A CFD STUDY OF THE SWIRL NUMBER INDUCED BY A DIESEL ENGINE INTAKE

VALVE PORTS Ana Elisa Fernandes Tobal

1, Cláudia Regina de Andrade

2, Edson Luiz Zaparoli

3, Fábio Yukio Kurokawa

4

1 Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brasil, anaeft@ita.br 2 Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brasil, Claudia@ita.br 3 Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brasil, zaparoli@it.br 4 MWM Internacional Motors, São Paulo, SP, Brasil, Fabio.kurokawa@navistar.com.br

Abstract: This work focuses on a numerical study of a diesel engine valve ports steady-state compressible flow to calculate the mixing effects due to the presence of the filling and spiral intake ducts. These valve ports have an important role in engine charge exchange (exhaust and intake mechanisms), air-fuel mixture and combustion processes. Diesel engine industry developed a stationary bench flow tests which has been very useful to improve the preliminary design of valve ports. In this bench methodology, a stationary airflow is induced through valve ports by a exhaust fan where pressure drops and swirl flow patterns are measured maintaining a fixed valve aperture. At this context, the present CFD (Computational Fluid Dynamic) work intends to show fluid flow patterns and to calculate the Swirl number induced by the secondary flow. A 3D turbulent steady compressible flow is solved employing a finite volume technique with a density based approach. Keywords: engineering applications, CFD, swirl number. 1. INTRODUCTION

The industry is always in search of improving the combustion process of diesel engine in order to reduce pollutants emission, low consumption and better performance.

The combustion process quality depends on the air and fuel mixture which should be as homogeneous as possible, for this, there are a rotational flow known as swirling flow and rotates around the axis of the cylinder. Due to the importance of the swirl number in diesel engines the need for the industry to control its intensity is clear as shown in [1]

F. Payri et al. [2] presented a study about the influence of the air flow movement in the combustion process of a direct injection diesel engine, modifying three design parameters, the cylinder head, the piston and the inlet duct in order to obtain different intensities of swirl in the cylinder. To measure the flow characteristics produced by the inlet port geometry of the cylinder heads, tests in a steady flow test rig have been carried out. This experiments have been performed by means of the paddle wheele technique, as proposed by the A.V.L method, and with

Laser-Doppler Anemometry (LDA). They have concluded that the an almost linear relation between swirl numbers calculated by both techniques was found, and these values were used as input data for in-cylinder flow models.

To analyzes different definitions of the swirl number and their application to control the mixing process in the cylinder of direct injection diesel engines Crnojevic et al. [3] discuss the origins of the existing methods used to control swirl, which are usually based on the presence of a stirring device, or rotameter, in the cylinder head. They have proposed a new possibility for determining the swirl number, based on equivalent angular velocity, and a comparison made of results obtained using the different techniques available for measuring swirl in motor cylinders.

Oishi et al. [4] studied an application of CFD for predicting intake swirl intensity. The accuracy of prediction is evaluated by comparing calculation results with results measured on a swirl test rig when using a CAM system to produce 11 variations of intake ports. Accordingly, the accuracy with which both flow rate and swirl intensity are estimated can be improved by these empirical equations to correct the estimated values.

At the present work, a numerical simulation is used to evaluate the flow patterns and determinate the swirl number at different positions along the diesel engine cylinder axis. The objective is to analyze the air mixing flow process without fuel, i.e, the combustion phenomenon is not evaluated. The studied geometry is a typical two intake valves engine, with a spiral and a filling inlet ducts. The numerical solution is achieved by constructing a three dimensional mesh and using a commercial CFD code based on the finite volume method.

2. PROBLEM STATEMENT

2.1. Geometry and boundary conditions

Figure 1 shows the studied geometry where a typical engine cylinder with two intake valves is represented. The computational domain includes an entry region (plenum) where the boundary conditions are specified (total pressure, total temperature and turbulent quantities specified values). The airflow reaches the spiral and filling intake ducts and the outlet boundary conditions are applied at the cylinder

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http://dx.doi.org/10.5540/DINCON.2011.001.1.0178

A CFD Study of the Swirl Number Induced by a Diesel Engine Intake Valve Ports A.E.F. Tobal , C.R. Andrade, E.L. Zaparoli, F.Y. Kurakawa.

exit (pressure and turbulent quantities). Non-slip conditions are applied at solid walls.

(a)

(b) (c)

Fig. 1. (a) Isometric view, (b) frontal view and (c) lateral view of

the engine cylinder

2.2. Mathematical Formulation

To simulate the compressible turbulent airflow, the following governing equations (RANS-Reynolds-Averaged Navier-Stokes, energy and realizable k- turbulence model) are used.

𝜕𝜌

𝜕𝑡+ ∇. (𝜌𝑣 ) = 0 (1)

𝜕

𝜕𝑡(𝜌𝑣 ) + ∇. (𝜌𝑣 𝑣 ) = −∇𝑝 + ∇. (𝜏 𝑒𝑓𝑓 ) (2)

where: 𝜌= fluid density; 𝑣 = velocity vector; 𝑝=pressure; 𝜏 𝑒𝑓𝑓 = viscous stress tensor. The stress tensor is determined by:

(𝜏 𝑒𝑓𝑓 ) = 𝜇𝑒𝑓𝑓 ∇𝑣 + ∇𝑣 𝑇 −

2

3∇. 𝑣 𝐼 (3)

with: 𝜇𝑒𝑓𝑓 = effective viscosity; 𝐼= unit tensor. 𝜕

𝜕𝑡 𝜌𝐸 +

𝜕

𝜕𝑥𝑖 𝑢𝑖 𝜌𝐸 + 𝑝 =

=𝜕

𝜕𝑥𝑗 𝑘𝑒𝑓𝑓

𝜕𝑇

𝜕𝑥𝑗+ 𝑢𝑖 𝜏𝑖𝑗 𝑒𝑓𝑓

+ 𝑆ℎ (4)

where 𝐸= total energy, 𝑘𝑒𝑓𝑓 = effective thermal conductivity 𝜏𝑖𝑗 𝑒𝑓𝑓

= stress tensor components of the 𝜏 𝑒𝑓𝑓 .

The term 𝑢𝑖 𝜏𝑖𝑗 𝑒𝑓𝑓 represents the viscous dissipation. In

the 𝑘 − 𝜖 model, the effective thermal conductivity is calculated by:

𝑘𝑒𝑓𝑓 = 𝑘 +

𝑐𝑝𝜇 𝑡

𝑃𝑟𝑡

(5)

where 𝑘, is the molecular thermal conductivity, 𝑃𝑟𝑡 is the turbulent Prandtl number. The realizable 𝑘 − 𝜖 turbulence model equations are: 𝜌𝑘 +

𝜕

𝜕𝑥𝑗 𝜌𝑘𝑢𝑗 =

=𝜕

𝜕𝑥𝑗 𝜇 +

𝜇 𝑡

𝜎𝑘

𝜕𝑘

𝜕𝑥𝑗 + 𝐺𝑘 + 𝐺𝑏 − 𝜌𝜖 − 𝑌𝑀 (6)

𝜕

𝜕𝑡 𝜌𝜖 +

𝜕

𝜕𝑥𝑗 𝜌𝜖𝑢𝑗 =

=𝜕

𝜕𝑥𝑗 𝜇 +

𝜇 𝑡

𝜎𝜖

𝜕𝜖

𝜕𝑥𝑗 + 𝜌𝐶1𝑆𝜖 − 𝜌𝐶2

𝜖2

𝑘+ 𝑣𝜖+ 𝐶1𝜖

𝜖

𝑘𝐶3𝜖

𝐺𝑏 (7)

where 𝐶1 = 𝑚𝑎𝑥 0.43,

𝜂

𝜂+5 , 𝜂 = 𝑆

𝑘

𝜖, 𝑆 = 2𝑆𝑖𝑗 𝑆𝑖𝑗

In equations 6 and 7, 𝐺𝑘 represents the generation of turbulence kinetic energy due to the mean velocity gradients. 𝐺𝑏 is the generation of turbulence kinetic energy due to buoyancy. 𝑌𝑀 represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. 𝐶2 and 𝐶1𝜖 are constants. 𝜎𝑘 and 𝜎𝜖 are the turbulent Prandtl numbers for k and 𝜖, respectively. In 𝑘 − 𝜖 model the turbulent viscosity is calculated by: 𝜇𝑡 = 𝜌𝐶𝜇

𝑘2

𝜖 (8)

𝐶𝜇 is given by: 𝐶𝜇 =

1

𝐴0+𝐴𝑠𝑘𝑈∗

𝜖

(9)

where

𝑈∗ ≡ 𝑆𝑖𝑗 𝑆𝑖𝑗 + 𝛺 𝑖𝑗𝛺 𝑖𝑗 (10)

and 𝛺 𝑖𝑗 = 𝛺𝑖𝑗 − 2𝜖𝑖𝑗𝑘 𝜔𝑘 (11)

The model constants 𝐴0 e 𝐴𝑠 are: 𝐴0 = 4.04, 𝐴𝑠 = 6𝑐𝑜𝑠∅ (12) where ∅ =

1

3𝑐𝑜𝑠−1 6𝑊 , 𝑊 =

𝑆𝑖𝑗 𝑆𝑗𝑘 𝑆𝑘𝑖

𝑆 3, 𝑆 = 𝑆𝑖𝑗 𝑆𝑖𝑗 and

𝑆𝑖𝑗 =1

2 𝜕𝑢𝑗

𝜕𝑥𝑖+

𝜕𝑢𝑖

𝜕𝑥𝑗

It can be seen that 𝐶𝜇 is a function of the mean strain and

rotation rates, the angular velocity of the system rotation,

and the turbulence fields (𝑘 e 𝜖). The realizable 𝑘 − 𝜖 model has been intensively used to

capture turbulence effects in the CFD calculations due to its cost effectiveness (lower CPU time).

Outlet

Inlet

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A CFD Study of the Swirl Number Induced by a Diesel Engine Intake Valve Ports A.E.F. Tobal , C.R. Andrade, E.L. Zaparoli, F.Y. Kurakawa.

2.3. Swirl number definition

It is known that the mixing rotation depends on several factors and the most important of which are the position of the valve with respect to the cylinder axis and the intake geometry. The swirl intensity is characterized by a dimensionless number known as the swirl number.

Fig. 2. Flow with swirl. [5]

To determine the swirl number, it is required to

determine the ratio between (i) the moment of axial momentum flux and (ii) the product of cylinder radius by axial momentum flux. These can be calculated theoretically for a steady flow, which is the most convenient case of flow for industrial applications. In this case, expression (13) for the swirl number can be written in the following form:

𝑆 = 𝑈 𝑊 𝑟𝑑𝐴

𝐴𝑅 𝑈 2𝑑𝐴

𝐴 (13)

where 𝑈 and 𝑊 are respectively the axial and tangential components of the velocity as can be seen in Figure 2.

3. SOLUTION STRATEGY

The system equations (1-7) is numerically solved employing a CFD code based on the finite volume method, Fluent Inc, [5]. The solution procedure comprises three steps:

(i) Pre-processor: 3D domain construction; polyedrical mesh generation, as depicted in Figure 3; boundary conditions and fluid properties settings;

(ii) Solver: in the second step, the compressible flow is calculated using a density based approach with first order discretization to evaluate the convective terms. The SIMPLE algorithm is employed to pressure-velocity coupling. A pseudo-transient approach is used to obtain the desired steady-state condition values. The converged numerical solution is reached when all variable (𝑈, 𝑉, 𝑊, 𝑃 and 𝑇) residues achieve 10-5. A workstation with two Intel QuadCore 2.66GHz processors and 8GB memory was used and a CPU time was approximately 5 hours.

(iii) Post-processing: at this last step, velocity, temperature and pressure fields were visualized and the. Swirl number was calculated.

Figure 3. Computational domain: example of a used mesh.

Figure 3 also shows a vertical and three horizontal

sections along the cylinder where the results will be presented.

4. RESULTS

Numerical results were obtained with a pressure differential equal to 55,000 Pa (determined by the difference between the inlet total pressure and outlet static pressure). The inlet total temperature is 300K and the turbulence intensity level is 5% (both inlet and outlet backflow). For the realizable 𝑘 − 𝜖 model is also necessary to impose the turbulent to laminar viscosity ratio (set as t/ = 10).

Figure 4 shows pressure and velocity magnitude contours at the vertical section shown in Figure 3. Note that the suction area and maximum velocity occur close to the valves region at the cylinder head due to the high velocity induced by the small area the valve and its seat.

(a)

(b)

Fig. 4. (a) Pressure fields contours and (b) Velocity magnitude

contours at a plane crossing the cylinder central axis.

The airflow pass through two intake ducts: the first one,

with lower pressure drop is designed to provide a good cylinder air filling, as presented in the streamlines of the upper-left duct airflow shown in Figure 5. To allow a good mixing process, another air stream acquires a strong angular

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A CFD Study of the Swirl Number Induced by a Diesel Engine Intake Valve Ports A.E.F. Tobal , C.R. Andrade, E.L. Zaparoli, F.Y. Kurakawa.

moment passing through the swirl lower-right duct, depicted in Figure 5. The characteristics of these intake ducts have a significant importance in the behavior of the swirl number.

Fig. 5. Top view of the intake air ducts: streamlines color-mapped

with velocity magnitude

Figure 6 exhibits the swirl number distribution along the

engine cylinder centerline. Close to valves region the airflow suffer the effects of the intake ducts and has non uniform feature and the calculated swirl number is low. Similar airflow patterns were reported in [6]. It is observed that the greatest value for the swirl number occurs at z/L = 0.55 (dashed line in Figure 6) that is the calculated in central cross-section area presented in Figure 3, where the airflow rotation is more ordered. After this central region, the swirl number decays and the fluid rotation is more disturbed.

Fig. 6. Swirl number variation along the cylinder central axis.

4. FINAL REMARKS

This work presented turbulent compressible air flow CFD results applied to a diesel engine intake valve ports with the main objective to evaluate the swirl number that is an important clue of the air-fuel mixing process quality.

Future studies intend to simulate other valves lift to obtain flow coefficients to allow comparison with available flowbench tests.

ACKNOWLEDGMENTS

Authors are grateful to MWM International Motors by the financial support for the development of the present work.

REFERENCES

[1]DOI H.EDRES, H.J.NEUSSER, R.WURMS,“Influence of swirl and tumble on economy and emissions of multi-valve SI engines.” SAE paper No. 920516, 1992.

[2]DOI F. PAYRI, J. BENAJES, X. MARGOT, A. GIL, “CFD modeling of the in-cylinder flow in direct-injection diesel engines.” Computers & fluids, Vol.33, pp.995-1021, 2004.

[3]DOI C. CRNOJEVIC, F. DECOOL, P. FLORENT, “Swirl measurements in a motor cylinder”. Experiments in fluids, Vol.26, pp.542-548, 1999.

[4]PUB Y. OISHI, M. OTAKE, Y. WATANABE, “Prediction of intake swirl applying CFD technique”. International symposium COMODIA Vol.94, pp.325-330, 1994.

[5] FLUENT INC. Theory guide, version 12.0, 2008. Available in <www.fluent.com>. Accessed may 20, 2011.

[6]DOI H. CUI, M. LI, Y. Han, “The Steady Flow Test and CFD Numerical Simulation on Improving Research of Locomotive Diesel Engine Helical Intake Port.” WASE International Conference on Information Engineering, Vol. 4, pp. 255-259, 14 - 15 August 2010

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sw

irl

Nu

mb

er

z/L

702