92 1.98 1.74

0.0127 Plain tube 9.96 100.6 10.6 10.4 10.4 11.0 5.2 5.2 5.2 5.1 0.23 0.30 0.37 0.45 1.86 1.90 1.92 1.72

0.0127 Plain tube 9.94 99.1 10.6 10.3 10.3 10.9 5.2 5.2 5.2 5.2 0.29 0.37 0.44 0.51 1.84 1.96 1.95 1.75

0.0127 Plain tube 9.92 101.9 10.6 10.4 10.3 10.8 4.9 4.9 4.9 4.9 0.33 0.40 0.47 0.55 1.77 1.83 1.87 1.70

0.0127 Plain tube 9.94 99.9 10.7 10.4 10.4 10.8 5.0 5.0 5.0 5.0 0.38 0.46 0.53 0.61 1.78 1.85 1.87 1.73

0.0127 Plain tube 10.01 100.7 10.7 10.5 10.3 10.7 5.1 5.1 5.1 5.1 0.43 0.50 0.58 0.65 1.80 1.88 1.92 1.78

0.0127 Plain tube 9.93 100.2 10.7 10.5 10.3 10.7 5.1 5.0 5.0 5.0 0.49 0.56 0.64 0.71 1.77 1.85 1.90 1.76

0.0127 Plain tube 9.88 101.0 10.8 10.4 10.3 10.8 5.1 5.1 5.1 5.1 0.53 0.61 0.68 0.75 1.76 1.88 1.93 1.75

0.0127 Plain tube 9.93 99.4 10.7 10.3 10.1 10.8 5.0 5.0 5.0 5.0 0.59 0.67 0.74 0.82 1.77 1.89 1.94 1.71

0.0127 Plain tube 9.96 99.7 10.8 10.4 10.3 11.1 5.1 5.1 5.1 5.1 0.65 0.72 0.79 0.87 1.79 1.92 1.95 1.67

0.0127 Plain tube 9.99 99.3 10.6 10.3 10.2 12.1 5.0 5.0 5.0 5.0 0.70 0.77 0.85 0.92 1.81 1.93 1.93 1.42

0.0127 Plain tube 150.6 9.90 9.8 9.3 9.2 9.7 4.9 4.9 4.9 4.8 0.10 0.15 0.20 0.25 2.02 2.24 2.31 2.05

0.0127 Plain tube 149.6 9.96 10.0 9.6 9.4 10.0 5.1 5.1 5.1 5.1 0.15 0.20 0.25 0.30 2.04 2.22 2.30 2.03

0.0127 Plain tube 150.2 9.96 9.8 9.6 9.4 9.9 5.0 5.0 5.0 4.9 0.20 0.25 0.30 0.35 2.07 2.19 2.28 2.01

0.0127 Plain tube 150.6 9.96 9.8 9.6 9.4 9.9 5.0 5.0 5.0 5.0 0.26 0.31 0.35 0.40 2.11 2.19 2.29 2.03

A

ppendix B

233

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 Plain tube 149.8 9.90 9.9 9.6 9.4 9.8 5.0 5.0 5.0 5.0 0.30 0.35 0.40 0.45 2.04 2.16 2.28 2.06

0.0127 Plain tube 150.4 9.92 9.8 9.3 9.0 9.4 5.0 5.0 5.0 4.9 0.36 0.41 0.46 0.51 2.09 2.30 2.50 2.27

0.0127 Plain tube 150.7 9.97 9.8 9.4 9.0 9.3 5.0 5.0 5.0 5.0 0.40 0.45 0.50 0.55 2.10 2.31 2.51 2.32

0.0127 Plain tube 149.9 9.97 9.8 9.3 8.9 9.2 5.1 5.1 5.1 5.0 0.45 0.50 0.55 0.60 2.15 2.39 2.65 2.43

0.0127 Plain tube 151.2 9.94 9.6 9.1 8.6 8.7 5.1 5.1 5.0 5.0 0.50 0.55 0.60 0.65 2.25 2.51 2.82 2.66

0.0127 Plain tube 150.5 9.89 9.5 8.9 8.3 8.5 5.3 5.2 5.2 5.1 0.56 0.61 0.66 0.71 2.36 2.68 3.21 2.92

0.0127 Plain tube 150.8 9.93 9.3 8.7 8.0 8.5 5.3 5.3 5.2 5.2 0.61 0.66 0.71 0.76 2.52 2.88 3.59 3.03

0.0127 Plain tube 149.5 9.90 8.9 8.3 7.9 8.6 5.1 5.1 5.0 5.0 0.66 0.71 0.76 0.81 2.68 3.17 3.57 2.74

0.0127 Plain tube 151.1 9.92 8.2 8.1 7.8 8.8 5.1 5.0 5.0 4.9 0.72 0.77 0.81 0.86 3.28 3.33 3.56 2.56

0.0127 Plain tube 150.2 9.89 8.2 8.1 7.9 9.0 5.3 5.2 5.1 5.1 0.75 0.80 0.85 0.90 3.47 3.51 3.64 2.54

0.0127 Plain tube 200.7 9.92 9.7 9.3 9.1 9.5 5.1 5.1 5.1 5.0 0.09 0.13 0.16 0.20 2.15 2.35 2.51 2.26

0.0127 Plain tube 199.6 9.95 9.5 9.1 8.8 9.2 4.9 4.9 4.9 4.9 0.14 0.18 0.21 0.25 2.22 2.42 2.59 2.33

0.0127 Plain tube 199.1 9.94 9.4 9.2 8.9 9.3 5.1 5.1 5.0 5.0 0.19 0.23 0.27 0.30 2.31 2.44 2.59 2.35

0.0127 Plain tube 200.3 9.96 9.5 9.2 8.9 9.2 5.2 5.1 5.1 5.1 0.24 0.28 0.32 0.35 2.29 2.47 2.67 2.41

0.0127 Plain tube 199.4 9.99 9.5 9.0 8.6 8.9 5.1 5.0 5.0 5.0 0.30 0.34 0.38 0.41 2.29 2.54 2.80 2.56

0.0127 Plain tube 200 10.00 9.3 8.9 8.4 8.6 5.1 5.1 5.0 5.0 0.34 0.38 0.42 0.45 2.40 2.65 2.99 2.80

0.0127 Plain tube 199.3 10.01 9.1 8.7 8.0 8.5 5.2 5.2 5.1 5.1 0.40 0.43 0.47 0.51 2.58 2.86 3.46 2.96

0.0127 Plain tube 199.2 9.95 8.7 8.2 7.9 8.5 5.4 5.3 5.2 5.2 0.45 0.49 0.52 0.56 2.99 3.48 3.75 3.02

0.0127 Plain tube 200.6 10.00 7.9 7.8 7.5 8.1 5.1 5.0 5.0 4.9 0.50 0.53 0.57 0.61 3.69 3.63 3.97 3.18

0.0127 Plain tube 200.5 9.95 8.0 7.9 7.6 8.1 5.3 5.2 5.1 5.0 0.55 0.58 0.62 0.66 3.78 3.72 4.06 3.24

0.0127 Plain tube 199.5 9.98 8.0 8.0 7.7 8.2 5.5 5.4 5.3 5.2 0.61 0.64 0.68 0.72 3.98 3.89 4.27 3.33

0.0127 Plain tube 200.2 10.02 8.0 7.9 7.6 8.2 5.5 5.4 5.3 5.2 0.65 0.68 0.72 0.76 4.15 4.04 4.44 3.41

0.0127 Plain tube 199.4 9.98 7.8 7.8 7.5 8.1 5.6 5.5 5.4 5.3 0.69 0.72 0.76 0.80 4.47 4.27 4.70 3.60

0.0127 14 74.9 4.99 8.2 8.1 7.8 8.3 4.9 4.9 4.9 4.8 0.11 0.16 0.21 0.26 1.50 1.57 1.68 1.46

0.0127 14 75.8 4.94 8.3 8.2 7.9 8.4 5.1 5.1 5.1 5.0 0.16 0.20 0.25 0.30 1.54 1.61 1.73 1.49

0.0127 14 75.0 4.97 8.5 8.3 8.0 8.6 5.0 5.0 5.0 4.9 0.21 0.25 0.30 0.35 1.43 1.52 1.64 1.38

0.0127 14 75.4 5.01 8.3 8.3 8.1 8.6 5.0 5.0 5.0 5.0 0.26 0.31 0.36 0.41 1.53 1.55 1.64 1.39

0.0127 14 75.4 4.96 8.4 8.1 8.2 8.6 4.9 4.8 4.8 4.8 0.31 0.35 0.40 0.45 1.40 1.53 1.46 1.32

234

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 14 75.7 4.98 8.4 8.1 8.4 8.5 4.9 4.9 4.9 4.9 0.35 0.40 0.45 0.50 1.46 1.57 1.43 1.39

0.0127 14 75.0 4.96 8.2 8.1 8.5 8.3 4.9 4.9 4.9 4.9 0.41 0.46 0.51 0.56 1.52 1.58 1.38 1.46

0.0127 14 75.1 5.00 8.2 8.1 8.6 8.3 4.9 4.9 4.9 4.9 0.48 0.53 0.58 0.63 1.55 1.60 1.36 1.47

0.0127 14 75.4 4.96 8.3 8.2 8.8 8.4 5.1 5.1 5.1 5.1 0.50 0.55 0.60 0.65 1.58 1.62 1.36 1.49

0.0127 14 74.3 4.95 8.3 8.0 8.6 8.3 4.8 4.7 4.7 4.7 0.59 0.64 0.69 0.74 1.43 1.55 1.27 1.39

0.0127 14 75.6 4.93 8.2 8.0 8.6 8.2 4.8 4.8 4.8 4.8 0.62 0.67 0.72 0.77 1.48 1.58 1.29 1.45

0.0127 14 75.8 4.99 8.6 8.3 9.1 9.4 5.0 5.0 5.0 4.9 0.67 0.72 0.76 0.81 1.42 1.51 1.22 1.13

0.0127 14 75.8 5.00 8.6 8.6 9.4 11.1 4.9 4.9 4.9 4.9 0.74 0.79 0.84 0.88 1.37 1.36 1.10 0.80

0.0127 14 73.0 4.99 8.6 8.7 9.5 10.7 5.1 5.1 5.0 5.0 0.81 0.86 0.91 0.96 1.42 1.39 1.13 0.88

0.0127 14 100.6 4.97 8.0 7.8 7.6 8.0 5.0 5.0 4.9 4.9 0.09 0.13 0.16 0.20 1.68 1.77 1.89 1.64

0.0127 14 100.5 4.96 8.3 8.1 7.8 8.2 5.2 5.2 5.2 5.2 0.14 0.18 0.21 0.25 1.61 1.75 1.91 1.67

0.0127 14 99.1 4.97 7.8 7.7 7.6 8.0 5.0 5.0 5.0 5.0 0.20 0.23 0.27 0.31 1.79 1.84 1.93 1.67

0.0127 14 102.3 4.98 7.5 7.4 7.4 7.6 4.9 4.8 4.8 4.8 0.25 0.28 0.32 0.35 1.90 1.98 1.92 1.76

0.0127 14 149.9 4.95 7.8 7.7 7.4 7.8 5.1 5.1 5.0 5.0 0.08 0.10 0.13 0.15 1.82 1.91 2.07 1.81

0.0127 14 149.7 4.96 7.5 7.5 7.3 7.7 5.1 5.1 5.1 5.1 0.13 0.15 0.18 0.20 2.08 2.10 2.23 1.92

0.0127 14 149.8 4.98 7.4 7.5 7.2 7.5 5.2 5.2 5.2 5.1 0.18 0.20 0.23 0.25 2.32 2.24 2.47 2.08

0.0127 14 150.3 5.00 7.1 7.2 6.9 7.3 5.0 5.0 5.0 4.9 0.23 0.25 0.28 0.30 2.50 2.28 2.56 2.14

0.0127 14 151.4 5.00 7.2 7.4 7.0 7.5 5.3 5.2 5.2 5.1 0.28 0.30 0.32 0.35 2.63 2.36 2.76 2.16

0.0127 14 151.9 4.98 6.8 7.0 6.7 7.1 5.2 5.1 5.0 5.0 0.33 0.36 0.38 0.40 2.98 2.64 3.01 2.33

0.0127 14 199.7 5.02 7.4 7.3 7.1 7.5 5.0 5.0 5.0 5.0 0.07 0.09 0.11 0.13 2.15 2.18 2.42 2.03

0.0127 14 200.2 5.01 7.1 7.2 6.9 7.3 5.0 5.0 5.0 5.0 0.12 0.14 0.16 0.18 2.45 2.36 2.78 2.18

0.0127 14 199.9 4.93 6.9 7.0 6.7 7.2 5.1 5.1 5.0 5.0 0.17 0.19 0.21 0.22 2.74 2.51 3.03 2.30

0.0127 14 199.6 4.94 7.0 7.1 6.7 7.3 5.3 5.3 5.3 5.3 0.23 0.24 0.26 0.28 3.05 2.81 3.43 2.48

0.0127 14 200 4.97 6.8 6.8 6.5 7.0 5.3 5.2 5.2 5.2 0.27 0.29 0.31 0.33 3.36 3.18 3.92 2.70

0.0127 14 199.7 5.01 6.6 6.7 6.4 6.8 5.3 5.2 5.2 5.1 0.33 0.34 0.36 0.38 3.76 3.54 4.17 3.00

0.0127 14 199.8 4.98 6.7 6.6 6.4 6.8 5.5 5.4 5.3 5.3 0.37 0.39 0.41 0.43 4.27 4.11 4.84 3.33

0.0127 14 75.6 9.90 9.8 9.3 9.1 10.2 4.9 4.9 4.9 4.8 0.15 0.25 0.34 0.44 2.03 2.27 2.33 1.86

0.0127 14 75.6 9.87 9.8 9.3 9.2 10.1 5.1 5.1 5.1 5.1 0.20 0.30 0.40 0.49 2.13 2.38 2.47 1.99

A

ppendix B

235

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 14 75.5 9.96 10.1 9.3 9.6 10.3 5.0 5.0 4.9 4.9 0.25 0.35 0.45 0.55 1.97 2.34 2.17 1.86

0.0127 14 75.3 9.93 10.1 9.4 9.8 10.3 5.1 5.1 5.0 5.0 0.31 0.41 0.51 0.60 1.98 2.34 2.09 1.89

0.0127 14 76.3 9.95 10.2 9.3 9.7 9.7 5.1 5.1 5.1 5.0 0.34 0.44 0.54 0.63 1.97 2.37 2.17 2.13

0.0127 14 75.6 9.95 9.7 8.9 9.5 9.5 4.9 4.9 4.8 4.8 0.39 0.49 0.59 0.69 2.09 2.49 2.18 2.14

0.0127 14 74.4 9.93 9.6 8.9 9.5 9.4 4.9 4.9 4.9 4.8 0.44 0.54 0.64 0.74 2.12 2.47 2.17 2.21

0.0127 14 75.4 9.92 9.8 9.0 9.7 9.7 4.9 4.9 4.8 4.8 0.46 0.56 0.66 0.76 2.04 2.40 2.07 2.04

0.0127 14 100.4 9.89 9.4 8.9 8.8 9.3 5.0 5.0 5.0 5.0 0.13 0.20 0.28 0.35 2.28 2.56 2.62 2.28

0.0127 14 100.5 9.90 9.5 8.9 9.0 9.4 5.1 5.1 5.1 5.0 0.18 0.25 0.33 0.40 2.29 2.62 2.53 2.31

0.0127 14 99.47 9.98 9.3 8.9 9.1 9.2 5.1 5.1 5.0 5.0 0.23 0.30 0.38 0.45 2.37 2.65 2.46 2.38

0.0127 14 100.1 9.97 9.0 8.7 9.2 9.0 5.0 5.0 4.9 4.9 0.29 0.36 0.43 0.51 2.48 2.71 2.38 2.42

0.0127 14 97.81 10.01 8.8 8.6 8.6 8.7 5.2 5.2 5.2 5.1 0.34 0.42 0.50 0.57 2.85 3.01 2.92 2.81

0.0127 14 102.1 9.92 8.5 8.3 8.6 8.4 5.0 5.0 4.9 4.9 0.37 0.45 0.52 0.59 2.92 3.05 2.73 2.87

0.0127 14 150.4 9.93 9.0 8.6 8.6 8.7 5.2 5.1 5.1 5.1 0.10 0.15 0.20 0.25 2.61 2.88 2.92 2.74

0.0127 14 150.8 9.96 8.8 8.6 8.5 8.7 5.3 5.2 5.2 5.2 0.15 0.20 0.25 0.30 2.82 3.04 3.05 2.87

0.0127 14 149.7 9.94 8.3 8.2 8.0 8.2 5.0 4.9 4.9 4.8 0.20 0.25 0.30 0.35 3.02 3.13 3.23 2.95

0.0127 14 150.8 9.96 8.3 8.2 8.0 8.2 5.1 5.0 5.0 4.9 0.25 0.30 0.35 0.40 3.12 3.21 3.34 3.03

0.0127 14 148.7 9.87 7.9 7.9 7.6 7.7 5.5 5.4 5.3 5.2 0.41 0.46 0.51 0.56 4.07 4.03 4.50 4.01

0.0127 14 200.5 9.89 8.6 8.3 8.1 8.3 5.1 5.1 5.1 5.1 0.09 0.13 0.16 0.20 2.89 3.10 3.32 3.06

0.0127 14 199.7 9.98 8.39 8.30 8.01 8.30 5.22 5.20 5.19 5.17 0.14 0.18 0.22 0.25 3.19 3.26 3.59 3.23

0.0127 14 200.1 9.88 8.23 8.22 7.91 8.19 5.27 5.25 5.22 5.19 0.19 0.23 0.27 0.30 3.38 3.38 3.74 3.34

0.0127 14 200.4 9.91 8.22 8.17 7.84 8.17 5.44 5.41 5.37 5.33 0.24 0.28 0.31 0.35 3.61 3.65 4.08 3.53

0.0127 14 200.4 9.93 8.11 8.03 7.72 8.04 5.48 5.44 5.39 5.33 0.29 0.33 0.37 0.40 3.84 3.91 4.34 3.71

0.0127 14 198.8 9.94 8.12 8.02 7.70 8.02 5.63 5.57 5.50 5.42 0.35 0.39 0.42 0.46 4.07 4.14 4.62 3.89

0.0127 14 200.6 9.82 8.02 7.89 7.60 7.86 5.74 5.67 5.58 5.48 0.39 0.43 0.47 0.50 4.39 4.51 4.97 4.20

0.0127 14 201.6 9.87 7.80 7.70 7.41 7.68 5.61 5.52 5.42 5.30 0.44 0.47 0.51 0.55 4.60 4.63 5.07 4.23

0.0127 14 200.9 9.98 7.82 7.73 7.45 7.75 5.64 5.54 5.42 5.29 0.48 0.52 0.55 0.59 4.68 4.64 5.02 4.13

0.0127 9 75.5 5.02 8.92 8.15 8.03 8.73 5.00 4.99 4.98 4.97 0.10 0.15 0.20 0.25 1.29 1.60 1.66 1.34

0.0127 9 76.5 5.00 8.81 8.05 7.93 8.56 4.97 4.96 4.95 4.94 0.16 0.20 0.25 0.30 1.31 1.63 1.69 1.39

236

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 9 75.2 5.01 8.59 8.19 7.85 8.60 4.94 4.93 4.92 4.91 0.20 0.25 0.30 0.35 1.38 1.55 1.73 1.37

0.0127 9 75.3 4.98 8.69 8.68 8.13 9.03 5.25 5.24 5.23 5.21 0.26 0.31 0.35 0.40 1.46 1.46 1.73 1.31

0.0127 9 74.8 4.93 8.52 8.63 8.13 8.68 5.22 5.20 5.19 5.17 0.31 0.36 0.41 0.45 1.50 1.45 1.69 1.41

0.0127 9 76.0 4.99 8.59 8.73 8.10 8.74 5.15 5.14 5.12 5.11 0.35 0.40 0.45 0.50 1.46 1.40 1.69 1.38

0.0127 9 75.8 4.99 8.67 8.62 8.10 8.62 5.12 5.11 5.09 5.07 0.40 0.45 0.50 0.55 1.42 1.43 1.67 1.41

0.0127 9 74.3 4.96 8.71 8.68 8.25 8.85 5.18 5.16 5.14 5.12 0.46 0.51 0.56 0.61 1.41 1.42 1.61 1.33

0.0127 9 74.9 4.97 8.71 8.44 8.01 8.52 4.92 4.90 4.88 4.86 0.50 0.55 0.60 0.65 1.32 1.41 1.60 1.36

0.0127 9 75.8 4.98 9.02 8.71 8.35 8.74 5.20 5.18 5.16 5.13 0.56 0.61 0.66 0.70 1.31 1.42 1.57 1.39

0.0127 9 75.7 4.96 8.73 8.36 7.96 8.23 4.86 4.83 4.81 4.78 0.61 0.66 0.71 0.76 1.29 1.41 1.59 1.45

0.0127 9 75.5 4.95 8.84 8.44 8.13 8.66 5.02 5.00 4.97 4.94 0.66 0.71 0.76 0.81 1.31 1.45 1.58 1.34

0.0127 9 101.1 4.95 8.50 8.07 7.21 7.96 4.79 4.78 4.77 4.75 0.09 0.12 0.16 0.20 1.34 1.51 2.04 1.55

0.0127 9 99.4 4.94 8.24 7.99 7.10 7.76 4.72 4.71 4.69 4.67 0.15 0.19 0.22 0.26 1.42 1.52 2.07 1.61

0.0127 9 101.5 4.98 8.51 8.46 7.48 8.18 5.09 5.08 5.06 5.04 0.18 0.22 0.26 0.29 1.47 1.48 2.07 1.60

0.0127 9 100.0 4.96 8.40 8.52 7.57 8.03 5.25 5.23 5.21 5.19 0.24 0.28 0.31 0.35 1.58 1.52 2.12 1.76

0.0127 9 100.9 4.96 8.11 8.17 7.04 7.50 4.82 4.80 4.78 4.75 0.29 0.33 0.37 0.40 1.52 1.48 2.22 1.82

0.0127 9 100.0 4.97 8.31 8.29 7.16 7.56 5.05 5.03 5.00 4.97 0.34 0.38 0.42 0.46 1.54 1.53 2.32 1.94

0.0127 9 99.7 4.96 8.19 8.17 7.00 7.27 5.02 5.00 4.96 4.93 0.39 0.43 0.46 0.50 1.58 1.57 2.46 2.14

0.0127 9 100.0 4.96 7.99 7.96 6.83 7.05 4.92 4.89 4.85 4.81 0.44 0.48 0.52 0.55 1.63 1.63 2.53 2.23

0.0127 9 99.8 5.02 8.09 8.05 6.93 7.21 5.15 5.11 5.07 5.03 0.49 0.53 0.57 0.61 1.72 1.72 2.74 2.33

0.0127 9 99.9 5.02 8.05 7.78 6.98 7.22 5.18 5.14 5.10 5.06 0.55 0.58 0.62 0.66 1.77 1.92 2.70 2.34

0.0127 9 150.2 4.96 8.13 8.03 7.43 7.93 5.25 5.23 5.21 5.18 0.08 0.10 0.13 0.15 1.74 1.78 2.25 1.82

0.0127 9 149.8 5.00 7.27 7.39 6.92 7.32 4.88 4.85 4.82 4.79 0.13 0.16 0.18 0.21 2.11 1.98 2.41 1.99

0.0127 9 150.7 4.99 7.22 7.29 7.08 7.41 5.12 5.09 5.05 5.01 0.18 0.20 0.23 0.25 2.40 2.29 2.48 2.10

0.0127 9 150.9 4.94 6.97 6.95 6.85 7.17 5.02 4.98 4.93 4.88 0.23 0.26 0.28 0.30 2.56 2.52 2.61 2.18

0.0127 9 149.6 5.00 7.13 7.05 6.89 7.30 5.22 5.17 5.12 5.07 0.29 0.31 0.34 0.36 2.64 2.69 2.85 2.26

0.0127 9 200.4 5.00 7.32 7.37 7.11 7.47 5.07 5.04 5.01 4.97 0.07 0.09 0.11 0.13 2.25 2.17 2.40 2.02

0.0127 9 200.1 5.01 7.07 7.16 6.84 7.32 5.07 5.03 4.98 4.93 0.12 0.14 0.16 0.18 2.53 2.37 2.73 2.12

0.0127 9 200.4 4.98 7.10 7.14 6.84 7.33 5.24 5.19 5.12 5.06 0.17 0.19 0.21 0.23 2.72 2.57 2.94 2.21

A

ppendix B

237

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 9 199.6 4.97 7.08 7.08 6.83 7.22 5.34 5.27 5.19 5.10 0.22 0.24 0.26 0.28 2.89 2.78 3.06 2.36

0.0127 9 202 4.98 6.96 6.93 6.72 7.14 5.23 5.14 5.04 4.93 0.27 0.28 0.30 0.32 2.91 2.81 2.99 2.28

0.0127 9 74.9 9.94 10.20 9.84 9.28 10.5 5.21 5.20 5.18 5.17 0.15 0.25 0.35 0.45 2.02 2.16 2.45 1.87

0.0127 9 75.2 9.92 9.82 9.71 9.11 10.4 4.99 4.98 4.96 4.95 0.20 0.30 0.40 0.49 2.07 2.12 2.42 1.83

0.0127 9 74.8 9.98 9.89 9.79 9.25 10.4 5.13 5.12 5.10 5.08 0.26 0.36 0.46 0.55 2.12 2.16 2.43 1.90

0.0127 9 76.3 9.96 9.66 9.37 9.13 10.1 4.99 4.97 4.96 4.93 0.30 0.40 0.50 0.59 2.15 2.29 2.41 1.94

0.0127 9 101.1 9.93 9.39 9.20 8.59 9.51 4.99 4.97 4.95 4.93 0.13 0.20 0.27 0.34 2.28 2.37 2.76 2.19

0.0127 9 98.2 9.89 9.44 9.32 8.79 9.49 5.11 5.09 5.07 5.05 0.19 0.26 0.34 0.41 2.31 2.36 2.69 2.25

0.0127 9 100.5 9.90 9.35 9.24 8.77 9.21 5.14 5.12 5.10 5.07 0.23 0.30 0.37 0.45 2.38 2.43 2.73 2.42

0.0127 9 101.6 9.87 9.07 8.69 8.42 8.49 5.05 5.02 5.00 4.96 0.27 0.35 0.42 0.49 2.48 2.73 2.92 2.83

0.0127 9 99.3 9.91 8.84 8.53 8.23 8.39 5.00 4.97 4.94 4.90 0.34 0.41 0.48 0.56 2.61 2.82 3.05 2.87

0.0127 9 100.0 9.96 9.20 8.65 8.45 8.61 5.23 5.19 5.16 5.11 0.40 0.47 0.55 0.62 2.53 2.91 3.06 2.89

0.0127 9 101.6 9.95 9.64 8.76 8.37 8.43 5.02 4.98 4.94 4.90 0.45 0.53 0.60 0.67 2.17 2.66 2.94 2.85

0.0127 9 150.4 9.94 9.33 9.07 8.42 8.91 5.13 5.11 5.08 5.04 0.10 0.15 0.20 0.25 2.39 2.54 3.01 2.60

0.0127 9 150.9 9.88 9.07 8.92 8.32 8.76 5.18 5.15 5.11 5.07 0.15 0.20 0.25 0.30 2.57 2.65 3.12 2.70

0.0127 9 150.3 9.92 8.52 8.42 8.04 8.47 5.03 4.99 4.94 4.89 0.21 0.25 0.30 0.35 2.87 2.92 3.24 2.80

0.0127 9 150.1 9.89 8.66 8.63 8.28 8.70 5.32 5.27 5.22 5.16 0.25 0.30 0.35 0.40 3.00 2.98 3.28 2.84

0.0127 9 151.2 9.90 8.33 8.33 8.02 8.47 5.13 5.08 5.02 4.96 0.30 0.35 0.40 0.45 3.13 3.09 3.35 2.86

0.0127 9 147.8 9.94 8.08 8.02 7.74 8.38 5.08 5.02 4.96 4.90 0.39 0.44 0.49 0.54 3.36 3.36 3.63 2.89

0.0127 9 200.1 9.95 8.48 8.29 8.00 8.39 5.02 4.99 4.94 4.88 0.09 0.13 0.17 0.20 2.92 3.05 3.29 2.87

0.0127 9 199.9 9.89 8.16 8.06 7.71 8.17 4.95 4.90 4.84 4.76 0.14 0.18 0.22 0.25 3.12 3.17 3.49 2.93

0.0127 9 200.9 9.90 8.28 8.23 7.87 8.31 5.28 5.21 5.13 5.04 0.19 0.23 0.26 0.30 3.34 3.33 3.68 3.07

0.0127 9 200 9.88 8.24 8.13 7.79 8.18 5.34 5.25 5.15 5.03 0.24 0.28 0.32 0.35 3.46 3.49 3.81 3.18

0.0127 9 199.6 9.92 8.06 7.99 7.68 7.99 5.31 5.21 5.08 4.95 0.29 0.33 0.37 0.40 3.66 3.61 3.88 3.31

0.0127 9 200.1 9.92 7.89 7.81 7.46 7.76 5.27 5.14 4.99 4.84 0.34 0.38 0.42 0.45 3.84 3.77 4.10 3.44

0.0127 9 200.7 9.90 7.75 7.70 7.36 7.65 5.34 5.20 5.04 4.87 0.39 0.42 0.46 0.50 4.18 4.02 4.35 3.61

0.0127 9 201.4 9.89 7.72 7.60 7.25 7.61 5.38 5.21 5.04 4.85 0.44 0.48 0.51 0.55 4.30 4.22 4.56 3.64

0.0127 9 199.3 9.91 7.75 7.64 7.24 7.47 5.63 5.45 5.26 5.06 0.49 0.53 0.57 0.60 4.76 4.62 5.12 4.19

238

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 4 75.4 4.95 7.14 7.45 7.14 7.64 4.87 4.85 4.83 4.82 0.10 0.15 0.20 0.25 2.21 1.93 2.17 1.77

0.0127 4 74.8 4.97 7.35 7.54 7.23 7.76 5.07 5.06 5.04 5.02 0.16 0.21 0.26 0.30 2.21 2.02 2.30 1.83

0.0127 4 75.4 4.99 7.21 7.38 7.11 7.60 5.00 4.98 4.96 4.94 0.20 0.25 0.30 0.35 2.28 2.09 2.34 1.89

0.0127 4 75.3 4.99 7.12 7.30 7.02 7.48 4.93 4.91 4.89 4.87 0.26 0.31 0.35 0.40 2.30 2.11 2.37 1.93

0.0127 4 76.2 4.97 7.18 7.39 7.08 7.55 5.14 5.12 5.10 5.07 0.30 0.35 0.40 0.45 2.46 2.21 2.53 2.03

0.0127 4 75.4 5.02 7.19 7.45 7.16 7.57 5.22 5.20 5.17 5.15 0.35 0.40 0.45 0.50 2.58 2.25 2.55 2.09

0.0127 4 74.9 4.93 6.83 7.07 6.78 7.22 4.93 4.90 4.88 4.85 0.41 0.46 0.51 0.56 2.63 2.29 2.61 2.09

0.0127 4 74.7 4.96 7.02 7.22 6.89 7.39 5.13 5.11 5.08 5.05 0.47 0.51 0.56 0.61 2.66 2.38 2.77 2.14

0.0127 4 75.3 4.99 7.02 7.14 6.92 7.38 5.16 5.13 5.10 5.07 0.50 0.55 0.60 0.65 2.72 2.52 2.77 2.18

0.0127 4 75.0 4.98 7.04 7.19 7.01 7.41 5.26 5.23 5.20 5.16 0.57 0.62 0.66 0.71 2.85 2.58 2.78 2.24

0.0127 4 100.2 5.00 7.11 7.38 7.13 7.58 4.97 4.95 4.93 4.90 0.09 0.13 0.16 0.20 2.36 2.07 2.29 1.88

0.0127 4 101.1 4.98 7.29 7.54 7.28 7.74 5.18 5.15 5.13 5.10 0.14 0.17 0.21 0.25 2.38 2.11 2.33 1.91

0.0127 4 99.7 5.01 6.99 7.18 6.96 7.42 4.92 4.89 4.86 4.83 0.19 0.23 0.27 0.30 2.44 2.21 2.42 1.95

0.0127 4 99.4 4.99 7.06 7.25 7.05 7.47 5.11 5.08 5.04 5.01 0.25 0.28 0.32 0.36 2.58 2.32 2.51 2.05

0.0127 4 100.0 5.00 7.02 7.12 6.98 7.41 5.06 5.02 4.99 4.95 0.29 0.33 0.36 0.40 2.58 2.41 2.54 2.05

0.0127 4 100.3 5.01 7.08 7.15 7.02 7.45 5.15 5.11 5.07 5.03 0.34 0.38 0.41 0.45 2.63 2.49 2.60 2.08

0.0127 4 98.9 4.99 6.83 6.88 6.77 7.19 4.97 4.92 4.87 4.82 0.40 0.44 0.48 0.52 2.71 2.57 2.67 2.13

0.0127 4 100.5 5.06 7.03 7.10 6.96 7.40 5.16 5.11 5.06 5.01 0.45 0.49 0.53 0.56 2.73 2.58 2.69 2.13

0.0127 4 97.9 5.03 6.96 7.06 6.86 7.39 5.22 5.16 5.11 5.06 0.51 0.55 0.59 0.62 2.92 2.68 2.91 2.17

0.0127 4 150.3 4.95 7.22 7.43 7.24 7.62 5.20 5.17 5.13 5.10 0.08 0.10 0.13 0.15 2.47 2.21 2.38 1.97

0.0127 4 149.8 4.94 7.20 7.38 7.18 7.55 5.23 5.19 5.15 5.10 0.13 0.15 0.18 0.20 2.54 2.28 2.46 2.04

0.0127 4 149.5 4.97 6.98 7.08 6.89 7.25 5.05 5.01 4.95 4.89 0.18 0.20 0.23 0.25 2.61 2.42 2.59 2.12

0.0127 4 149.8 4.94 6.90 6.96 6.73 7.13 5.07 5.01 4.94 4.87 0.23 0.26 0.28 0.31 2.72 2.56 2.80 2.21

0.0127 4 201.1 5.01 7.16 7.34 7.09 7.46 5.17 5.14 5.09 5.04 0.07 0.09 0.11 0.13 2.55 2.30 2.54 2.08

0.0127 4 200.5 4.99 7.11 7.18 6.92 7.30 5.20 5.14 5.07 5.00 0.12 0.14 0.16 0.18 2.64 2.47 2.73 2.19

0.0127 4 200.5 4.95 6.86 6.92 6.67 7.00 5.17 5.09 5.00 4.90 0.17 0.19 0.21 0.23 2.97 2.73 2.99 2.38

0.0127 4 199.9 4.95 6.83 6.89 6.59 6.94 5.35 5.25 5.13 5.01 0.22 0.24 0.26 0.28 3.39 3.06 3.45 2.59

0.0127 4 199.9 4.96 6.79 6.87 6.61 6.93 5.41 5.28 5.14 5.00 0.27 0.29 0.31 0.33 3.63 3.17 3.43 2.59

A

ppendix B

239

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 4 200.1 4.99 6.51 6.60 6.30 6.60 5.37 5.21 5.04 4.87 0.33 0.35 0.37 0.39 4.42 3.66 4.04 2.92

0.0127 4 199.2 4.83 6.75 6.78 6.47 6.81 5.66 5.49 5.31 5.12 0.36 0.38 0.40 0.42 4.49 3.80 4.25 2.90

0.0127 4 197.9 4.97 6.71 6.73 6.41 6.73 5.71 5.52 5.31 5.09 0.41 0.43 0.45 0.47 5.08 4.17 4.60 3.08

0.0127 4 75.7 10.0 8.81 8.77 8.59 8.92 5.07 5.05 5.03 5.00 0.15 0.25 0.35 0.44 2.7 2.7 2.8 2.6

0.0127 4 75.6 10.1 8.87 8.80 8.59 8.86 5.21 5.19 5.17 5.14 0.21 0.31 0.41 0.51 2.8 2.8 3.0 2.7

0.0127 4 75.4 10.0 8.41 8.34 8.04 8.32 4.84 4.82 4.79 4.76 0.26 0.36 0.45 0.55 2.8 2.9 3.1 2.8

0.0127 4 74.6 9.9 8.49 8.43 8.14 8.44 5.03 5.01 4.98 4.95 0.32 0.42 0.52 0.62 2.9 2.9 3.2 2.9

0.0127 4 74.9 10.0 8.61 8.60 8.34 8.70 5.37 5.34 5.31 5.28 0.38 0.48 0.58 0.67 3.1 3.1 3.4 3.0

0.0127 4 100.3 9.87 8.66 8.57 8.34 8.79 5.17 5.14 5.11 5.08 0.12 0.20 0.27 0.34 2.8 2.9 3.1 2.7

0.0127 4 100.4 9.86 8.49 8.43 8.17 8.61 5.10 5.07 5.04 5.00 0.18 0.25 0.33 0.40 2.9 2.9 3.2 2.7

0.0127 4 99.3 9.86 8.38 8.30 8.03 8.49 5.06 5.03 4.99 4.94 0.23 0.31 0.38 0.45 3.0 3.0 3.3 2.8

0.0127 4 99.1 9.86 8.10 8.06 7.79 8.21 5.01 4.97 4.92 4.87 0.31 0.38 0.45 0.53 3.2 3.2 3.4 3.0

0.0127 4 99.5 9.93 8.34 8.33 8.15 8.57 5.36 5.31 5.26 5.20 0.38 0.46 0.53 0.61 3.3 3.3 3.4 3.0

0.0127 4 150.7 9.97 8.42 8.35 8.10 8.43 5.12 5.08 5.03 4.98 0.10 0.15 0.20 0.25 3.0 3.1 3.3 2.9

0.0127 4 150.1 9.96 8.45 8.39 8.14 8.49 5.32 5.27 5.21 5.14 0.15 0.20 0.25 0.30 3.2 3.2 3.4 3.0

0.0127 4 150.1 9.99 8.03 7.94 7.70 8.04 4.96 4.91 4.84 4.75 0.21 0.26 0.30 0.35 3.3 3.3 3.5 3.1

0.0127 4 149.6 9.93 7.99 7.97 7.73 8.02 5.09 5.02 4.94 4.85 0.26 0.31 0.36 0.41 3.4 3.4 3.6 3.1

0.0127 4 150 9.91 8.02 8.05 7.81 8.13 5.40 5.32 5.22 5.12 0.31 0.36 0.41 0.46 3.8 3.6 3.9 3.3

0.0127 4 200.6 10.0 8.49 8.45 8.28 8.63 5.36 5.31 5.24 5.15 0.09 0.13 0.17 0.20 3.2 3.2 3.3 2.9

0.0127 4 200.1 9.9 8.01 7.95 7.72 8.09 5.09 5.02 4.92 4.82 0.14 0.18 0.22 0.25 3.5 3.4 3.6 3.1

0.0127 4 200.6 9.9 8.17 8.09 7.84 8.16 5.42 5.32 5.21 5.08 0.19 0.23 0.27 0.30 3.7 3.6 3.8 3.3

0.0127 4 199.8 10.0 7.86 7.81 7.48 7.79 5.34 5.22 5.08 4.92 0.25 0.29 0.32 0.36 4.0 3.9 4.2 3.5

0.0127 4 200.7 9.9 8.05 8.01 7.67 7.96 5.70 5.56 5.40 5.22 0.29 0.33 0.37 0.40 4.3 4.1 4.4 3.7

0.0127 4 199.2 9.9 7.73 7.66 7.26 7.50 5.69 5.51 5.32 5.11 0.35 0.39 0.43 0.46 5.0 4.7 5.2 4.2

0.0127 4 199.3 10.0 7.75 7.72 7.31 7.53 5.84 5.64 5.42 5.19 0.41 0.44 0.48 0.52 5.3 4.9 5.4 4.3

0.0127 4 200.1 9.85 7.57 7.50 7.03 7.31 5.89 5.67 5.44 5.19 0.45 0.48 0.52 0.56 6.0 5.5 6.3 4.7

0.0127 4 201.7 9.89 7.37 7.23 6.74 7.08 5.69 5.45 5.20 4.94 0.49 0.53 0.56 0.60 6.0 5.7 6.6 4.7

0.0127 3 75.6 5.01 8.07 8.12 7.70 8.03 5.26 5.24 5.22 5.19 0.09 0.14 0.19 0.24 1.79 1.75 2.04 1.78

240

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 3 75.5 5.03 7.55 7.70 7.42 7.67 4.96 4.94 4.92 4.89 0.15 0.20 0.25 0.30 1.96 1.84 2.03 1.83

0.0127 3 75.1 4.95 7.31 7.45 7.20 7.46 4.84 4.81 4.79 4.76 0.21 0.26 0.30 0.35 2.02 1.89 2.07 1.85

0.0127 3 74.6 5.00 7.38 7.53 7.29 7.61 5.04 5.01 4.99 4.96 0.26 0.31 0.36 0.41 2.16 2.00 2.19 1.90

0.0127 3 75.0 5.00 7.22 7.33 7.07 7.49 4.94 4.91 4.88 4.85 0.31 0.36 0.41 0.46 2.21 2.09 2.30 1.91

0.0127 3 74.5 4.96 7.33 7.43 7.27 7.66 5.23 5.20 5.17 5.14 0.36 0.41 0.46 0.51 2.39 2.25 2.39 1.99

0.0127 3 75.7 5.06 7.17 7.31 7.10 7.50 5.07 5.03 5.00 4.97 0.41 0.46 0.51 0.56 2.43 2.25 2.44 2.02

0.0127 3 74.8 5.00 7.31 7.47 7.28 7.66 5.27 5.24 5.20 5.17 0.47 0.52 0.57 0.62 2.48 2.26 2.44 2.03

0.0127 3 75.5 5.00 7.07 7.30 7.09 7.48 5.11 5.07 5.04 5.00 0.50 0.55 0.60 0.65 2.58 2.26 2.45 2.03

0.0127 3 74.4 4.97 7.15 7.36 7.13 7.51 5.30 5.26 5.22 5.18 0.57 0.62 0.67 0.72 2.71 2.39 2.62 2.15

0.0127 3 100.3 4.98 7.55 7.67 7.34 7.61 4.94 4.92 4.89 4.86 0.07 0.11 0.14 0.18 1.92 1.82 2.05 1.82

0.0127 3 100.3 4.98 7.67 7.81 7.51 7.79 5.17 5.14 5.11 5.08 0.10 0.14 0.17 0.21 2.01 1.88 2.10 1.86

0.0127 3 100.1 4.99 7.37 7.46 7.24 7.56 5.03 5.01 4.98 4.94 0.14 0.18 0.21 0.25 2.16 2.05 2.23 1.92

0.0127 3 100.7 4.95 7.12 7.22 7.01 7.39 4.90 4.87 4.84 4.80 0.17 0.21 0.24 0.28 2.26 2.13 2.31 1.94

0.0127 3 101.1 4.94 7.35 7.42 7.22 7.61 5.23 5.20 5.16 5.12 0.22 0.25 0.29 0.33 2.36 2.24 2.43 2.00

0.0127 3 101.2 4.97 7.12 7.24 7.04 7.43 5.05 5.01 4.97 4.92 0.28 0.32 0.35 0.39 2.43 2.26 2.42 2.00

0.0127 3 101.9 4.95 7.16 7.35 7.18 7.50 5.19 5.14 5.09 5.04 0.35 0.39 0.43 0.46 2.54 2.27 2.40 2.03

0.0127 3 150.2 4.96 9.01 8.67 8.45 8.89 4.97 4.97 4.96 4.95 0.08 0.10 0.13 0.15 1.24 1.35 1.43 1.27

0.0127 3 150.0 5.02 9.07 8.67 8.49 8.91 4.96 4.95 4.94 4.93 0.13 0.16 0.18 0.21 1.23 1.36 1.42 1.27

0.0127 3 150.0 5.01 8.84 8.54 8.39 8.85 5.01 5.00 4.99 4.98 0.18 0.20 0.23 0.25 1.31 1.42 1.48 1.30

0.0127 3 149.5 4.98 8.78 8.57 8.45 8.90 4.98 4.96 4.95 4.93 0.23 0.26 0.28 0.31 1.32 1.39 1.43 1.26

0.0127 3 150.4 4.94 8.77 8.55 8.38 8.83 4.98 4.97 4.95 4.93 0.28 0.30 0.33 0.35 1.31 1.39 1.45 1.27

0.0127 3 150.2 5.02 8.79 8.55 8.43 8.80 5.00 4.98 4.96 4.94 0.33 0.36 0.38 0.41 1.33 1.41 1.45 1.31

0.0127 3 150.4 5.01 8.86 8.62 8.38 8.81 5.21 5.19 5.17 5.14 0.38 0.41 0.43 0.46 1.38 1.47 1.57 1.37

0.0127 3 149.8 4.98 8.59 8.42 8.15 8.57 5.13 5.11 5.08 5.05 0.43 0.46 0.48 0.50 1.45 1.52 1.63 1.42

0.0127 3 150.1 4.94 8.30 8.18 7.88 8.35 5.13 5.10 5.07 5.03 0.48 0.50 0.53 0.55 1.57 1.61 1.77 1.50

0.0127 3 150.7 5.01 7.89 7.80 7.48 7.98 5.02 4.98 4.94 4.91 0.53 0.55 0.58 0.60 1.76 1.79 2.00 1.64

0.0127 3 150.1 4.97 7.65 7.57 7.23 7.62 5.10 5.06 5.02 4.98 0.58 0.60 0.63 0.65 1.97 2.00 2.28 1.90

0.0127 3 148.8 4.94 7.13 6.87 6.55 7.12 5.13 5.08 5.04 4.99 0.64 0.66 0.69 0.71 2.50 2.80 3.32 2.34

A

ppendix B

241

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 3 150.1 4.94 6.67 6.69 6.52 7.13 5.22 5.17 5.12 5.07 0.68 0.70 0.73 0.75 3.46 3.29 3.57 2.42

0.0127 3 150.3 4.96 6.71 6.77 6.57 7.14 5.30 5.25 5.20 5.14 0.73 0.75 0.78 0.80 3.58 3.32 3.66 2.50

0.0127 3 150.1 4.99 6.61 6.63 6.43 7.02 5.26 5.21 5.15 5.09 0.78 0.81 0.83 0.86 3.78 3.57 3.97 2.62

0.0127 3 151.2 5.00 6.43 6.48 6.44 7.31 5.14 5.08 5.02 4.96 0.84 0.87 0.89 0.92 3.94 3.62 3.59 2.15

0.0127 3 199.9 4.93 8.57 8.57 8.36 8.56 4.89 4.89 4.88 4.86 0.07 0.09 0.11 0.12 1.35 1.35 1.43 1.34

0.0127 3 199.6 4.97 8.27 8.39 8.11 8.43 4.95 4.93 4.92 4.91 0.12 0.14 0.16 0.18 1.51 1.44 1.57 1.42

0.0127 3 199.7 4.98 8.37 8.45 8.20 8.39 5.09 5.08 5.06 5.04 0.17 0.19 0.21 0.23 1.53 1.49 1.60 1.50

0.0127 3 200.3 5.01 8.14 8.24 7.86 8.12 4.95 4.93 4.91 4.88 0.22 0.24 0.26 0.28 1.58 1.52 1.71 1.56

0.0127 3 199.5 4.98 8.02 8.07 7.57 7.88 4.99 4.96 4.93 4.90 0.27 0.29 0.31 0.33 1.65 1.61 1.91 1.69

0.0127 3 199.9 4.97 7.79 7.78 7.42 7.82 5.26 5.23 5.19 5.16 0.32 0.34 0.36 0.38 1.98 1.97 2.25 1.88

0.0127 3 200.1 4.94 7.25 7.45 7.01 7.38 5.26 5.22 5.18 5.13 0.37 0.39 0.41 0.43 2.52 2.24 2.73 2.21

0.0127 3 200.2 4.96 6.83 6.93 6.79 7.25 5.26 5.21 5.16 5.10 0.42 0.44 0.46 0.48 3.21 2.92 3.08 2.34

0.0127 3 201 5.01 6.83 6.93 6.74 7.14 5.26 5.20 5.14 5.08 0.47 0.49 0.51 0.53 3.23 2.93 3.17 2.45

0.0127 3 200.3 4.99 6.72 6.81 6.63 6.97 5.27 5.20 5.13 5.06 0.53 0.54 0.56 0.58 3.50 3.14 3.38 2.64

0.0127 3 200.6 4.97 6.65 6.72 6.53 6.87 5.32 5.24 5.17 5.08 0.57 0.59 0.61 0.63 3.79 3.42 3.70 2.82

0.0127 3 200.3 4.97 6.73 6.79 6.60 6.93 5.51 5.43 5.34 5.25 0.62 0.64 0.66 0.68 4.15 3.72 4.02 3.00

0.0127 3 73.9 9.93 9.02 8.98 8.59 8.81 5.20 5.18 5.15 5.12 0.14 0.24 0.34 0.44 2.63 2.64 2.93 2.72

0.0127 3 74.6 9.88 9.00 8.95 8.70 9.06 5.07 5.04 5.02 4.99 0.15 0.25 0.35 0.45 2.54 2.56 2.72 2.45

0.0127 3 75.8 9.85 8.67 8.54 8.08 8.35 4.84 4.82 4.79 4.76 0.19 0.29 0.38 0.48 2.60 2.68 3.03 2.77

0.0127 3 74.3 9.90 8.87 8.78 8.30 8.60 5.12 5.09 5.06 5.03 0.24 0.34 0.44 0.54 2.67 2.72 3.10 2.80

0.0127 3 75.9 9.90 8.48 8.34 8.01 8.30 4.87 4.84 4.81 4.77 0.28 0.38 0.47 0.57 2.77 2.87 3.13 2.84

0.0127 3 76.5 9.88 8.67 8.74 8.42 8.71 5.32 5.29 5.26 5.22 0.31 0.41 0.50 0.60 2.99 2.90 3.17 2.87

0.0127 3 100.1 9.92 8.53 8.41 8.04 8.35 4.90 4.87 4.84 4.80 0.11 0.18 0.25 0.33 2.76 2.84 3.14 2.83

0.0127 3 100.2 9.92 8.68 8.53 8.13 8.47 5.03 5.00 4.96 4.92 0.12 0.20 0.27 0.34 2.75 2.84 3.18 2.83

0.0127 3 100.3 9.91 8.66 8.53 8.15 8.48 5.07 5.04 5.00 4.96 0.17 0.24 0.31 0.39 2.80 2.88 3.19 2.85

0.0127 3 101.6 9.87 8.53 8.48 8.23 8.52 5.17 5.14 5.10 5.05 0.20 0.27 0.34 0.41 2.98 2.98 3.19 2.87

0.0127 3 99.9 9.93 8.20 8.15 7.93 8.22 4.87 4.83 4.79 4.73 0.23 0.31 0.38 0.46 3.02 3.03 3.20 2.89

0.0127 3 100.6 9.94 8.42 8.36 8.16 8.44 5.24 5.20 5.15 5.10 0.27 0.34 0.41 0.49 3.17 3.19 3.35 3.02

242

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 3 99.2 9.93 8.32 8.27 8.06 8.38 5.25 5.20 5.15 5.09 0.32 0.39 0.47 0.54 3.28 3.28 3.47 3.06

0.0127 3 150.4 9.93 8.56 8.41 8.10 8.43 5.18 5.14 5.09 5.02 0.08 0.13 0.18 0.23 2.98 3.08 3.35 2.95

0.0127 3 150.1 9.95 8.69 8.49 8.21 8.57 5.34 5.29 5.22 5.15 0.12 0.17 0.22 0.27 3.01 3.15 3.38 2.95

0.0127 3 150.3 9.98 8.27 8.08 7.78 8.13 5.06 5.00 4.93 4.85 0.16 0.21 0.26 0.31 3.16 3.29 3.55 3.09

0.0127 3 150.4 9.92 8.33 8.12 7.82 8.19 5.20 5.13 5.05 4.96 0.20 0.25 0.30 0.35 3.22 3.36 3.64 3.11

0.0127 3 149.5 9.90 8.40 8.21 7.88 8.23 5.39 5.31 5.22 5.12 0.25 0.30 0.35 0.40 3.34 3.47 3.79 3.23

0.0127 3 148.5 10.00 8.34 8.14 7.87 8.12 5.45 5.35 5.25 5.10 0.31 0.36 0.41 0.46 3.51 3.64 3.88 3.36

0.0127 3 199.7 9.87 8.38 8.27 8.00 8.34 5.20 5.14 5.07 4.98 0.08 0.12 0.16 0.19 3.15 3.20 3.42 2.97

0.0127 3 199.1 9.85 8.44 8.32 8.02 8.39 5.30 5.23 5.15 5.05 0.10 0.14 0.17 0.21 3.18 3.24 3.48 2.99

0.0127 3 200.9 10.00 8.19 8.04 7.71 7.88 5.08 5.00 4.90 4.79 0.12 0.16 0.20 0.23 3.25 3.33 3.62 3.28

0.0127 3 200.7 9.92 8.13 8.04 7.74 7.90 5.17 5.09 4.98 4.85 0.14 0.18 0.22 0.26 3.40 3.41 3.65 3.31

0.0127 3 200.4 9.90 8.28 8.19 7.87 8.05 5.40 5.30 5.18 5.04 0.17 0.21 0.24 0.28 3.49 3.48 3.74 3.34

0.0127 3 200.4 9.92 8.31 8.22 7.88 8.07 5.61 5.49 5.36 5.20 0.20 0.24 0.28 0.31 3.73 3.69 3.99 3.51

0.0127 3 201.1 9.98 8.05 7.95 7.59 7.81 5.49 5.36 5.20 5.02 0.24 0.28 0.31 0.35 3.97 3.92 4.26 3.64

0.0127 3 200.5 9.99 7.77 7.69 7.28 7.54 5.39 5.23 5.05 4.85 0.28 0.32 0.36 0.39 4.27 4.13 4.57 3.78

0.0127 3 199.2 10.12 7.58 7.49 7.08 7.30 5.39 5.22 5.02 4.81 0.31 0.35 0.39 0.43 4.71 4.53 5.03 4.14 Table B.6 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 15 oC measured at each section of the of

the test section inside 12.7 mm internal diameter tube Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 Plain tube 75.0 9.92 20.2 20.2 20.4 21.0 15.0 15.0 15.0 15.0 0.21 0.31 0.42 0.52 1.95 1.95 1.87 1.67

0.0127 Plain tube 75.1 9.88 20.4 20.4 20.6 21.2 15.1 15.1 15.1 15.1 0.31 0.41 0.52 0.62 1.89 1.91 1.82 1.62

0.0127 Plain tube 75.1 9.90 20.5 20.6 20.9 21.4 15.1 15.1 15.1 15.1 0.41 0.52 0.62 0.72 1.85 1.82 1.73 1.57

0.0127 Plain tube 75.4 9.94 20.6 20.7 21.0 21.6 15.1 15.1 15.1 15.1 0.46 0.56 0.66 0.76 1.83 1.81 1.71 1.56

0.0127 Plain tube 75.1 9.94 20.8 20.9 21.1 21.8 15.2 15.2 15.2 15.2 0.52 0.62 0.72 0.83 1.79 1.78 1.70 1.51

0.0127 Plain tube 100.2 9.94 19.8 19.7 19.9 20.3 15.0 15.0 15.0 15.0 0.18 0.26 0.34 0.41 2.09 2.12 2.05 1.89

0.0127 Plain tube 100.8 9.95 20.1 20.1 20.3 20.7 15.1 15.1 15.1 15.1 0.28 0.36 0.43 0.51 2.02 2.00 1.91 1.77

A

ppendix B

243

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 Plain tube 100.3 9.95 20.2 20.2 20.4 20.8 15.1 15.1 15.1 15.1 0.39 0.46 0.54 0.62 1.98 1.98 1.89 1.76

0.0127 Plain tube 150.6 9.92 19.3 19.1 19.2 19.5 14.9 14.9 14.9 14.9 0.15 0.20 0.25 0.31 2.32 2.39 2.35 2.19

0.0127 Plain tube 150.8 9.96 19.3 19.3 19.4 19.7 15.1 15.1 15.0 15.0 0.25 0.31 0.36 0.41 2.37 2.37 2.33 2.13

0.0127 Plain tube 149.9 9.91 19.4 19.4 19.5 19.8 15.0 15.0 15.0 15.0 0.36 0.41 0.46 0.51 2.28 2.27 2.23 2.08

0.0127 Plain tube 150.2 9.88 19.6 19.5 19.5 19.7 15.1 15.1 15.1 15.1 0.46 0.51 0.56 0.61 2.23 2.25 2.24 2.15

0.0127 Plain tube 150.4 9.90 19.5 19.4 19.3 19.4 15.1 15.1 15.1 15.1 0.55 0.60 0.65 0.71 2.29 2.34 2.40 2.33

0.0127 Plain tube 150.5 9.94 19.4 19.2 19.1 19.1 15.2 15.2 15.2 15.1 0.66 0.71 0.76 0.81 2.41 2.50 2.58 2.51

0.0127 Plain tube 150.4 9.92 19.0 18.8 18.7 19.0 15.1 15.1 15.1 15.0 0.74 0.79 0.84 0.89 2.58 2.70 2.78 2.51

0.0127 Plain tube 200 10.01 18.8 18.7 18.5 19.0 14.9 14.9 14.9 14.9 0.09 0.13 0.17 0.21 2.60 2.66 2.78 2.44

0.0127 Plain tube 200.3 9.92 19.0 18.9 18.8 19.2 15.1 15.1 15.0 15.0 0.14 0.18 0.22 0.25 2.56 2.60 2.63 2.43

0.0127 Plain tube 200.6 9.88 18.8 18.7 18.6 19.0 14.9 14.9 14.9 14.9 0.19 0.23 0.27 0.30 2.61 2.61 2.68 2.43

0.0127 Plain tube 200.2 9.94 18.9 18.9 18.8 19.1 15.1 15.0 15.0 15.0 0.24 0.28 0.32 0.36 2.61 2.62 2.64 2.44

0.0127 Plain tube 201 9.96 19.0 18.9 18.8 19.1 15.1 15.0 15.0 15.0 0.29 0.33 0.37 0.40 2.56 2.59 2.64 2.47

0.0127 Plain tube 199.5 9.92 19.1 18.9 18.8 19.1 15.1 15.1 15.1 15.0 0.34 0.38 0.42 0.46 2.53 2.60 2.65 2.46

0.0127 Plain tube 200.9 9.87 19.0 18.9 18.8 18.9 15.1 15.1 15.0 15.0 0.39 0.43 0.47 0.50 2.55 2.63 2.67 2.56

0.0127 Plain tube 200.5 9.96 18.9 18.7 18.5 18.5 15.1 15.1 15.0 15.0 0.44 0.48 0.52 0.56 2.62 2.74 2.91 2.88

0.0127 Plain tube 200.1 9.93 18.8 18.7 18.3 18.3 15.2 15.1 15.1 15.1 0.49 0.53 0.57 0.61 2.76 2.85 3.11 3.13

0.0127 Plain tube 200.5 9.91 18.6 18.4 18.0 18.2 15.2 15.1 15.1 15.1 0.54 0.58 0.62 0.66 2.94 3.10 3.48 3.24

0.0127 Plain tube 200.7 9.96 18.2 18.0 18.0 18.2 15.2 15.2 15.1 15.1 0.59 0.63 0.67 0.71 3.35 3.59 3.58 3.27

0.0127 Plain tube 199.8 9.95 17.8 18.0 18.0 18.2 15.3 15.3 15.2 15.1 0.64 0.68 0.72 0.76 4.01 3.66 3.60 3.33

0.0127 14 74.3 9.85 19.2 19.0 18.7 20.1 15.2 15.1 15.1 15.1 0.16 0.26 0.37 0.47 2.44 2.61 2.77 1.99

0.0127 14 75.9 9.88 19.3 18.9 18.6 20.0 14.8 14.8 14.8 14.8 0.21 0.31 0.41 0.51 2.21 2.41 2.58 1.89

0.0127 14 75.4 9.96 19.6 19.1 18.9 20.1 15.2 15.1 15.1 15.1 0.26 0.36 0.46 0.56 2.26 2.55 2.65 2.00

0.0127 14 75.6 9.94 19.5 18.9 19.1 20.0 15.0 15.0 15.0 15.0 0.31 0.41 0.51 0.61 2.23 2.62 2.48 2.02

0.0127 14 75.4 9.92 19.6 18.8 19.2 20.0 15.0 15.0 15.0 15.0 0.36 0.46 0.56 0.66 2.19 2.61 2.38 2.00

0.0127 14 101.6 9.96 18.8 18.3 18.1 19.1 14.9 14.9 14.9 14.9 0.13 0.20 0.28 0.36 2.60 2.96 3.14 2.37

0.0127 14 100.4 9.90 18.8 18.4 18.3 19.0 15.0 15.0 15.0 15.0 0.18 0.26 0.33 0.41 2.65 2.99 3.07 2.49

0.0127 14 100.7 10.00 18.8 18.4 18.5 19.0 15.1 15.1 15.0 15.0 0.23 0.31 0.39 0.47 2.68 3.02 2.94 2.53

244

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 14 100.4 9.95 18.8 18.4 18.7 19.0 15.1 15.1 15.1 15.0 0.29 0.36 0.44 0.52 2.71 3.01 2.78 2.57

0.0127 14 99.5 9.89 18.6 18.2 18.6 18.7 15.0 15.0 15.0 14.9 0.34 0.41 0.49 0.57 2.78 3.06 2.76 2.68

0.0127 14 101.1 9.91 18.4 18.2 18.4 18.5 15.3 15.3 15.2 15.2 0.38 0.46 0.53 0.61 3.18 3.47 3.15 3.03

0.0127 14 101.2 9.95 18.2 18.0 18.0 18.2 15.3 15.3 15.3 15.2 0.44 0.52 0.60 0.67 3.53 3.69 3.63 3.36

0.0127 14 97.8 9.93 18.2 18.1 18.1 18.3 15.4 15.4 15.4 15.4 0.52 0.59 0.67 0.75 3.60 3.73 3.74 3.47

0.0127 14 150.9 9.90 18.4 18.2 18.1 18.5 15.2 15.2 15.1 15.1 0.10 0.15 0.21 0.26 3.08 3.27 3.36 2.95

0.0127 14 148.7 9.88 18.1 18.0 17.9 18.2 14.9 14.9 14.9 14.9 0.16 0.21 0.26 0.32 3.20 3.29 3.27 3.02

0.0127 14 150.3 9.92 18.1 18.0 18.1 18.2 15.1 15.1 15.0 15.0 0.21 0.26 0.31 0.36 3.29 3.40 3.31 3.11

0.0127 14 150.6 9.89 18.0 17.9 18.0 18.1 15.1 15.1 15.0 15.0 0.25 0.30 0.36 0.41 3.42 3.54 3.44 3.20

0.0127 14 151.9 9.92 18.1 18.1 18.4 18.3 15.2 15.2 15.2 15.1 0.35 0.40 0.45 0.50 3.49 3.53 3.13 3.15

0.0127 14 150.1 9.96 18.0 18.0 18.1 18.0 15.3 15.3 15.2 15.1 0.42 0.47 0.52 0.58 3.71 3.70 3.40 3.38

0.0127 14 201.1 9.90 18.1 17.9 17.7 18.1 15.0 15.0 15.0 15.0 0.09 0.13 0.17 0.20 3.28 3.47 3.66 3.20

0.0127 14 201.9 9.96 18.1 18.1 17.9 18.2 15.3 15.2 15.2 15.2 0.14 0.18 0.22 0.26 3.52 3.60 3.78 3.30

0.0127 14 200.8 9.98 18.0 17.9 17.7 18.1 15.2 15.2 15.1 15.1 0.19 0.23 0.27 0.30 3.65 3.69 3.91 3.38

0.0127 14 200 9.88 17.6 17.7 17.5 17.8 15.0 15.0 14.9 14.9 0.25 0.28 0.32 0.36 3.86 3.74 3.97 3.44

0.0127 14 200.3 9.91 17.7 17.7 17.5 17.8 15.1 15.1 15.0 15.0 0.29 0.33 0.37 0.41 3.99 3.85 4.08 3.52

0.0127 14 199.8 9.88 17.8 17.9 17.7 18.0 15.4 15.3 15.3 15.2 0.34 0.38 0.42 0.46 4.15 3.92 4.15 3.56

0.0127 14 200.2 9.90 17.6 17.6 17.4 17.7 15.2 15.2 15.1 15.0 0.39 0.43 0.47 0.51 4.28 4.08 4.31 3.68

0.0127 9 75.1 9.93 19.6 19.3 19.2 19.4 15.2 15.2 15.2 15.2 0.16 0.26 0.36 0.47 2.29 2.47 2.49 2.41

0.0127 9 75.1 9.92 19.1 19.2 18.7 19.1 14.9 14.9 14.9 14.9 0.21 0.31 0.41 0.52 2.38 2.33 2.60 2.39

0.0127 9 75.0 9.96 19.5 19.5 19.1 19.4 15.1 15.0 15.0 15.0 0.26 0.36 0.46 0.57 2.28 2.27 2.49 2.31

0.0127 9 74.7 9.93 19.3 19.5 18.6 19.2 14.9 14.8 14.8 14.8 0.31 0.42 0.52 0.62 2.26 2.18 2.67 2.30

0.0127 9 100.6 9.93 19.2 19.0 18.2 19.0 15.2 15.2 15.2 15.2 0.13 0.21 0.28 0.36 2.52 2.63 3.30 2.60

0.0127 9 100.8 9.94 19.2 19.1 18.3 19.0 15.2 15.1 15.1 15.1 0.18 0.25 0.33 0.41 2.50 2.53 3.23 2.57

0.0127 9 98.62 9.88 19.1 19.1 18.1 18.9 15.1 15.1 15.0 15.0 0.24 0.32 0.39 0.47 2.50 2.48 3.30 2.57

0.0127 9 100.4 9.87 19.1 19.1 18.0 18.9 15.1 15.1 15.0 15.0 0.28 0.35 0.43 0.50 2.44 2.47 3.40 2.56

0.0127 9 100.4 9.94 19.1 19.2 18.1 19.0 15.1 15.1 15.1 15.1 0.33 0.41 0.48 0.56 2.53 2.48 3.41 2.59

0.0127 9 101.6 9.86 19.2 19.1 18.0 18.6 15.1 15.1 15.1 15.1 0.37 0.44 0.52 0.59 2.44 2.51 3.46 2.84

A

ppendix B

245

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 9 98.9 9.96 18.8 19.0 17.9 19.2 15.0 15.0 15.0 15.0 0.46 0.54 0.62 0.70 2.66 2.50 3.50 2.39

0.0127 9 151.1 9.92 18.6 18.5 17.9 18.4 15.2 15.2 15.2 15.1 0.10 0.15 0.20 0.26 2.92 3.07 3.68 3.09

0.0127 9 149.9 9.88 18.6 18.5 17.8 18.3 15.1 15.1 15.1 15.1 0.15 0.21 0.26 0.31 2.93 3.00 3.74 3.11

0.0127 9 150 9.95 18.1 18.1 17.4 17.9 14.9 14.8 14.8 14.8 0.21 0.26 0.31 0.36 3.13 3.12 3.84 3.23

0.0127 9 150.6 9.90 18.1 18.1 17.6 18.0 15.1 15.0 15.0 15.0 0.26 0.31 0.36 0.41 3.35 3.28 3.92 3.31

0.0127 9 149.5 9.92 18.1 18.2 17.8 18.2 15.3 15.3 15.2 15.2 0.31 0.36 0.41 0.46 3.52 3.38 3.94 3.36

0.0127 9 149.2 9.95 17.9 17.9 17.5 17.9 15.1 15.1 15.1 15.0 0.37 0.42 0.47 0.52 3.62 3.64 4.11 3.47

0.0127 9 200.8 9.92 18.3 18.0 17.8 18.3 15.1 15.1 15.1 15.0 0.09 0.13 0.17 0.20 3.20 3.50 3.72 3.10

0.0127 9 200.6 9.89 18.3 18.1 17.9 18.3 15.3 15.3 15.3 15.2 0.14 0.18 0.22 0.25 3.42 3.64 3.89 3.24

0.0127 9 200.2 9.94 18.1 18.0 17.8 18.2 15.3 15.3 15.2 15.2 0.19 0.23 0.27 0.31 3.66 3.73 3.98 3.33

0.0127 9 199.8 9.96 18.1 17.9 17.7 18.2 15.4 15.3 15.3 15.2 0.24 0.28 0.32 0.36 3.79 3.87 4.19 3.37

0.0127 9 199.6 9.89 17.9 17.8 17.5 18.0 15.3 15.2 15.2 15.1 0.29 0.33 0.37 0.41 3.89 4.00 4.33 3.45

0.0127 9 201.8 9.93 17.7 17.6 17.3 17.9 15.1 15.0 15.0 14.9 0.33 0.37 0.41 0.45 3.94 3.96 4.24 3.34

0.0127 4 75.0 9.92 18.0 18.0 17.8 18.3 15.0 15.0 15.0 15.0 0.13 0.24 0.34 0.44 3.36 3.34 3.57 3.04

0.0127 4 75.3 9.91 17.9 17.9 17.7 18.1 14.8 14.8 14.8 14.8 0.15 0.25 0.35 0.45 3.23 3.27 3.49 2.99

0.0127 4 75.2 9.90 18.0 18.0 17.8 18.2 14.9 14.9 14.9 14.9 0.16 0.26 0.37 0.47 3.21 3.24 3.43 2.98

0.0127 4 75.9 9.90 18.1 18.0 17.8 18.2 14.9 14.9 14.9 14.9 0.20 0.30 0.40 0.50 3.18 3.19 3.39 3.01

0.0127 4 76.2 9.88 18.2 18.1 17.9 18.3 15.0 15.0 15.0 15.0 0.22 0.32 0.42 0.52 3.17 3.24 3.43 2.98

0.0127 4 74.5 9.89 18.2 18.1 17.9 18.3 15.0 15.0 14.9 14.9 0.27 0.37 0.47 0.58 3.13 3.20 3.44 3.00

0.0127 4 75.2 9.89 18.2 18.1 17.9 18.3 15.0 15.0 15.0 15.0 0.30 0.40 0.50 0.61 3.15 3.24 3.41 3.05

0.0127 4 75.1 9.92 18.3 18.3 18.1 18.5 15.2 15.1 15.1 15.1 0.33 0.43 0.53 0.64 3.15 3.19 3.35 2.95

0.0127 4 100.5 9.86 17.8 17.9 17.7 18.1 14.9 14.9 14.9 14.9 0.08 0.16 0.23 0.31 3.43 3.38 3.53 3.13

0.0127 4 100.4 9.95 18.0 18.0 17.8 18.2 15.0 15.0 15.0 15.0 0.10 0.18 0.25 0.33 3.43 3.38 3.55 3.15

0.0127 4 100.5 9.94 18.2 18.1 18.0 18.3 15.2 15.2 15.1 15.1 0.13 0.20 0.28 0.36 3.39 3.38 3.57 3.20

0.0127 4 100.7 9.91 18.0 17.9 17.8 18.1 15.0 15.0 15.0 14.9 0.16 0.24 0.32 0.39 3.38 3.38 3.57 3.20

0.0127 4 101.3 9.96 18.1 18.0 17.8 18.1 15.0 15.0 15.0 14.9 0.20 0.27 0.35 0.43 3.30 3.37 3.60 3.20

0.0127 4 100.3 9.94 18.0 18.0 17.7 18.1 15.0 15.0 15.0 15.0 0.25 0.33 0.40 0.48 3.38 3.40 3.65 3.25

0.0127 4 100.1 9.95 18.1 18.1 17.9 18.2 15.2 15.2 15.2 15.1 0.31 0.39 0.46 0.54 3.47 3.47 3.75 3.28

246

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 4 99.83 9.96 17.8 17.8 17.7 18.0 15.0 15.0 15.0 15.0 0.37 0.45 0.53 0.60 3.64 3.60 3.77 3.32

0.0127 4 150.8 9.88 17.9 17.9 17.7 18.0 15.1 15.0 15.0 15.0 0.05 0.10 0.16 0.21 3.53 3.49 3.72 3.29

0.0127 4 149.8 9.97 17.8 17.8 17.6 17.9 14.9 14.9 14.9 14.9 0.07 0.12 0.17 0.22 3.57 3.53 3.76 3.35

0.0127 4 150.8 9.94 18.1 18.1 17.9 18.3 15.3 15.3 15.2 15.2 0.09 0.14 0.19 0.24 3.55 3.52 3.74 3.30

0.0127 4 150.9 9.91 18.1 18.1 17.9 18.2 15.2 15.2 15.2 15.1 0.13 0.18 0.23 0.28 3.54 3.51 3.74 3.34

0.0127 4 150.1 9.91 17.9 17.9 17.7 18.0 15.1 15.1 15.0 15.0 0.18 0.23 0.28 0.33 3.60 3.59 3.81 3.37

0.0127 4 150.4 9.88 18.0 18.0 17.8 18.1 15.3 15.2 15.2 15.1 0.23 0.28 0.33 0.38 3.70 3.66 3.87 3.42

0.0127 4 150.3 9.87 17.7 17.7 17.5 17.7 15.0 15.0 14.9 14.9 0.27 0.32 0.37 0.42 3.75 3.74 3.95 3.47

0.0127 4 150.5 9.89 17.8 17.8 17.7 17.9 15.2 15.2 15.1 15.1 0.32 0.37 0.42 0.47 3.88 3.77 3.97 3.50

0.0127 4 149.2 9.85 17.7 17.7 17.5 17.7 15.2 15.2 15.1 15.1 0.38 0.43 0.49 0.54 4.06 3.91 4.20 3.83

0.0127 4 200.8 9.90 17.8 17.8 17.6 17.9 15.0 15.0 15.0 14.9 0.07 0.11 0.15 0.19 3.60 3.62 3.84 3.40

0.0127 4 200.5 9.92 17.9 17.8 17.6 17.9 15.1 15.1 15.1 15.0 0.09 0.13 0.17 0.21 3.62 3.68 3.95 3.45

0.0127 4 199.9 9.91 18.0 17.9 17.7 18.0 15.2 15.2 15.2 15.1 0.12 0.16 0.20 0.24 3.71 3.73 3.95 3.46

0.0127 4 199.7 9.87 17.9 17.8 17.6 17.9 15.3 15.2 15.2 15.1 0.16 0.19 0.23 0.27 3.78 3.84 4.10 3.57

0.0127 4 200 9.88 17.7 17.6 17.4 17.7 15.1 15.1 15.0 14.9 0.21 0.25 0.29 0.32 3.96 3.94 4.22 3.65

0.0127 4 200.6 9.87 17.6 17.6 17.3 17.6 15.2 15.1 15.0 14.9 0.26 0.29 0.33 0.37 4.15 4.06 4.38 3.77

0.0127 4 199.2 9.98 17.7 17.7 17.4 17.7 15.4 15.3 15.2 15.1 0.31 0.35 0.39 0.43 4.36 4.29 4.68 3.96

0.0127 3 74.7 9.96 18.1 18.1 17.8 18.1 14.9 14.9 14.9 14.9 0.14 0.24 0.34 0.45 3.16 3.19 3.50 3.14

0.0127 3 75.3 9.95 18.3 18.3 18.0 18.3 15.2 15.2 15.2 15.1 0.17 0.27 0.38 0.48 3.25 3.26 3.58 3.22

0.0127 3 75.5 9.93 18.0 18.0 17.6 18.0 14.8 14.7 14.7 14.7 0.22 0.32 0.42 0.53 3.12 3.09 3.47 3.05

0.0127 3 74.3 9.90 18.3 18.3 17.9 18.3 15.1 15.1 15.1 15.1 0.27 0.37 0.48 0.58 3.10 3.17 3.53 3.13

0.0127 3 101.0 9.92 18.0 17.9 17.7 18.0 14.9 14.9 14.9 14.9 0.11 0.18 0.26 0.34 3.30 3.36 3.64 3.25

0.0127 3 99.6 9.89 18.0 17.9 17.6 17.9 14.9 14.9 14.9 14.8 0.13 0.21 0.28 0.36 3.29 3.38 3.68 3.27

0.0127 3 100.9 9.93 18.1 17.9 17.7 18.0 15.0 15.0 15.0 14.9 0.17 0.25 0.32 0.40 3.29 3.40 3.71 3.25

0.0127 3 100.0 9.93 18.1 18.1 17.8 18.1 15.2 15.2 15.1 15.1 0.22 0.29 0.37 0.45 3.42 3.46 3.75 3.33

0.0127 3 100.0 9.97 18.2 18.1 17.9 18.2 15.3 15.2 15.2 15.2 0.26 0.34 0.42 0.50 3.47 3.48 3.73 3.30

0.0127 3 99.8 9.95 17.8 17.7 17.6 17.9 14.9 14.9 14.9 14.9 0.31 0.39 0.47 0.55 3.53 3.52 3.74 3.34

0.0127 3 101.7 9.92 18.1 18.2 18.0 18.3 15.3 15.3 15.3 15.3 0.35 0.42 0.50 0.57 3.54 3.50 3.73 3.36

A

ppendix B

247

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0127 3 150.7 9.96 17.9 17.9 17.7 18.1 15.0 15.0 14.9 14.9 0.07 0.12 0.17 0.22 3.52 3.48 3.61 3.12

0.0127 3 150.1 9.94 17.8 17.9 17.7 18.1 15.0 15.0 15.0 14.9 0.10 0.15 0.20 0.25 3.58 3.52 3.64 3.17

0.0127 3 149.7 9.94 18.1 18.1 18.0 18.3 15.3 15.3 15.2 15.2 0.14 0.19 0.24 0.29 3.61 3.54 3.68 3.21

0.0127 3 151 9.91 17.7 17.8 17.6 18.0 15.0 15.0 14.9 14.9 0.16 0.22 0.27 0.32 3.65 3.58 3.68 3.24

0.0127 3 150.4 9.96 17.8 17.9 17.8 18.1 15.1 15.1 15.0 15.0 0.20 0.25 0.31 0.36 3.74 3.60 3.69 3.27

0.0127 3 150.3 9.92 18.0 18.1 17.9 18.2 15.4 15.3 15.3 15.2 0.25 0.30 0.35 0.40 3.79 3.68 3.80 3.33

0.0127 3 149.5 9.90 17.9 18.0 17.9 18.2 15.4 15.4 15.3 15.2 0.30 0.35 0.40 0.45 3.96 3.80 3.91 3.42

0.0127 3 200.5 9.88 17.8 17.8 17.6 18.0 15.0 15.0 14.9 14.9 0.07 0.11 0.15 0.18 3.65 3.57 3.72 3.26

0.0127 3 199.3 9.91 17.9 17.9 17.7 18.0 15.2 15.1 15.1 15.0 0.10 0.14 0.18 0.21 3.72 3.69 3.83 3.35

0.0127 3 199.6 9.91 17.9 17.9 17.8 18.1 15.3 15.2 15.2 15.1 0.14 0.17 0.21 0.25 3.80 3.73 3.85 3.33

0.0127 3 200.2 9.90 17.9 17.9 17.7 18.0 15.3 15.2 15.2 15.1 0.16 0.20 0.24 0.28 3.89 3.84 4.00 3.43

0.0127 3 199.4 9.90 17.8 17.8 17.7 18.0 15.3 15.3 15.2 15.1 0.19 0.23 0.27 0.31 4.03 3.92 4.06 3.51

0.0127 3 200 9.91 17.7 17.7 17.5 17.9 15.3 15.2 15.1 15.0 0.24 0.28 0.32 0.36 4.23 4.06 4.20 3.58

0.0127 3 200.2 9.88 17.4 17.5 17.3 17.6 15.2 15.1 15.0 14.9 0.29 0.32 0.36 0.40 4.47 4.19 4.34 3.69

0.0127 3 200.9 9.88 17.5 17.5 17.3 17.7 15.3 15.2 15.1 15.0 0.32 0.36 0.40 0.44 4.61 4.30 4.49 3.74

0.0127 3 199.6 9.91 17.5 17.5 17.3 17.6 15.4 15.3 15.2 15.1 0.37 0.40 0.44 0.48 4.86 4.54 4.75 3.98 Table B.7 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 5 oC measured at each section of the of the

test section inside 15.9 mm internal diameter tube. Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 Plain tube 5.00 74.8 10.2 11.2 11.4 11.7 4.65 4.65 4.64 4.64 0.14 0.18 0.22 0.26 0.897 0.768 0.741 0.710

0.0159 Plain tube 5.03 74.9 11.4 11.1 11.3 11.4 4.62 4.62 4.61 4.61 0.25 0.29 0.33 0.37 0.741 0.775 0.756 0.739

0.0159 Plain tube 5.01 75.4 11.1 11.0 11.3 11.3 4.67 4.66 4.66 4.65 0.35 0.38 0.42 0.46 0.778 0.787 0.756 0.758

0.0159 Plain tube 5.03 74.8 10.8 10.8 11.1 11.0 4.62 4.62 4.61 4.60 0.44 0.48 0.52 0.56 0.820 0.816 0.777 0.787

0.0159 Plain tube 5.00 74.7 10.6 10.7 11.0 10.8 4.70 4.70 4.69 4.68 0.55 0.59 0.63 0.67 0.854 0.837 0.799 0.824

0.0159 Plain tube 5.01 75.3 10.1 10.3 10.5 10.3 4.45 4.44 4.43 4.42 0.65 0.69 0.73 0.77 0.889 0.861 0.830 0.855

0.0159 Plain tube 5.03 74.7 10.1 10.3 10.5 10.5 4.56 4.55 4.54 4.53 0.75 0.79 0.83 0.87 0.914 0.871 0.840 0.840

248

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 Plain tube 5.00 74.9 9.4 10.0 10.6 11.0 4.12 4.11 4.10 4.09 0.85 0.89 0.93 0.97 0.942 0.857 0.773 0.721

0.0159 Plain tube 5.03 101.1 10.0 11.2 11.7 11.3 4.89 4.89 4.88 4.88 0.13 0.16 0.19 0.22 0.99 0.80 0.74 0.79

0.0159 Plain tube 5.02 100.0 11.0 10.8 11.0 10.7 4.91 4.91 4.90 4.89 0.23 0.26 0.29 0.32 0.83 0.85 0.83 0.86

0.0159 Plain tube 5.00 100.6 10.4 10.3 10.5 10.2 4.57 4.56 4.55 4.54 0.33 0.36 0.39 0.42 0.85 0.88 0.85 0.89

0.0159 Plain tube 5.01 99.6 10.4 10.2 10.4 10.1 4.82 4.81 4.79 4.78 0.44 0.47 0.50 0.53 0.90 0.92 0.90 0.95

0.0159 Plain tube 5.03 99.8 10.1 10.0 10.0 9.7 4.93 4.91 4.90 4.88 0.54 0.57 0.60 0.63 0.98 0.99 0.99 1.04

0.0159 Plain tube 5.02 100.1 9.7 9.6 9.7 9.5 5.12 5.10 5.08 5.06 0.64 0.67 0.70 0.73 1.11 1.11 1.09 1.14

0.0159 Plain tube 5.04 100.8 8.9 9.1 9.1 8.9 4.79 4.78 4.76 4.74 0.74 0.77 0.80 0.83 1.22 1.16 1.16 1.21

0.0159 Plain tube 4.98 99.9 8.5 8.8 9.0 9.2 4.77 4.76 4.75 4.75 0.84 0.87 0.89 0.92 1.34 1.24 1.17 1.11

0.0159 Plain tube 5.03 99.6 8.7 9.1 9.4 9.8 4.99 4.98 4.98 4.99 0.89 0.92 0.95 0.98 1.36 1.23 1.13 1.05

0.0159 Plain tube 4.99 150.0 9.49 10.05 10.12 9.55 4.84 4.84 4.83 4.82 0.12 0.14 0.16 0.18 1.07 0.96 0.94 1.06

0.0159 Plain tube 5.03 150.4 9.46 9.91 9.98 9.56 5.00 4.98 4.97 4.96 0.22 0.24 0.26 0.28 1.13 1.02 1.01 1.09

0.0159 Plain tube 4.97 150.0 9.66 9.96 9.86 9.38 5.21 5.19 5.17 5.15 0.32 0.34 0.36 0.38 1.12 1.04 1.06 1.18

0.0159 Plain tube 5.02 149.9 8.90 9.11 8.91 8.49 5.03 5.01 4.98 4.95 0.43 0.45 0.46 0.48 1.30 1.23 1.28 1.42

0.0159 Plain tube 5.04 149.8 8.48 8.65 8.49 8.16 5.32 5.29 5.25 5.21 0.53 0.55 0.57 0.59 1.60 1.50 1.56 1.71

0.0159 Plain tube 4.99 149.7 7.70 7.80 7.65 7.40 5.28 5.23 5.19 5.14 0.63 0.65 0.67 0.69 2.06 1.95 2.03 2.22

0.0159 Plain tube 4.99 149.6 6.90 7.15 7.12 7.00 5.00 4.95 4.90 4.84 0.73 0.75 0.77 0.79 2.64 2.28 2.26 2.32

0.0159 Plain tube 5.00 150.7 6.87 7.13 7.09 6.97 5.07 5.01 4.95 4.89 0.82 0.84 0.86 0.88 2.78 2.37 2.35 2.41

0.0159 Plain tube 5.05 149.1 7.14 7.40 7.41 7.36 5.33 5.27 5.21 5.15 0.88 0.90 0.92 0.94 2.79 2.37 2.30 2.30

0.0159 Plain tube 4.97 148.7 6.94 7.31 7.34 7.33 5.18 5.12 5.06 5.01 0.93 0.95 0.97 0.99 2.82 2.27 2.19 2.14

0.0159 Plain tube 5.03 200.0 8.60 9.04 9.07 8.86 4.82 4.81 4.80 4.79 0.07 0.08 0.10 0.11 1.33 1.19 1.18 1.24

0.0159 Plain tube 5.01 200.1 8.30 8.38 8.49 8.42 4.89 4.88 4.87 4.85 0.12 0.13 0.15 0.16 1.47 1.43 1.39 1.41

0.0159 Plain tube 4.95 200.2 8.30 8.45 8.35 8.27 4.90 4.89 4.87 4.85 0.17 0.18 0.20 0.21 1.46 1.40 1.43 1.45

0.0159 Plain tube 5.03 199.9 8.52 8.53 8.44 8.18 5.08 5.06 5.03 5.01 0.22 0.24 0.25 0.27 1.46 1.45 1.48 1.59

0.0159 Plain tube 4.98 200.0 8.22 8.30 8.12 7.81 5.10 5.08 5.05 5.02 0.27 0.28 0.30 0.31 1.60 1.55 1.62 1.79

0.0159 Plain tube 5.03 199.7 8.02 8.12 7.92 7.67 5.27 5.24 5.21 5.17 0.32 0.33 0.35 0.36 1.84 1.75 1.86 2.02

0.0159 Plain tube 5.00 200.0 7.57 7.71 7.59 7.35 5.27 5.23 5.19 5.14 0.37 0.38 0.40 0.41 2.18 2.02 2.09 2.27

0.0159 Plain tube 4.97 199.8 7.38 7.42 7.39 7.24 5.43 5.39 5.34 5.29 0.42 0.43 0.45 0.46 2.56 2.46 2.43 2.55

A

ppendix B

249

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 Plain tube 5.08 200.0 7.09 7.21 7.23 7.17 5.34 5.29 5.23 5.17 0.47 0.48 0.50 0.51 2.91 2.65 2.55 2.54

0.0159 Plain tube 4.97 199.9 6.56 6.66 6.63 6.65 5.03 4.97 4.90 4.83 0.52 0.53 0.55 0.56 3.27 2.95 2.88 2.73

0.0159 Plain tube 4.91 200.7 6.53 6.62 6.59 6.55 5.05 4.98 4.90 4.83 0.57 0.58 0.60 0.61 3.35 3.00 2.92 2.85

0.0159 Plain tube 5.28 197.9 6.93 6.98 6.98 6.94 5.43 5.35 5.26 5.17 0.63 0.64 0.66 0.68 3.54 3.24 3.09 3.00

0.0159 Plain tube 10.07 75.2 11.8 12.5 12.8 13.2 4.47 4.47 4.46 4.46 0.10 0.18 0.26 0.34 1.38 1.26 1.21 1.15

0.0159 Plain tube 9.95 76.3 11.9 12.3 12.6 13.1 4.33 4.33 4.33 4.32 0.16 0.24 0.31 0.39 1.32 1.25 1.20 1.14

0.0159 Plain tube 9.98 75.4 11.7 12.2 12.7 13.2 4.40 4.40 4.39 4.38 0.22 0.30 0.38 0.46 1.36 1.28 1.21 1.13

0.0159 Plain tube 9.90 75.5 11.7 12.1 12.6 13.2 4.38 4.37 4.37 4.36 0.28 0.36 0.44 0.52 1.35 1.29 1.21 1.13

0.0159 Plain tube 9.97 75.3 11.7 12.1 12.6 13.2 4.29 4.29 4.28 4.27 0.38 0.46 0.54 0.62 1.36 1.28 1.20 1.12

0.0159 Plain tube 9.99 75.4 11.7 12.3 12.8 13.7 4.35 4.34 4.33 4.32 0.48 0.56 0.64 0.72 1.36 1.26 1.19 1.07

0.0159 Plain tube 9.89 75.2 11.6 12.4 13.0 14.7 4.12 4.11 4.10 4.09 0.59 0.67 0.74 0.82 1.33 1.19 1.12 0.93

0.0159 Plain tube 9.92 74.8 11.8 12.7 13.3 14.8 4.26 4.25 4.24 4.23 0.61 0.69 0.77 0.85 1.32 1.17 1.10 0.94

0.0159 Plain tube 10.01 75.2 11.6 12.6 13.3 15.2 3.96 3.94 3.93 3.91 0.67 0.75 0.83 0.91 1.32 1.16 1.07 0.89

0.0159 Plain tube 9.9 100.3 11.6 12.1 12.1 12.4 4.50 4.50 4.49 4.48 0.16 0.22 0.28 0.34 1.39 1.32 1.30 1.26

0.0159 Plain tube 10.0 99.6 11.7 11.8 12.1 12.5 4.67 4.66 4.65 4.64 0.26 0.32 0.38 0.44 1.44 1.40 1.35 1.29

0.0159 Plain tube 10.0 99.8 11.7 12.0 12.5 12.8 4.71 4.70 4.69 4.67 0.36 0.42 0.48 0.54 1.42 1.37 1.28 1.23

0.0159 Plain tube 10.0 99.4 12.0 12.4 12.7 12.8 4.81 4.80 4.78 4.76 0.47 0.53 0.59 0.65 1.41 1.33 1.27 1.25

0.0159 Plain tube 10.0 100.4 11.9 12.2 12.5 12.6 4.87 4.85 4.83 4.81 0.56 0.62 0.68 0.74 1.43 1.36 1.31 1.29

0.0159 Plain tube 10.0 100.0 11.7 12.0 12.4 12.8 4.80 4.78 4.76 4.74 0.67 0.73 0.79 0.85 1.44 1.38 1.31 1.25

0.0159 Plain tube 10.1 99.9 11.3 11.7 12.3 12.1 4.57 4.55 4.54 4.54 0.78 0.84 0.90 0.96 1.51 1.42 1.31 1.34

0.0159 Plain tube 9.99 150.3 11.5 11.6 11.7 11.8 4.88 4.87 4.86 4.85 0.08 0.12 0.16 0.20 1.51 1.50 1.46 1.44

0.0159 Plain tube 10.08 149.4 11.3 11.4 11.6 11.7 4.84 4.83 4.82 4.80 0.14 0.18 0.22 0.26 1.55 1.54 1.50 1.47

0.0159 Plain tube 9.91 149.6 11.1 11.1 11.4 11.5 4.92 4.91 4.89 4.87 0.24 0.28 0.32 0.36 1.60 1.61 1.53 1.51

0.0159 Plain tube 9.89 150.0 11.2 11.1 11.4 11.3 4.96 4.94 4.92 4.89 0.34 0.38 0.42 0.46 1.58 1.61 1.54 1.55

0.0159 Plain tube 9.91 149.9 11.0 10.8 10.9 10.7 4.91 4.88 4.85 4.81 0.44 0.48 0.52 0.56 1.63 1.69 1.65 1.70

0.0159 Plain tube 9.92 150.1 10.6 10.3 10.3 10.0 5.10 5.06 5.02 4.97 0.54 0.58 0.62 0.66 1.82 1.90 1.89 1.97

0.0159 Plain tube 9.96 149.8 9.7 9.4 9.4 9.2 5.04 4.99 4.94 4.89 0.65 0.69 0.73 0.76 2.16 2.26 2.25 2.31

0.0159 Plain tube 9.99 151.9 8.5 8.6 9.0 9.0 4.95 4.89 4.83 4.77 0.81 0.84 0.88 0.92 2.84 2.68 2.41 2.34

250

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 Plain tube 9.84 149.3 8.6 8.7 9.1 9.2 5.07 5.01 4.95 4.88 0.82 0.86 0.90 0.94 2.83 2.65 2.37 2.26

0.0159 Plain tube 10.02 200.3 11.1 11.1 11.4 11.4 4.68 4.67 4.65 4.64 0.07 0.10 0.13 0.16 1.58 1.55 1.50 1.48

0.0159 Plain tube 9.93 200.8 10.8 10.6 10.8 10.7 4.93 4.92 4.90 4.88 0.16 0.19 0.22 0.25 1.70 1.74 1.70 1.70

0.0159 Plain tube 9.96 200.3 10.8 10.5 10.5 10.3 5.00 4.97 4.94 4.90 0.26 0.29 0.32 0.35 1.73 1.81 1.81 1.85

0.0159 Plain tube 9.93 199.4 10.8 10.9 10.5 10.4 5.17 5.13 5.08 5.03 0.36 0.39 0.41 0.44 1.76 1.72 1.84 1.85

0.0159 Plain tube 9.99 199.9 9.4 9.5 9.4 9.1 5.22 5.17 5.10 5.03 0.46 0.49 0.52 0.55 2.40 2.30 2.33 2.47

0.0159 Plain tube 9.91 200.9 8.8 8.9 9.0 8.8 5.28 5.20 5.12 5.04 0.56 0.59 0.61 0.64 2.82 2.69 2.54 2.65

0.0159 14 4.99 75.1 8.78 8.79 9.35 8.74 4.85 4.84 4.84 4.82 0.14 0.18 0.22 0.26 1.27 1.27 1.11 1.28

0.0159 14 5.01 75.1 8.33 8.66 9.29 8.61 4.98 4.96 4.95 4.94 0.25 0.29 0.33 0.37 1.50 1.36 1.16 1.37

0.0159 14 5.04 74.8 8.55 8.75 9.26 8.57 4.97 4.96 4.95 4.93 0.34 0.39 0.43 0.47 1.41 1.33 1.17 1.38

0.0159 14 5.00 74.7 8.80 8.64 9.01 8.44 5.00 4.98 4.97 4.95 0.44 0.48 0.52 0.56 1.32 1.37 1.24 1.43

0.0159 14 5.02 74.7 8.85 8.47 8.90 8.29 4.91 4.89 4.87 4.84 0.54 0.58 0.62 0.66 1.28 1.41 1.25 1.46

0.0159 14 5.02 74.5 9.42 8.69 9.37 8.61 5.09 5.07 5.04 5.02 0.65 0.69 0.73 0.77 1.16 1.39 1.16 1.40

0.0159 14 5.02 74.8 9.45 8.38 9.56 8.91 4.81 4.78 4.76 4.74 0.75 0.79 0.83 0.87 1.08 1.40 1.05 1.21

0.0159 14 5.00 75.1 9.38 8.60 9.57 10.10 4.50 4.48 4.47 4.47 0.85 0.89 0.93 0.97 1.02 1.22 0.98 0.89

0.0159 14 5.01 100.3 8.33 8.49 8.65 8.39 5.21 5.19 5.18 5.16 0.13 0.16 0.19 0.22 1.61 1.52 1.45 1.56

0.0159 14 5.03 100.4 7.86 8.20 8.35 7.99 5.10 5.08 5.06 5.04 0.23 0.26 0.29 0.32 1.82 1.61 1.53 1.71

0.0159 14 5.02 100.3 7.78 8.00 7.96 7.68 5.04 5.02 5.00 4.97 0.34 0.37 0.40 0.43 1.84 1.69 1.70 1.85

0.0159 14 5.00 100.6 7.63 7.77 7.56 7.48 5.04 5.01 4.98 4.95 0.44 0.47 0.50 0.53 1.94 1.82 1.94 1.98

0.0159 14 5.00 100.1 7.73 7.77 7.55 7.56 5.17 5.13 5.09 5.05 0.54 0.56 0.59 0.62 1.95 1.90 2.03 2.00

0.0159 14 5.02 99.4 7.81 7.71 7.60 7.62 5.26 5.22 5.18 5.14 0.64 0.67 0.70 0.73 1.97 2.02 2.07 2.02

0.0159 14 5.01 99.9 7.97 7.64 7.65 7.70 5.19 5.15 5.12 5.09 0.74 0.77 0.80 0.83 1.81 2.02 1.98 1.92

0.0159 14 5.02 99.3 8.42 7.57 8.00 8.28 5.17 5.15 5.14 5.15 0.84 0.87 0.90 0.93 1.55 2.08 1.76 1.60

0.0159 14 5.01 150.5 7.42 7.70 7.68 7.54 5.05 5.03 5.00 4.97 0.12 0.14 0.16 0.18 2.12 1.88 1.87 1.95

0.0159 14 5.00 149.5 7.48 7.77 7.68 7.61 5.33 5.30 5.26 5.21 0.23 0.25 0.27 0.29 2.33 2.03 2.07 2.09

0.0159 14 5.00 150.3 7.05 7.39 7.29 7.21 5.18 5.13 5.08 5.02 0.33 0.35 0.37 0.39 2.68 2.22 2.27 2.29

0.0159 14 4.98 149.6 7.02 7.45 7.31 7.18 5.35 5.28 5.21 5.13 0.43 0.45 0.47 0.49 2.99 2.30 2.38 2.44

0.0159 14 5.03 150.9 6.83 7.23 7.10 6.99 5.40 5.31 5.21 5.10 0.53 0.55 0.57 0.59 3.53 2.63 2.67 2.66

A

ppendix B

251

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 14 4.97 150.4 6.55 6.91 6.77 6.64 5.22 5.08 4.93 4.76 0.63 0.64 0.66 0.68 3.76 2.72 2.71 2.66

0.0159 14 5.00 149.0 6.77 7.13 6.99 6.87 5.45 5.22 4.96 4.68 0.73 0.75 0.77 0.79 3.81 2.62 2.48 2.29

0.0159 14 5.01 149.3 6.61 7.04 6.91 6.85 5.31 4.95 4.54 4.08 0.82 0.84 0.86 0.88 3.88 2.40 2.11 1.81

0.0159 14 5.00 150.0 6.50 6.96 6.88 6.86 5.20 4.72 4.19 3.59 0.88 0.90 0.91 0.93 3.85 2.24 1.86 1.53

0.0159 14 5.00 200.4 7.72 7.91 7.85 7.77 5.51 5.51 5.50 5.49 0.12 0.13 0.15 0.16 2.27 2.08 2.13 2.20

0.0159 14 5.01 199.7 7.07 7.35 7.25 7.11 5.26 5.24 5.22 5.19 0.22 0.24 0.25 0.27 2.77 2.39 2.48 2.63

0.0159 14 4.99 199.8 7.10 7.42 7.25 7.08 5.58 5.54 5.49 5.44 0.32 0.34 0.35 0.37 3.30 2.66 2.85 3.04

0.0159 14 4.99 200.5 6.75 6.99 6.83 6.65 5.56 5.48 5.40 5.31 0.42 0.43 0.45 0.46 4.21 3.33 3.50 3.75

0.0159 14 5.03 200.7 6.60 6.76 6.56 6.38 5.62 5.51 5.39 5.27 0.52 0.54 0.55 0.57 5.18 4.04 4.33 4.55

0.0159 14 10.0 75.4 10.51 9.41 9.94 10.51 4.64 4.63 4.62 4.60 0.19 0.26 0.34 0.42 1.71 2.10 1.88 1.70

0.0159 14 10.0 75.2 10.17 9.32 9.85 10.48 4.66 4.65 4.63 4.61 0.29 0.37 0.44 0.52 1.82 2.15 1.92 1.71

0.0159 14 10.0 74.5 10.69 9.57 10.15 10.78 4.89 4.87 4.85 4.83 0.39 0.47 0.55 0.63 1.73 2.13 1.89 1.68

0.0159 14 10.0 74.8 10.52 9.04 9.69 10.44 4.39 4.37 4.35 4.32 0.49 0.57 0.65 0.73 1.64 2.15 1.88 1.64

0.0159 14 10.0 74.6 11.04 9.38 10.30 11.18 4.49 4.47 4.44 4.42 0.59 0.67 0.75 0.83 1.53 2.04 1.71 1.48

0.0159 14 10.0 74.8 11.29 9.25 10.73 12.71 4.06 4.03 4.01 3.99 0.69 0.77 0.85 0.93 1.39 1.92 1.49 1.15

0.0159 14 10.0 100 9.9 10.2 10.3 10.1 4.88 4.86 4.84 4.82 0.16 0.22 0.28 0.34 1.98 1.88 1.83 1.92

0.0159 14 10.0 100 9.8 10.2 10.2 9.9 5.01 4.99 4.97 4.94 0.26 0.32 0.38 0.44 2.10 1.93 1.91 2.02

0.0159 14 10.0 100 9.9 10.1 10.1 9.8 4.95 4.93 4.89 4.86 0.36 0.42 0.48 0.54 2.03 1.93 1.94 2.03

0.0159 14 10.0 99 10.1 10.2 10.1 10.0 5.05 5.02 4.98 4.94 0.47 0.53 0.59 0.65 1.99 1.95 1.95 2.00

0.0159 14 10.0 99 9.9 10.0 9.9 9.9 4.89 4.85 4.81 4.76 0.57 0.63 0.69 0.75 2.01 1.96 1.98 1.96

0.0159 14 10.0 100 9.9 9.8 9.9 10.0 4.79 4.74 4.70 4.67 0.67 0.73 0.79 0.85 1.96 1.97 1.94 1.88

0.0159 14 10.0 99 10.7 10.0 10.8 11.4 4.80 4.77 4.75 4.75 0.77 0.83 0.89 0.95 1.72 1.92 1.66 1.51

0.0159 14 10.0 150.4 9.48 9.89 9.83 9.75 5.22 5.19 5.16 5.12 0.14 0.18 0.22 0.26 2.36 2.14 2.15 2.17

0.0159 14 10.0 150.0 8.98 9.35 9.27 9.30 5.03 4.99 4.94 4.88 0.24 0.28 0.32 0.36 2.55 2.31 2.33 2.28

0.0159 14 10.0 150.6 9.10 9.46 9.42 9.38 5.37 5.31 5.25 5.18 0.34 0.38 0.42 0.46 2.68 2.41 2.40 2.38

0.0159 14 10.0 149.8 8.94 9.24 9.21 9.18 5.42 5.34 5.26 5.16 0.44 0.48 0.52 0.56 2.86 2.57 2.54 2.50

0.0159 14 10.0 150.7 8.24 8.72 8.70 8.64 5.17 5.07 4.94 4.80 0.54 0.58 0.62 0.66 3.27 2.75 2.67 2.61

0.0159 14 10.1 150.6 7.97 8.43 8.47 8.41 5.10 4.93 4.73 4.49 0.65 0.69 0.73 0.77 3.52 2.89 2.70 2.57

252

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 14 10.0 150.1 8.09 8.61 8.67 8.67 5.25 4.98 4.66 4.26 0.75 0.79 0.83 0.86 3.54 2.77 2.51 2.28

0.0159 14 10.0 149.8 7.35 7.96 8.17 8.24 4.65 4.19 3.64 2.95 0.85 0.89 0.93 0.97 3.72 2.66 2.21 1.89

0.0159 14 10.1 200.2 9.27 9.71 9.58 9.50 5.31 5.30 5.29 5.27 0.13 0.16 0.19 0.22 2.55 2.29 2.35 2.39

0.0159 14 10.0 199.9 8.68 9.13 8.98 8.89 5.26 5.23 5.20 5.16 0.24 0.27 0.30 0.33 2.94 2.58 2.66 2.69

0.0159 14 10.0 199.9 8.50 8.97 8.83 8.67 5.50 5.45 5.39 5.32 0.33 0.36 0.39 0.42 3.36 2.86 2.93 3.01

0.0159 14 10.0 199.8 8.20 8.49 8.36 8.17 5.49 5.41 5.31 5.20 0.44 0.47 0.50 0.53 3.73 3.27 3.30 3.39

0.0159 14 10.0 199.4 7.78 7.96 7.83 7.64 5.40 5.28 5.15 5.01 0.54 0.57 0.60 0.62 4.23 3.74 3.74 3.83

0.0159 9 4.98 75.0 8.73 9.07 8.80 8.78 4.93 4.92 4.91 4.90 0.14 0.18 0.22 0.26 1.32 1.20 1.29 1.29

0.0159 9 5.00 75.3 8.75 9.09 8.99 8.90 5.03 5.01 5.00 4.99 0.24 0.28 0.32 0.36 1.35 1.23 1.25 1.28

0.0159 9 4.99 74.9 9.39 9.43 9.50 8.99 5.10 5.08 5.07 5.05 0.35 0.39 0.43 0.47 1.16 1.15 1.13 1.27

0.0159 9 4.99 74.8 9.20 9.33 9.50 8.82 5.05 5.03 5.01 4.99 0.45 0.48 0.52 0.56 1.21 1.16 1.11 1.31

0.0159 9 4.98 75.1 8.92 9.51 9.67 8.76 5.18 5.16 5.14 5.11 0.55 0.59 0.63 0.67 1.33 1.15 1.10 1.37

0.0159 9 4.99 75.1 7.95 9.16 9.30 8.56 5.05 5.02 5.00 4.97 0.65 0.69 0.73 0.77 1.73 1.21 1.16 1.39

0.0159 9 4.97 75.0 7.54 8.94 9.22 9.01 4.77 4.74 4.71 4.68 0.75 0.79 0.83 0.87 1.80 1.19 1.11 1.15

0.0159 9 5.01 76.2 8.10 9.61 10.02 10.32 4.97 4.94 4.91 4.88 0.77 0.81 0.85 0.88 1.61 1.08 0.98 0.92

0.0159 9 5.03 99.1 8.36 8.60 8.37 8.20 5.07 5.05 5.04 5.02 0.13 0.16 0.19 0.22 1.53 1.42 1.51 1.58

0.0159 9 5.03 100.1 8.58 8.45 8.15 7.94 5.14 5.12 5.10 5.08 0.23 0.26 0.29 0.32 1.46 1.51 1.65 1.76

0.0159 9 5.03 100.2 8.33 8.16 7.85 7.66 5.17 5.15 5.12 5.09 0.34 0.37 0.40 0.43 1.59 1.67 1.85 1.96

0.0159 9 4.99 99.9 7.92 7.95 7.73 7.63 5.29 5.26 5.22 5.19 0.44 0.47 0.50 0.53 1.90 1.86 1.99 2.05

0.0159 9 5.00 100.0 7.28 7.56 7.44 7.36 5.10 5.06 5.02 4.98 0.54 0.57 0.60 0.63 2.30 2.00 2.07 2.10

0.0159 9 4.99 100.0 7.27 7.55 7.43 7.52 5.15 5.11 5.07 5.03 0.64 0.67 0.69 0.72 2.36 2.05 2.12 2.01

0.0159 9 4.99 99.7 6.87 7.16 7.12 7.25 4.94 4.91 4.87 4.85 0.74 0.77 0.80 0.83 2.60 2.22 2.23 2.09

0.0159 9 4.99 149.9 7.61 7.71 7.72 7.50 5.08 5.06 5.03 5.00 0.12 0.14 0.16 0.18 1.98 1.89 1.86 2.01

0.0159 9 4.99 149.3 7.48 7.78 7.59 7.36 5.19 5.15 5.11 5.06 0.22 0.24 0.26 0.28 2.19 1.90 2.01 2.18

0.0159 9 5.00 149.8 7.19 7.61 7.39 7.20 5.26 5.21 5.16 5.10 0.32 0.34 0.36 0.38 2.60 2.09 2.25 2.40

0.0159 9 5.01 150.5 7.08 7.49 7.28 7.09 5.35 5.30 5.24 5.19 0.43 0.44 0.46 0.48 2.90 2.29 2.46 2.63

0.0159 9 4.99 150.2 7.00 7.30 7.17 7.00 5.50 5.44 5.38 5.32 0.52 0.54 0.56 0.58 3.34 2.70 2.79 2.98

0.0159 9 5.02 150.3 6.78 7.11 6.94 6.76 5.42 5.34 5.25 5.16 0.63 0.65 0.67 0.69 3.70 2.84 2.99 3.15

A

ppendix B

253

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 9 5.03 152.4 6.64 6.91 6.78 6.61 5.44 5.31 5.17 5.00 0.72 0.74 0.76 0.78 4.21 3.16 3.14 3.14

0.0159 9 5.00 149.8 6.19 6.47 6.34 6.19 4.99 4.85 4.69 4.51 0.73 0.75 0.77 0.79 4.20 3.10 3.04 2.99

0.0159 9 5.02 200.2 7.64 7.78 7.70 7.44 5.40 5.37 5.32 5.28 0.12 0.13 0.15 0.16 2.25 2.08 2.12 2.33

0.0159 9 5.01 199.9 7.07 7.23 7.18 7.04 5.33 5.25 5.18 5.09 0.22 0.24 0.25 0.27 2.88 2.54 2.50 2.58

0.0159 9 4.98 199.7 6.69 6.85 6.80 6.64 5.30 5.18 5.06 4.93 0.33 0.34 0.36 0.37 3.58 3.00 2.87 2.93

0.0159 9 4.99 200.5 6.61 6.78 6.79 6.54 5.52 5.37 5.21 5.05 0.43 0.44 0.46 0.47 4.58 3.54 3.17 3.36

0.0159 9 5.02 201.3 6.53 6.66 6.66 6.37 5.68 5.50 5.31 5.13 0.52 0.53 0.55 0.56 5.90 4.32 3.75 4.04

0.0159 9 9.99 75.1 10.9 11.3 11.6 12.1 4.60 4.59 4.58 4.56 0.18 0.26 0.34 0.42 1.59 1.49 1.42 1.32

0.0159 9 10.00 74.9 11.0 11.3 12.5 12.3 4.66 4.65 4.63 4.61 0.29 0.37 0.45 0.52 1.59 1.52 1.27 1.30

0.0159 9 10.04 75.0 11.3 11.6 12.8 12.3 4.74 4.73 4.71 4.68 0.39 0.47 0.55 0.63 1.53 1.46 1.25 1.32

0.0159 9 9.99 74.7 11.3 11.8 12.8 12.5 4.78 4.76 4.74 4.71 0.48 0.56 0.64 0.72 1.54 1.43 1.24 1.29

0.0159 9 10.02 74.6 10.5 11.6 12.9 13.0 4.56 4.54 4.51 4.48 0.59 0.67 0.75 0.83 1.70 1.42 1.19 1.18

0.0159 9 10.0 99.4 10.3 10.2 10.4 10.5 4.84 4.83 4.81 4.79 0.17 0.23 0.29 0.35 1.83 1.87 1.81 1.76

0.0159 9 10.0 99.8 10.7 10.2 10.4 10.1 4.88 4.86 4.83 4.80 0.27 0.33 0.39 0.45 1.73 1.89 1.80 1.89

0.0159 9 10.0 100.1 10.6 10.0 10.1 9.8 5.05 5.03 4.99 4.96 0.36 0.42 0.48 0.54 1.82 2.02 1.95 2.05

0.0159 9 10.0 99.6 9.9 9.9 9.9 9.8 5.11 5.08 5.04 4.99 0.47 0.53 0.59 0.65 2.10 2.08 2.07 2.09

0.0159 9 10.0 99.6 9.3 9.6 9.6 9.7 5.04 5.00 4.95 4.91 0.57 0.63 0.69 0.75 2.37 2.19 2.14 2.10

0.0159 9 10.0 100.0 8.9 9.4 9.8 9.9 4.71 4.66 4.63 4.60 0.67 0.73 0.78 0.84 2.39 2.12 1.94 1.90

0.0159 9 10.0 149.9 9.36 9.09 9.13 9.22 4.90 4.87 4.83 4.79 0.15 0.19 0.23 0.27 2.25 2.38 2.34 2.27

0.0159 9 10.0 149.8 9.36 9.19 9.15 9.29 5.34 5.29 5.24 5.19 0.25 0.29 0.33 0.36 2.50 2.58 2.57 2.45

0.0159 9 10.1 149.9 8.69 8.92 8.94 8.87 5.23 5.17 5.12 5.06 0.35 0.39 0.43 0.47 2.91 2.69 2.64 2.65

0.0159 9 10.0 149.9 8.34 8.74 8.77 8.63 5.20 5.14 5.08 5.01 0.45 0.49 0.53 0.57 3.19 2.79 2.71 2.77

0.0159 9 10.0 150 7.72 7.72 7.98 8.05 5.15 5.08 5.01 4.92 0.55 0.59 0.63 0.67 3.91 3.82 3.39 3.21

0.0159 9 10.0 150.9 7.82 7.89 8.13 8.19 5.27 5.18 5.07 4.92 0.64 0.68 0.72 0.76 3.93 3.69 3.27 3.07

0.0159 9 10.1 149.9 7.72 7.91 8.15 8.26 5.19 5.02 4.79 4.50 0.75 0.79 0.83 0.87 4.00 3.49 3.00 2.68

0.0159 9 10.0 150.9 7.50 7.76 8.08 8.09 5.01 4.77 4.46 4.06 0.80 0.84 0.88 0.92 4.04 3.36 2.78 2.49

0.0159 9 10.1 199.2 9.43 9.43 9.41 9.19 5.32 5.27 5.22 5.15 0.13 0.16 0.19 0.22 2.46 2.43 2.40 2.50

0.0159 9 10.0 199.2 9.05 9.13 9.00 8.83 5.41 5.33 5.24 5.14 0.23 0.26 0.29 0.32 2.75 2.63 2.66 2.71

254

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 9 10.0 199.9 8.56 8.63 8.57 8.39 5.51 5.39 5.25 5.11 0.34 0.37 0.40 0.43 3.31 3.10 3.03 3.06

0.0159 9 10.0 199.3 7.95 8.07 7.94 7.71 5.27 5.11 4.93 4.75 0.44 0.47 0.50 0.53 3.74 3.38 3.33 3.39

0.0159 9 9.9 200 7.88 8.03 7.96 7.73 5.38 5.20 5.00 4.81 0.53 0.56 0.59 0.62 4.01 3.52 3.38 3.41

0.0159 4 4.99 75.5 7.59 7.88 8.07 7.99 4.85 4.83 4.81 4.79 0.15 0.19 0.23 0.27 1.82 1.64 1.53 1.56

0.0159 4 5.03 75.4 7.38 7.74 7.97 7.84 5.07 5.05 5.03 5.01 0.25 0.29 0.33 0.37 2.19 1.87 1.71 1.78

0.0159 4 5.01 75.0 7.25 7.67 7.88 7.62 5.09 5.07 5.05 5.02 0.35 0.39 0.43 0.47 2.33 1.93 1.77 1.94

0.0159 4 4.98 74.7 7.10 7.43 7.55 7.46 5.04 5.01 4.98 4.95 0.45 0.49 0.53 0.57 2.42 2.07 1.95 2.00

0.0159 4 5.01 74.6 6.97 7.23 7.35 7.39 4.96 4.93 4.89 4.86 0.55 0.59 0.63 0.67 2.50 2.19 2.04 1.98

0.0159 4 5.05 74.7 6.97 7.27 7.42 7.52 4.96 4.93 4.89 4.85 0.65 0.69 0.73 0.77 2.52 2.16 2.00 1.90

0.0159 4 5.00 74.8 6.97 7.30 7.57 7.69 5.00 4.96 4.92 4.87 0.75 0.79 0.83 0.87 2.55 2.14 1.89 1.78

0.0159 4 5.00 75.4 6.64 6.97 7.32 7.68 4.66 4.62 4.57 4.52 0.82 0.86 0.90 0.94 2.53 2.13 1.82 1.59

0.0159 4 4.99 101.1 7.49 7.66 7.77 7.63 5.14 5.12 5.10 5.07 0.13 0.16 0.19 0.22 2.13 1.97 1.87 1.96

0.0159 4 5.01 99.82 7.35 7.49 7.55 7.48 5.23 5.20 5.17 5.13 0.24 0.27 0.30 0.33 2.37 2.19 2.10 2.14

0.0159 4 5.01 100.3 7.38 7.54 7.57 7.53 5.34 5.30 5.26 5.22 0.34 0.37 0.40 0.43 2.47 2.24 2.18 2.17

0.0159 4 5.01 100.9 7.10 7.26 7.28 7.24 5.13 5.08 5.03 4.98 0.44 0.47 0.50 0.52 2.55 2.31 2.24 2.23

0.0159 4 4.99 99.88 6.96 7.15 7.18 7.14 5.10 5.04 4.99 4.94 0.53 0.56 0.59 0.62 2.69 2.38 2.29 2.27

0.0159 4 5.02 99.59 6.96 7.17 7.24 7.18 5.19 5.14 5.11 5.08 0.64 0.67 0.70 0.73 2.84 2.49 2.36 2.41

0.0159 4 5.01 99.9 6.89 7.06 7.16 7.11 5.19 5.19 5.22 5.27 0.74 0.77 0.80 0.83 2.96 2.69 2.58 2.72

0.0159 4 5.00 100.6 6.73 6.90 7.06 7.03 5.17 5.22 5.30 5.42 0.80 0.83 0.86 0.89 3.22 2.98 2.84 3.11

0.0159 4 4.98 150.9 7.49 7.58 7.69 7.60 5.42 5.38 5.34 5.30 0.12 0.14 0.16 0.18 2.41 2.28 2.13 2.17

0.0159 4 4.98 149.9 7.42 7.55 7.60 7.42 5.53 5.47 5.41 5.35 0.23 0.25 0.27 0.28 2.64 2.41 2.28 2.41

0.0159 4 4.97 151.2 7.17 7.26 7.28 7.11 5.55 5.47 5.39 5.30 0.32 0.34 0.36 0.38 3.07 2.79 2.64 2.76

0.0159 4 5.04 149.5 6.86 7.06 7.16 6.88 5.44 5.34 5.22 5.11 0.43 0.45 0.47 0.49 3.56 2.93 2.62 2.85

0.0159 4 5.03 149.7 6.57 6.70 6.75 6.49 5.33 5.19 5.03 4.86 0.53 0.55 0.57 0.59 4.09 3.35 2.94 3.11

0.0159 4 4.98 149.8 6.67 6.80 6.83 6.57 5.55 5.33 5.09 4.83 0.63 0.65 0.67 0.69 4.45 3.40 2.87 2.86

0.0159 4 5.01 151.1 6.55 6.66 6.67 6.48 5.47 5.12 4.73 4.29 0.72 0.74 0.76 0.78 4.65 3.26 2.59 2.30

0.0159 4 5.02 199.7 7.39 7.57 7.56 7.33 5.29 5.23 5.17 5.10 0.12 0.13 0.15 0.16 2.40 2.15 2.11 2.26

0.0159 4 5.03 199.3 7.19 7.29 7.22 7.02 5.54 5.44 5.33 5.21 0.22 0.24 0.25 0.27 3.06 2.73 2.67 2.79

A

ppendix B

255

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 4 4.99 200 6.78 6.82 6.77 6.51 5.53 5.39 5.23 5.06 0.32 0.34 0.35 0.37 4.02 3.48 3.26 3.47

0.0159 4 5.00 200.3 6.58 6.59 6.46 6.23 5.66 5.46 5.26 5.04 0.42 0.43 0.45 0.46 5.44 4.46 4.19 4.23

0.0159 4 5.02 200.7 6.48 6.48 6.30 6.04 5.78 5.54 5.30 5.05 0.52 0.54 0.55 0.56 7.20 5.40 5.03 5.10

0.0159 4 10.0 75.2 9.26 9.60 9.70 9.65 4.63 4.62 4.59 4.57 0.18 0.26 0.34 0.42 2.17 2.02 1.97 1.98

0.0159 4 10.0 75.5 9.05 9.68 9.73 9.60 4.98 4.96 4.93 4.90 0.28 0.36 0.44 0.52 2.47 2.13 2.10 2.14

0.0159 4 10.0 74.6 9.03 9.55 9.64 9.51 4.87 4.84 4.81 4.78 0.39 0.47 0.55 0.63 2.41 2.13 2.08 2.12

0.0159 4 10.0 75.5 8.81 9.33 9.44 9.47 4.82 4.79 4.75 4.72 0.49 0.57 0.65 0.73 2.52 2.22 2.15 2.12

0.0159 4 10.0 75.4 8.57 9.12 9.43 9.74 4.57 4.53 4.49 4.45 0.59 0.67 0.75 0.83 2.51 2.19 2.04 1.90

0.0159 4 10.1 74.6 8.61 9.16 9.64 9.91 4.63 4.60 4.55 4.50 0.67 0.75 0.83 0.91 2.53 2.21 1.98 1.86

0.0159 4 10.0 101.1 9.07 9.46 9.76 9.47 4.90 4.87 4.84 4.81 0.16 0.22 0.28 0.34 2.41 2.19 2.04 2.15

0.0159 4 10.0 101.5 8.88 9.14 9.37 9.23 4.85 4.82 4.78 4.74 0.26 0.32 0.38 0.44 2.49 2.32 2.18 2.23

0.0159 4 10.0 100.9 8.98 9.10 9.32 9.28 5.00 4.96 4.91 4.86 0.37 0.43 0.49 0.54 2.52 2.42 2.28 2.26

0.0159 4 10.0 101.0 8.92 9.09 9.33 9.35 5.06 5.01 4.95 4.90 0.47 0.53 0.59 0.65 2.60 2.46 2.29 2.25

0.0159 4 10.0 99.8 8.54 8.83 9.09 9.18 4.83 4.77 4.73 4.70 0.57 0.63 0.69 0.75 2.71 2.48 2.30 2.24

0.0159 4 10.0 101.0 8.42 8.71 9.09 9.20 4.82 4.79 4.79 4.83 0.67 0.73 0.79 0.85 2.79 2.56 2.34 2.30

0.0159 4 10.0 100.8 8.23 8.48 8.97 9.53 4.70 4.73 4.82 5.01 0.77 0.83 0.89 0.95 2.83 2.67 2.42 2.21

0.0159 4 10.0 150 8.88 9.01 9.19 9.21 5.14 5.10 5.04 4.98 0.15 0.19 0.23 0.27 2.69 2.57 2.42 2.38

0.0159 4 10.1 149.5 8.94 9.06 9.23 9.11 5.36 5.29 5.22 5.14 0.25 0.29 0.33 0.37 2.82 2.67 2.51 2.54

0.0159 4 10.0 150.5 8.44 8.56 8.70 8.56 5.23 5.14 5.05 4.94 0.35 0.39 0.43 0.47 3.14 2.94 2.75 2.77

0.0159 4 10.0 150 8.23 8.24 8.41 8.17 5.33 5.22 5.09 4.93 0.45 0.49 0.53 0.57 3.47 3.33 3.02 3.11

0.0159 4 10.0 150.6 8.07 8.14 8.32 8.08 5.37 5.21 5.02 4.79 0.55 0.59 0.63 0.67 3.73 3.44 3.05 3.06

0.0159 4 10.0 150.5 8.00 8.04 8.22 8.03 5.43 5.18 4.87 4.49 0.65 0.69 0.73 0.77 3.90 3.50 3.00 2.83

0.0159 4 10.0 150.5 7.53 7.59 7.75 7.68 5.01 4.58 4.04 3.37 0.75 0.79 0.83 0.87 4.00 3.35 2.71 2.34

0.0159 4 10.0 150.2 7.60 7.71 7.97 7.93 5.01 4.43 3.70 2.79 0.81 0.85 0.89 0.93 3.89 3.07 2.36 1.95

0.0159 4 10.0 200.7 9.16 9.23 9.35 9.07 5.38 5.31 5.23 5.14 0.13 0.16 0.19 0.22 2.66 2.56 2.44 2.56

0.0159 4 10.1 199.7 8.46 8.50 8.59 8.30 5.31 5.20 5.07 4.93 0.23 0.26 0.29 0.32 3.21 3.06 2.87 3.00

0.0159 4 10.0 200.8 7.93 7.93 8.04 7.74 5.33 5.17 4.99 4.80 0.33 0.36 0.39 0.42 3.89 3.65 3.31 3.42

0.0159 4 10.0 201.7 7.60 7.50 7.54 7.25 5.41 5.20 4.97 4.73 0.43 0.46 0.49 0.52 4.59 4.38 3.91 3.98

256

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 4 10.0 200.7 7.66 7.55 7.59 7.31 5.74 5.49 5.23 4.97 0.54 0.57 0.59 0.62 5.25 4.89 4.28 4.30

0.0159 3 4.99 75.1 8.06 8.07 8.13 7.83 5.25 5.23 5.20 5.18 0.15 0.19 0.23 0.26 1.78 1.76 1.71 1.89

0.0159 3 5.02 75.2 7.59 7.69 7.79 7.68 5.32 5.29 5.27 5.24 0.25 0.29 0.33 0.37 2.22 2.10 2.00 2.06

0.0159 3 4.99 74.9 7.44 7.53 7.74 7.60 5.25 5.22 5.20 5.17 0.35 0.39 0.43 0.47 2.29 2.17 1.97 2.05

0.0159 3 4.99 75.0 7.35 7.53 7.70 7.55 5.21 5.18 5.14 5.11 0.45 0.49 0.53 0.57 2.34 2.13 1.96 2.05

0.0159 3 4.99 75.3 7.04 7.15 7.33 7.29 4.93 4.89 4.85 4.81 0.55 0.59 0.63 0.67 2.36 2.21 2.02 2.02

0.0159 3 4.98 75.3 7.25 7.51 7.69 7.63 5.15 5.11 5.07 5.02 0.65 0.69 0.73 0.77 2.38 2.08 1.90 1.91

0.0159 3 4.98 74.9 6.98 7.26 7.49 7.46 4.89 4.85 4.80 4.75 0.75 0.79 0.83 0.87 2.39 2.07 1.85 1.84

0.0159 3 5.03 100.9 7.59 7.68 7.79 7.56 5.20 5.17 5.14 5.11 0.13 0.16 0.19 0.22 2.11 2.01 1.91 2.06

0.0159 3 5.00 100.9 7.32 7.52 7.64 7.41 5.24 5.20 5.16 5.12 0.23 0.26 0.29 0.32 2.40 2.16 2.02 2.19

0.0159 3 5.00 100.6 7.25 7.41 7.49 7.33 5.18 5.14 5.09 5.04 0.33 0.36 0.39 0.42 2.42 2.20 2.09 2.19

0.0159 3 5.02 100.4 7.20 7.34 7.43 7.28 5.17 5.12 5.07 5.01 0.44 0.47 0.50 0.53 2.48 2.27 2.13 2.22

0.0159 3 4.98 100.5 7.27 7.44 7.50 7.36 5.35 5.30 5.24 5.19 0.54 0.57 0.59 0.62 2.61 2.33 2.22 2.31

0.0159 3 5.00 99.48 6.88 7.10 7.17 7.01 5.15 5.11 5.07 5.05 0.64 0.67 0.70 0.73 2.91 2.52 2.39 2.55

0.0159 3 5.01 99.7 6.76 7.01 7.11 7.00 5.23 5.22 5.24 5.28 0.75 0.78 0.81 0.84 3.28 2.82 2.69 2.94

0.0159 3 4.97 100.4 6.71 7.02 7.13 7.15 5.32 5.38 5.48 5.62 0.84 0.87 0.90 0.93 3.57 3.06 3.04 3.27

0.0159 3 4.98 150.3 7.49 7.61 7.68 7.44 5.40 5.35 5.30 5.25 0.12 0.14 0.16 0.18 2.38 2.21 2.10 2.28

0.0159 3 5.00 149.8 7.21 7.29 7.33 7.12 5.36 5.29 5.22 5.14 0.23 0.25 0.27 0.28 2.71 2.51 2.37 2.53

0.0159 3 5.03 149.5 7.15 7.23 7.21 7.00 5.50 5.41 5.31 5.21 0.33 0.35 0.37 0.39 3.05 2.77 2.66 2.82

0.0159 3 5.01 149.4 6.79 6.89 6.90 6.68 5.50 5.36 5.20 5.01 0.42 0.44 0.46 0.48 3.89 3.27 2.95 3.00

0.0159 3 5.00 151.2 6.57 6.67 6.68 6.41 5.43 5.13 4.76 4.32 0.52 0.54 0.56 0.58 4.42 3.25 2.61 2.40

0.0159 3 5.01 200.6 7.48 7.56 7.58 7.26 5.48 5.41 5.34 5.26 0.12 0.13 0.15 0.16 2.51 2.35 2.25 2.51

0.0159 3 5.01 199.5 6.88 6.91 6.88 6.62 5.34 5.22 5.09 4.96 0.22 0.24 0.25 0.27 3.26 2.98 2.81 3.03

0.0159 3 5.02 199.9 6.80 6.86 6.78 6.52 5.67 5.50 5.32 5.14 0.32 0.33 0.35 0.36 4.46 3.70 3.46 3.64

0.0159 3 4.99 200.5 6.58 6.63 6.51 6.22 5.80 5.59 5.36 5.14 0.42 0.43 0.45 0.46 6.39 4.81 4.37 4.63

0.0159 3 4.98 199.3 7.59 7.71 7.55 7.49 5.48 5.41 5.34 5.26 0.12 0.14 0.15 0.17 2.37 2.18 2.26 2.24

0.0159 3 5.02 200.2 7.08 7.09 7.11 6.89 5.53 5.41 5.29 5.15 0.22 0.24 0.25 0.27 3.26 3.01 2.77 2.90

0.0159 3 5.00 200.2 6.71 6.66 6.63 6.43 5.56 5.39 5.22 5.03 0.32 0.33 0.35 0.36 4.39 3.95 3.55 3.58

A

ppendix B

257

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 3 5.02 200.4 6.73 6.72 6.73 6.43 5.80 5.60 5.40 5.20 0.37 0.38 0.40 0.41 5.38 4.51 3.81 4.10

0.0159 3 10.0 75.4 9.40 9.17 9.08 9.37 4.55 4.52 4.49 4.47 0.18 0.26 0.34 0.42 2.07 2.16 2.19 2.04

0.0159 3 10.0 74.9 9.20 9.29 9.34 9.55 4.77 4.74 4.71 4.68 0.29 0.37 0.45 0.53 2.26 2.20 2.16 2.05

0.0159 3 10.0 75.2 9.20 9.29 9.37 9.63 4.84 4.81 4.77 4.74 0.38 0.46 0.54 0.62 2.30 2.24 2.18 2.05

0.0159 3 10.0 75.4 8.84 8.86 9.11 9.53 4.54 4.50 4.46 4.42 0.49 0.57 0.65 0.73 2.34 2.31 2.16 1.97

0.0159 3 10.0 75.0 8.86 9.05 9.39 9.83 4.56 4.51 4.47 4.42 0.59 0.67 0.75 0.83 2.34 2.22 2.04 1.86

0.0159 3 10.0 75.3 8.34 8.90 9.34 10.9 4.12 4.07 4.02 3.97 0.69 0.77 0.84 0.92 2.38 2.08 1.89 1.44

0.0159 3 10.0 99.96 9.18 9.37 9.43 9.41 4.99 4.96 4.92 4.88 0.16 0.22 0.28 0.34 2.39 2.27 2.22 2.21

0.0159 3 10.0 99.87 8.85 9.18 9.22 9.27 4.93 4.89 4.85 4.80 0.26 0.32 0.38 0.44 2.56 2.34 2.29 2.24

0.0159 3 10.0 99.98 8.92 9.07 9.11 9.24 4.99 4.94 4.89 4.83 0.37 0.43 0.49 0.55 2.57 2.44 2.38 2.28

0.0159 3 10.0 99.87 8.53 8.83 8.85 8.99 4.78 4.72 4.67 4.61 0.47 0.53 0.59 0.65 2.69 2.45 2.41 2.30

0.0159 3 10.0 100.6 8.58 9.07 9.11 9.23 5.04 4.98 4.94 4.91 0.57 0.63 0.69 0.75 2.84 2.46 2.41 2.33

0.0159 3 10.0 100.2 8.35 8.92 9.10 9.19 4.97 4.94 4.93 4.97 0.67 0.73 0.79 0.85 2.98 2.53 2.42 2.39

0.0159 3 10.0 100.5 8.09 8.65 8.96 9.80 4.83 4.85 4.92 5.06 0.77 0.83 0.89 0.95 3.08 2.64 2.48 2.12

0.0159 3 10.0 150.4 8.79 8.98 9.01 8.80 5.07 5.02 4.95 4.88 0.14 0.18 0.22 0.26 2.71 2.54 2.48 2.57

0.0159 3 10.0 149.5 8.78 8.98 8.94 8.77 5.29 5.21 5.13 5.04 0.24 0.28 0.32 0.36 2.88 2.66 2.63 2.69

0.0159 3 10.0 149.9 8.28 8.48 8.39 8.26 5.17 5.07 4.95 4.80 0.34 0.38 0.42 0.46 3.22 2.94 2.92 2.90

0.0159 3 10.0 150.6 7.97 8.22 8.20 8.02 5.27 5.09 4.84 4.49 0.45 0.49 0.53 0.57 3.74 3.22 3.00 2.85

0.0159 3 10.0 150.2 7.75 8.00 7.97 7.78 5.13 4.73 4.16 3.35 0.54 0.58 0.62 0.66 3.85 3.09 2.64 2.27

0.0159 3 10.0 200.9 8.51 8.41 8.32 8.31 5.20 5.12 5.02 4.92 0.13 0.16 0.19 0.22 3.03 3.06 3.06 2.97

0.0159 3 10.0 199.7 8.10 8.09 8.00 7.91 5.32 5.19 5.04 4.87 0.24 0.27 0.30 0.33 3.61 3.47 3.40 3.31

0.0159 3 10.0 199.7 7.78 7.88 7.76 7.56 5.40 5.21 5.01 4.80 0.34 0.37 0.39 0.42 4.23 3.78 3.66 3.65

0.0159 3 10.1 200.1 7.71 7.80 7.67 7.40 5.68 5.45 5.21 4.96 0.44 0.47 0.50 0.52 4.97 4.30 4.10 4.13

0.0159 3 10.0 200.3 7.64 7.73 7.60 7.29 5.80 5.55 5.28 4.99 0.52 0.55 0.58 0.61 5.49 4.62 4.35 4.40

258

Appendix B

Table B.8 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 15 oC measured at each section of the of the test section inside 15.9 mm internal diameter tube.

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 Plain tube 9.95 74.9 21.5 22.0 22.6 23.4 14.3 14.3 14.3 14.3 0.10 0.18 0.27 0.35 1.39 1.29 1.21 1.09

0.0159 Plain tube 9.98 75.1 21.7 22.2 22.5 23.3 14.1 14.1 14.1 14.1 0.16 0.24 0.33 0.41 1.32 1.23 1.19 1.08

0.0159 Plain tube 9.98 75.1 22.3 22.8 23.1 24.1 14.3 14.3 14.3 14.3 0.22 0.30 0.39 0.47 1.26 1.19 1.14 1.03

0.0159 Plain tube 10.00 75.3 22.2 22.6 22.9 23.8 14.1 14.1 14.1 14.1 0.28 0.36 0.44 0.53 1.23 1.17 1.14 1.03

0.0159 Plain tube 9.99 75.3 22.4 22.8 23.4 24.3 14.2 14.2 14.2 14.2 0.38 0.46 0.55 0.63 1.22 1.16 1.08 0.99

0.0159 Plain tube 9.99 75.2 22.3 22.9 23.7 23.9 13.9 13.9 13.9 13.9 0.47 0.56 0.64 0.72 1.19 1.12 1.03 1.00

0.0159 Plain tube 10.04 75.7 22.4 22.9 24.0 25.4 13.7 13.7 13.7 13.7 0.58 0.66 0.74 0.82 1.15 1.09 0.98 0.86

0.0159 Plain tube 9.94 74.4 22.4 22.9 23.8 24.4 13.6 13.6 13.6 13.6 0.60 0.69 0.77 0.85 1.13 1.07 0.98 0.92

0.0159 Plain tube 10.06 76.5 22.9 23.7 25.2 23.1 14.0 14.0 14.0 14.0 0.65 0.73 0.81 0.89 1.13 1.04 0.90 1.11

0.0159 Plain tube 9.99 100.1 22.0 22.3 22.6 22.7 14.8 14.8 14.8 14.8 0.10 0.16 0.23 0.29 1.39 1.32 1.28 1.25

0.0159 Plain tube 9.96 99.59 21.8 22.1 22.3 22.3 14.5 14.5 14.5 14.5 0.14 0.20 0.26 0.33 1.36 1.31 1.28 1.27

0.0159 Plain tube 9.98 100.1 21.7 21.8 22.2 22.4 14.5 14.5 14.5 14.5 0.21 0.27 0.33 0.39 1.41 1.37 1.30 1.26

0.0159 Plain tube 9.93 99.98 21.6 21.7 22.1 22.3 14.5 14.5 14.5 14.5 0.31 0.37 0.43 0.50 1.40 1.38 1.30 1.27

0.0159 Plain tube 9.88 100.8 21.6 21.7 22.2 22.4 14.5 14.5 14.5 14.5 0.41 0.47 0.53 0.59 1.39 1.36 1.28 1.24

0.0159 Plain tube 9.93 99.89 21.9 22.0 22.5 22.7 14.5 14.5 14.5 14.5 0.51 0.57 0.63 0.69 1.35 1.32 1.25 1.21

0.0159 Plain tube 9.91 99.95 21.9 22.1 22.6 22.8 14.5 14.4 14.4 14.4 0.61 0.67 0.73 0.79 1.33 1.30 1.22 1.18

0.0159 Plain tube 9.93 100.7 21.9 22.0 22.6 23.0 14.4 14.4 14.3 14.3 0.68 0.74 0.80 0.86 1.33 1.29 1.21 1.15

0.0159 Plain tube 9.97 99.65 21.7 22.0 22.7 23.9 14.2 14.1 14.1 14.1 0.75 0.81 0.87 0.93 1.32 1.28 1.17 1.02

0.0159 Plain tube 10.0 150.4 21.1 21.2 21.4 21.4 14.7 14.7 14.7 14.7 0.08 0.12 0.16 0.20 1.55 1.54 1.48 1.49

0.0159 Plain tube 9.9 150.2 21.2 21.1 21.2 21.3 14.7 14.7 14.7 14.7 0.14 0.18 0.22 0.26 1.54 1.55 1.52 1.50

0.0159 Plain tube 9.9 150.6 21.3 21.3 21.6 21.5 14.9 14.9 14.9 14.9 0.24 0.28 0.32 0.36 1.55 1.56 1.49 1.51

0.0159 Plain tube 9.9 150.1 21.5 21.5 21.7 21.6 14.9 14.9 14.9 14.9 0.34 0.38 0.42 0.46 1.52 1.51 1.46 1.48

0.0159 Plain tube 10.0 149.6 21.5 21.4 21.7 21.4 14.8 14.8 14.8 14.7 0.44 0.48 0.52 0.56 1.50 1.50 1.44 1.50

0.0159 Plain tube 10.0 149.4 21.4 21.3 21.5 21.2 14.9 14.9 14.9 14.9 0.54 0.58 0.62 0.66 1.55 1.58 1.53 1.59

0.0159 Plain tube 10.0 149.8 20.8 20.7 20.8 20.6 14.9 14.8 14.8 14.8 0.64 0.68 0.72 0.76 1.68 1.72 1.67 1.72

0.0159 Plain tube 10.0 149.6 21.3 21.0 20.9 20.8 14.9 14.8 14.8 14.8 0.74 0.78 0.82 0.86 1.56 1.61 1.64 1.66

A

ppendix B

259

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 Plain tube 10.0 150.1 20.4 20.3 20.3 20.6 14.8 14.8 14.8 14.8 0.82 0.86 0.90 0.94 1.80 1.84 1.81 1.71

0.0159 Plain tube 10.0 200 19.1 19.1 19.2 19.0 15.4 15.3 15.3 15.2 0.13 0.17 0.20 0.23 2.72 2.62 2.52 2.63

0.0159 Plain tube 10.0 200.9 18.5 18.6 18.7 18.5 15.3 15.3 15.2 15.1 0.24 0.27 0.30 0.33 3.19 3.01 2.89 2.92

0.0159 Plain tube 10.0 201.2 18.2 18.3 18.4 18.3 15.5 15.4 15.3 15.2 0.33 0.37 0.40 0.43 3.73 3.43 3.24 3.21

0.0159 Plain tube 10.0 200.7 17.9 18.1 18.1 17.9 15.5 15.4 15.3 15.2 0.44 0.47 0.50 0.53 4.23 3.73 3.56 3.66

0.0159 Plain tube 10.1 200.6 17.4 17.6 17.6 17.4 15.3 15.3 15.3 15.4 0.54 0.57 0.60 0.64 4.81 4.38 4.37 4.89

0.0159 14 10.0 75.0 20.4 20.9 21.8 21.3 14.6 14.6 14.6 14.6 0.19 0.27 0.35 0.44 1.73 1.59 1.40 1.51

0.0159 14 10.0 74.4 20.4 21.1 21.8 21.5 14.8 14.8 14.8 14.8 0.29 0.38 0.46 0.54 1.79 1.59 1.43 1.49

0.0159 14 10.0 74.9 20.4 20.9 21.8 21.6 14.7 14.7 14.7 14.7 0.39 0.47 0.55 0.64 1.77 1.62 1.40 1.46

0.0159 14 10.0 75.0 20.7 21.0 22.1 21.8 14.5 14.5 14.5 14.5 0.49 0.57 0.65 0.74 1.64 1.56 1.32 1.38

0.0159 14 10.0 75.2 21.2 21.2 22.5 22.0 14.6 14.6 14.6 14.6 0.59 0.67 0.75 0.83 1.53 1.53 1.26 1.36

0.0159 14 10.0 75.0 21.7 21.4 23.3 23.6 14.2 14.2 14.2 14.2 0.68 0.77 0.85 0.93 1.33 1.40 1.10 1.07

0.0159 14 10.1 100.1 20.3 20.7 20.9 20.5 15.0 14.9 14.9 14.9 0.17 0.23 0.29 0.35 1.90 1.75 1.68 1.79

0.0159 14 10.0 100.5 19.7 20.3 20.7 20.3 14.9 14.9 14.9 14.9 0.26 0.33 0.39 0.45 2.09 1.85 1.73 1.85

0.0159 14 10.0 101.3 20.0 20.5 20.7 20.2 14.8 14.8 14.7 14.7 0.37 0.43 0.49 0.55 1.93 1.75 1.69 1.81

0.0159 14 10.0 99.6 20.3 20.6 20.9 20.3 14.9 14.9 14.8 14.8 0.47 0.53 0.59 0.66 1.86 1.74 1.66 1.82

0.0159 14 10.0 100.9 20.2 20.4 20.8 20.2 14.8 14.8 14.7 14.7 0.56 0.62 0.69 0.75 1.84 1.79 1.66 1.82

0.0159 14 10.0 100.0 20.7 20.4 21.1 20.6 14.7 14.6 14.6 14.6 0.66 0.72 0.79 0.85 1.67 1.74 1.55 1.69

0.0159 14 10.0 99.5 21.7 20.4 21.7 21.3 14.6 14.6 14.6 14.6 0.77 0.83 0.90 0.96 1.42 1.72 1.41 1.49

0.0159 14 10.0 150.5 19.2 19.8 19.8 19.7 15.0 15.0 15.0 15.0 0.15 0.19 0.23 0.27 2.38 2.09 2.10 2.10

0.0159 14 10.0 150.2 19.0 19.5 19.4 19.4 15.0 15.0 15.0 14.9 0.25 0.29 0.33 0.37 2.50 2.21 2.28 2.23

0.0159 14 10.0 149.8 19.0 19.4 19.2 19.3 15.1 15.1 15.0 15.0 0.35 0.39 0.43 0.47 2.57 2.33 2.40 2.31

0.0159 14 10.0 150.2 18.8 19.2 19.0 19.1 15.0 14.9 14.9 14.7 0.45 0.49 0.53 0.57 2.66 2.39 2.41 2.32

0.0159 14 10.0 150.2 18.7 19.0 18.9 18.9 15.0 14.8 14.6 14.4 0.54 0.59 0.63 0.67 2.68 2.42 2.36 2.20

0.0159 14 10.0 150.7 18.3 18.6 18.6 18.6 14.6 14.3 13.9 13.3 0.65 0.69 0.73 0.77 2.73 2.36 2.12 1.87

0.0159 14 10.0 151.1 18.3 18.9 18.9 19.0 14.7 14.1 13.2 12.0 0.74 0.78 0.82 0.86 2.77 2.09 1.75 1.43

0.0159 14 10.0 149.3 17.8 18.3 18.5 18.7 13.9 12.5 10.8 8.4 0.85 0.89 0.93 0.97 2.57 1.73 1.29 0.98

0.0159 14 10.0 200.4 18.9 19.4 19.3 19.3 15.0 15.0 14.9 14.9 0.14 0.17 0.20 0.23 2.57 2.25 2.30 2.31

260

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 14 9.9 200.4 18.9 19.4 19.4 19.3 15.3 15.3 15.2 15.2 0.23 0.26 0.29 0.33 2.78 2.44 2.42 2.44

0.0159 14 10.0 200 18.3 18.8 18.8 18.7 15.1 15.0 14.9 14.9 0.34 0.37 0.41 0.44 3.06 2.65 2.63 2.62

0.0159 14 10.1 199.1 18.1 18.6 18.6 18.5 15.1 15.0 14.9 14.8 0.44 0.47 0.50 0.54 3.34 2.80 2.79 2.78

0.0159 14 10.0 200.5 18.2 18.6 18.6 18.5 15.4 15.3 15.2 15.0 0.54 0.57 0.60 0.63 3.62 3.09 2.93 2.89

0.0159 14 10.0 201.1 17.9 18.2 18.3 18.1 15.3 15.1 14.8 14.6 0.64 0.67 0.70 0.73 3.79 3.18 2.94 2.81

0.0159 14 10.0 199.9 17.8 18.1 18.2 18.1 15.2 14.9 14.5 14.0 0.73 0.77 0.80 0.83 3.84 3.09 2.69 2.46

0.0159 14 10.0 200.7 17.3 17.7 17.9 17.9 14.6 14.1 13.4 12.6 0.83 0.86 0.89 0.93 3.82 2.76 2.24 1.89

0.0159 9 9.99 75.3 21.2 21.7 22.3 23.1 14.7 14.7 14.6 14.6 0.19 0.27 0.35 0.43 1.53 1.42 1.32 1.19

0.0159 9 9.98 75.0 21.4 21.7 22.8 23.1 14.6 14.6 14.6 14.6 0.29 0.37 0.45 0.53 1.46 1.41 1.22 1.18

0.0159 9 10.03 75.2 21.4 21.6 22.9 23.1 14.6 14.6 14.5 14.5 0.39 0.47 0.55 0.64 1.46 1.43 1.20 1.17

0.0159 9 10.04 75.0 21.2 21.6 23.2 23.5 14.1 14.1 14.1 14.1 0.49 0.57 0.65 0.74 1.41 1.33 1.10 1.07

0.0159 9 9.98 74.9 21.5 22.1 23.6 24.4 14.3 14.2 14.2 14.2 0.59 0.67 0.75 0.84 1.39 1.27 1.07 0.98

0.0159 9 10.0 99.9 20.6 20.6 21.0 21.4 15.0 15.0 14.9 14.9 0.17 0.23 0.29 0.35 1.79 1.77 1.66 1.56

0.0159 9 10.0 100.1 20.8 20.5 21.0 21.2 14.9 14.9 14.9 14.8 0.27 0.33 0.39 0.45 1.70 1.77 1.63 1.58

0.0159 9 10.0 100.9 21.0 20.5 20.9 20.9 14.9 14.9 14.9 14.8 0.36 0.42 0.49 0.55 1.66 1.78 1.67 1.66

0.0159 9 10.1 100.1 20.7 20.5 20.8 20.4 14.9 14.8 14.8 14.8 0.47 0.53 0.59 0.66 1.73 1.80 1.69 1.80

0.0159 9 10.1 100.6 19.8 20.1 20.4 20.0 14.7 14.7 14.7 14.7 0.57 0.63 0.70 0.76 1.98 1.88 1.77 1.87

0.0159 9 10.0 100.6 19.2 20.0 20.6 20.2 14.6 14.6 14.6 14.5 0.67 0.73 0.79 0.85 2.19 1.85 1.67 1.79

0.0159 9 10.1 99.5 19.3 20.6 21.9 22.5 14.7 14.7 14.7 14.7 0.77 0.83 0.89 0.95 2.17 1.70 1.39 1.29

0.0159 9 10.0 150.4 19.8 19.6 19.8 20.0 15.1 15.1 15.1 15.1 0.14 0.18 0.22 0.27 2.15 2.23 2.13 2.04

0.0159 9 10.0 149.9 19.6 19.3 19.5 19.6 15.2 15.2 15.1 15.1 0.25 0.29 0.33 0.37 2.29 2.44 2.32 2.26

0.0159 9 10.0 150.4 18.7 18.8 18.9 19.0 15.0 14.9 14.9 14.9 0.35 0.39 0.44 0.48 2.68 2.63 2.54 2.42

0.0159 9 10.1 150.7 18.4 18.8 19.0 19.0 15.1 15.0 15.0 15.0 0.45 0.49 0.53 0.57 3.02 2.68 2.53 2.50

0.0159 9 10.0 149.8 18.2 18.6 18.9 18.9 15.1 15.1 15.0 15.0 0.55 0.59 0.63 0.67 3.27 2.81 2.60 2.58

0.0159 9 10.0 148.7 18.1 18.6 18.9 18.9 15.1 15.1 15.1 15.1 0.66 0.70 0.74 0.78 3.40 2.91 2.65 2.64

0.0159 9 10.0 149.5 17.9 18.4 18.5 18.6 15.1 15.1 15.1 15.1 0.75 0.79 0.83 0.87 3.53 3.01 2.93 2.84

0.0159 9 10.0 147.6 17.9 18.4 18.8 19.2 14.9 14.9 15.0 15.0 0.85 0.89 0.93 0.98 3.42 2.92 2.60 2.41

0.0159 9 10.0 200.4 19.3 19.1 19.2 19.2 15.1 15.0 15.0 15.0 0.13 0.17 0.20 0.23 2.39 2.49 2.38 2.36

A

ppendix B

261

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

h [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 9 10.0 200.8 18.9 18.8 18.9 18.9 15.2 15.1 15.1 15.0 0.23 0.26 0.30 0.33 2.70 2.75 2.67 2.59

0.0159 9 9.9 200.9 18.4 18.3 18.4 18.5 15.2 15.1 15.1 15.0 0.33 0.37 0.40 0.43 3.07 3.12 2.95 2.81

0.0159 9 9.8 202.2 17.9 17.8 18.0 18.0 15.0 15.0 14.9 14.8 0.43 0.46 0.49 0.52 3.45 3.50 3.15 3.06

0.0159 9 10.0 200.4 18.1 18.4 18.4 18.2 15.3 15.2 15.1 15.0 0.54 0.57 0.61 0.64 3.56 3.20 3.04 3.08

0.0159 9 10.0 200.6 17.9 18.2 18.2 18.0 15.2 15.1 15.0 14.8 0.63 0.67 0.70 0.73 3.71 3.26 3.15 3.16

0.0159 9 10.0 200.1 17.8 18.0 18.0 17.9 15.3 15.2 15.1 14.9 0.74 0.77 0.80 0.83 4.08 3.49 3.36 3.36

0.0159 9 9.9 199.5 17.7 18.1 18.2 18.1 15.4 15.3 15.2 15.1 0.83 0.86 0.89 0.92 4.29 3.51 3.37 3.37

0.0159 9 10.0 199.8 17.5 18.1 18.2 18.1 15.3 15.2 15.2 15.1 0.88 0.92 0.95 0.98 4.49 3.51 3.36 3.37

0.0159 4 10.1 74.8 19.6 19.8 20.3 20.6 14.7 14.7 14.7 14.7 0.19 0.27 0.35 0.44 2.05 1.96 1.80 1.70

0.0159 4 10.0 75.0 19.2 20.0 20.5 20.6 14.6 14.6 14.6 14.5 0.29 0.38 0.46 0.54 2.16 1.86 1.70 1.66

0.0159 4 10.0 75.0 19.3 20.1 20.6 20.5 14.7 14.7 14.6 14.6 0.38 0.47 0.55 0.63 2.18 1.83 1.67 1.70

0.0159 4 10.0 75.0 19.3 20.0 20.3 20.5 14.8 14.8 14.7 14.7 0.49 0.57 0.66 0.74 2.23 1.92 1.80 1.74

0.0159 4 10.0 74.7 19.0 19.8 20.1 20.2 14.6 14.6 14.5 14.5 0.59 0.67 0.76 0.84 2.27 1.91 1.81 1.76

0.0159 4 10.0 99.4 19.1 19.4 19.6 19.7 15.0 15.0 14.9 14.9 0.17 0.23 0.29 0.35 2.42 2.27 2.15 2.12

0.0159 4 10.1 100.5 18.9 19.2 19.4 19.4 14.9 14.9 14.9 14.9 0.27 0.33 0.39 0.45 2.56 2.38 2.26 2.22

0.0159 4 10.0 100.4 18.7 19.0 19.2 19.2 14.8 14.8 14.7 14.7 0.37 0.43 0.49 0.55 2.58 2.35 2.25 2.21

0.0159 4 10.0 99.8 18.7 18.9 19.2 19.3 14.8 14.8 14.8 14.7 0.47 0.53 0.59 0.66 2.60 2.44 2.27 2.20

0.0159 4 10.1 100.7 18.8 19.0 19.4 19.5 15.0 14.9 14.9 14.9 0.57 0.63 0.69 0.76 2.67 2.46 2.28 2.19

0.0159 4 10.0 99.6 18.5 18.9 19.3 19.6 14.8 14.8 14.9 15.0 0.67 0.74 0.80 0.86 2.73 2.46 2.26 2.18

0.0159 4 10.0 100.7 18.2 18.6 19.2 19.6 14.6 14.6 14.7 15.0 0.77 0.83 0.89 0.95 2.77 2.52 2.28 2.17

0.0159 4 10.1 151 18.7 19.0 19.2 19.4 15.1 15.1 15.1 15.0 0.14 0.18 0.23 0.27 2.80 2.57 2.43 2.33

0.0159 4 10.1 150.1 18.5 18.6 18.8 18.9 15.0 15.0 14.9 14.8 0.25 0.29 0.33 0.37 2.86 2.78 2.59 2.51

0.0159 4 10.0 151.5 18.5 18.7 19.0 19.0 15.3 15.2 15.2 15.1 0.35 0.39 0.43 0.47 3.13 2.90 2.66 2.61

0.0159 4 10.0 150.5 18.0 18.2 18.4 18.4 15.1 15.0 15.0 15.0 0.45 0.49 0.53 0.57 3.38 3.20 2.94 2.93

0.0159 4 10.0 149.7 18.1 18.2 18.4 18.5 15.3 15.3 15.5 15.7 0.55 0.59 0.63 0.67 3.63 3.52 3.37 3.63

0.0159 4 10.1 199.9 19.1 19.1 19.3 19.3 15.4 15.3 15.3 15.2 0.13 0.17 0.20 0.23 2.72 2.64 2.53 2.47

0.0159 4 10.0 200.9 18.4 18.5 18.6 18.6 15.2 15.1 15.1 15.0 0.23 0.26 0.29 0.33 3.11 2.99 2.81 2.79

0.0159 4 10.0 200 18.1 18.1 18.3 18.2 15.3 15.2 15.1 15.0 0.34 0.37 0.40 0.43 3.52 3.42 3.14 3.13

262

Appendix B

Twall [oC]

Twall [oC]

Twall [oC]

Twall [oC]

Tref [oC]

Tref [oC]

Tref [oC]

Tref [oC]

x [-]

x [-]

x [-]

x [-]

h [kW/m2oC]

h [kW/m2 oC]

h [kW/m2 oC]

H [kW/m2 oC]

D

[m]

y

[-]

[kW/m2]

G

[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.0159 4 10.0 200.6 18.1 18.1 18.3 18.2 15.5 15.4 15.3 15.2 0.43 0.46 0.49 0.52 3.92 3.74 3.39 3.36

0.0159 4 10.0 199.8 17.6 17.6 17.7 17.7 15.3 15.1 15.0 14.7 0.53 0.56 0.60 0.63 4.29 4.05 3.61 3.44

0.0159 4 10.0 201.2 17.6 17.6 17.7 17.6 15.3 15.0 14.7 14.3 0.63 0.66 0.69 0.72 4.43 3.96 3.35 3.01

0.0159 3 9.99 75.6 19.8 19.7 19.7 19.8 14.8 14.8 14.7 14.7 0.19 0.27 0.35 0.44 2.00 2.02 2.02 1.96

0.0159 3 10.0 74.6 19.2 19.6 19.6 19.8 14.7 14.7 14.7 14.6 0.29 0.38 0.46 0.54 2.23 2.05 2.02 1.94

0.0159 3 10.0 75.3 19.0 19.4 19.6 19.5 14.5 14.4 14.4 14.4 0.39 0.48 0.56 0.64 2.19 2.00 1.94 1.95

0.0159 3 10.0 75.1 19.2 19.7 19.9 20.0 14.7 14.7 14.7 14.7 0.49 0.57 0.66 0.74 2.25 2.02 1.94 1.89

0.0159 3 10.0 76.0 19.0 19.5 19.8 19.9 14.7 14.6 14.6 14.6 0.58 0.67 0.75 0.83 2.32 2.07 1.96 1.89

0.0159 3 10.0 75.0 19.1 19.7 20.1 20.3 14.5 14.5 14.5 14.5 0.71 0.80 0.88 0.96 2.17 1.93 1.78 1.71

0.0159 3 10.1 100.0 19.2 19.3 19.2 19.4 14.8 14.8 14.8 14.8 0.17 0.23 0.29 0.35 2.33 2.27 2.27 2.19

0.0159 3 10.0 100.2 18.9 19.3 19.4 19.5 15.0 15.0 14.9 14.9 0.27 0.33 0.39 0.45 2.58 2.33 2.28 2.21

0.0159 3 10.0 100.9 18.7 19.0 19.2 19.4 14.9 14.9 14.9 14.9 0.36 0.43 0.49 0.55 2.62 2.41 2.32 2.22

0.0159 3 10.0 100.4 18.5 18.8 19.1 19.3 14.8 14.8 14.8 15.0 0.47 0.53 0.60 0.66 2.67 2.49 2.38 2.32

0.0159 3 10.0 99.9 18.6 19.0 19.3 19.6 15.0 15.1 15.3 15.7 0.57 0.63 0.69 0.75 2.73 2.52 2.50 2.58

0.0159 3 10.0 150.2 18.8 19.2 19.4 19.2 15.2 15.2 15.1 15.1 0.14 0.18 0.23 0.27 2.78 2.51 2.39 2.48

0.0159 3 10.0 150.1 18.1 18.5 18.7 18.6 14.9 14.9 14.8 14.8 0.25 0.29 0.33 0.37 3.20 2.81 2.61 2.64

0.0159 3 10.0 151.1 18.2 18.6 18.8 18.7 15.3 15.2 15.1 15.1 0.34 0.38 0.43 0.47 3.42 2.96 2.76 2.77

0.0159 3 10.0 150 17.9 18.3 18.4 18.4 15.2 15.1 15.0 15.0 0.45 0.49 0.53 0.57 3.76 3.21 2.97 2.92

0.0159 3 10.0 149.9 17.7 18.1 18.4 18.3 15.2 15.1 15.0 14.9 0.55 0.59 0.63 0.68 4.03 3.37 3.04 2.96

0.0159 3 10.0 149.9 17.7 18.1 18.3 18.3 15.3 15.2 15.0 14.9 0.64 0.68 0.73 0.77 4.11 3.40 3.02 2.88

0.0159 3 10.0 149.7 17.7 18.1 18.4 18.3 15.2 15.0 14.8 14.6 0.75 0.79 0.83 0.87 4.08 3.28 2.84 2.67

0.0159 3 10.0 200 19.1 19.1 19.2 19.0 15.4 15.3 15.3 15.2 0.13 0.17 0.20 0.23 2.72 2.62 2.52 2.63

0.0159 3 10.0 200.9 18.5 18.6 18.7 18.5 15.3 15.3 15.2 15.1 0.24 0.27 0.30 0.33 3.19 3.01 2.89 2.92

0.0159 3 10.0 201.2 18.2 18.3 18.4 18.3 15.5 15.4 15.3 15.2 0.33 0.37 0.40 0.43 3.73 3.43 3.24 3.21

0.0159 3 10.0 200.7 17.9 18.1 18.1 17.9 15.5 15.4 15.3 15.2 0.44 0.47 0.50 0.53 4.23 3.73 3.56 3.66

0.0159 3 10.1 200.6 17.4 17.6 17.6 17.4 15.3 15.3 15.3 15.4 0.54 0.57 0.60 0.64 4.81 4.38 4.37 4.89

0.0159 3 10.0 199.7 17.3 17.5 17.5 17.3 15.5 15.7 16.0 16.4 0.64 0.67 0.70 0.73 5.63 5.60 6.63 11.11

Publications 263

Appendix C – Publications

Personal informations:

Name:Taye Stephen Mogaji

Place and date of birth: Akure,Ondo State,Nigeria, 1974

Academic training and qualifications:

Doctor of Science in Mechanical Engineering Area of concentration;Térmicos e

fluidos., Universidade de São Paulo, São Carlos,Brazil, 2010-2014.

Master’s degree: Master of Engineering in Mechanical Engineering (building Services

Option) - The Federal University of Technology, Akure - Nigéria – 2008.

First degree:Mechanical Engineering:The Federal University of Technology Akure,

Nigeria-2002.

Given below are the journal articles produced during this study:

MOGAJI, T.S., KANIZAWA, F.T., BANDARRA FILHO, E.P. RIBATSKI, G. Experimental study of the effect of twisted-tape inserts on flow boiling heat transfer enhancement and pressure drop penalty. International Journal of Refrigeration, Vol. 36, pp. 504-515, 2013.

MOGAJI, T.S., RIBATSKI, G., Enhancement and prediction of flow boiling heat transfer inside horizontal tubes containing twisted-tape inserts. Proceedings of the 22nd International Congress of Mechanical Engineering November, Ribeirão Preto, SP, Brazil ,COBEM: ISNN 2176-5480, , p. 190-201, 2013

KANIZAWA, F.T., MOGAJI, T.S., RIBATSKI, G Evaluation of the heat transfer enhancement and pressure drop penalty during flow boiling inside tubes containing twisted-tape inserts. Applied Thermal Engineering, 2014 (accepted for publication).

MOGAJI, T.S., RIBATSKI, G. Flow boiling heat transfer enhancement inside horizontal tubes containing twisted-tape inserts. International Journal of Heat and Mass Transfer, 2014 (Under review).

MOGAJI, T.S., KANIZAWA, F.T., BANDARRA FILHO, E.P. RIBATSKI, G. Experimental study of the effect of twisted-tape inserts on flow boiling heat transfer enhancement and pressure drop penalty.Proceedings of ECI 8th International Conference on Boiling and Condensation Heat Transfer, Lausanne, Switzerland (ECI,2012), 2012.

KANIZAWA, F.T., MOGAJI, T.S., RIBATSKI, G. Estudo experimental de transferência de carlor durante escoamento bifásico de R134a em tubo com fita retorcidas. Proceedings of 3o Encontro brasileiro sobre ebulição, condensação e escoamento multifasicos. Curitiba, PR, Brazil;2012.

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