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Navia, Juliana Andrea Niño

Preliminary design methodology for multi fuel gas turbine combustors / Juliana Andrea Niño Navia.

São José dos Campos, 2010.

152f.

Thesis of master in science – Program of Aeronautics and Mechanics Engineering – Field of Aerodynamics, Propulsion, and Energy – Aeronautical Institute of Technology, 2009. Advisor: Prof. Dr. Pedro Teixeira Lacava.

1 .Gas Turbine Combustor. 2. Design methodology. 3. Chemical Reactor Network. I. General Command

for Aerospace Technology. Aeronautics Institute of Technology. Division of Aeronautical and Mechanical

Engineering. II.Title

BIBLIOGRAPHIC REFERENCE

Navia, Juliana Andrea Niño. Preliminary design methodology for multi fuel gas turbine combustor. 2010. 152f. Thesis of master in Aerodynamics, Propulsion, and Energy – Aeronautics Institute of Technology, São José dos Campos.

CESSION OF RIGHTS

AUTHOR NAME: Juliana Andrea Niño Navia

PUBLICATION TITLE: Preliminary design methodology for multi-fuel gas turbine combustor.

PUBLICATION KIND/YEAR: Thesis of master / 2010

It is granted to Aeronautics Institute of Technology permission to reproduce copies of

this thesis to only loan or sell copies for academic and scientific purposes. The author

reserves other publication rights and no part of this thesis can be reproduced without

the authorization of the author.

___________________________

Juliana Andrea Niño Navia

Rua Siria, 95

CEP 12216-530 – São José dos Campos–SP–Brasil

PRELIMINARY DESIGN METHODOLOGY FOR MULTI

FUEL GAS TURBINE COMBUSTORS

Juliana Andrea Niño Navia

Thesis committee composition:

Prof. Dra. Cristiane Aparecida Martins Chairperson - ITA

Prof. Dr. Pedro Texeira Lacava Advisor - ITA

Prof. Dr. Ezio Castejon Garcia Membro - ITA

Prof. Dr. Helder Fernando de Franca Mendes Carneiro

Membro - IAE

Prof. Dr. João Roberto Barbosa Membro - ITA

Prof. Dr. Marco Aurélio Ferreira Membro - INPE

ITA

Dedico este trabajo a mis padres Norberto

and Mercedes, y a mi hermana Aura.

Acknowledgements

First and foremost, I would like thanks to my advisor Prof. Pedro Lacava for his assistance

and guidance through this work, I would also like to thank to Alexandre Alves and Felipe

Tauk for their assistance and help during this work.

I would like thank too Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior

CAPES, for to grant me a scholarship.

Also, I would like express to my acknowledgements to the staff of Department of Graduate

Studies of ITA and professors of the Division of Aeronautical and Mechanical Engineering

for their help.

Finally, I would like to thanks my family and my friends for their support during throughout

my life and this research.

“Nature never breaks her own laws”

– Leonardo da Vinci

Resumo

As câmaras de combustão para turbinas a gás têm sido tradicionalmente projetadas por

tentativa e erro, o qual é um processo que consome tempo e custo. Com o desenvolvimento

dos computadores e novas técnicas de simulação, o desenvolvimento do projeto foi melhorado

consideravelmente, no entanto continua sendo um processo iterativo que requer um amplo

conhecimento das condições de operação do motor e da interação de todos componentes do

motor.

Este trabalho apresenta o estabelecimento de uma metodologia de projeto preliminar para

câmaras de combustão para turbinas a gás baseada na metodologia proposta por Melconian

and Moldak [1] e a aplicação de uma cadeia de reatores químicos (CRN) que tem com

objetivo estabelecer o perfil de temperatura dos gases dentro destes dispositivos.

Tal proposta usa querosene como combustível. Por esta razão, a metodologia apresentada

no presente trabalho foi adaptada para considerar diferentes tipos de combustível, e baseia-se

no estabelecimento de parâmetros geométricos básicos e fornecimento de uma configuração

básica de um combustor considerando as mudanças nas cargas operacionais.

Foram desenvolvidos alguns exemplos, que permitiram verificar a aplicação da

metodologia proposta e da cadeia de reatores. O primeiro caso foi usado como método de

validação empregando-se uma câmara de combustão tipo tubular, que funciona com

querosene como combustível, baseado no exemplo proposto por Melconian e Moldak[1]. O

segundo caso corresponde a um combustor tipo anular para um motor de aviação que

funciona com querosene e etanol. Para cada um desses combustíveis, desenvolveu-se um

projeto preliminar de combustor. O terceiro caso trata de um combustor do tipo anular para

aplicação em turbinas a gás industrial que utilizam gás natural, querosene e etanol como

combustível.

A metodologia de projeto é apresentada passo a passo neste trabalho. É importante

mencionar que a metodologia proposta é para combustores convencionais.

Abstract

The combustors for gas turbines have been traditionally designed through trial and error,

which is a time consuming and expensive process. With the development of computers and

new simulation techniques the design process has been improved considerably. However, the

design of combustors for gas turbines still remains an iterative process, which requires a broad

knowledge of engine operating conditions and the interaction of their components with the

engine components.

This work presents the establishment of a methodology for preliminary design for gas

turbine combustor, based on the methodology proposed by Melconian e Moldak [1] and the

application of a chemical reactors network (CRN), this last one in order to establish the

temperature profile of the gases into combustor.

Originally, the methodology proposed by Melconian e Moldak [1] uses kerosene as fuel.

For this reason, the proposed methodology in this work was adapted to consider different

types of fuel. This methodology is capable to set the basic geometric parameters and

providing a basic configuration of a combustor considering changes in operational loads.

Some cases have been developed, which allowed verifying the implementation of the

proposed methodology and the CRN. The first case was used as validation method and was

employing a multi–can combustor type, which operates with kerosene as fuel based on

example proposed by Melconian e Moldak [1]. The second case corresponds to an annular

combustor for an aircraft engine which operates with kerosene, natural gas and ethanol. For

each of these fuels was carried out a preliminary design of combustor. The third case is a can

annular combustor for application in an industrial gas turbine using natural gas, ethanol and

kerosene as fuels.

A step by step design methodology is presented in this work. It is important to mention

that the proposed methodology is for conventional combustors

Contents

LIST OF FIGURES ............................................................................................................... XI

LIST OF TABLES .............................................................................................................. XIII

LIST OF ABBREVIATIONS AND ACRONYMS ......................................................... XVII

LIST OF SYMBOL ......................................................................................................... XVIII

1 INTRODUCTION ............................................................................................................... 17

1.1 GAS TURBINE COMBUSTOR DESIGN PROCESS .................................................................. 17

1.1.1 Preliminary design ........................................................................................................ 17

1.1.2 Detailed design ............................................................................................................. 19

1.1.3 Rig testing ..................................................................................................................... 19

1.2 OBJECTIVE ........................................................................................................................ 20

1.3 MOTIVATION .................................................................................................................... 20

1.4 DESIGN METHODOLOGIES FOR GAS TURBINE COMBUSTORS .............................................. 21

1.4.1 Empirical methodology ................................................................................................ 21

1.4.2 Semi-empirical methodology ....................................................................................... 22

1.4.3 Semi-analytical methodology ....................................................................................... 23

1.4.4 Analytical methodology ............................................................................................... 23

1.5 THESIS OUTLINE ............................................................................................................... 24

2.1 GAS TURBINE COMBUSTOR ............................................................................................... 25

2.1.1 Combustor types ........................................................................................................... 26

2.1.2 Basic configuration of the combustor ........................................................................... 28

2.2 DESIGN METHODOLOGY.................................................................................................... 31

2.2.1 Theoretical limits for equivalence ratio ........................................................................ 31

2.2.2 Basic dimensions for combustor. ................................................................................. 38

2.2.3 Aerodynamics Considerations ...................................................................................... 40

2.2.4 Chemical Considerations .............................................................................................. 41

2.2.5 Determination of combustor area ................................................................................. 43

2.2.6 Preliminary estimate of air distribution ........................................................................ 44

2.2.7 Length of combustors zones ......................................................................................... 45

2.2.8 Diffuser design ............................................................................................................. 47

2.2.9 Swirler design ............................................................................................................... 50

2.2.10 Recirculation zone ........................................................................................................ 53

2.2.11 Flame temperature calculations .................................................................................... 54

2.2.12 Film cooling .................................................................................................................. 61

2.2.13 Design of air admission holes ....................................................................................... 69

3. METHODOLOGY IMPLEMENTATION ..................... ................................................. 76

3.1 METHODOLOGY STRUCTURE............................................................................................. 76

3.1.1 Theoretical limits for equivalence ratio ........................................................................ 76

3.1.2 Equivalence ratio for primary zone ................................................................................. 79

3.1.4 Calculation of basic dimensions ................................................................................... 79

3.1.5 Calculation of air flow and length of zones .................................................................. 80

3.1.6 Calculation of diffuser parameters ............................................................................... 81

3.1.7 Calculation swirler parameters ..................................................................................... 81

3.1.8 Calculation of recirculation zone .................................................................................. 81

3.1.9 Calculation of flame temperature ................................................................................. 82

3.1.10 Film cooling calculation ............................................................................................... 83

3.1.11 Air admission holes ...................................................................................................... 83

4. VALIDATION AND RESULTS ....................................................................................... 85

4.1 VALIDATION ........................................................................................................................ 85

4.2 RESULTS .............................................................................................................................. 94

4.2.1 Annular combustor operating with kerosene ................................................................... 95

4.2.2 Annular combustion chamber operating with ethanol ................................................... 104

4.2.3 Can-annular combustion chamber operating with natural gas ...................................... 114

4.2.4 Can-annular combustion chamber operating with ethanol ............................................ 122

4.2.5 Can annular combustor operating with kerosene .......................................................... 129

5. CONCLUSIONS ............................................................................................................ 140

BIBLIOGRAPHY ................................................................................................................. 142

List of Figures

FIGURE 2.1 – Cross section of three main combustor type. ................................................... 27

FIGURE 2.2 – Basic combustor features. ................................................................................ 29

FIGURE 2.3 – Flame limit temperature for flammable mixture. ........................................... 332

FIGURE 2.4 – Dref and Dft for flame tube arrangements .......................................................... 39

FIGURE 2.5 – Theta parameter correlation ............................................................................. 42

FIGURE 2.6 – Dilution zone mixing performance .................................................................. 46

FIGURE 2.7 – Basic geometry of combustor ..........................................................................48

FIGURE 2.8 – Swirler basic geometry ..................................................................................... 51

FIGURE 2.9 – Recirculation zone ............................................................................................ 53

FIGURE 2.10 – Diagram of the combustor model ................................................................... 55

FIGURE 2.11 – Perfectly Stirred Reactor (PSR) ..................................................................... 57

FIGURE 2.11 – Perfectly Stirred Reactor (PSR) ..................................................................... 59

FIGURE 2.13 – Film cooling device geometry ........................................................................ 61

FIGURE 2.14 – Heat transfer model for flame tube ................................................................ 65

FIGURE 3.1 – Schematic overview of preliminary desing procedure ..................................... 77

FIGURE 3.2 – Example of adiabatic temperature curves ........................................................ 78

FIGURE 3.3 – Equivalence ratio for primary zone .................................................................. 79

FIGURE 3.4 – Calculation of reference area and flame tube ................................................... 80

FIGURE 3.5 – Calculation of air flow and length of the zones ............................................... 80

FIGURE 3.6 – Calculation of difusser parameters ................................................................... 81

FIGURE 3.7 – Calculations of swirler parameters ................................................................... 81

FIGURE 3.8 – Calculation of recirculation zone ..................................................................... 82

FIGURE 3.9 – Calculation of flame temperature ..................................................................... 82

FIGURE 3.10 – Film cooling calculation ................................................................................. 83

FIGURE 3.11 – Air admission holes ........................................................................................ 89

FIGURE 4.1 – Temperature profiles by Melconian and Modak [1] methodology ..................90

FIGURE 4.2 – Temperature profiles by CRN methodology ...................................................91

FIGURE 4.3 – Temperature profile for annular combustor operating with kerosene .............. 99

FIGURE 4.4 – Temperature profile for annular combustor operating with kerosene ............ 100

FIGURE 4.5 – Temperature profile for annular combustor operating with ethanol .............. 108

FIGURE 4.6 – Temperature profile for annular combustor operating with ethanol .............. 110

FIGURE 4.7– Temperature profile for can-annular combustor operating with natural gas... 118

FIGURE 4.8– Temperature profile for can-annular combustor operating with natural gas... 119

FIGURE 4.9 – Temperature profile for can-annular combustor operating with ethanol ....... 126

FIGURE 4.10 – Temperature profile for can-annular combustor operating with ethanol ..... 134

FIGURE 4.11 – Temperature profile for can-annular combustor operating with kerosene ... 134

FIGURE 4.12 – Temperature profile for can-annular combustor operating with kerosene ... 134

List of Tables

TABLE 2.1 - Representative values of pressure loss [8]……………………………………. 40

TABLE 2.2 - LDZ/Dft as a function of TQ for different values of pressure loss factor ………47

TABLE 3.1 – Limits for equivalence ratio as function of T3……………………………....... 78

TABLE 4.1– Example operating condition [1]………………………………………………86

TABLE 4.2– Equivalence ratio limits comparison [1]……………………………………….86

TABLE 4.3– Combustor liner airflow and outer casing airflow reference values ………......87

TABLE 4.4 – Combustor liner airflow and outer casing airflow final values ……………….88

TABLE 4.5– Combustor length zone and preliminary air distribution ……………………...88

TABLE 4.6 – Diffuser example parameters …………………………………………………88

TABLE 4.7 – Swirler example parameters …………………………………………………..89

TABLE 4.8 – Temperature profile ……………………………………...……………………91

TABLE 4.9 – Slot position …………………………………………………………………..92

TABLE 4.10 – Wall temperature …………………………………………………………… 93

TABLE 4.11 – Air admission holes parameters……………………………………………. .93

TABLE 4.12 – Operating condition for annular combustor operating with kerosene ……….95

TABLE 4.13 – Theoretical equivalence limits for annular combustor operating with

kerosene………………………………………………………………………………………96

TABLE 4.14 – Combustor liner airflow and outer casing airflow reference values ………...96

TABLE 4.15 – Combustor liner airflow and outer casing airflow final values for annular

combustor ………………………………………………………………………………….....97

TABLE 4.16 – Combustor length zone and preliminary air distribution for annular

combustor……………………………………………………………………………………..97

TABLE 4.17 – Diffuser parameter for annular combustor …………………………………..98

TABLE 4.18 – Swirler parameter for annular combustor …………………………………...98

TABLE 4.19 – Temperature profile …………………………………………...……………100

TABLE 4.20 – Wall temperature ……………………………………………...……………102

TABLE 4.21 – Air admission holes parameters ………………………………..…………. 103

TABLE 4.22 – Air admission holes distribution ……………………………...……………103

TABLE 4.23 – Operating condition for annular combustor operating with ethanol …….....105

TABLE 4.24 – Theoretical limits for annular combustor operating with ethanol ………….105

TABLE 4.25 – Combustor liner airflow and outer casing airflow reference values ……….106


combustor operating with ethanol …………………………………………………………..107

TABLE 4.27– Combustor length zone and preliminary air distribution for natural gas ...…107

TABLE 4.28– Diffuser parameter for annular combustor operating with ethanol …………108

TABLE 4.29 – Temperature profile for annular combustor operating with ethanol …...…109

TABLE 4.30 – Cooling slot position and wall temperature for annular combustor with

operating with ethanol ………………………………………………………………………111

TABLE 4.31 – Air admission holes for annular combustor operating with ethanol …….....112

TABLE 4.32 – Air admission holes distribution for can-annular combustor operating with

ethanol ………………………………………………………………………………………112

TABLE 4.33 – Basic layout for annular combustors ……………………………………...113

TABLE 4.34 – Operating condition for can-annular combustor operating with natural gas..114

TABLE 4.35 – Theoretical limits for annular combustor operating with natural gas ……...115

TABLE 4.36 – Combustor liner airflow and outer casing airflow reference values …..….115

TABLE 4.37 – Combustor liner airflow and outer casing airflow final values for can-annular

combustor operating with natural gas ……………………………………………………..116

TABLE 4.38 – Combustor length zone and preliminary air distribution for can-annular

combustor operating with natural gas …………………………….…...……………………116

TABLE 4.39 – Diffuser parameter for can-annular combustor operating with natural gas ..117

TABLE 4.40– Swirler parameter for can-annular combustor operating with natural gas ….118

TABLE 4.41 – Temperature profile for can annular combustor operating with natural gas .118

TABLE 4.42– Cooling slot position and wall temperature for can-annular combustor with

operating with natural gas …………………………………………………………………..120

TABLE 4.43 – Air admission holes for annular combustor operating with natural gas …....121

TABLE 4.44 – Operating conditions for can-annular combustor operating with ethanol ….122

TABLE 4.45 – Theoretical limits for annular combustor operating with ethanol ………….123


TABLE 4.47– Combustor liner airflow and outer casing airflow final values for can-annular

combustor operating with ethanol …………………………………………….………….…124

TABLE 4.48 – Combustor length zone and preliminary air distribution for can-annular

combustor operating with ethanol…………………………………………………………...124

TABLE 4.49– Diffuser parameter for can-annular combustor operating with ethanol …….125

TABLE 4.50 – Swirler parameter for can-annular combustor operating with ethanol ……..125

TABLE 4.51 – Temperature profile for can annular combustor operating with ethanol

….............................................................................................................................................126


operating with ethanol ………………………………………………………………………128

TABLE 4.53 – Air admission holes for annular combustor operating with ethanol ……… 129

TABLE 4.54 – Operating condition for annular combustor operating with kerosene .……..130

TABLE 4.55 – Theoretical limits for can annular combustor operating with kerosene ……130



combustor operating with kerosene ………………………………………………………...132

TABLE 4.58 – Combustor length zone and preliminary air distribution for kerosene …….132

TABLE 4.59 – Diffuser parameter for can annular combustor operating with kerosene …..133

TABLE 4.60 – Swirler parameter for can annular combustor operating with kerosene ……133

TABLE 4.61 – Temperature profile for can annular combustor operating with kerosene….133

TABLE 4.62 – Cooling slot position and wall temperature for can annular combustor with

operating with kerosene …………………………………………………………………….136

TABLE 4.63 – Air admission holes parameters for annular combustor operating with natural

gas …………………………………………………………………………………………..137

TABLE 4.64 – Basic layout for can annular combustors ………..…………………….…...138

List of Abbreviations and Acronyms

3-D Three - dimensional

CCD Computational Combustion Dynamic

CFD Computational Fluid Dynamic

CRN Chemical Reactor Network

FAR Fuel Air Ratio

LHV Lower Heating Value

PFR Plug Flow Reactor

PSR Perfectly Stirred Reactor

List of Symbol

Latin Characters

A Area

Aft Cross sectional area of flame tube

Aref Maximum casing cross sectional area

AR Area ratio

b Inlet temperature factor

C1 Convection heat flux from combustion to gas liner

C2 Convection heat flux from liner to annulus air

Cd Coefficient of discharge

Cd,s Coefficient of discharge of snout

Cp Gas specific heat at constant pressure

D Diameter

Dref Maximum casing diameter or width

DZ Dilution zone

D Diameter

Ea Activation Energy

EI Emission index

H Enthalpy

K Hole pressure loss factor

K1-2 Conduction heat flux through liner wall

Ksw A constant used in swirler blade design

K Thermal conductivity

L Length

Lu Luminosity factor

m& Mass flow rate

M Molecular weight

Nh Numbers of holes

P Total Pressure

Pr Pressure Ratio

p Static pressure

Q Heat Flux

q Dynamic pressure

R Universal gas constant

R1 Radiation heat flux from combustion gas to liner

R2 Radiation heat flux from combustor

Ra Gas constant for air

R Radius

s Slot height

TQ Traverse quality temperature

T Temperature

t Time

tw Wall thickness

U,u Velocity

V Volume

V Reference velocity

W Slot gap width

X Distance

Y Molecular fraction

Z Type of hole parameter

Greek Characters

α Hole area ratio

αsw Swirler blade stagger angle

β Hole bleed ratio

βsw Swirler air turning angle

∆P Pressure drop

∆T Temperature difference

∆ Momentum loss factor

ε Emissivity

η Combustion efficiency

θ Efficiency combustion correlation factor

θ Inclination angle of dome

µ Dynamic viscosity

µ Hole area ratio

ρ Density

σ Stefan-Boltzmann constant

ϕ Equivalence ratio

ψ Angle of divergence wall and axis

ω& Production rate

Subscripts

3 Inlet

4 Outlet

ad Adiabatic

an Annular

con Condition

cool Cooling

cv Control Volume

Diff Diffuser

DZ Dilution Zone

ft Flame tube

g Gas

h Hole

in Internal

inn Inner

Max Maximum

mix Mixture

Out Outer

Prod Products

PZ Primary Zone

Reac Reactant

Ref Reference

s Snout

sto Stoichometric

sw Swirler

SZ Secondary Zone

w Wall

1 Introduction

The gas turbine design traditionally has been a combination of empirical relations,

numerical modeling and extensive variety of component testing, with the goal of obtaining an

acceptable solution between the different design challenges. As the gas turbine operates in a

wide range of conditions the combustor must be designed to operate stable over wide range of

conditions. Some items that must be considered at each operating condition are: combustion

efficiency, loss of pressure, maximum allowed wall temperature, exit temperature quality and

emissions of pollutants [1]. In addition it is necessary to be considered into design process the

physical limitations of combustor, the interaction of the combustor with other engine

components specially the compressor and turbine, and different possible types of fuels that

will be used in the gas turbine.

1.1 Gas Turbine Combustor Design Process

The design process of a combustion chamber for gas turbine design involves different

stages and is directly related to the design methodologies for combustor [2],[3] and it can vary

according with the used methodology. But in general the design process can be divided into

three main stages which correspond to the preliminary design, detailed design and rig testing.

1.1.1 Preliminary design

The preliminary design is a process that involves several stages and it can be divided

into basic sizing, evaluation and modification.

Chapter 1. INTRODUCTION 18

The basic sizing of a combustor is given by a series of parameters and requirements

that the combustor should accomplish according with the operating conditions, those

conditions are given depending upon application (aeronautical or industrial). For an aircraft

engine it is necessary to know the aircraft mission and cycle analysis of engine; however, for

industrial turbines it is necessary just to know cycle analysis to establish these conditions.

The items that must be specified in each operating condition are: air mass flow rate,

fuel mass flow, combustor inlet conditions (temperature, pressure and velocity), outlet

temperature and transversal quality, pressure loss allowed, limits on the combustion

efficiency, maximum allowable wall temperature, fuel type. In addition it is necessary to carry

into consideration aspects such as weight, space limitations, and combustor type.[1]

At this stage of design are established the geometric parameters and basic dimensions

of combustor. These basic dimensions include the total length of combustor, length of each

one of combustor zones, flame tube diameter, number and position of air admission holes and

the geometric parameters for diffuser and swirler based in the aforementioned information.

Using the main geometrical parameters and the dimensions of combustor it is possible

to carry out a design evaluation. The assessment of the preliminary design is usually done by

simulation techniques, using CFD codes that provides an overview of the aerodynamic,

thermodynamic and chemical processes that occurring inside of combustor; the assessment is

performed for all operating conditions to assure that combustor accomplish the specified

requirements at each operating condition, also it is possible submit the preliminary design to a

structural analysis to avoid future structural damage in the combustor.

With the results of this evaluation are possible perform the necessary modifications in

the design layout to obtain the best overall configuration. This process is iterative in nature;

therefore it is important that from the beginning of the project the designer must be set the


initial conditions closer as possible to the real operating conditions; in this way the spent time

in the refining process of the model will be significantly reduced. [4]

1.1.2 Detailed design

Assuming a favorable preliminary design, the detailed design begins in which all

combustor parts to be fabricated are designed. During the detailed design the combustor will

be separated into parts and components, each one of which must be designed and analyzed

separately.

Another important part of detailed design is the production design. At this stage a

specialist determine how each part of the combustor will be manufactured, he establishes the

construction process and assembly for each one. Also he establishes the final assembly

process.

Sometimes the design can be modified to make easier the manufacture; this implies a

new evaluation in the design, and it is done to verify that the modification does not interfere

with the original requirements.

1.1.3 Rig testing

Basically the rig test consists on a series of tests that are made to each of combustor

components, with the purpose of checking the correct operation and performance of

combustor and each component separately; these tests are made for all operating conditions.

These tests are carried out before the combustor is coupled to the gas turbine engine.


1.2 Objective

The objective of this work is to establish a preliminary design methodology for gas

turbines combustors that operates with a variety of fuels based in the model proposed by

Melconian and Moldak [1]. This methodology should be capable to set the basic geometric

parameters and provide a basic configuration of a combustor considering possible changes of

fuel and operational loads. The proposed methodology also includes the use of a chemical

reactor network (CRN) to calculate the gas temperature inside the combustor, in addition of

the model proposed by Melconian and Moldak [1].

1.3 Motivation

The increased in global energy demand [5] mainly caused by the growth in electric

generation industries and aviation, the last one with an increment of the worldwide fleet of

aircraft about 5% annually [6]. Has been caused an increased in the use of gas turbine engine.

Thus different countries seek to consolidate an energetic structure that gives them security,

but also oriented towards reducing the environmental impact and the production costs.

In gas turbines used for electrical generation much like in the aeronautic industry has

been exploring a wide variety of fuels, from the most traditional as natural gas and petroleum

derivatives, through alcohol and biodiesel and even some non-traditional fuel as syngas and

synfuels. As a direct result of these searches it is necessary that new gas turbines have the

ability to operate with a wide variety of fuels [7], [8].


1.4 Design methodologies for gas turbine combustors

There are currently several methodologies used for the design of gas turbine

combustors, these methodologies has been developed through time and has evolved from

empirical models to more analytical and complex models that using advanced numerical

methods. These combustor design methodologies can be classified according to the level of

complexity. This level of complexity is mainly associated with the dimensionality [1], and fall

in four categories: empirical models, semi-empirical, semi-analytical and analytical which is

the most advanced; this one use numerical techniques for analyzing multidimensional

combustion processes [9]. Each one of these methodologies has its strengths and weakness.

1.4.1 Empirical methodology

The empirical methodology tend to be the simplest model and are based on the

empirical relationships which were obtained through a variety of tests of different components

of the combustor and a wide variety of configurations, within this methodology is also used a

series of statistical data of successful combustion systems that compound a base line, this base

line is used to establish basic parameters of a combustor.

The major advantage of that methodology is the simplicity of calculations, through it

is possible determinate basic parameters of combustors just with the inlet conditions based in

the mission and engine cycle analysis. This methodology is considered as a method of rapid

implementation [4],[10]. In the same way with the use of statistics base lines it is possible to

identify a combination of parameters that allow obtaining configuration of the most suitable


combustion chamber according to the initial parameters set, so the time spent on the

optimization process will reduced [4].

However, this methodology being a basic model has a number of restrictions,

especially related to the characteristics of the fluid and its behavior within the combustor, this

behavior is related to turbulence levels, with the fuel injection process, fuel evaporation and

combustion process. Some limitations of empirical models are: scaling combustor, calculating

combustor with non conventional or new concepts in combustion, and if are required

significant changes in technological levels (combustor performance, combustor temperature

rise and durability) [11].

1.4.2 Semi-empirical methodology

Semi-empirical methodology consists of equations that contained empirically

determinate constants, and is an evolution of empirical methodology. Generally in this

methodology is added chemical reactors network (CRN). This network is usually a series of

perfectly stirred reactor which simulate the primary and secondary region of the combustor,

where the composition, velocity, temperature of the gas and heat flux is uniform throughout

the studied region. The reaction mechanism used in this model is usually one step global

mechanisms. It is important to note that although this model is more complex than the

previous one the basic empirical relationships are also used to obtain basic geometric

parameters of combustor. With this model it is possible to obtain a better correlation between

the emission of pollutants and combustion efficiency [1],[9]. As well as the previous

methodology, the major advantage is the reduced time of implementation, and does not

require a higher computational effort.


1.4.3 Semi-analytical methodology

The semi-analytical methodology is more complex that the previous ones. It includes

the empirical relations, constants and equations that have already been used in the previous

methodologies and also includes a chemical reactor network. The main difference between

this methodology and the semi-empirical methodology is the complexity in the chemical

reaction network, which is given by the number of reactors that are used into the network and

how they are interconnected, i.e. for each region of the combustor is represented by a

chemical reactor network, which are interconnected. One of the main objectives of this type

of modelling is to obtain an estimate of emissions of pollutants, particularly NOx and CO [9].

This methodology also includes model of turbulence, reactions rates and a simplified model

of heat transfer [1]. This type of methodology requires a considerable computational effort

and a broad knowledge of each one of the phenomena that occurs into the combustor [12].

1.4.4 Analytical methodology

The analytical methodologies are related to multidimensional models. In these models

is taking into account not only physical process, but also chemical process. This means that

within the model there are usually sub-models that improve prediction accuracy for design

combustor [13]. Some of the sub-models include turbulence and scalar transport models,

spray dynamics, evaporation and mixing, heat transfer.

This type of methodology generally uses CFD code or a computational combustion

dynamics (CCD) code [12] that use detailed chemical kinetic mechanisms and different

numerical techniques to simulate combustors with complex geometries in 3-D. However, for


its implementation requires a detailed knowledge of combustor geometry and operating

conditions, besides requiring an extremely high computational effort.

1.5 Thesis outline

Chapter 2 discusses the development of a preliminary design methodology for multi-

fuel gas turbine combustor used in this work. Chapter 3 focuses in the implementation of

methodology. Chapter 4 presents the methodology validation and show the results obtained

for different combustor configurations as well a discussion of these results. Chapter 5 contains

general conclusions about the work.

2 Developing of preliminary design methodology for multi

fuel gas turbine combustor

This chapter discusses the development of a preliminary design methodology for multi-

fuel gas turbine combustor; which is based on the formulation proposed by Melconian and

Modak [1]. This model is based on a series of empirical and semi-empirical correlations that

have been developmed through the time, and allows obtain a first approach of combustor

model. The methodology assumes that the inlet combustor conditions are known from the

engine cycle analyses.

2.1 Gas turbine combustor

The basic combustion chamber or combustor is an engine component and it is

basically a single circular tube, where the chemical energy contained in a fuel is transformed

into heat energy. This energy is drawn through the turbine and the engine keeps running. The

burning process must be continuous during engine operation from the ignition until engine

shutdown.

A combustor must satisfy a wide range of requirements [1],[12], which may vary

according to type of application. However, the basic requirements for all combustors are:

• high combustion efficiency;

CHAPTER 2. DEVELOPING OF DESIGN METHODOLOGY FOR MULTI

FUEL GAS TURBINE COMBUSTOR

26

• high reliability and smooth ignition, both on the ground (especially at low

temperatures) and high altitude after a flameout for aircraft gas turbine;

• optimal flame stability in all operating conditions;

• homogeneous temperature distribution at combustor chamber outlet (pattern factor);

• minimal formation of pollutants at all operating conditions;

• minimum pressure loss;

• low manufacturing cost, easy maintenance and long operating life;

• fit and compatibility with the engine size and low weight for certain cases;

• low fuel consumption;

• multi-fuel capability.

2.1.1 Combustor types

The combustion chambers can be classified according to three design features:

by geometry, air distribution, and type of fuel injector. For the present work was adopted the

classification by geometry, that it corresponds to the most used classification.

Combustor classification by geometry

There are three basic configurations of combustors, multi-can (can, tubular), annular,

can-annular (tuboannular). See Figure 2.1



27

FIGURE 2.1 – Cross section of three main combustor type.

Multi-can combustors

Also called can or tubular, consist of a flames tubes mounted concentrically within a

cylindrical casing, which are arranged around the engine axis. The interconnector is necessary

to ensure the ignition of all cans during the start-up by the flame propagation through

interconnecting tubes.

This type of construction provides a combustor with high pressure drop, heavy, large

length, and large frontal area. It is often used with centrifugal compressors. The advantage of

this combustor is its mechanical resistant and the developing and testing of the combustor can

be made with one can.

Annular combustors

The annular combustion chamber consists of a single annular flame tube (liner), which is

located within an inner and outer wall forming the combustor casing. The space between the



28

compressor and turbine is maximized, using it primarily for the combustion process. The size

and the front section are minor compared with other types of combustors; therefore, the

pressure loss is reduced and the area to be refrigerated too. For this reason the additional

amount of air can be used in primary and secondary zones of the chamber, improving the

combustion efficiency. The design process and development of an annular combustor is

complex and rig testing is complex too. Structurally is weaker compared with the others

configurations, so that buckling can occur in the hot walls of flame tube.

Can-annular combustor

The can-annular combustor consists of several flame tubes (cans), within a single

cylindrical casing. As a result of this configuration, the length and weight are lower than a

multi-can combustor. However, it is more difficult obtain a uniform distribution of air

combustion between the flame tubes when compared with the multi-can and is possible affirm

that this type of combustor is an intermediate design between multi-can and annular

combustors.

2.1.2 Basic configuration of the combustor

The combustion chamber is divided into the following regions or components:

Diffuser, Primary zone, Secondary zone and Dilution zone. These regions and main

components of a typically combustor is shown in the following schematic representation of

Figure 2.2



29

FIGURE 2.2 – Basic combustor features [14].

Diffuser

The function of the diffuser is reducing the air flow velocity from the compressor, besides

taking part in the distribution of airflow in the combustor, i.e. the airflow delivery for primary

and secondary zone. It is also used to recover some of the dynamic pressure.

The diffuser section is located directly after the compressor and is presented as a

divergent channel. There are two main types of diffuser: soft expansion or aerodynamic long

diffuser and sudden expansion also called "dump or step". The first configuration allows

reach up to 35% reduction in speed before the airflow reaches the snout where it is divided in

three parts. The dump diffuser consists of a short conventional diffuser in its forward part, the

walls of which are suddenly broken, where the velocity is reduced by about 50%. At the

output of this the airflow is divided creating a ring of air that surrounds the contour of the

flame tube and part of the airflow entering to the dome of the combustor.



30

Primary zone

The main function of the primary zone is to anchor the flame and to provide the adequate

conditions for complete combustion of air- fuel mixture. Within this area there is a

recirculation zone which consists of a flow reversal zone generated by the low pressure that

generated due to high levels of turbulence. A portion of the incoming air flow is mixed with

hot gases from the recirculation zone and fuel steam, and this mixture is ignited by the high

temperature of the gas, As result is a self-sustaining of burning process is established after

initial ignition.

This recirculation zone can be generated through different methods such as swirlers,

opposed air jets, mechanical and combined stabilizers. These methods not only help to

stabilize the flame also increase the rate of mixture air/fuel to improve combustion.

Secondary zone

The temperature of the gases and products leaving the primary zone is around 2000K. At

these temperatures and as consequence of the dissociation the combustion products may

contain unburned hydrocarbons (UHC) and species as H2 and CO in high concentrations.

Should these gases pass directly into the dilution of these would be rapidly cooled by the

addition of large amount of air, gas composition would “frozen” and will be appear pollutants

as CO, H2 and UHC. The secondary zone then reduces these species by the addition of air,

reducing the temperature and encourages the formation of CO2, H2O and complete

combustion. In the case of aircraft at high altitude the reaction rate becomes slower as a

consequence of pressure reduction and largely of the combustion occurs in this region.



31

Dilution Zone

The main role of this zone is to receive the remaining air and gases from the combustion

and mixing them, in order to obtain an appropriate temperature distribution for the turbine

entrance. This temperature distribution is usually associated with pattern factor or transverse

temperature quality (TQ), which is a parameter, used to determine the quality of the mixing

process in the dilution zone and is defined as:

34

4max

TT

TTTQ

−−= (2.1)

Where Tmax is the maximum or peak temperature, T4 is the average exit temperature and T3

is the combustion inlet temperature and usually corresponds to the compressor discharge

temperature. A satisfactory value for transverse temperature quality is around 0.25.

The amount of air available for dilution zone normally is 20% to 50% of the total air flow

from the compressor. The air injection is performed through one or more rows of holes in the

wall of flame tube.

2.2 Design methodology

2.2.1 Theoretical limits for equivalence ratio

The equivalence ratio for the primary zone should be chosen assuming that the air and

fuel injected in this region will form a flammable mixture before ignition; so the equivalence

ratio for the primary zone should be within the mixture flammable envelope for the reactants



32

established. According with Melconian and Modak [1], temperatures above 1600K for lean

and rich mixtures guaranteeing that combustion always will happen, as is show in the Figure

2.3.

FIGURE 2.3 – Flame limit temperature for flammable mixture. [1].

Thus the equivalence ratio for the primary zone should be within the limits of the

equivalence ratio rich and lean, producing a temperature of 1600K, it is evident that these

limits depends of air temperature at inlet of combustor or outlet from compressor (T3), which

varies according to engine operating condition. Then, it is necessary obtain the behaviour of

the equivalence ratio limits, called ϕrich and ϕlean as a function of temperature (T3).

It is important to emphasize that for each engine operating condition is obtained a

different equivalence ratio limits, so it is necessary to calculate these limits for the most

critical operating condition and choose the percentage of airflow from the compressor to

satisfy completely the condition of flammable mixture.

To obtain the limits ϕrich and ϕlean as a function of temperature (T3) is used chemical

equilibrium calculations.



33

Adiabatic Flame Temperature

Adiabatic flame temperature it is the highest temperature reached by the products of

combustion, where all the energy released by the reactions is contained in the products,

considering absence of any external heat transfer. The adiabatic flame temperature depends on

the initial conditions of the reactants (pressure, temperature, composition, equivalence ratio)

and the type of process (pressure or volume constant); generally the maximum adiabatic flame

temperature is obtained close to the stoichiometric condition.

Applying the first law of thermodynamics and considering a fuel-air mixture burning at

constant pressure:

Hreac ( Ti,P) = H prod (Tad,P) (2.2)

where Hreact is the reactants enthalpy and Hprod is the products enthalpy or, equivalently, in

intensive form

hreac (Ti,P) = hprod (Tad,P) (2.3)

Where the molar absolute enthalpy for species i, can be write as:

T

Trefi,s0

i,f0

i hh)T(h ∆+= (2.4)

where 0

i,fh is enthalpy of formation and i,sh∆ is the change of sensible enthalpy, and Tref is the

reference temperature, in general is assumed as 298K.



34

Chemical Equilibrium

In high temperature combustion processes, the products of combustion are not a simple

mixture of ideal products, i.e. major species dissociate, producing a variety of multiple minor

species. For this reason the major problem is the calculation of the mole fraction of all product

species at given pressure and temperature, subject to the conservation of number of moles of

each of the elements that compound the initial mixture. There are several ways to calculate

the equilibrium composition; in this work was used Gibbs function as follows,

TSHG −= (2.5)

For adiabatic systems without work, the second law of thermodynamics can be written as;

0)dG( m,P,T ≤ (2.6)

In this way the Gibbs function decreases for spontaneous changes, and reached the

minimum value at equilibrium. Thus,

0)dG( m,P,T = (2.7)

The Gibbs function for the i species is given by,

)P/Pln(.Rgg 0i

0T,iT,i += (2.8)



35

where 0T,ig is the Gibbs function of the pure species at standard pressure and temperature,

where the standard pressure P0 is assumed as 1 atm, and can be calculate through,

])g()g([)g(g Tref0iT

0iTref

0fi,

0Ti, −+=

(2.9)

where the ( 0fi,g )Tref is the Gibbs function of formation and Tref

0iT

0i )g()g( − is the change of

sensible Gibbs function and the values can be obtained from tabulated values for each species

according with the temperature of interest.

For an ideal gas mixture, the Gibbs function can be written as,

)]P/Pln(.Rg.[NgNG 0i

0T,i

k

1iiT,i

k

1iimix +== ∑∑

==

(2.10)

where Ni is the number of moles of the ith species.

For a given temperature and pressure dGmix = 0, i.e. for the equilibrium condition

becomes,

0)]P/Pln(.Rg[d.N)]P/Pln(.Rg.[dN 0i

0T,i

k

1ii

0i

0T,i

k

1ii =+++ ∑∑

==

(2.11)

where it is possible to say that d(lnPi) = dPi / Pi and ΣdPi = 0, since the change in partial

pressure is zero because the total pressure is constant, then



36

)]P/Pln(.Rg.[dN0dG 0i

0T,i

k

1iimix +== ∑

= (2.12)

For a general system, where

a.A + b.B + ...⇔ e.E + f.F + … , (2.13)

the change in the number of moles of each species is proportional to its stoichiometric

coefficient,

dNA = -k.a

dNB = -k.b

⁞ ⁞

dNE = +k.e

dNF = +k.f

(2.14)

Substituting the equation 2.14 into 2.12 and cancelling the proportionality constant k,

0...)]P/Pln(.Rg.[f)]P/Pln(.Rg.[e

...)]P/Pln(.Rg.[b)]P/Pln(.Rg.[a0

F0

T,F0

E0

T,E

0B

0T,B

0A

0T,A

=+++++

−+−+− (2.15)

Rearranging the equation 2.15:



37

( )

=−−−++−

...)P/P.()P/P(

...)P/P.()P/P(ln.T.R...gbga...gfge

b0B

a0A

f0F

e0E0

T,B0

T,A0

T,F0

T,E (2.16)

where the left hand side term of the equation 2.16 is called the change of standard state Gibbs,

i.e.,

( )...gbga...gfgeG 0B,f

0A,f

0F,f

0E,f

0T −−−++≡∆ (2.17)

the right hand side term of the equation 2.16 is defined as the equilibrium constant Kp for the

reaction establish at the equation 2.13

=

...)P/P.()P/P(

...)P/P.()P/P(K

b0B

a0A

f0F

e0E

p (2.18)

Finally the statement of chemical equilibrium at constant pressure and temperature,

becomes,

p0T Kln.T.RG −=∆ (2.19)

or

)T.R/Gexp(K 0Tp ∆−= (2.20)



38

2.2.2 Basic dimensions for combustor.

To determinate the basic geometry of combustor, firstly it must be determinated the

reference area (Aref), which is defined as the maximum transversal area of combustor casing in

absence of flame tube. This area is limited by chemical and aerodynamics parameters. From

the chemical parameters is desired a higher volume to complete the chemical reactions and

from the aerodynamics parameters it is desired a lower volume because it represents a smaller

length and, consequently, a smaller contact surface with the flow, which reduces the total

pressure loss.

The Figure 2.4 shows the reference height or the reference diameter for the different

combustor configurations. The Figure also shows the liner height and diameter according with

the combustor configuration, Dft is the liner or flame tube height or diameter, Dref is defined as

the height or diameter of the casing and Dint is defined as the height or internal diameter of

internal combustor casing.

Based on the geometry of each combustor, the equations for the reference area Aref are

obtained

For annular and can-annular combustor:

( )

⋅−

+=

44

2 22

ininrefref

DDD.A

ππ

(2.21)

For multi-can combustor:



39

⋅=

4

2ref

ref

DA

π

(2.22)

FIGURE 1.4 – Dref and Dft for flame tube arrangements [1].

The selection of the reference area is made based in the obtained data for a selected

operating conditions and taking into account the chemical and aerodynamic considerations.



40

2.2.3 Aerodynamics Considerations

The aerodynamics considerations are relationed with the ratio of combustor total pressure

loss and the total pressure at the combustor inlet )P/P( 343−∆ and with the ratio given by the

total pressure loss and dynamic reference pressure )q/P( ref43−∆ . Rearranging the equation

(2.23) is possible obtained the reference area (Aref) value through the equation 2.24.

2

3ref

0.533AR

ref

43

3

43

PA

Tm

2

R

q

∆P

P

∆P

= −− &

(2.23)

50

3

43

43

3

33

2

.

refarref

P

P

q

P

P

T.mRA

⋅

⋅=

−

−

∆

∆&

(2.24)

Typical values used for Aref calculation are showed in Table 2.1

TABLE 2.1 - Representative values of pressure loss [8]

Combustor type

%P

∆P

3

43−

ref

43

q

∆P−

3ref

3

PA

Tm 3&

Multi-can 5.3 40 3.0 x 10-3

Annular 6.0 20 4.5 x 10-3 Can-annular 5.4 30 3.5 x 10-3



41

2.2.4 Chemical Considerations

The chemical considerations are based on the combustion efficiency η and are correlating

with the reference area (Aref) through parameter θ, according with the equation 2.25. For any

given air/fuel ratio the combustion efficiency (η) is function of θ Lefebvre [14] and

Melconian and Modak [8] represent it as an empirical relation and is show by the equation

(.25) in the Figure. 2.5

3

375.075.13 exp

m

b

TDAP refref

&

⋅⋅⋅=θ

(2.25)

where θ is the correlating parameter of combustion efficiency η.

The parameter b in the equation 2.25 is a temperature correction factor and is defined by

de empirical equations 2.26 and 2.27, and it depends of primary zone equivalence ratio.

)ln39.1(245 PZb φ+⋅= for 0.6< PZφ ≤1.0 (2.26)

)ln00.2(170 PZb φ+⋅= for 1.0< PZφ ≤1.4 (2.27)



42

FIGURE 2.5 – Theta parameter correlation. [1].

Primary zone equivalence ratio

The primary zone equivalence ratio (ϕPZ) can be calculated using the equation 2.28,

where PZm& is the mass airflow rate in the primary zone, ϕGlobal is the total equivalence ratio

and ṁo fuel flow rate.

=

o

PZ

GlobalPZ

m

m

&

&

φφ

(2.28)



43

ϕGlobal is represented by equation (2.29)

.stoo

f

con.opto

f

.est

con.optglobal

m

m

m

m

==

&

&

&

&

φφ

φ

(2.29)

Is important remember that the total equivalence ratio global (ϕGlobal) will change

according with the engine operating conditions, hence the primary zone equivalence ratio (ϕpz)

also change, and taking into account this condition the primary zone equivalence ratio (ϕpz)

must be into the fuel flammability limits envelope, for temperatures above 1600K.

2.2.5 Determination of combustor area

Based on the estimed values obtained through the equations 2.22, 2.23, 2.24 and 2.25

there will be two different values for any operating condition. In this case the reference area

(Aref) must be chosen as the highest value found between the aerodynamic and chemical

calculation, Melconial e Modak [1].

The combustor area is given by the relationship:

refft AA ⋅= 7.0 (2.30)

This relationship is seems to be quite satisfactory for single can, multi-can, annular

combustors. For can-annular combustor a value between 0.65-0.67[1] is more appropriate for

the constant.



44

With the value of the combustor area (Aft) is possible calculate the Dft that correspond to

the height or diameter of flame tube according with the type of combustor see Figure 2.1

For annular combustor,

( ) π⋅+=

refin

ftft DD

AD (2.31)

For multi-can and can-annular combustors,

0,54

⋅=

πft

ft

AD (2.32)

2.2.6 Preliminary estimate of air distribution

In this section the air distribution is estimated, when is determined the limits of

flammability of the mixture also is determined the percentage of air from the compressor that

entering in the primary zone for each one of the operating conditions through the equation

2.28.

To determine the amount of air entering the secondary zone is applied the condition that

the combustion process must be completed at the end of this region. Then is used as a

reference the most critical condition of operation or the richest operating condition. This

refers to the condition with the lowest mass airflow. It is assumed that until the end of the



45

secondary zone the global equivalence ratio should be around 0.8[1], using the following

equation;

( )33 8.0 m

m

m

m PZrichglobalSZ

&

&

&

&−= +

φ (2.33)

where PZm& is mass airflow rate in the primary zone, ṁ3 is the air mass flow rate from

compressor, and (ϕglobal)+rich is the global equivalence ratio at richest operating condition.

In the calculation sequence, must be estimated the amount of film cooling air, according

with the equation 2.34 proposed by Odgers [15]. This portion of air can be calculated by;

30T1.0m

m3

3

cool −=&

& (2.34)

where T3 is the temperature in K at the design point condition.

Finally the amount of air ṁDZ, used in the dilution zone is given by;

( )33

1m

mmm

m

m coolSZPZDZ

&

&&&

&

& ++−= (2.35)

2.2.7 Length of combustors zones

The length of the primary zone and secondary zone can be assumed as ¾Dft and ½Dft

respectively, according with Melconian and Modak [1],[15]. The length of the zone of

dilution is a function of temperature traverse quality (TQ) and pressure loss (∆P3-4/qref,). The



46

temperature traverse quality is defined as a relationship between the highest expected

temperature at the combustor outlet and the average temperature of the combustor relative to

the mean temperature change in the combustor;

Usually this parameter must be between 0.05 and 0.30.

The relationship between pressure loss factor, temperature traverse quality and the length

of the dilution zone is shown in the Figure 2.6, Melconian and Modak[1].

FIGURE 2.6 – Dilution zone mixing performance. [1].

The Table 2.2 shows the equations that characterize the curves shown in the Figure. 2.6.

[17].

At this point of calculation has been defined. if within the calculation of the dilution zone

is included the nozzle box, it corresponds a transition piece between the combustor secondary



47

zone and nozzle guide vane, in this case the designer should evaluate whether the length of

the zone of dilution takes into account or not this nozzle box

TABLE 2.2 - LDZ/Dft as a function of TQ for different values of pressure loss factor

∆∆∆∆P 3–4/qref LDZ/Dft

15 3.78 – 6TQ

20 3.83 – 11.83TQ + 13.42TQ

30 2.96 – 9.86TQ + 13.32TQ

50 2.718 – 12.64TQ + 28.512TQ

Finally the total length of the combustor is defined as the length from the outlet of fuel

injector to the end of the dilution zone, and is given by:

LCC= LPZ + LSZ + LDZ (2.36)

2.2.8 Diffuser design

The diffuser design is more restricted due to the space of the engine, but the ultimate goal

is to design the most efficient diffuser within the given space with the least possible pressure

loss. The basic geometry of the diffuser is shown in Figure 2.7. At this stage of the design the

compressor outlet profile is unknown and it is assumed as uniform. For conventional designs

of combustion chamber is assumed that about a half of the air entering to the primary zone

enters through the swirler and slot dome cooling of the primary zone, that is passing through

the snout area (As), therefore the remaining percentage air would pass through the annular

area (Aan). The annular area is given by the equation:



48

Aan = Aref – Aft (2.37)

The air mass flow rate at the annular area (Aan) is:

( )SWdome3an mmmm &&&& +−= (2.38)

where ṁdome is the air mass flow rate passing thought the dome and ṁSW is the air mass flow

rate passing through the swirler.

The area A0 is calculated assuming that the air velocity in this section corresponds to the

air velocity through the annular area Aan, therefore:

anan

30 A

m

mA ⋅=

&

& (2.39)

FIGURE 2.7 – Basic geometry of diffuser. [1].

The expansion ratio can be calculated as follows:



49

3

0

A

AAR= (2.40)

The divergence angle (ψ) of the diffuser should be the ideal to minimize total pressure

loss of the flow. For a long diffuser with a low angle of divergence the total pressure loss is

high due to the skin friction along the walls, in the opposite case a diffuser with a high angle

of divergence reduces the length of the diffuser and consequently the pressure loss due to skin

friction, but increase the stall losses due to the boundary layer separation. The equation

developed by Kretschemer and used by Melconian and Modak [1], to obtain the total pressure

loss, is adopted:

( ) 2

o

32

3

1.222

3

33a

3

dif

A

A1

A

tanψ

P

TmR1.75

P

∆P

−

⋅=

& (2.41)

where 1.75Ra = 502.4 J/kgK. The typical value for pressure loss is about 1%; in this way, it

can be adopted as a value of design, and the divergence angle (ψ) can be calculated through

the equation 2.41.

The snout area As, is given by:

Sd,3

S

0

S

C

1.

m

m

A

A&

&= (2.42)

where As is the snout area, Cd,S is the coefficient of discharge of snout and ṁs air mass flow

rate



50

Then the length of the diffuser can be obtained through:

Ldif = (R0 – R3)/tanψ (2.43)

where R0 and R3 correspond to D0/2 and D3/, respectively. For the calculation of the diffuser

are used the parameters at most critical operating condition.

2.2.9 Swirler design

The main role of the swirler is create a zone of low pressure where the products of

burning flow in the opposite direction relative to the general motion of the airflow, creating a

recirculation zone into the primary zone of combustor to stabilize the flame in this region. The

intensity of the recirculation zone is function of degree of swirl, number and type of blades,

and airflow through the blade channel.

For swirler design should be considered that the momentum of the quantity of air passing

through is equal to momentum generates by the air entering into the zone of recirculation

through the holes in the primary zone. According to experimental results by Melconian and

Modak [1], it is recommended that the air mass flow rate of swirler must be between 3 and

12% of total air. Most swirlers are made with set at a constant angle blade. Based on

experimental results the stagger angle of blades can be considered equal to the turning angle

of air flow (βsw). Usually the stagger angle of blades lie between 45 and 70 degrees [16].

Typical configuration of swirler and their components is show in the Figure 2.8.



51

FIGURE 2.8 – Swirler basic geometry. [1].

The pressure loss factor through of swirler can be obtained by the equation 2.44,

2

3

2

2

2

.sec

−

=∆

m

m

A

A

A

AK

q

P sw

ft

refsw

sw

refsw

ref

sw

&

&β (2.44)

where ṁsw is the total air mass flow rate passing through the swirler, the constant Ksw

correspond to blade form factor of the swirler, 1.30 for straight blades and 1.15 for curved

blades.

The pressure loss factor through the swirler can be written as,

ref

diff

ref

s

refref

ftsw

ref

sw

q

P

q

P

q

P

q

PP

q

P ∆∆∆∆ −−=−

= −43 (2.45)



52

The equation 2.45 considers the diffuser pressure loss, the pressure loss inside the snout

(∆Ps) and the total loss of pressure along the combustor (∆P3-4/qref). The diffuser pressure loss

factor is given by the equation 2.46,

3

43

43

3

1

P

Pq

P.

P

P

q

P

ref

diff

ref

diff

−

−= ∆∆∆∆

(2.46)

Since ∆Pdiff/qref is about 1% for the diffuser design, and the total pressure loss depends on

the combustor geometry and their typical values are shown in Table 2.2 at section 2.2.7. The

pressure loss (∆P3_4/P3) can be calculated by equation 2.3, and then the term of pressure loss

in the snout is calculated by equation 2.47,

2

0

∆=∆=∆A

A

q

P

q

q

q

P

q

P ref

s

s

ref

s

s

s

ref

s (2.47)

where ∆Ps / qs ≅ 0.25.[1]

With the value of ∆Psw/qref it is possible to calculate the swirler area value (Asw) through

equation 2.45. The next step is estimate the value of the fuel atomizer casing (DI,sw). In

general this value correspond 10 to 15 % of reference diameter (DREF), typically outer

diameter (D0,sw) is about 30% of the flame tube diameter (Dft)



53

2.2.10 Recirculation zone

The length of the recirculation zone (LRZ) is based on statistical data and it must be assumed a

value between the primary zone length (LZP) and twice the outer diameter of swirler (D0,sw), as

is show the Figure 2.9. Once the length of the recirculation zone (LRZ) is calculated the

inclination angle (θ) and length of the dome (LDOME) can be obtained by the equations 2.48

and 2.49, [17] respectively

( ) ( )

+−+−

+−+−−−−−=

2ZRZRft

2swswft

2ft

2ZRZRft

2swswft

2ftZRftswftft

L.16L.D.8D.4D.D.4D.2

L.16L.D.8D.4D.D.4D.L.4DD.2D.Dcosaθ (2.48)

( )θtan

DDL SWft

DOME ⋅−

=2

(2.49)

The equations 2.48 and 2.49 represent just geometric relationships.

FIGURE 2.9 – Recirculation zone



54

2.2.11 Flame temperature calculations

For the combustor cooling system design, it is necessary to determine the temperature

profile of the gases throughout the combustor. The objective of this calculation is obtain the

points of the combustor where the temperature will be higher and in which region is located,

to allow the designer to know where can be localized the cooling slots.

In the methodology proposed by Melconian and Modak [1], the calculation of flame

temperature is given by a series of empirical equations that only takes into account the

efficiency of combustion; otherwise it is assumed that the temperature profile varies linearly

between inlet temperature (Tin) and outlet temperature (Tout) for each region. For those reasons

in the methodology here proposed, the calculation of the flame temperature will be made by

the use of a chemical reactors network (CRN).

In this methodology the combustor is divided into four main regions: recirculation

zone, remain primary zone, secondary zone and dilution zone, where the recirculation zone is

represented by one perfectly stirred reactor (PSR) at given temperature, the remain primary

zone are represented by five PSR, the secondary zone have five PSR and dilution zone has

been modelled as a plug flow reactor; as is show in the Figure 2.10. This approach allows take

into account the chemical reaction and gives a more appropriate temperature profile.



55

FIGURE 2.10 – Diagram of the combustor model

Chemical reactors network methodology

The CRN is generally used for the prediction of pollutants in the combustor [18], as much

as in the design stage as in combustors already built. The use of the CRN in the combustor

design allows a fast analysis of different configurations and chemical processes that occurs in

it.

The modelling of the combustor using CRN is based on the simulation of different

regions of the combustor using simplified reactors models as PSR, PFR, etc, which are

interconnected to form a network, each of which is fed by the products of the preceding one.

The configuration of the reactor network depends on the geometry and operating

conditions of combustor [19]. Currently there are various models of reactors network, a

typical model is proposed by Turns [20]. This model is a combination of PSR and PFR, in this

case specifically the combustor is modelled by two PSR and PFR, which are connected in



56

series; the first reactor is the primary zone, the second PSR represents the secondary zone and

dilution zone PFR. Turns [20] also argues that the model's accuracy depends on the proper

proportion of reagents used in each of the cases.

Another model used frequently is the proposed by Ruta and Malte [21] in which the

primary zone is modelling as PSR, the secondary zone and dilution zone of the chamber are

represented by a two PFR, i.e., the total model includes a PSR and PFR connected in series.

Models more complex of reactor network have been developed in order to describe better

each of the areas of the combustor, such as the model proposed by Allaire [19] where the

primary zone of the combustor has been divided in nine PSR connected in parallel, the

secondary zone and dilution are represented as two PFR connected in series with each other

and with the network of reactors in the primary zone. Another case is the model proposed by

Novoselov [18] in which the combustor has been modelled as series of thirty-one reactors.

The perfectly stirred reactor (PSR)

It is an ideal reactor in which a perfect mixture is obtained inside of it, where the

phenomenon of mixture is neglected into the reaction, because is considered that this

phenomenon occurs extremely fast due to the high level of turbulence. It is also assumed that

temperature and species composition within the reactor are constant.

Conservation equations for the perfectly stirred reactor (PSR)

Following the approach proposed by Turns [20], the equations for the PSR can be written

as follows, based on the control volume shown in Figure 2.11



57

FIGURE 2.11 – Perfectly Stirred Reactor (PSR). [20].

The conservation of mass for any species i can be written as:

out,iin,i'''

i mmVm0 &&& −+⋅= (2.50)

where ṁi’’’ is the rate of mass generation for ith species, V the reactor volume, ṁi,in is the mass

flow rate of the species into the control volume, and ṁi,out is the mass flow rate of the species

out of the control volume.

The rate of generation of the species can be written as;

ii'''

i .MWm ω&& = (2.51)

where iω& is the production rate of ith species and MWi is the molecular weight. The total mass

flow within the control volume is the product of total mass flow by the initial mass fraction of

species, or



58

Y in,iin,i mm ⋅= && (2.52)

Similarly can be written to the out total mass flow of species i,

Y out,iout,i mm ⋅= && (2.53)

For a steady-state, steady flow energy equation applied to a perfectly stirred reactor can

be written as,

)h(hmQ RPCV −⋅= && (2.54)

In terms of species ith is rewritten as,

−⋅= ∑∑==

)T(h.Y)T(hYmQ ini

N

1iin,iouti

N

1iout,iCV && (2.55)

where the specific enthalpy for species can be written as,

dT)T(Cph(T)hT

Trefi

0f,ii ∫+= (2.56)

where the term hof,i is the enthalpy of formation of species ith and Cpi(T) is the specific heat,

which is a function of temperature .



59

The equations specified above may involve several species and reactions, in this specific

case and to simplify calculations, is considered a one-step global chemical reaction of fuel and

air the products will be,

VMm iii ω&& = (2.57)

The consumption rate for the overall chemical reaction is calculated as,

bO

ai

ai )(n)(n

RT

E-expA.

2

−=ω& (2.58)

The plug flow reactor (PFR)

The plug-flow reactor is a reactor whose main ideal assumptions are ideal gas behavior,

steady state, inviscid flow, one- dimensional, not mixed in the axial direction. The

conservation equations for control volume shown in the Figure 2.12 can be written as:

FIGURE 2.12 – Perfectly Stirred Reactor (PSR). [20].

Conservation of mass:



60

0dx

)v.A.(d x =ρ (2.59)

where ρ is the density, A is reactor area and vx is the velocity in axial direction.

Conservation of momentum:

0dx

dv.v.

dx

dP xx =+ ρ (2.60)

where P is the reactor pressure.

Conservation of species:

0v.

MW.

dx

dY

x

iii =−ρ

ω& (2.61)

where Yi is the mass fraction of species, iω& the production rate of ith species and MWi is the

molecular weight.

Conservation of energy:

ii

k

1ii

x

2x

2x MW.h.

Cp..v

1

dx

dA.

A

1.

Cp

v

dx

d.

Cp.

v

dx

dT ωρ

ρρ

&∑−

+==

(2.62)

where T is the gas temperature, hiis the specific enthalpy of species, Cp is the heat capacity.



61

2.2.12 Film cooling

The film cooling system is created by a thin film of air between the flame tube wall and

hot gases from the combustion. It is created by stream of cold air from the compressor that

enters through holes to the surface tangential and parallel to the hot gases, as the cooling air

mix with the hot gases it must be renewed through another set of slots located in a the

following section of combustor.

To design the cooling system with film cooling it is necessary select the height of the slot

(s), the slot lip thickness (t), flame tube wall thickness (tw), establish the position of the dome

cooling slot, the number of slots along the remainder of the flame tube and their positions as

well as material from the casing. The Figure 2.12 shows the geometry of the film cooling

device.

FIGURE 2.13 – Film cooling device geometry. [1].

And for annular combustors;

( ) ( )sDD.2DsDDA anrefintanintslot −+++= (2.63)

In the case of annular combustors, the area calculated by this equation represents the sum

of the areas of the slots of the outer and inner walls of the combustor.



62

The air mass flow rate that enters by each slot is given by,

an

slotanslot A

A.mm && = (2.64)

The last equation does not take into account the mass airflow from the slot of dome, a

recommended value for this mass flow is around 3% of mass airflow from compressor.

The next step corresponds to the calculation of the product between the density and

velocity of air through annular area (Aan), and for this calculations are used the values

obtained from equations 2.63 and 2.64.

slot

slotanan A

mU.

&=ρ (2.65)

The equation 2.63 allows calculate the product between gas density and velocity into the

flame tube,

ft

ggg A

mU

&=.ρ (2.66)

where ṁg correspond to mass gas flow into region of flame tube at position of the slot.



63

To evalue the effectiveness of cooling (ηc), it is necessary calculate the temperature in

one position immediately prior to the next, and can be obtained through the equation 2.67 and

2.68, [22]

3.1m5.0fors

t

s

xm10.1

2.02.015.0

g

a65.0c <<

=

−−

µµη (2.67)

0.4m3.1fors

t

s

x28.1

2.02.015.0

g

ac <<

=

−−

µµη (2.68)

where m is calculated by,

gg

anan

A.

.m

ρΑρ= (2.69)

and x corresponds to the distance between the slots. For the last slot is assumed as the distance

until the end of the combustor. The terms µa and µg from the equations 2.70 and 2.71 are the

dynamic viscosity of air and gas into the flame tube, respectively. To calculated the dynamic

viscosity of air µa, the temperature of the slot is assumed as the inlet temperature (T3), as is

show in the equation 2.68,[22]



64

543

1333

9

23

63a

10)T10600774.4T107769.2...

...T108564.5T00749.003863.0(−−−

−

×⋅×−⋅×+

+⋅×−⋅+=µ (2.70)

For the dynamic viscosity of gas µg[22], the temperature of gas used this calculation is

given by the temperature profile obtained in the previous section,

54g

133g

9

2g

6gg

10)T10600774.4T107769.2...

...T108564.5T00749.003863.0(

−−−

−

×⋅×−⋅×

+⋅×−⋅+=µ (2.71)

With the efficiency of film cooling is possible calculate the gas temperature (Tw,ad) at the

wall; as follows,

( )3ggad,w TT.TT −−= η (2.72)

For internal and external temperatures of the flame tube at the point immediately before

the next slot, it is necessary to make a balance of heat flux through the tube wall of flame. The

flame tube is heated by radiation and convection from the hot gas inside, and it is cooled by

convection to the annulus air and by radiation to the outer casing. Under equilibrium

condition the internal and external heat fluxes are equal at any point; the loss of heat by

conduction along the flame tube is very small and usually is neglected. The Figure 2.14 shows

the heat transfer model along the flame tube.



65

F FIGURE 2.14 – Heat transfer model for flame tube. [14].

Under steady-state, the rate of heat transfer into a wall must be balanced by the rate of

heat transfer out, [11] as is show in the equation 2.73,

( ) ( ) 1w212w221w11 AKAKCRAKCR ∆∆∆ −=++=++ (2.73)

where the heat conduction along the flame tube (K) is neglected, and the flame tube wall is

usually so thin that can be consider as ∆Aw1 = ∆Aw2. The equation 2.73 can be simplified to,

( ) ( ) 212211 KCRCR −=+=+ (2.74)

and K1-2 is the conduction heat transfer through the flame tube wall due to temperature

gradient, and is given by:



66

( )2121 . www

w TTt

kK −=− (2.75)

where kw is the thermal conductivity of material of flame tube, and Tw1 and Tw2 are the

temperatures in the inner surface and outer surface of flame tube.

The radiation heat flux from combustion gas to flame tube is given by:

( ) ( )5.21w

5.2g

5.1ggw1 TTT15.0R −+= εεσ (2.76)

where σ is the Stefan-Boltzmann constant whose value is 5.67 x 10-8 W/ (m2K4), εw is the

flame tube wall emissivity and εg is the gas emissivity at temperature Tg can be obtained

through,

[ ]5.1g

5.0b3g T.)l.FAR(P290.0exp1 −−−=ε (2.77)

where FAR is the fuel air ratio by mass, lb is mean beam length of radiation path that is

determinate by the shape and size of the gas volume, for annular combustors are lb = 0.90Dft

and for multi-can and can-annular lb = 0.75Dft [11]. It is important to emphasize that the

equation 2.77 is used for nonluminous gases, for luminous gases is used the following

equation,



67

[ ]5.1g

5.0bu3g T.)l.FAR(LP290.0exp1 −−−=ε (2.78)

where Lu is a luminosity factor and can be calculated by the expression proposed by Mongia

[23],

365.7

8

u H

10964.5L

×= (2.79)

where H is the fuel hydrogen content (by mass) in percent.

The convection heat gas flux from gas for hot side wall of flame tube is calculated

depending on the value of m,

( ) 3.1m5.0forTTRex

k069.0C 1wad,w

7.0x

g1 <<−

= (2.80)

( ) 0.4m3.1forTTs

xRe

x

k010.0C 1wad,w

36.08.0

xg

1 <<−

=

−

(2.81)

where the Reynolds number (Rex) has as a reference length the distance between the slots,



68

aaax

xURe

µρ= (2.82)

The term kg in the equations 2.80 and 2.81represents the gas conductivity into the flame

tube, and is defined as,

33

1123

83

54g T105011410,1T1089398,4T1080957,91092657.5k −−−− ×+×−×+×= (2.83)

The radiation heat flux from flame tube to casing is calculated by,

( )43

42w2 TTZR −= σ (2.84)

where Z is equal to 0.4 for aluminium air casing, or 0.6 for steel air casing. The convection

heat flux to annulus air is given by,

( )32w

8.0

aan

an2.0

an

an2 TT

A

m

D

k020.0C −

=

µ&

(2.85)

where kan is the conductivity of air at the annular area, and can be obtained through the

equation 2.81 substituting Tg by T3, as follow,



69

3g

112g

8g

54an T105011410,1T1089398,4T1080957,91092657.5k −−−− ×+×−×+×= (2.86)

To determine the temperatures in the inner and outer wall of flame tube is necessary solve

the system show in the equation 2.74 through an iterative process. The calculation should be

carried out for all operating conditions and it is recommended that in any case the temperature

of inner wall of flame tube should be not greater than 1100 K, it is recommended that the

position of the dome slot would be such that its projection on the length of the dome

represents one third of this distance.

2.2.13 Design of air admission holes

Firstly it is necessary verifying the remaining air mass flow rate available for admission

holes in each zone of combustor. It is carried out discounting the air mass flow rate of air at

each zone less the air that enters through the cooling slots; after this is possible determines the

available air mass flow rate that it will enter for each row of holes.

In the primary zone the air mass flow rate (ṁh,PZ) that goes into the holes is given by,

PZ,slotdome,slotswPZPZ,h mmmmm &&&&& −−−= (2.87)



70

where ṁslot,dome is the air mass flow rate that enters in the primary zone by the slot located in

the dome and ṁslot,PZ is the total air mass flow rate that enters by all the slot located into the

primary zone. The air mass flow rate for the secondary zone (ṁh,SZ) is calculated through,

SZ,slotSZSZ,h mmm &&& −= (2.88)

where ṁslot,SZ is the total air mass flow rate that enters by all the slot located into the

secondary zone. Finally, for the dilution zone will be,

DZ,slotSZPZ3DZ,h mmmmm &&&&& −−−= (2.89)

After determining the air mass flow rate that will enter into each zone, it is necessary to

specify the type of hole. The determination of the hole size is done through by iterative

process, this process is due to the of discharge coefficient value (Cd,h) is unknown. The

sequence of calculation is presented below:

1. Calculation of bleed ratio (β), that is defined as,

an

h

m

m

&

&=β (2.90)

where ṁh is the hole mass flow and ṁan is the annulus mass flow.



71

2. Establish a reasonable value of discharge coefficient (Cd,h).

3. Determine the total area of holes (Ah), for each row using the equation 2.91, and

assuming the pressure loss through a hole (∆Pft/P3)as 0.6

h2

d2

3

32

h

3

ft

ACP

Tm5.143

P

P &=

∆ (2.91)

4. Calculate the hole area ratio (α) and (µ) that is the relation between hole bleed ratio (β)

and hole area ratio (α).

AreaAnnulus

AreaHole

A

A

an

h ==α (2.92)

RatioAreaHore

RatioBleed==αβµ (2.93)

5. Calculate the pressure loss factor (K) using the equation 2.94,

( )

−

++==

5.0

22

2422 4421K ββ

δµµµδ (2.94)

where δ is the momentum loss factor, that varies according with the type of hole, using

0.8 for plain holes and 0.6 for plunged holes[24].



72

6. Replace into the equation 2.95, the value of pressure loss factor (K) to obtain the value

of discharge coefficient (Cd,h).

( )( )[ ] 5.022

h,d2KK4

1KC

βδ −−

−= (2.95)

If the discharge coefficient established in the step two is equal to the value obtained in by

the equation 2.95, then the correct value has been selected. If not, the iterative process must

be followed until correct values are found.

From the sequence showed, it is obtained the total area of a row of holes. After this is

established the number of holes per row (Nh) and the number of rows for each zone, to

determinate those numbers it is important take in to account the total length of each zone and

the distance between the rows and the number of holes, to avoid possible structural damage.

With the hole number (Nh) is possible found the diameter of holes (dh), as follow,

h

hh N.

A.2d

π= (2.96)

For multi-can and can-annular combustor the yielding position of the holes is the even

distribution of these along the circumference taking as the centre of it, the fuel nozzle. For

annular combustor the holes should be distributed in the inner and outer walls of flame tube of

combustor, where the inner wall has the lower diameter that the outer wall. For this reason is



73

necessary calculated the annular areas of the combustor. The outer annular area (Aan,out) can

be determined by [25]:

( ) ( )

++−+=

4

DDDD2DA

2ftrefin

2refin

out,an π (2.97)

For the inner annular area (Aan,inn),

( )

−−+=

4

DDDDA

2in

2ftrefin

inn,an π (2.98)

Then it is possible calculate the internal hole area of the inner wall of the flame tube

through the following equation,

+

=

inn,an

out,an

hinn,h

A

A1

AA

(2.99)

The outer hole area is the result of the difference between the total area of holes (Ah) and

internal hole area (Ah,inn),



74

inn,hhext,h AAA −= (2.100)

The number of internal holes for the inner wall of tube flame is calculated by the

equation:

+

=

inn,h

out,h

hinn,h

A

A1

NN

(2.101)

The holes for outer wall are given by;

inn,hhout,h NNN −= (2.102)

Then is necessary verified whetter the number of holes fit the internal and external

circumferences of flame tube, as follows:

( )( )2

DDD.C ftrefint

inn,ft

−+= π (2.103)

( )( )2

DDD.C ftrefint

out,ft

++= π (2.104)

assuming that;



75

out,hinn,hh ddd ≅≅ (2.105)

then;

inn,hinn,hinn,ft N.dC > (2.106)

out,hout,hout,ft N.dC > (2.107)

3 Methodology Implementation

The proposed methodology allows calculate the basic geometric parameters of

combustors as: the total length of the combustor, length of each zone of the combustor,

diameter or height of the flame tube and the casing, dimensions of the diffuser, geometric

parameters of swirler, yielding positioning and size of primary and secondary air admission

holes, film cooling system and temperature profile.

The design methodology for a gas turbine combustor operating with different types of

fuels is presented through the use of a schematic view that is shown in the Figure 3.1 which

specifies the sequence followed.

3.1 Methodology structure

As shown in Figure 3.1 the methodology is divided into several stages, for each stage of

calculation is necessary to establish which parameters are inputs and which ones are outputs.

Next are described each one.

3.1.1 Theoretical limits for equivalence ratio

To establish the limits for equivalence ratio is necessary set the type of fuel to be used

and its composition, enthalpy of formation of fuel and the lower heating value. With these

CHAPTER 3. METHODOLOGY IMPLEMENTATION 77

data is possible obtain the adiabatic flame temperature as a function of equivalence ratio, for

different inlet temperatures (T3). For this work was assumed that the inlet temperature varies

from 300 to 1000 K and equivalence ratio varies from 0.5 to 1.5, as is shown in the Figure

3.2.

FIGURE 3.1 – Schematic overview of preliminary design procedure


The Figure 3.2 shows the results obtained for adiabatic flame temperature as function of

equivalence ratio, where ∆T -= 1600 – T3,

FIGURE 3.2 – Example of adiabatic temperature curves

After determining the curves for each temperature (T3), and to obtain the function that

relates the inlet temperature for the limits ϕrich and ϕlean it is necessary make a linear

interpolation to find a equation that relates the temperature and the limits.The results of this

relationship are show as example in the Table 3.1.

TABLE 3.1 – Limits for equivalence ratio as function of T3

Fuel ϕrich ϕlean Kerosene 0.67 - .0004T3

1.82 -0.0006T3

Natural gas 2.458 - 0.0004 T3 0.399 – 0.0001 T3

Ethanol 1.4596 - 0.0015 T3 0.7229-0.0005T3

1000

1200

1400

1600

1800

2000

2200

0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6

∆T =

(1

60

0-T

3)K

Equivalence ratio ϕ

300K

400K

500K

600K

700K

800K

900K

1000K

T3


3.1.2 Equivalence ratio for primary zone

Having defined the theoretical limits it is necessary to establish the operating limits for

equivalence ratio. These limits are related itself with the engine operating conditions, where

the inputs and outputs for calculation are shown in the Figure 3.3. In this section are taken

into account chemical and aerodynamic considerations.

FIGURE 3.3 – Equivalence ratio for primary zone

3.1.4 Calculation of basic dimensions

This section shows the input and output parameters for the calculation of basic

dimensions of the combustion chamber, these basic dimensions mainly concern to the

reference area and flame tube area, and reference diameter and flame tube diameter. See

Figure 3.4.


FIGURE 3.4 – Calculation of reference area and flame tube

It is important to remember that from the values obtained for the Dft is necessary choose

the value that is used in subsequent calculations. The value of Dft must be at least equal to the

higher value obtained for all operating conditions, to ensure that satisfy the aerodynamic and

chemical conditions. In addition with the value of Dft established are recalculate the values of

reference area (Aref) , area of the flame tube(Aft); and the diameter or height as it is necessary.

3.1.5 Calculation of air flow and length of zones

At this stage is defined the percentage of air that enter into each of the regions of the

combustor and besides is obtained the length of each of these regions. See Figure 3.5.

FIGURE 3.5 – Calculation of air flow and length of the zones


3.1.6 Calculation of diffuser parameters

In this section are shown the inputs and outputs of the design parameters for diffuser, as

shown in Figure 3.6.

FIGURE 3.6 – Calculation of diffuser parameters

3.1.7 Calculation swirler parameters

To calculate swirler parameters are considered some aspects specially the available space,

because the swirler size is strongly relational with the fuel injector size. The inputs and

outputs in this section are shown in Figure 3.7.

FIGURE 3.7 – Calculations of swirler parameters

3.1.8 Calculation of recirculation zone

The input data and output for calculation of recirculation are show in the Figure 3.8.


FIGURE 3.8 – Calculation of recirculation zone

3.1.9 Calculation of flame temperature

As was established in the previous chapter the calculation of the flame temperature is

carry out through the use of a CRN, consequently is necessary establish the initials values for

inputs parameters. These values only feeds the first reactor the remainder reactor are fed by

the product of the previous one.

The Figure 3.9 shows the inputs and output for flame temperature.

FIGURE 3.9 – Calculation of flame temperature

The execution of the CRN was carry out using software CHEMKIN Collection 3.7 code, the

package AURORA [28] was used for simulated the PSR and package PLUG [29] to simulated

PFR.


3.1.10 Film cooling calculation

The calculation of film cooling system is carried out for the most critical operating

condition, i.e. the values adopted for this calculation correspond to this situation. With the

temperature profile along the combustor established in the previous section it is possible to

determine the hottest area of the combustor, so it becomes easier to determine the position and

number of cooling slots along the combustor. The profile of temperature used corresponds for

most critical operating condition too. The Figure 3.10 shows the inputs and outputs for film

cooling.

FIGURE 3.10 – Film cooling calculation

3.1.11 Air admission holes

The inputs and outputs of the calculation of air admission holes are shown in the Figure

3.11. As was established in the previous chapter the calculation of air admission holes is an

iterative process, and may require several attempts before finding the appropriate values.


FIGURE 3.11 – Air admission holes

CHAPTER 4. 85

4. Validation and results

This chapter deals with the validation of the adequacy of methodology proposed during

this research, as well as with its validation and the results obtained for different configurations

of combustors using different types of fuel.

4.1 Validation

To validate the proposed methodology was used the example given by Melconian and

Modak [1]. The example presents the calculation process. The results are compared with the

reference literature. In this way it is possible to verify the accuracy of the proposed

methodology.

In the example, it is assumed a multican configuration with six combustors for a turbojet

aircraft; which cruise speed is assumed as 1.4 Mach, with a compressor exit area of 0.096 m2

and exit velocity of 150 m/s at the normal cruise condition, using kerosene as fuel.

The inlet parameters used for the calculation are showed in the Table 4.1

CHAPTER 4. VALIDATION AND RESULTS 86

TABLE 4.1– Example operating condition [1]

Operating Condition

P3 [Mpa]

p3 [Mpa]

T3 [K] M 3

[kg/s] φ

Overall Pattern Factor

Comb. Eff. % Min

mf3 [kg/s]

∆P3-4/P3

1 2 1.93 814 18.1 0.347 20 99.7 0.427 0.07

2 0.7 0.68 707 6.8 0.286 20 99.5 0.132 0.07

3 1.8 1.77 1060 14.2 0.145 20 99.5 0.14 0.07

4 0.15 0.148 343 1.05 0.128 20 99 0.0091 0.07

Where the condition 1 represents design point maximum thrust SLS, condition 2 is

maximum altitude, condition 3 is the normal cruise and the condition 4 is the ground idle

Additionally the value of pressure loss factor (∆P3-4/qref) was established as 53.

The amount of air required in the primary zone is obtained by through of the use of

theoretical limits for equivalence ratio. For kerosene these limits are given by the equations

4.1 and 4.2. [17].Using the methodology described in the section 2.2.1 and 3.1.1.

φlean = 0.67 – 0.0004 T3 (4.1)

φrich = 1.82 + 0.0006 T3 (4.2)

The Table 4.2 shown a comparison between the values obtained for equivalence ratio

limits using the equations 4.1, 4.2 and the method proposed by Melconian and Modak [1]

TABLE 4.2– Equivalence ratio limits comparison [1]

Condition

Ratio Φ Overall/ Φlimit

by Melconian Ratio Φ Overall/ Φlimit

By proposed equations

Lean Rich Lean Rich 1 1.01 0.14 1.01 0.15

2 0.73 0.12 0.74 0.13

3 0.60 0.05 0.59 0.06

4 0.24 0.06 0.24 0.06


Comparing the results obtained with the example values is observed that the variation is

about 1% and the limits do not vary significantly. Therefore the approach that was carried out

by using the equations 4.1 and 4.2 is appropriate.

The amount of air required in the primary zone is among the greatest value obtained from

the rich condition, in this case 0.15, and the lowest value obtained in the poor condition, 0.24

for this case. The example considerer a value of 0.25 corresponding to 25% of the total

amount of air that enters to the combustor.

The reference values of combustors (area and diameter) were obtained taking into

account the aerodynamic and chemical considerations discussed in the sections 2.2.3 and

2.2.4. The values for each of the operating conditions are shown in the Table 4.3.

TABLE 4.3– Combustor liner airflow and outer casing airflow reference values Condition Aref [m

2] Aft [m2] Dft [m] Dref [m]

Aerodynamic Chemical Aerodynamic Chemical Aerodynamic Chemical Aerodynamic Chemical

1 8.51E-02 4.80E-03 5.96E-02 3.36E-03 2.75E-01 6.54E-02 3.29E-01 7.81E-02

2 8.51E-02 1.42E-02 5.96E-02 9.94E-03 2.75E-01 1.12E-01 3.29E-01 1.34E-01

3 8.47E-02 8.92E-04 5.93E-02 6.24E-04 2.75E-01 2.82E-02 3.28E-01 3.37E-02

4 4.27E-02 3.19E-02 2.99E-02 2.23E-02 1.95E-01 1.69E-01 2.33E-01 2.02E-01

The Table 4.3 shows that the highest value for the flame tube diameter Dft in the four

conditions corresponding to a value of 0.275 m and is given by aerodynamics conditions

Table 4.4 shows the values of the example and the results obtained; there is a slight

difference between them about of 4%. This difference may be due to the calculation that was

performed without any approximation; the example suggests that some approximations were

made. For further calculations, the values adopted correspond to the values used in the

example.


TABLE 4.4 – Combustor liner airflow and outer casing airflow final values Example values Results

Reference area Aref 0.088 m2 0.085 m2

Flame tube area Aft 0.0617 m2 0.060 m2 Reference diameter Dref 0.335 m 0.329 m

Flame tube diameter Dft 0.280 m 0.275 m

Table 4.5 shows the values obtained for the length of the combustor and the percentage of

air for each of the regions of the combustor, whereas the equivalence ratio ϕ should not

exceed 0.8 in the secondary zone. These values are equals to the example.

TABLE 4.5– Combustor length zone and preliminary air distribution

Zone

Percent of Air (%)

Length [m]

Primary Zone 25 0.21

Secondary Zone 18.38 0.14

Dilution Zone 5.22 0.37

The total length of the combustor is 0.723m and air available for cooling is the 51.40%.

Table 4.6 presents the design parameters of the diffuser, where it was considered that half

of the air entering the primary zone is admitted through the swirl and the dome slot cooling,

i.e. 12.5 % passes through the swirl and the slot. Then 87.5% of total air passes through the

combustor annular area (Aan). The calculation assumes that the pressure loss in the diffuser is

1% and the coefficient of discharge of the snout is 1.

TABLE 4.6 – Diffuser example parameters

Diffuser Parameter

Air percent through the section Aan 87.5

Divergence angle ψ [°] 23

Snout area As [m2] 0.0038

Snout diameter Ds [m] 0.069

Ldif [m] 0.064


Table 4.7 presents the parameters obtained for the swirler, assuming the following

conditions: stagger angle of 60o, air mass flow rate through the swirler is 7%, loss of pressure

inside the snout of 25%, atomizer diameter of 0.042 m, wall thickness of 0.0015 m and

straight blade type.

TABLE 4.7 – Swirler example parameters

Swirler parameters

Swirler Area Asw [m2] 3.21E-03

Swirler Diameter Dsw [m] 0.078

Dsw/Dft 0.28

The recirculation zone parameters were obtained assuming that the length of the

recirculation zone should be between two times the outer diameter of the swirler and the

length of the primary area, for this example were taken as 0.168 m. Obtaining that the dome

angle θ= 48.43o and the length of the dome is 0.0895 m.

The temperature profile along the combustor was obtained using two methodologies, the

first profile corresponds to the methodology proposed by Melconian and Modak [1]. The

combustor is divided into four zones: recirculation zone, primary zone, secondary zone and

dilution zone. For each zone, the local temperature will be assumed to vary linearly between

the zone inlet temperature (Tin) and zone outlet temperature (Tout). the results are presented in

Figure 4.1


FIGURE 4.1 – Temperature profiles by Melconian and Modak [1] methodology

As shown in Figure 4.1 for the conditions 1, 3 and 4 the highest temperatures are at the

exit of the primary zone, which most part of the combustion process takes places. However, in

condition 2 the highest temperature is reached in the secondary zone, suggesting that for this

condition the combustion process was not completed in the primary zone and part of it takes

place in the secondary zone.

The Table 4.8 shows the inlet and outlet temperature at each zone of combustor, as the

mean temperature at recirculation zone.

The second methodology is based on the CRN, to obtain the temperature profile it was

carried out the temperature calculation by use of software CHEMKIN 3.7, package AURORA

[28] and PLUG [29]. This code used a detailed mechanism for kerosene.[30].

The input data of this calculation are based in the molar fraction of reactants. The

recirculation zone was modelled as a single PSR at given temperature, the temperature in the

recirculation zone was assumed as the mean temperature of the recirculation zone that was

found using the methodology proposed by Melconian and Modak [1] since the inlet

temperature (T3) it is too low compared with the real temperature, as it is known the

recirculation zone it is mixture of recirculating hot gases from the remainder primary zone

700

1200

1700

2200

2700

3200

0,00 0,20 0,40 0,60 0,80

Tem

per

atur

e [K

]

Distance [m]

Temperature profile

Condition 1Condition 2Condition 3Condition 4


and new reactant. For the inlet of primary zone was assumed the output parameters from the

PSR of recirculation zone.

TABLE 4.8 – Temperature profile

Condition Recirculation zone

Primary zone Secondary zone Dilution Zone

1 Tin 814.00 2534.4 2145,6 1520,7

Tout 2398.7 2080 1501

Tmean 1822.81 - - -

2 Tin 707.00 2412.7 2103.2 1468.7

Tout 2345.6 1979.2 1468.2

Tmean 1619.90

3 Tin 1060.00 2867.6 2426.8 1654.2

Tout 2752.2 2333.1 1645.3

Tmean 2076.73

4 Tin 343.00 1467.8 1198.1 987.7

Tout 1428.9 1101.2 967.4

Tmean 889.50

The Figure 4.2 presents the results obtained by the used of CNR

FIGURE 4.2 – Temperature profiles by CRN methodology

700

1200

1700

2200

2700

3200

0,00 0,20 0,40 0,60 0,80

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



Comparing the Figure 4.1 with Figure 4.2 is observed that the temperature using the CRN

methodology is greater that the methodology used by Melconian and Modak [1]. It is mainly

due to that in CRN is considered all chemical reactions. There are two main differences

between the two methodologies. Firstly, in the primary zone occurs, as is observed using the

methodology of Melconian and Modak [1], into the primary zone the temperature is increased

slowly, in the CNR methodology the temperature present a sudden increase at the first reactor,

after this reactor the temperature became to decrease. The second difference is in the dilution

in the methodology proposed by Melconian and Modak [1] the temperature decreased slowly.

Using the CNR the temperature in this zone remains almost constant, what means that for this

zone of the combustor does not happen any chemical reaction.

To calculate the film cooling system, it is assumed that the film cooling surfaces have the

same shape and size. The following parameters were assumed: slot height (s) = 0.0025m, slot

lip thickness (t) = 0.002m, wall thickness (tw) = 0.0012 m, the wall material is nimonic and

the casing material is aluminum. The calculation was carried out for the two types of gases,

i.e., non luminous gases and luminous gases. The Temperature profile adopted for the

calculation of cooling system corresponds to the CRN methodology.

The calculation was carried out with six cooling slots including the slot located in the

dome. The position of the slots is shown in Table 4.9. The position of each slot corresponds to

the position given by the example.

TABLE 4.9 – Slot position

Slot Distance [m]

Flare cooling 0.068

Slot 1 0.168

Slot 2 0.220

Slot 3 0.360

Slot 4 0.450

Slot 5 0.714


Table 4.10 presents the values obtained for the temperature of the inner and outer wall,

for two types of gas i.e. for luminous and non luminous gases, where the calculation was

carried out for all operating conditions.

From the Table 4.10 it can be observed that the temperature in the wall for luminous

gas is higher that non luminous gas, it is due that during the calculation is taking in to account

the emission of small particles that going to accumulate in to the wall, increasing the

temperature. It is important remark that the calculation for film cooling was performed with

the Temperature profile obtain by de CNR method, and the temperatures at the wall are higher

that the presented in the example.

TABLE 4.10 – Wall temperature Operating Condition

Position [m] Luminous gas Non luminous gas

Tw1 [K] Tw2 [K] Tw1 [K] Tw2 [K]

1 0.168 1061.92 1036.35 1042.39 1018.86

2 924.41 913.93 896.26 887.17

3 1326.86 1301.37 1290.90 1268.93

4 437.49 436.54 429.72 428.85

1 0.220 1256.27 1184.17 1178.52 1119.27

2 1111.49 1075.71 1022.82 995.06

3 1522.00 1441.04 1420.19 1357.40

4 548.57 545.35 517.64 514.92

1 0.360 985.83 972.86 973.90 961.85

2 1006.21 994.26 949.15 939.57

3 1382.09 1351.08 1325.69 1300.28

4 464.73 463.52 451.73 450.65

1 0.450 982.75 970.95 970.72 959.77

2 974.34 964.45 929.02 920.87

3 1336.52 1314.08 1293.20 1274.38

4 461.12 460.06 449.88 448.92


1 0.714 983.43 972.51 967.84 957.93

2 889.52 884.04 860.36 855.78

3 1216.41 1207.43 1194.93 1187.21

4 440.17 439.41 429.26 428.59

To calculate the air admission holes firstly was established the percentage of air available

for each zone, obtaining 14.83% for primary zone, 18.30% for secondary zone and 42.10%

for dilution zone. Eight holes was established as the number of holes in each of those zones,

as a first approximation the discharge coefficient was set at 0.5 for each of those zones of the

combustor. The results are shown in the Table 4.11:

TABLE 4.11 – Air admission holes parameters Zone Nholes dh [m] Ah,t [m2] Cd

Primary Zone 8 0.0231 0.00336 0.558

Secondary Zone 8 0.0257 0.00416 0.556

Dilution Zone 8 0.0394 0.00978 0.544

The modifications done in the methodology proposed by Melconian and Modak [1] does

not vary considerably the results in the basic layout and the geometry of combustor, the

difference is not significant. For these reasons the methodology proposed in this work shows

a good accuracy and its recommendable.

4.2 Results

This section describes some preliminary designs for two combustors configurations

that operate with different fuels. The first combustor is an annular combustor which operates

with ethanol and kerosene. The second combustor is a can-annular combustor for a stationary


turbine operating with natural gas, kerosene and ethanol. These are some hypothetical to

present how use the design methodology for multifuel combustors.

4.2.1 Annular combustor operating with kerosene

The parameters used for the preliminary design are based on the combustor used as

example by Melconian Modak [1], i.e., was assumed similar operating conditions and used

the typical values proposed for an annular combustor. The fuel used was kerosene.

Input design parameters are presented in Table 4.12

The value of pressure loss factor (∆P3-4/qref) was assumed as 25. The internal diameter of

combustor was setting as 0.25 m.

TABLE 4.12 – Operating condition for annular combustor operating with kerosene

Operating Condition

P3 [Mpa]

p3 [Mpa] T3 [K]

M 3 [kg/s]

φ Overall

Pattern Factor

Comb. Eff. % Min

mf3 [kg/s] ∆P3-4/P3

1 2 1.93 814 18.1 0.347 20 99.7 0.427 0.06

2 0.7 0.68 707 6.8 0.286 20 99.5 0.132 0.06

3 1.8 1.77 1060 14.2 0.145 20 99.5 0.14 0.06

4 0.15 0.148 343 1.05 0.128 20 99 0.0091 0.06

The amount of air required in the primary zone was established using the equations 4.1

and 4.2 for kerosene [17], obtaining the results show in Table 4.13.


TABLE 4.13 – Theoretical equivalence limits for annular combustor operating with kerosene

Condition

Theoretical Limits Ratio Φ Overall/ Φlimit


2 0.39 2.24 0.74 0.13

3 0.24 2.46 0.59 0.06

4 0.53 2.02 0.24 0.06

The amount of air required in the primary zone is a value between 0.15 and 0.24. For this

case we assumed a value of 0.24 corresponding to 24% of the total amount of air entering into

the combustor. It is also noted that under the same operating conditions. The theoretical limits

ΦOverall / Φlimit ratio does not vary with respect to the previous example due to those limits

depends on the inlet temperature and theoretical equivalence limits.

The table 4.14 show the results obtained for the areas and diameters of reference and

flame tube.

TABLE 4.14 – Combustor liner airflow and outer casing airflow reference values Condition Aref [m

2] A ft [m2] Dft [m] Dref [m]


1 6.31E-02 1.41E-02 4.42E-02 9.88E-03 3.47E-02 1.18E-02 1.56E-01 1.68E-02

2 6.32E-02 3.47E-02 4.42E-02 2.43E-02 3.47E-02 2.68E-02 1.56E-01 3.83E-02

3 6.28E-02 4.40E-03 4.40E-02 3.08E-03 3.45E-02 3.84E-03 1.55E-01 5.49E-03

4 3.17E-02 7.52E-02 2.22E-02 5.26E-02 2.06E-02 5.17E-02 9.25E-02 7.39E-02

Table 4.15 presents the suggested values and the final values adopted for further

calculations. The suggested values are the minimum reference values (area and diameter) that

must have the combustor. The final values correspond to the recalculated values for a flame

tube diameter (Dft) of 0.180 m. This value was chosen because it is the one that better fit for

further calculations and fulfills with all considerations.


TABLE 4.15 – Combustor liner airflow and outer casing airflow final values for annular combustor

Suggested Values Final Values Reference area Aref 0.075 m2 0.409 m2

Flame tube area Aft 0.053 m2 0.286 m2

Reference diameter Dref 0.156 m 0.257 m


Table 4.16 shows the values obtained for the length of the combustor and the

percentage of air for each combustor zone.

TABLE 4.16 – Combustor length zone and preliminary air distribution for annular combustor

Zone

Percent of Air (%)

Length [m]




The total length of the combustor is 0.542 m and the percentage of air available for

cooling is 51.40%, this value is equal to the value found in the previous example. It happens

because the value depends only of the inlet temperature (T3).

The diffuser design parameters are shown in the Table 4.17, where 12% of total air

passing through the swirl and the slot. Then 87.5% of total air passes through the annular area

of the combustor (Aan). The calculation assumes that the total pressure loss in the diffuser is

1%, the discharge coefficient of the snout is 1 and the compressor exit area is 0.096 m2.


TABLE 4.17 – Diffuser parameter for annular combustor

Diffuser Parameter





Ldif [m] 0.001

It is observed that the divergence angle of diffuser is closer to the 90o and the diffuser

length is very small, this is due to the configuration of combustor it is not fit completely to

compressor exit area. However, the diffuser can be assumed as a sudden expansion diffuser,

in which the walls have high angles of divergence. These types of diffusers are used in most

contemporary turbines. Also can be assumed that it is not necessary the use of diffuser.

The Table 4.18 shows the parameters obtained for the swirler. For the calculation was

assumed the following conditions: stagger angle of the 55o, mass air flow through the swirler

5%, loss pressure inside of the snout of 25%, atomizer diameter of 0.032 m corresponding to

12.5% of the reference diameter, wall thickness of 0.0015m and blades type curved.

TABLE 4.18 – Swirler parameter for annular combustor

Swirler parameters



Dsw/Dft 0.30

The parameters of the recirculation zone were obtained assuming the length of the

recirculation zone as 0.110 m. Obtaining that the dome angle θ is 48.12o and the length of the

dome (LDom) is 0.0622 m.

The Figure 4.3 shows the results for the temperature profile using the methodology of

Modak and Melconian [1].


FIGURE 4.3– Temperature profile for annular combustor operating with kerosene

The Figure 4.3 presented that for conditions 1, 3, and 4 the highest temperature is reached

at the end of the primary zone. However in the condition 2 the highest temperature condition

is reached in the secondary zone, present the same behaviour that the previous case.

The Table 4.19 shows the inlet and outlet temperature at each zone of combustor and also


The Figure 4.4 shows the temperature profile using the proposed CRN, as the previous

case the calculation was carry out use of software CHEMKIN 3.7, package AURORA [28]

and PLUG.[29] This code used a detailed mechanism for kerosene.[30]. As in the previous

case the temperature in the recirculation zone was assumed as the mean temperature,

calculated by the methodology of Modak and Melconian [1]

700

1200

1700

2200

2700

3200

0,00 0,10 0,20 0,30 0,40 0,50 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



TABLE 4.19 – Temperature profile



1 Tin 814.00 25567.4 2212.4 1676.1

Tout 2412.10 2101.2 1670.1

Tmean 1822.81

2 Tin 707.00 2498.7 2199.2 1553.3

Tout 2378.1 2087.9 1545.8

Tmean 1619.90

3 Tin

2798.6 2562.1 1702.1

Tout 2736.9 2465 1697.7

Tmean 2076.73

4 Tin 343.00 1567.38 1278.1 1042

Tout 1476.1 1188.8 1036.3

Tmean 889.50 - - -

FIGURE 4.4– Temperature profile for annular combustor operating with kerosene

Comparing the Figure 4.3 and Figure 4.4 can be observed that the temperature reached

using the CRN is always higher for all operating conditions, in the same way it is observed

that the changes in the temperatures between the zones is evident, this it is mainly related with

the inlet temperature at each zone of the combustor. For the calculation in the CRN is taking

in to account the air that enter in each zone, this influence can be observed in the behaviour of

700

1200

1700

2200

2700

3200

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



the temperature line. It is interesting observe that in the dilution the temperature remains

almost constant.

Comparing with the combustor multican used in the previous case is observed that under

the same operating condition the Temperature profile changes slightly mainly due to the

volume of the combustor. Based on the Figure 4.2 and 4.4 the temperature is higher in the

annular combustor that in the multican combustor.

To calculate the film cooling system, it is assumed that the film cooling surfaces have the

same shape and size. And was assumed the same parameters used in the previous example.

slot height (s) = 0.0025m, slot lip thickness (t) = 0.002m, wall thickness (tw) = 0.0012, the

wall material is nimonic and the aluminum for casing material.

The calculation was carried out with six cooling slots including slot located in the dome.

The positioning of the cooling slots is based on the example and are the same that the

previous case. The position of the slots and results obtained for wall temperature at four

operating conditions are shown in Table 4.20. As the previous case the calculation was carried

out for luminous and non luminous gases.


TABLE 4.20 – Wall temperature

Operating Condition Position

[m] Luminous gas Non luminous gas

Tw1 [K] Tw2 [K] Tw1 [K] Tw2 [K]

1 0.09 1172.35 1158.80 1132.30 1120.38

2 1021.49 1015.83 961.85 957.37

3 1440.32 1425.38 1372.08 1360.11

4 464.63 464.23 444.08 443.74

1 0.110 1084.71 1075.12 1044.75 1036.64

2 939.23 935.35 887.42 884.46

3 1350.77 1340.11 1287.87 1279.69

4 426.99 426.72 411.61 411.40

1 0.150 1533.55 1489.33 1377.93 1344.28

2 1323.90 1308.02 1154.98 1144.18

3 1733.60 1690.77 1561.67 1531.11

4 642.46 640.89 567.98 566.84

1 0.190 1469.14 1434.16 1329.38 1302.66

2 1284.77 1271.15 1130.01 1120.65

3 1681.21 1646.11 1524.38 1499.26

4 606.47 605.26 544.12 543.22

1 0.240 1287.43 1269.72 1202.87 1188.65

2 1159.46 1151.88 1049.42 1044.00

3 1542.87 1522.85 1433.14 1418.27

4 519.51 518.91 484.85 484.37

1 0.310 1252.03 1237.12 1252.03 1237.12

2 1121.90 1115.41 1121.90 1115.41

3 1485.29 1469.75 1485.29 1469.75

4 511.89 511.35 511.89 511.35

From the Table 4.20 can be observed that the temperature in the wall for luminous gas

is higher that non luminous gas, this behavior is the same that in the previous case. It is

important remark that the calculation for film cooling was performed with the Temperature


profile obtain by de CNR method, and the temperatures on the wall are higher that the

presented in the example.

The percentage of air available for zone of combustors is: 13.85% or the primary zone,

19.25% for the secondary zone and 42.10% for dilution zone. To obtain the remainder

parameters for air admission, the number of holes per zone was established as follows: sixteen

holes in the primary zone, sixteen in the secondary zone and twenty in the dilution zone. As a

first approximation, the discharge coefficient was set at 0.5. The results are shown in the table

4.21.

TABLE 4.21 – Air admission holes parameters Zone Nholes dh [m] Ah,t [m2] Cd

Primary Zone 16 0.0155 0.0030 0.622

Secondary Zone 16 0.0172 0.0037 0.622

Dilution Zone 20 0.0233 0.0085 0.621

From the Table 4.21 we can see that the diameter of the holes varies, being in this

example the smaller the primary zone and the larger the dilution zone, this is due to the

amount of air that must enter in each zone.

The number of holes in each zone is distributed in the inner and outer wall; the

distribution is show in the Table 4.22.

TABLE 4.22 – Air admission holes distribution Zone Nholes Nh,inn Nh,out

Primary Zone 16 5 11

Secondary Zone 16 5 11

Dilution Zone 20 6 14

Where Nholes is the total number of holes, Nh, inn is the number of holes in the inner wall

and Nh,out is the number of holes in the outer wall. The number of holes arranged in each zone


fits within the internal and external circumference. To obtain a high efficiency in the

combustion process, the distribution of the holes in the primary zone must take into account

the positions of the fuel injectors and the all air that enters should be used in combustion

process.

4.2.2 Annular combustion chamber operating with ethanol

For this example assumes that the combustor burned ethanol as fuel. The input

parameters are the same to the previous example. To maintain the same equivalence ratio that

the previous case it is necessary to establish a new mass flow of fuel due to change in the fuel.

Assuming that equivalence global ratio and mass air flow (M3) are constant i.e. does not

vary with respect to the previous example and FAR for ethanol is assumed as 9. A new mass

fuel flow is obtained through the equations 4.3 and 4.4

stoo

f

cono

f

sto

conglobal

m

m

m

m

==

&

&

&

&

φφφ

(4.3)

Where ṁo is the mass air flow and ṁf is the mass fuel flow.

f

oGlobal m

mFAR

&

&= (4.4)


The Table 4.23 shows the operating conditions

TABLE 4.23 – Operating condition for annular combustor operating with ethanol

Operating Condition

P3 [Mpa]

p3 [Mpa]

T3 [K] M 3

[kg/s] φ


Comb. Eff. % Min

mf3 [kg/s]

∆P3-4/P3

1 2 1.93 814 18.1 0.347 20 99.7 0.698 0.06

2 0.7 0.68 707 6.8 0.286 20 99.5 0.216 0.06

3 1.8 1.77 1060 14.2 0.145 20 99.5 0.229 0.06

4 0.15 0.148 343 1.05 0.128 20 99 0.015 0.06

The values of pressure loss (∆P3-4/qref) and internal diameter was assumed as the same

values of the previous cases. Where pressure loss is 25 and internal diameter is 0.25m.

The amount of air necessary for the primary zone was established through the

equations 4.5 and 4.6 for theoretical limits for equivalence ratio for ethanol. These equations

were found using methodology described in the section 2.2.1 and 3.1.1.

φlean = 0.7229-0.0005T3 (4.5)

φrich = 1.4596 - 0.0015 T3 (4.6)

The Table 4.24 presents the results for theoretical limits.

TABLE 4.24 – Theoretical limits for annular combustor operating with ethanol

Condition



2 0.37 2.52 0.78 0.12

3 0.20 3.05 0.75 0.05

4 0.55 1.98 0.23 0.06


The amount of air required in the primary zone is between 0.13 and 0.23. The

calculation assumed a value of 0.24 which corresponds to 24% of the total amount of air

entering to the combustor.

The results for the areas and diameters of reference and flame tube are shown in the

Table 4.25.




1 6.31E-02 1.41E-02 4.42E-02 9.88E-03 3.47E-02 1.18E-02 1.56E-01 1.68E-02

2 6.32E-02 3.47E-02 4.42E-02 2.43E-02 3.47E-02 2.68E-02 1.56E-01 3.83E-02

3 6.28E-02 4.40E-03 4.40E-02 3.08E-03 3.45E-02 3.84E-03 1.55E-01 5.49E-02

4 3.17E-02 7.52E-02 2.22E-02 5.26E-02 2.06E-02 5.17E-02 9.25E-02 7.39E-01

Where the minimum value that must have the flame tube diameter (Dft) for this case is

0.052 m. In this case, like previous two cases the flame tube diameter Dft is determined by

chemical considerations and the reference diameter Dref by aerodynamic conditions. The

flame tube diameter for this case is lower than that of the combustor operating with natural

gas, but higher than the combustor operating with kerosene.

The flame tube diameter (Dft) was assumed as 0.200m, this value fulfills the

aerodynamic and chemical considerations. Table 4.26 shows the suggested values and the

final values adopted for further calculations. The suggested values are the minimum reference

values (area and diameter) for combustor. The final values correspond to the recalculated

values for a flame tube diameter Dft of 0.200 m.


TABLE 4.26 – Combustor liner airflow and outer casing airflow final values for annular combustor operating with ethanol

Suggested Values Final Values Reference area Aref 0.075 m2 0.480m2




The Table 4.27 shows the values obtained for combustor length zone and percentage of

air for each zone of the combustor.

TABLE 4.27– Combustor length zone and preliminary air distribution for ethanol

Zone

Percent of Air (%)

Length [m]





cooling is 51.40. The percent of air for cooling is the same that the previous cases, because it

depends of inlet temperature (T3).

For the diffuser design was considered that 12% of the total air entering the chamber

passes through the swirler and dome slot. Then the remaining 88% of total air passes through

the annular area of the combustor (Aan). The calculation assumes that the pressure loss in the

diffuser is 1%, the discharge coefficient of the snout is 1 and the compressor exit area is 0.096

m2. The results are shown in the Table 4.28.


TABLE 4.28– Diffuser parameter for annular combustor operating with ethanol

Diffuser Parameter

Air percent through the section Aan 88




Ldif [m] 0.002

As in the previous cases the divergence angle shows that it is closer to the 90o and the

diffuser length is very small. This is due mainly to the compressor exit area that is not

completely compatible with the combustor configuration.

For the calculation of swirler the following conditions were assumed: Stagger angle =

55o, mass air through swirler = 5%, total loss of pressure inside the snout of 25%, atomizer

diameter of 0.036 m which corresponds to 12.5% of reference diameter, thickness of the wall

=0.0015m and curved blades.

The length of the chamber of the recirculation zone was established as 0.125m. The dome

angle θ is 43.60o and the resultant length of the dome is 0.0727 m.

The Figure 4.5 shows the results obtained for the temperature profile using the

methodology proposed by Melconian and Modak [1].

FIGURE 4.5– Temperature profile for annular combustor operating with ethanol.

700

1200

1700

2200

2700

3200

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile




mean temperature at recirculation zone

TABLE 4.29 – Temperature profile for annular combustor operating with ethanol



1

Tin 814.00 2413.2 2277.1 1613.5

Tout 2306.3 2187.7 1608.9

Tmean 1822.81

2

Tin 707.00 2587.42 2363.4 1689.9

Tout 2478.5 2252.1 1678.4

Tmean 1619.90

3

Tin 1060.00 2606.2 2135.7 1587.6

Tout 2471.7 2017 1576.0

Tmean 2076.73

4

Tin 343.00 1281.1 1076 876

Tout 1198 978.5 875.6

Tmean 889.50

The Figure 4.6 show the temperature profile using the proposed CRN, as the previous

case the calculation was carry out use of CHEMKIN 3.7, package AURORA[28] and

PLUG[29]. This code used a detailed mechanism for ethanol [32]. As in the previous cases

the temperature in the recirculation zone was assumed as the mean temperature, calculated by

the methodology of Modak and Melconian [1].


using the CRN is always higher for all operating conditions, in the same way it is observed

that the changes in the temperatures between the zones is evident. This it is mainly related

with the inlet temperature at each zone of the combustor. In the CRN calculation is taking in

to account the air that enter in each zone, the influence of the air inlet can be observed in the

behaviour of the temperature line. As in the previous case it was observed that the

temperature in the dilution zone remains almost constant


FIGURE 4.6– Temperature profile for annular combustor operating with ethanol.

The positioning of cooling slots was perform based on the temperature profile, placing a

greater number of slots in hottest area of the combustor, in this case three slots are positioned

into recirculation zone and primary zone. For calculations were assumed the following values:

Slot height (s) = 0.0025m, the Slot Lip Thickness (t) = 0.002m, wall thickness (tw) = 0.0012

m, wall material is nimonic and material of the steel casing. The gas is assumed as non-

luminous.

The position of the slots and temperature of the inner and outer wall are shown in Table

4.30.

700

1200

1700

2200

2700

3200

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



TABLE 4.30 – Cooling slot position and wall temperature for annular combustor with operating with ethanol.

Operating condition Position [m] Tw1 [K] Tw2 [K]

1 0.090 1172.35 1158.80

2 1021.49 1015.83

3 1440.32 1425.38

4 464.63 464.23

1 0.110 1084.71 1075.12

2 939.23 935.35

3 1350.77 1340.11

4 426.99 426.72

1 0.150 1533.55 1489.33

2 1323.90 1308.02

3 1733.60 1690.77

4 642.46 640.89

1 0.190 1469.14 1434.16

2 1284.77 1271.15

3 1681.21 1646.11

4 606.47 605.26

1 0.250 1287.43 1269.72

2 1159.46 1151.88

3 1542.87 1522.85

4 519.51 518.91

1 0.310 1252.03 1237.12

2 1121.90 1115.41

3 1485.29 1469.75

4 511.89 511.35

From the Table 4.30 can be observed that the temperature in the wall are above that

1300K, for this reason it is necessary modify the position of the cooling slots. The position of

the slot was adopted from the previous cases. The calculation of film cooling was performed

with the Temperature profile obtained by de CNR method.


To calculate the air admission holes parameters, firstly was established the percentage of

air available for each area. Obtaining that for the primary zone is 13.85% for primary zone,

19.25% for the secondary zone and 42.10% for dilution zone. To obtain the remainder

parameters for air admission holes, the number of holes per zone was established as follows:

sixteen holes for primary zone, sixteen holes for secondary zone and twenty holes in the

dilution zone. As a first approximation, the discharge coefficient was set at 0.5. Finally, the

results are shown in the Table 4.31.

TABLE 4.31 – Air admission holes for annular combustor operating with ethanol Zone Nholes dh [m] Ah,t [m2] Cd

Primary Zone 16 0,0149 0,00281 0,623

Secondary Zone 16 0,0176 0,00390 0,623

Dilution Zone 20 0,0233 0,00854 0,622

The distribution of the holes in the inner and outer wall is shown in Table 4.32.

TABLE 4.32 – Air admission holes distribution for can-annular combustor operating with ethanol

Zone Nholes Nh,inn Nh,out Primary Zone 16 4 12

Secondary Zone 16 4 12

Dilution Zone 20 5 15

Where Nholes is the total number of holes, Nh,inn is the number of holes in the inner wall

and Nh,out is the number of holes in the outer wall. As in the previous cases the number of air

admission holes in each zone fits within the outer and inner circle.

The Table 4.33 shows a comparison between the basic layout for the combustor operating

with kerosene and the combustor operating with ethanol.


TABLE 4.33 – Basic layout for annular combustors Combustor operating with Ethanol Combustor operating with kerosene

Reference diameter Dref [m] 2,85E-01 Reference diameter Dref [m] 2,57E-01

Flame tube diameter Dft [m] 2,00E-01 Flame tube diameter Dft [m] 1,80E-01

Internal diameter di [m] 2,50E-01 Internal diameter di [m] 2,50E-01

Total length [m] 6,02E-01 Total length [m] 5,42E-01

Primary zone length [m] 1,50E-01 Primary zone length [m] 1,35E-01

Secondary zone length [m] 1,00E-01 Secondary zone length [m] 9,00E-02

Dilution Zone Length [m] 3,52E-01 Dilution Zone Length [m] 3,17E-01

Length of recirculation zone [m]

1,25E-01 Length of recirculation zone [m]

1,10E-01

From the Table 4.33 it can be observed that the combustor operating with ethanol the size

is higher comparing with the combustor operating with kerosene. However, is possible that

either of the combustor under the given conditions it is able to operate without any problem,

because the amount of air admitted into the primary zone of the combustor is the same for

both cases and corresponds to 24 % of total air. This ensures that the combustors always

operated between flammability limits. In this way the combustion is guaranteed under all

operating conditions from the chemical point of view. From the aerodynamic point of view

and based on the calculations performed it was observed that also is also possible; however,

the total pressure loss is higher for the ethanol case. The difference in the flame tube diameter

is due mainly to diffuser calculation. Due to with a higher diameter the length of the diffuser

according with the calculations become negative, that it is not possible under any condition.

The parameters used to calculate the diffuser and swirler are the same for both cases, as well

the parameters used for film cooling calculation. For these specific cases it is necessary to

perform a modification in the position of cooling slot, since to for one of the cases the

temperature at the wall is above of 1300 K. The holes for admission air for the both cases are

the same. In general it is possible that for the same operating conditions the combustor have

the ability to operate without problem.


4.2.3 Can-annular combustion chamber operating with natural gas

The proposal combustor is for an industrial gas turbine type can-annular with six

combustors, which operates with natural gas. With a maximum power of 14.41 MW,

compressor exit area of 0.290 m2, air velocity at the outlet of the compressor is assumed to be

150 m/s.

Input parameters for each operating condition are shown in Table 4.34. The value of

pressure loss (∆P3-4/qref) was assumed as 30[1]. The internal diameter of the combustor was

set as 0.22m.

Where condition 1 corresponds to 100% of engine rotation, i.e. 11.200 rpm, the second

condition corresponding to 80% with 8.960 rpm, the third condition corresponds to 60% of

6.720 rpm rotation and the fourth condition corresponds to 40% of the 4.480 rpm rotation.

TABLE 4.34 – Operating condition for can-annular combustor operating with natural gas

Operating Condition

P3 [Mpa]

p3

[Mpa] T3 [K]

M 3 [kg/s]

φ Overall

Pattern Factor

Comb. Eff. %

Min

mf3 [kg/s]

∆P3-4/P3

1 1.732 1.696 678 50 0.314 20 99 0.9118 0.04

2 1.195 1.168 609 39 0.186 20 99 0.4285 0.04

3 0.831 0.81 547 28 0.162 20 98 0.2747 0.04

4 0.641 0.623 506 17 0.157 20 96 0.1601 0.04

The amount of air required in the primary zone was established using the theoretical

limits for equivalence ratio equations for gas natural equation 4.7 and 4.8

φlean = 0.399 – 0.0001 T3 (4.7)

φrich = 2.458 - 0.0004 T3 (4.8)


The theoretical limits for equivalence ratio are shown in the Table 4.35.

TABLE 4.35 – Theoretical limits for annular combustor operating with natural gas

Condition


Lean Rich Lean Rich

1 0.33 2.19 0.95 0.14

2 0.34 2.21 0.55 0.08

3 0.34 2.24 0.48 0.07

4 0.35 2.26 0.45 0.07

Consequently, the amount of air required in the primary zone lies between 0.14 and 0.45.

The calculation assumed a value of 0.46 which corresponds to the 46% of the total amount of

air entering the combustion chamber.

The Table 4.36 show the results obtained for the reference values of combustors (area and

diameter).




1 2.47E-01 2.10E-02 1,63E-01 1.39E-03 1.43E-01 1.85E-02 3.99E-01 2.71E-02

2 2.64E-01 8.42E-03 1.74E-01 5.56E-03 1.50E-01 7.77E-03 4.16E-01 1.04E-01

3 2.59E-01 1.33E-02 1.71E-01 8.79E-03 1.48E-01 1.21E-02 4.10E-01 1.30E-01

4 1.96E-01 1.39E-01 1.29E-01 9.16E-03 1.21E-01 1.25E-02 3.46E-02 1.33E-01

Based on the result from the Table 4.36 the minimum value that the tube must have for

this case is 0.150m. For this case the flame tube diameter is given by the aerodynamic

conditions as the reference diameter. For this example it was assumed a flame tube diameter

Dft of 0.230 m, accomplish with the minimum diameter given by the aerodynamic conditions.

The Table 4.37 shows the suggested values which are the minimum value that must have

the combustor and the values adopted for further calculations.


TABLE 4.37 – Combustor liner airflow and outer casing airflow final values for can-annular combustor operating with natural gas

Suggested Value Final Values Reference area Aref 0.264 m2 0.283 m2




The Table 4.38 shows the values obtained for the length of the combustor and the

preliminary air distribution.

TABLE 4.38 – Combustor length zone and preliminary air distribution for can-annular combustor operating with natural gas

Zone

Percent of Air (%)

Length [m]




The total length of the chamber is 0.637 m and the percentage of air available for cooling

is 37.80 %.

For the diffuser design was considered that half of the air entering the primary zone is

supported through the swirl and the dome slot cooling, i.e. 23% passes through the swirl and

the cooling of the dome slot. Then 77% of the total air passes through the annular area of the

combustor (Aan). The calculation assumes that the pressure loss in the diffuser is 1%, the

discharge coefficient of the snout is 1 and the compressor exit area is 0.290 m2. The results

are shown in the Table 4.39.


TABLE 4.39 – Diffuser parameter for can-annular combustor operating with natural gas

Diffuser Parameter





Ldif [m] 0.261

For this case it can be observed that the divergence angle of the diffuser is small,

resulting in a relatively long diffuser. This due to the outlet compressor area is not completely

fitted with the combustor.

For the calculation of swirled the following conditions were assumed: stagger angle =

60o, mass air flow rate through the swirler 6%, loss of pressure inside the snout of 25%, the

atomizer diameter of 0.032 m which corresponds to 10% of reference diameter, thickness of

the wall type was assumed as 0.0012m and blades type curved. The Table 4.40 shows the

results obtained for the swirler.

TABLE 4.40 – Swirler parameter for can-annular combustor operating with natural gas

Swirler Parameter



Dsw/Dft 0.29

The parameters of the recirculation zone were obtained assuming that the length of the

recirculation zone lies between two times the outer diameter of the swirl and the length of the

primary area for this example was taken as 0.135m. The calculated dome angle θ is 49.32o

and the length of the dome (LDom) is 0.0700 m.

The Figure 4.7 shows the results obtained for the temperature profile obtained using the



From the Figure 4.7 can be observed that the highest temperature inside the combustor

reaches the end of the primary zone for the first operating condition. Also is observed that for

conditions 1, 2, 4 the higher temperature is reached in the primary zone, however for

condition 2 this temperature also reaches in the secondary zone

FIGURE 4.7– Temperature profile for can-annular combustor operating with natural gas



TABLE 4.41 – Temperature profile for can annular combustor operating with natural gas

Condition Recirculation

zone Primary zone Secondary zone Dilution Zone

1 Tin 678.00 2345.7 2089.8 1576.4 Tout

2263.2 1945.1 1553.7 Tmean 1643.64

2 Tin 609.00 2265 1986.4 1576.3 Tout

2291.1 1876.3 1553.7 Tmean 1517.98

3 Tin 547.00 2010.7 1567.2 1463.3 Tout 1813.33 1892.2 1435.2 1450.8 Tmean

4 Tin 506.00 1879.9 1456.5 880.6 Tout

1791.7 1296.2 876.7 Tmean 1300.51 - - -

700

900

1100

1300

1500

1700

1900

2100

2300

2500

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



The Figure 4.8 show the temperature profile using the proposed CRN, as the previous

case the calculation was carried out use of CHEMKIN 3.7, package AURORA[28] and PLUG

[29]. This code adopts a detailed mechanism for natural gas GRImech 3.0.[31]. As in the

previous cases the temperature in the recirculation zone was assumed as the mean

temperature, calculated by the methodology of Modak and Melconian [1].


using the CRN is higher for all operating conditions. Also it is observed that the changes in

the temperatures between the zones is evident, and is mainly related with the inlet temperature

at each zone of the combustor. The influence of the air inlet can be observed in the behaviour

of the temperature line. As in the previous case it was observed that in the temperature in the

dilution zone remains almost constant.

FIGURE 4.8– Temperature profile for can-annular combustor operating with natural gas

To calculate the film cooling, we assumed the following values: Slot height (s) = 0002 m,

the Slot Lip Thickness (t) = 0.0012m, wall thickness (tw) = 0.0015 m, the wall material is

stainless steel and the steel casing material. The gas is assumed as non-luminous.

700

900

1100

1300

1500

1700

1900

2100

2300

2500

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



The positioning of the cooling slots are related to the temperature profile, locating a

greater number of slots in the hottest area of the combustor, in this case three slots were

located in the primary zone, two in the secondary zone and one in dilution zone, for a total of

six slots, here it is not includes the dome slot. The position of the slots is shown in the Table

4.42 and the results obtained for the temperature of the inner and outer wall.

TABLE 4.42 – Cooling slot position and wall temperature for can-annular combustor with

operating with natural gas Operating condition

Position [m] Tw1 [K] Tw2 [K]

1 0.090 866.80 849.42

2 770.90 758.78

3 689.73 681.56

4 639.99 634.78

1 0.120 835.66 821.51

2 744.02 734.18

3 666.26 659.61

4 618.15 613.91

1 0.160 921.57 894.50

2 814.42 800.61

3 721.66 710.21

4 672.54 665.16

1 0.200 984.07 939.95

2 862.77 841.17

3 773.66 753.76

4 729.30 715.83

1 0.280 974.73 938.49

2 859.60 841.43

3 756.74 742.05

4 707.52 698.00

1 0.350 905.82 884.69

2 783.81 775.71

3 684.09 677.26

4 624.93 621.06


From the Table 4.42 can be observed that the temperature in the wall is lower than

1300K. The calculation for film cooling was performed with the temperature profile obtains

by de CNR method

To calculate the air admission holes was established the percentage of air available for

each zone, obtaining that for the primary zone is 35.93%, 6.29% for the secondary zone and

18.90% dilution zone. For each zone of the combustor was set the number of holes as follows:

twelve holes in the primary zone, twenty-four in the secondary zone and twenty in the dilution

zone. As a first approximation, the discharge coefficient was set at 0.5 for each of those areas

of the combustor. The results are shown in the Table 4.43.

TABLE 4.43 – Air admission holes for annular combustor operating with natural gas Zone Nholes dh [m] Ah,t [m2] Cd

Primary Zone 18 0.0399 0.0023 0.586

Secondary Zone 24 0.0143 0.0039 0.595

Dilution Zone 20 0.0274 0.0118 0.591

The number of holes provided for each section of the combustor can be accommodated

within the circumference of the combustor. However, the diameter of the hole in the primary

zone is considerably greater than that of other diameter holes. In order to reduce this size is

necessary to increase the number of holes in the zone, but for this example a larger number of

holes in a row is not possible because not fit into to the circumference. Therefore is important

to determine if the number of holes will be distributed in one or two rows and if this

distribution does not affect structurally the combustor.


4.2.4 Can-annular combustion chamber operating with ethanol

The combustor proposed for this case has the same configuration that the previous case,

but operating with ethanol as fuel. The combustor has the same operating conditions and the

input parameters are similar, however to maintain the same total equivalence ratio and due to

the change in the fuel, it is necessary to calculate the mass flow for the new fuel by using the

equations 4.3 and 4.4, where ethanol FAR is 9. The Table 4.44 shows the operating conditions

for the proposed combustor.

For this example also assumes that output area 0.290 m2 compressor and air velocity at

the outlet of the compressor = 150 m/s.

The value of pressure loss (∆P3-4/qref) was assumed as 30[1]. The internal diameter of the

combustor was assumed as 0.220m.

TABLE 4.44 – Operating conditions for can-annular combustor operating with ethanol

Operating Condition

P3 [Mpa]

p3

[Mpa] T3 [K]

M 3 [kg/s]

φ Overall

Pattern Factor

Comb. Eff. %

Min

mf3 [kg/s]

∆P3-4/P3

1 1.732 1.696 678 50 0.314 20 99 1.744 0.04

2 1.195 1.168 609 39 0.186 20 99 0.807 0.04

3 0.831 0.81 547 28 0.162 20 98 0.5046 0.04

4 0.641 0.623 506 17 0.157 20 96 0.2971 0.04

The amount of air necessary for the primary zone was established using the the

theoretical limits for equivalence ratio equations 4.5 and 4.6 for ethanol. The Table 4.45

shown the results for equivalence ratio limits


TABLE 4.45 – Theoretical limits for annular combustor operating with ethanol

Condition



2 0.42 2.38 0.56 0.07

3 0.45 2.28 0.53 0.07

4 0.47 2.22 0.44 0.07

Consequently, the amount of air required in the primary zone lies between 0.13 and 0.44.

The calculation assumed a value of 0.44 which corresponds to 44% of the total amount of air

entering to the combustor.

The Table 4.46 presents the results obtained for combustor flame tube and outer casing

reference (area and diameter).




1 2.47E-01 2.26E-02 1.63E-01 1.49E-02 1.43E-01 1.98E-02 3.99E-01 2.89E-02

2 2.64E-01 2.29E-04 1.74E-01 1.51E-04 1.50E-01 2.18E-04 4.16E-01 1.71E-02

3 2.59E-01 1.04E-04 1.71E-01 6.90E-05 1.48E-01 9.97E-05 4.10E-01 1.15E-02

4 1.96E-01 9.59E-05 1.29E-01 6.33E-05 1.21E-01 9.15E-05 3.46E-02 1.10E-02

The minimum value that the flame tube should hav is 0.150 m. For this case, as in the

previous example, the flame tube diameter and reference diameter are given by the

aerodynamic conditions. Therefore the suggested values are the same that the last case,

because it is the aerodynamics consideration, which will determine the size of the combustor.

For this example assume a flame tube diameter of 0.230 m.

The Table 4.47 shows the suggested values and the values adopted for further

calculations, where final values corresponds to recalculated values for a flame tube diameter

of 0.230m.


TABLE 4.47– Combustor liner airflow and outer casing airflow final values for can-annular combustor operating with ethanol

Suggested Values Final Values Reference area Aref 0.264 m2 0.283 m2




The Table 4.48 shows the values obtained for combustor length zones and percentage of

air for each of the zone of the combustor.

TABLE 4.48 – Combustor length zone and preliminary air distribution for can-annular combustor operating with ethanol.

Zone

Percent of Air (%) Length [m]




The total length of the chamber is 0.637 m and the percentage of air available for cooling

is 37.80%, and this values is the same that the previous case. It is because the amount of air

available for film cooling depends of the inlet temperature (T3).

For the diffuser design was considered that the 22% of total mass air flow rate passes

through the swirl and the cooling of the dome slot. Then 78% of the total air passes through

the annular area of the combustor (Aan). For calculation it was assumed that the pressure loss

in the diffuser is 1%, the discharge coefficient of the snout is 1 and the compressor exit area is

0290 m2. The results are shown in the Table 4.49.


TABLE 4.49– Diffuser parameter for can-annular combustor operating with ethanol

Diffuser Parameter





Ldif [m] 0.253

From the Table 4.49 can be observed that the divergence angle is too small and as

consequence the diffuser is long, however, is less than in the previous case.

For swirler calculation the following conditions were assumed: stagger angle of 60o, mass

flow of air swirled through 6%. Loss of pressure in the snout of 25%, atomizer diameter of

0.042 m, which corresponds to 10% of the reference diameter, wall thickness of 0.0012m and

blades type curved. The results are shown in the Table 4.50.

TABLE 4.50 – Swirler parameter for can-annular combustor operating with ethanol

Swirler Parameter



Dsw/Dft 0.28

The length of the recirculation zone was assumed to 0.133m, the dome angle (θ) is 50.70o

and dome length (LDom) is 0.0669 m.

The Figure 4.9 shows the results obtained for the temperature profile obtained using the



FIGURE 4.9– Temperature profile for can-annular combustor operating with ethanol

The Table 4.51 shows the temperature profile for inlet and outlet temperature for each

zone and at each operating condition.

TABLE 4.51 – Temperature profile for can annular combustor operating with ethanol

Condition Recirculation zone Primary zone Secondary zone Dilution Zone

1 Tin 678.00 2441.2 2208.5 1478.8 Tout

2376.4 2106.1 1477.2 Tmean 1643.64

2 Tin 609.00 2245.7 1867.6 1319.6 Tout

2132.4 1762.5 1319.4 Tmean 1517.98

3 Tin 547.00 2176.7 1699.8 1176 Tout

2076.3 1587.2 1172.9 Tmean 1391.22

4 Tin 506.00 1979.9 1448.5 986.7 Tout

1897.7 1343.5 986.1 Tmean 1300.51 - - -

From the Figure 4.9 can be observed that the highest temperature inside the combustor is

reaches the end of the primary zone for the first operating condition. Also it is observed that

700

900

1100

1300

1500

1700

1900

2100

2300

2500

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



for conditions 1, 2, 4 the higher temperature is reached in the primary zone, however for

condition 2 this temperature is reached in the secondary zone.

The Figure 4.10 shows the temperature profile using the proposed CRN, as the previous

case the calculation was carry out use of CHEMKIN 3.7, package AURORA [28] and PLUG

[29]. This code used a detailed mechanism for ethanol.[32]. As in the previous cases the

temperature in the recirculation zone was assumed as the mean temperature, calculated by the

methodology of Modak and Melconian [1]. See Table 4.50. Comparing the Figure 4.9 and

Figure 4.10 can be observed that the temperature reached using the CRN is higher for all

operating conditions. The influence of the air inlet can be observed in the behaviour of the

temperature line. As in the previous case was observed that in the temperature in the dilution

zone remains almost constant.

FIGURE 4.10– Temperature profile for can-annular combustor operating with ethanol

To calculate the film cooling, is assumed the following values: slot height (s) = 0002 m,

the slot lip thickness (t) = 0.0012m, wall thickness (tw) = 0.0015 m, the wall material is

stainless steel and the steel casing material. The gas is assumed as non-luminous. This

700

900

1100

1300

1500

1700

1900

2100

2300

2500

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



conditions are the same that the previous case. The calculation of film cooling system was

carried out with six cooling slots and in this calculation it is not include the slot located in the

dome. The position of the slots is shown in the Table 4.52 and the results obtained for the

temperature of the inner and outer wall.


operating with ethanol Operating condition Position [m] Tw1 [K] Tw2 [K]

1 0.090 887.42 867.27

2 789.19 775.08

3 705.20 695.72

4 655.51 649.42

1 0.120 861.48 844.20

2 766.86 754.75

3 685.96 677.81

4 637.39 632.17

1 0.160 982.76 945.07

2 841.57 825.24

3 769.48 752.80

4 712.89 702.71

1 0.200 1062.61 1000.97

2 906.16 880.85

3 836.86 805.83

4 789.69 769.55

1 0.280 1045.83 994.54

2 888.43 868.35

3 808.65 786.68

4 751.78 738.48

1 0.350 962.45 932.13

2 804.71 795.81

3 721.13 711.05

4 647.09 641.98


From the Table 4.52 can be observed that the temperature in the wall is lower than 1300K

for all operating conditions. The calculation for film cooling was performed with the

Temperature profile obtains by de CNR method.


each zone, obtaining that for the primary zone is 33.93%, 8.27% for the secondary zone and

18.90% dilution zone. For each zone of the combustor was setting the number of holes as

follows: eighteen holes in the primary zone, twenty-four in the secondary zone and twenty in

the dilution zone. As a first approximation, the discharge coefficient was setting at 0.5 for

each of those areas of the combustor. The results are shown in the Table 4.53.

TABLE 4.53 – Air admission holes for annular combustor operating with ethanol Zone Nholes dh [m] Ah.t [m2] Cd

Primary Zone 18 0.0368 0.02130 0.585

Secondary Zone 24 0.0165 0.00512 0.593

Dilution Zone 26 0.0274 0.01178 0.590

The number of holes obtained for each section of the combustor can be fitted within the

circumference of the combustor. However, the diameter of the hole in the primary zone is

considerably greater than that of other diameter holes. In order to reduce this size it is

necessary to increase the number of holes in that zone, for these reason it is important to

determine if the number of holes will be distributed in one or two rows and if this distribution

does not affect structurally the combustor

4.2.5 Can annular combustor operating with kerosene

To carry out the calculation of the combustor operating with kerosene, was assumed the

same values that the previous case as input parameters. To maintain the same equivalence


ratio that the previous case it is necessary to establish a new mass flow of fuel due to change

in the fuel.

Assuming equivalence global ratio and mass air flow (M3) are constant i.e. does not vary

with respect to the previous example and FAR for kerosene is assumed as 14.7. A new mass

fuel flow is obtained through the equations 4.3 and 4.4

Input parameters used for design are presented in Table 4.54 including the new mass fuel

flow.

TABLE 4.54 – Operating condition for annular combustor operating with kerosene

Operating Condition

P3 [Mpa]

p3 [Mpa]

T3 [K] M 3

[kg/s] φ


Comb. Eff. % Min

mf3 [kg/s]

∆P3-4/P3

1 1.732 1.696 678 50 0.314 20 99 1.068 0.04

2 1.195 1.168 609 39 0.186 20 99 0.4945 0.04

3 0.831 0.81 547 28 0.162 20 98 0.309 0.04

4 0.641 0.623 506 17 0.157 20 96 0.1819 0.04

The value of pressure loss factor (∆P3-4/qref) was assumed as 30. The internal diameter of

the combustor was setting as 0.220m.

The amount of air required in the primary zone was established using the theoretical

limits for equivalence ratio equations 4.1 and 4.2 for kerosene,

The theoretical limits for equivalence ratio are shown in the Table 4.55.

TABLE 4.55 – Theoretical limits for can annular combustor operating with kerosene

Condition



2 0.426 2.185 0.436 0.085

3 0.451 2.148 0.359 0.075

4 0.468 2.124 0.336 0.074


The amount of air required in the primary zone is assumed as 0.43 which corresponds to

43% of the total amount of air entering to the combustor.

The Table 4.56 shows the results obtained for the reference values of combustors (area

and diameter)




1 2.47E-01 4.09E-02 1.63E-01 2.70E-02 1.43E-01 3.39E-02 3.99E-01 4.85E-02

2 2.64E-01 2.83E-04 1.74E-01 1.87E-04 1.50E-01 2.70E-04 4.16E-01 1.90E-02

3 2.59E-01 1.49E-04 1.71E-01 9.80E-05 1.48E-01 1.42E-04 4.10E-01 1.38E-02

4 1.96E-01 1.41E-04 1.29E-01 9.28E-05 1.21E-01 1.34E-04 3.46E-01 1.34E-02

The Table 4.56 shows that the highest value for the flame tube diameter Dft in the four

conditions corresponding to a value of 0.150 m and is given by aerodynamics conditions. The

reference diameter is determined by aerodynamic considerations too. It important say that this

values are the same for the combustor operating with gas natural and ethanol, that is,

meaning that for this combustor operating under the given conditions the change of fuel does

not influence the geometric and basic sizing of combustor.

The flame tube diameter Dft value adopted for further calculations corresponds to

0.230m. This value was adopted because fulfils with all considerations. The Table 4.57

presents the suggested values and the final values adopted for further calculations. The

suggested values are the minimum areas and diameters that must have the combustor. The

final values correspond to the recalculated values for a flame tube diameter Dft of 0.230 m.


TABLE 4.57 – Combustor liner airflow and outer casing airflow final values for annular combustor operating with kerosene

Suggested Values Final Values

Reference area Aref 0.264m2 0.283m2

Flame tube area Aft 0.174m2 0.187m2

Reference diameter Dref 0.416m 0.420m

Flame tube diameter Dft 0.150m 0.230m

Table 4.58 shows the values obtained for the length of the combustor and the percentage

of air for each combustor zone.

TABLE 4.58 – Combustor length zone and preliminary air distribution for kerosene

Zone

Percent of Air (%) Length [m]





cooling is 37.8%. The last one is the same for all examples since it depends of the inlet

temperature T3.

The diffuser design parameters are shown in the Table 4.59, assuming that 21.5% of total

air passing through the swirl and the slot. Then 78.5% of total air passes through the annular

area of the combustor Aan. For calculation was assumed that the pressure loss in the diffuser is

1%, the discharge coefficient of the snout is 1 and the compressor exit area is 0.290 m2.


TABLE 4.59 – Diffuser parameter for can annular combustor operating with kerosene

Diffuser Parameter





Ldif [m] 0.249

From the Table 4.59 can be observed that the divergence angle of diffuser the divergence

angle is too small and as consequence the diffuser is long. The diffuser for this case is a

intermediate value between the values for a combustor operating with ethanol and combustor

operating with natural gas.

The Table 4.60 shows the swirler parameters. For the calculation was assumed the

following conditions: stagger angle = 60o, mass air flow through the swirler 6%, total loss

pressure inside of the snout of 25%, the atomizer diameter of 0.042m corresponding to 10%

of the reference diameter, wall thickness of 0.0012m and blades type curved.

TABLE 4.60 – Swirler parameter for can annular combustor operating with kerosene

Swirler parameters



Dsw/Dft 0.29

The parameters of the recirculation zone were obtained assuming the length of the

recirculation zone as 0.135 m. Obtaining that the dome angle θ is 49.32o and the length of the

dome LDom is 0.07 m.

The Figure 4.11 shows the results for the temperature profile using the methodology

proposed by Modak and Melconian [1] .


FIGURE 4.11– Temperature profile for can annular combustor operating with kerosene

The Figure 4.11 shows that the highest temperature for conditions 1, 3 and 4 are reached

at the end of primary zone. And for condition 2 the highest temperature is reached at the

secondary zone.

As it is observed from the Figure 4.11 the temperature profile presents higher

temperatures in all operating condition, the curves have a similar behavior. The highest

temperature of gas is reached at the end of the recirculation zone, where is located the primary

zone, that meaning with the entering air the chemical reaction is completed.

The Figure 4.12 shown the result for the Temperature profile using the CNR, where is

adopted a detailed mechanism for kerosene.[30]. As all previous cases the temperature in the

recirculation zone was assumed as the mean temperature in the zone as was obtained by the

methodology proposed by Melconian and Modak [1] See Table 4.61.

700

900

1100

1300

1500

1700

1900

2100

2300

2500

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



The Table 4.61 shows the temperature profile for inlet and outlet temperature for each

zone and at each operating condition.

TABLE 4.61 – Temperature profile for can annular combustor operating with kerosene

Condition Recirculation

zone Primary zone Secondary zone Dilution Zone

1 Tin 678.00 2340.2 2096.2 1580.1 Tout

2256.4 1998.9 1579.7 Tmean 1643.64

2 Tin 609.00 2263.4 1873 1435.6 Tout 1972.47 2167.8 1791.5 1430.9

Tmean

3 Tin 547.00 2075.6 1676.3 1108.2 Tout

1956.3 155.8 1102.5 Tmean 1391.22

4 Tin 506.00 1879.9 1562.3 978.4 Tout

1787.7 1431.4 973.5 Tmean 1300.51 - - -

Comparing the Figure 4.11and Figure 4.12 can be observed that the temperature reached

using the CRN is higher for all operating conditions. The influence of the air inlet can be

observed in the behaviour of the temperature line. As in the previous case was observed that

the temperature in the dilution zone remains almost constant.

FIGURE 4.12– Temperature profile for annular combustor operating with natural gas

700

900

1100

1300

1500

1700

1900

2100

2300

2500

0,00 0,20 0,40 0,60

Tem

per

atur

e [K

]

Distance [m]

Temperature profile



To calculate the film cooling, is assumed the following values: slot height (s) = 0002 m,

the slot lip thickness (t) = 0.0012m, wall thickness (tw) = 0.0015 m, the wall material is

stainless steel and the steel casing material. The gas is assumed as non-luminous. These

parameters are the same that the two previous cases

The calculation of film cooling system was carried out with six cooling slots and in this

calculation it is not include the slot located in the dome.The positioning of the cooling slots is

based on the temperature profile, for this reason are positioned a greater number of slots in the

hottest areas of the combustor, for this case three slots are positioned between the

recirculation zone and primary zone, not including the dome slot. The position of the slots and

the results are shown in the Table 4.62.

TABLE 4.62 – Cooling slot position and wall temperature for can annular combustor with operating with kerosene

Operating condition

Position [m] Tw1 [K] Tw2 [K]

1 0.090 870.57 855.46

2 773.79 763.31

3 691.92 684.89

4 642.61 638.13

1 0.120 839.17 826.87

2 746.59 738.07

3 668.16 662.44

4 620.36 616.71

1 0.160 928.12 904.43

2 815.48 803.49

3 730.62 720.15

4 676.25 669.88

1 0.200 988.09 951.01

2 869.93 851.37

3 781.39 763.59

4 725.88 715.43


1 0.280 983.29 951.60

2 863.33 848.18

3 767.98 754.35

4 711.54 703.39

1 0.350 920.94 901.17

2 798.43 791.30

3 700.45 693.61

4 646.40 642.25

From the Table 4.62 is observed that the temperature in the wall is lower than 1300K for

all operating conditions. Is possible affirm that the position of slots area correct. The

calculation for film cooling was performed with the Temperature profile obtains by de CNR

method.


each area getting that for the primary zone is 32.91%, 9.24% for the secondary zone and

18.90% for dilution zone. To obtain the remainder parameters for air admission holes, the

number of holes per zone was established as follows: eighteen holes for primary zone, twenty

four for secondary zone and twenty in the dilution zone. As a first approximation, the

discharge coefficient was set at 0.5. The results are shown in the Table 4.63.

TABLE 4.63 – Air admission holes parameters for can annular combustor operating with kerosene

Zone Nholes dh [m] Ah,t [m2] Cd

Primary Zone 18 0.0382 0.02067 0.585

Secondary Zone 24 0.0174 0.00574 0.593

Dilution Zone 20 0.0274 0.01179 0.590

The number of holes obtained for each section of the combustor can be fitted within the

circumference of the combustor. However, the diameter of the hole in the primary zone is

considerably greater than that of other diameter holes, and in order to reduce this size is


necessary to increase the number of holes in the zone, for these reason it is important to

determine if the number of holes will be distributed in one or two rows and if this distribution

does not affect structurally the combustor.

TABLE 4.64 – Basic layout for can annular combustor Combustor operating with

natural gas Combustor operating with

ethanol Combustor operating with

kerosene Reference diameter

Dref [m] 4.20E-01

Reference diameter Dref [m]

4.20E-01 Reference diameter

Dref [m] 4.20E-01

Flame tube diameter Dft [m]

2.30E-01 Flame tube diameter

Dft [m] 2.30E-01

Flame tube diameter Dft [m]

2.30E-01

Internal diameter di [m]

n/a Internal diameter di

[m] n/a

Internal diameter di [m]

n/a

Total length [m] 6.37E-01 Total length [m] 6.37E-01 Total length [m] 6.37E-01 Primary zone

length [m] 1.73E-01

Primary zone length [m]

1.73E-01 Primary zone

length [m] 1.73E-01

Secondary zone length [m]

1.15E-01 Secondary zone

length [m] 1.15E-01

Secondary zone length [m]

1.15E-01

Dilution Zone Length [m]

3.50E-01 Dilution Zone Length [m]

3.50E-01 Dilution Zone Length [m]

3.50E-01

Length of recirculation zone

[m] 1.35E-01


[m] 1.35E-01


[m] 1.35E-01

From theTable 4.63 is possible said that this combustor has the ability to operate with the

three fuels without a significant modification, i.e. for those three cases the basic sizing and

configuration practically is the same, the theoretical limits for equivalence ratio are closer the

difference between them are approximately 2%, this small difference allows that the

configuration in the air admission will be the same.

Another important fact is that the flame tube diameter (Dft) is equal for all cases what

means that for this combustor the references values for combustor liner airflow and outer

casing airflow are determined by aerodynamic conditions and the change of fuel does not

affect considerably the size. In general for this combustor the parameters considerer into the

design process are the same.


It is important say that in each case presented in this work the parameters adopted were

based on typical values and are within the limits of the methodology. However, these values

may change according with the designer criteria. The goal of the selection of each parameter

is obtain the best possible configuration, allowing that the combustor operates with different

type of fuel without affecting combustor performance. It is possible that a combustor

operating with different types of fuels does not operate with one hundred percent efficiency.

However, the design looks that the combustor performance will be the maximum operating

with any type of fuel.

It is also important notice the difference shown in each of the combustors. For annular

combustor operating with kerosene and ethanol, the geometry is governed by aerodynamic

and chemical considerations. This makes the combustor designed for kerosene have not the

ability to operate with ethanol. But the combustor designed to operate with ethanol is in the

ability to operate with kerosene.

In the case of can annular combustor operating with natural gas, ethanol and kerosene the

geometry is governed purely by aerodynamic parameters. This is mainly due to the factor of

total pressure loss in the combustor is more restrictive than in the case of the annular

combustor. In this way it is possible say that with lower pressure loss factor into the

combustor, which have more influence in to the geometry are aerodynamic considerations.

However, it is important to remember that are the set of operating parameters are those who

will determine the basic geometry of the combustor and under certain conditions the

considerations that govern the design can vary from aerodynamics consideration to chemical

considerations o vice versa.

140

5. Conclusions

The proposed methodology for combustor design showed that has the ability to establish

basic geometric parameters and basic configuration of a combustor using fuels such as natural

gas and ethanol.

It also was shown that the design process requires a broad knowledge of operating

conditions. As is can be observed from the examples the design process not only consists in

adapting the operating conditions from one configuration to another. There must be a detailed

analysis of each operating condition and parameters to be used into design, considering not

only the type of fuel, also aspects such as compatibility between engine components,

especially with compressor.

It was found that although the change of fuel affects the combustor geometry is not

always a determining factor, are the set of initial parameters which will determine the basic

configuration. It is important to emphasize that the design operating conditions must be closer

as possible to real condition; the time spent in the design process will be less. Also it is

important remember that methodology here proposed allows obtained a preliminary design

and it is necessary continue with the optimization process through numerical analysis tools as

CFD codes.

According with the results obtained in this work it is possible to design a combustion

chamber to operate with three types of fuels cosidered in this work. However, it is important

to note that according with the results is possible obtain a basic layout for an aeronautical

CHAPTER 5. CONCLUSIONS 141

combustor that operates with kerosene and ethanol, and an industrial combustor that have the

ability to operate with natural gas, ethanol and kerosene. However, this requires an extensive

study of the conditions of combustor operating condition and the interaction with the

components of the gas turbine engine.

The use CRN proved to be a useful tool to calculate the temperature of the gases, which

takes into account not only the conditions of operation also takes into consideration the fuel

characteristics.

Finally as recommendations for future work, is suggested the use of CNR in the

prediction of pollutants.

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[3] STUTTAFORD, P.J.; RUBINI P.A. Assessment of a radiative heat transfer model for a new gas turbine combustor preliminary design tool. In: AEROSPACE SCIENCES MEETING & EXHIBIT, 35., 1997, Reno, Proceedings... Washington, D.C: AIAA, 1997. (AIAA Paper 97-0294).

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FOLHA DE REGISTRO DO DOCUMENTO

1. CLASSIFICAÇÃO/TIPO DM

2. DATA 24 de setembro de 2010

3. REGISTRO N° DCTA/ITA/DM-060/2010

4. N° DE PÁGINAS 152

5. TÍTULO E SUBTÍTULO: Preliminary design methodology for multi fuel gas turbine combustors

6. AUTOR(ES): Juliana Andrea Niño Navia 7. INSTITUIÇÃO(ÕES)/ÓRGÃO(S) INTERNO(S)/DIVISÃO(ÕES): Instituto Tecnológico de Aeronáutica - ITA 8. PALAVRAS-CHAVE SUGERIDAS PELO AUTOR: Gas Turbine Combustor; Design methodology; Chemical Reactor Network; Gas turbine 9.PALAVRAS-CHAVE RESULTANTES DE INDEXAÇÃO: Combustores; Turbinas a gás; Reatores químicos; Síntese de redes; Controle de processos; Engenharia mecânica 10. APRESENTAÇÃO: X Nacional Internacional ITA, São José dos Campos. Curso de Mestrado. Programa de Pós-Graduação em Engenharia Aeronáutica e Mecânica. Área de Aerodinâmica, Propulsão e Energia. Orientador: Pedro Texeira Lacava. Defesa em 21/09/2010. Publicada em 2010. 11. RESUMO:

The combustors for gas turbines have been traditionally designed through trial and error, which is a time consuming and expensive process. With the development of computers and new simulation techniques the design process has been improved considerably. However, the design of combustors for gas turbines still remains an iterative process, which requires a broad knowledge of engine operating conditions and the interaction of their components with the engine components.

This work presents the establishment of a methodology for preliminary design for gas turbine combustor, based on the methodology proposed by Melconian e Moldak and the application of a chemical reactors network (CRN), this last one in order to establish the temperature profile of the gases into combustor.

Originally, the methodology proposed by Melconian e Moldak uses kerosene as fuel. For this reason, the proposed methodology in this work was adapted to consider different types of fuel. This methodology is capable to set the basic geometric parameters and providing a basic configuration of a combustor considering changes in operational loads.

Some cases have been developed, which allowed verifying the implementation of the proposed methodology and the CRN. The first case was used as validation method and was employing a multi–can combustor type, which operates with kerosene as fuel based on example proposed by Melconian e Moldak. The second case corresponds to an annular combustor for an aircraft engine which operates with kerosene, natural gas and ethanol. For each of these fuels was carried out a preliminary design of combustor. The third case is a can annular combustor for application in an industrial gas turbine using natural gas, ethanol and kerosene as fuels.

A step by step design methodology is presented in this work. It is important to mention that the proposed methodology is for conventional combustors.

12. GRAU DE SIGILO: (X ) OSTENSIVO ( ) RESERVADO ( ) CONFIDENCIAL ( ) SECRETO

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