2006 Cooling Airflow Simulation for Passenger Cars Using Detailed Underhood Geometry

400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-0790 Web: www.sae.org

SAE TECHNICALPAPER SERIES 2006-01-3478

Cooling Airflow Simulation for Passenger Carsusing Detailed Underhood Geometry

Ales Alajbegovic and Raja SenguptaExa Corporation

Wilko JansenJaguar Cars Ltd./Land Rover

Commercial Vehicle EngineeringCongress and Exhibition

Chicago, IllinoisOctober 31-November 2, 2006

THIS DOCUMENT IS PROTECTED BY U.S. AND INTERNATIONAL COPYRIGHT.It may not be reproduced, stored in a retrieval system, distributed or transmitted, in whole or in part, in any form or by any means.

Downloaded from SAE International by Bo Feng, Friday, April 05, 2013 07:03:28 PM

The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAE's peer review process under the supervision of the session organizer. This process requires a minimum of three (3) reviews by industry experts.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE.

For permission and licensing requests contact:

SAE Permissions400 Commonwealth DriveWarrendale, PA 15096-0001-USAEmail: [email protected]: 724-772-4028Fax: 724-776-3036

For multiple print copies contact:

SAE Customer ServiceTel: 877-606-7323 (inside USA and Canada)Tel: 724-776-4970 (outside USA)Fax: 724-776-0790Email: [email protected]

ISSN 0148-7191Copyright 2006 SAE International

Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions.

Persons wishing to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract to Secretary, Engineering Meetings Board, SAE.

Printed in USA



2006-01-3478

Cooling Airflow Simulation for Passenger Cars using Detailed Underhood Geometry

Ales Alajbegovic and Raja Sengupta Exa Corporation

Wilko Jansen Jaguar Cars Ltd./Land Rover

Copyright 2006 SAE International

ABSTRACT

Air flow in the underhood area is the primary source of engine cooling. A quick look at the vehicle underhood reveals exceptionally complex geometry. In addition to the engine, there are fans, radiator, condenser, other heat exchangers and components. The air flow needs to have adequate access to all relevant parts that require cooling. Due to complex geometry, the task to ensure sufficient air cooling is not a simple one. The air flow entering from the front grille is affected by many components on its path through the underhood. Even small geometry details affect the flow direction and can easily cause recirculation regions which reduce the cooling efficiency. Therefore, air cooling flow analysis requires detailed treatment of the underhood geometry and at the same time accurate air flow modeling. Recent advances in the lattice-Boltzmann equation (LBE) modeling are allowing both. Presented is analysis of air-cooling flow over a passenger vehicle, Land Rover LR3, that includes detailed external and underhood geometry. Simulations were performed using PowerFLOW, an LBE based flow solver. Shown are flow structures that form at 95 km/h and their effect on the overall cooling flow rate and coolant temperatures in the heat exchangers.

INTRODUCTION

The most important goal for the new vehicle design is to reduce the number of prototypes and being able to make components selection and positioning early in the design process. All this is possible only with the use of simulation tools. Being able to have information on the cooling performance in the concept stage allows reduction in the number of needed prototypes and shortening of the design cycle.

The underhood thermal management plays an essential role in the design of vehicles. There needs to be sufficient airflow available to adequately cool the underhood components. The amount of airflow depends

on the positioning and size of the grilles, fan operation, and the positioning of the underhood components. There is a considerable ongoing effort to develop fluid flow simulation capability coupled with heat transfer calculations. Srinivasan et al. [1] presented an omni-tree meshing technology for rapid mesh generation for Navier-Stokes solvers. The cooling airflow simulations using Navier-Stokes solvers coupled with heat exchanger calculations for passenger cars were presented by [2], [3], [4], and for trucks by [5], [6], [7].

Fortunato et al. [8] used the lattice-Boltzmann equation (LBE) solver for the cold flow over the entire car including the underhood and a Navier-Stokes solver for the underhood flow. The velocity field on the entrance surfaces into the underhood area calculated by the LBE solver was used as the inlet boundary condition to the Navier-Stokes solver calculation. The present work is somewhat an extension of this work. The simulations here were performed using the LBE solver to simulate the flow over the passenger car exterior and through the underhood area including heat transfer. This approach leverages all advantages of an LBE solver applied to the simulation of the underhood thermal management.

MATHEMATICAL MODEL

One of the major challenges in performing fluid simulations in CAE is the difficulty to adequately discretize the flow domain and at the same time resolve surface details of complex geometries. The Navier-Stokes solvers that are mostly used in industrial applications are very demanding on the quality and size of the meshes for practical calculations. These requirements are a direct consequence of the properties of the finite volume method (FVM) which is the most used approach in the numerical solution of the Navier-Stokes equations. This method employs the pressure-correction algorithm for imposing the mass conservation. Pressure-correction is an iterative procedure that is expensive numerically and therefore limits the effective mesh size that can be used for practical



calculations. In order to limit the number of cells, unstructured meshes are used which allow the discretization of complex geometries while maintaining low cell counts. It is not uncommon for some generated cells in unstructured meshes to have very distorted shapes that cause calculation inaccuracies or even instabilities and subsequent divergence of the calculation. The varying cell shapes in unstructured meshes cause inevitable dependence of the results on the mesh size and quality. Mesh generation for the Navier-Stokes solvers made significant progress in the last years and considerable part of the process is automized. However, the preparation of surfaces and some mesh generation procedures still require users involvement. This part remains to be labor intensive and depends strongly on the skill of the user to manipulate meshes. The entire meshing process limits the level of geometry detail that can be handled in practical use and in most cases the geometry is simplified to reduce the preparation time and fulfill the design timelines.

Lattice-Boltzmann equation (LBE) solvers represent an alternative to the Navier-Stokes solvers. They dont need any special iterative procedure and fulfill mass, momentum, and energy conservation by design. As a result, LBE solvers are numerically very efficient and robust. The increased numerical efficiency allows handling of lattices with very large number of elements (or voxels). In addition, the properties of Boltzmann equation allow an improved treatment of the interaction of the fluid flow with the wall surface. Surface elements (or surfels) are designed as active elements that interact with the neighboring lattice elements. The combination of both large lattices and dynamic surface treatment allow accurate representation of surfaces without the need for geometry simplification. This feature is paramount for the deployment of simulation techniques in the design process. In addition, the LBE solvers are linearly scalable with the number of processors.

The lattice-Boltzmann equation approach to simulate fluid flows was demonstrated by Frisch, Hasslacher, and Pomeneau [9]. Since then, there was considerable effort invested into the development of a lattice-Boltzmann based flow solver and there are good reviews available on the current status [10], [11]. Here is presented only a very short overview of the method. The reader should consult the provided references in case of interest for more detailed information.

The Boltzmann equation can be written in the following form:

f ft x

+ =

rr (1)

where f is the velocity probability distribution function and is the collision operator. Boltzmann equation in the lattice form can be expressed as a set of algebraic equations for probability distribution at each state, if :

( , ) ( , ) ( , )i i i if t t x e t f t x t x+ + = + r r r r (2)

where the collision operator is modeled using the BGK form [12]:

(0)( , ) ( ( , ) ( , ))i i itt x f t x f t x

= r r r (3)

The equilibrium distribution function, ( )0if , is expanded with respect to the velocity [12]:

(0)2 2 2( , ) (1 ( ))2

i iii p

s s s

u u e ee uf t x t

c c c

= + + r (4)

Important feature of this approach is that the mean quantities like density, , and velocity, ur , are obtained from the calculated velocity probability distribution functions:

( , ) ( , )ii

t x f x t =r r (5) 1( , ) ( , )

( , ) i iiu t x f x t e

t x= r r r rr (6)

It can be shown that the described system yields the behavior of the Navier-Stokes equations. More precisely, the Navier-Stokes equations represent a subset of the behavior modeled by the Boltzmann equation in the limit of small Knudsen numbers. A nice feature of the lattice-Boltzmann equation solver is that the mass and momentum conservation are automatically fulfilled by enforcing the sum of the collision term for all states, i, to be equal zero:

( , ) 0ii

t x = r (7) ( , ) 0i i

i

t x e = r r (8) Turbulence effects are modeled using a modified k- model based on the original RNG formulation [13, 14]:

( )1 tDk k PDt x x

= + + r r (9)

( )( )

1

3 20

2 3

1

1 /

1

tD C PDt x x k

C Ck

= + +

+ +

r r (10)

The values for the dimensionless coefficients are the same as in the original model formulation [13, 14]. This



LBE based description of turbulent fluctuation carries flow history and upstream information, and contains high order terms to account for the nonlinearity of the Reynolds stress [15]. This is contrasted with typical Navier-Stokes solvers, which tend to use the conventional linear eddy viscosity based on the Reynolds stress closure models.

Temperature evolution is calculated using the PDE in the following form:

Pr Prp t p

pt

c cDT Tc QDt x x

= + +

&r r (11)

Turbulence and temperature equations are solved on the same lattice using a modified Lax-Wendroff-like explicit time marching finite difference scheme. Simulation presented in this work was performed using the solver described in the following references [16], [17], [18], [19]. The simulation tool is also available commercially [20].

SIMULATION DETAILS

Performed is the simulation of the airflow over the vehicle exterior and inside the underhood of the Land Rover LR3. The simulation is done using the LBE solver [20]. All geometry details are considered without any simplifications. Car geometry is shown from different perspectives in Figure 1. The geometry is clearly of considerable complexity and includes all underhood and underbody details. Lattice used in the simulation was generated automatically and without any intervention from the user. The resulting lattice size had around 8 million fine equivalent voxels (number of voxels that are updated every time step) and approximately the same number of surfels (Table 1).

The parameters used in the simulation are shown in Table 1. Vehicle was placed in the digital wind tunnel (DWT). The vehicle front area was about 2% of the overall wind tunnel front face. The air velocity of 95 km/h was imposed at the inlet boundary of the DWT resulting in uniform air distribution of the upstream air. In addition to the airflow, the heat transfer between airflow and heat exchangers is modeled as well. The interaction is calculated using the one-dimensional tool or 1D-tool [22]. The 1D-tool calculates the heat transfer between the coolant flow inside and airflow through the heat exchanger. The calculation approach considerably simplifies the flow configuration essentially assuming coolant flow as one dimensional this is the reason for the name 1D-tool.

Figure 1. Fully resolved Land Rover LR3 geometry used in the simulation showing external body, underhood and

underbody details.

Operating Condition 95GVW Air velocity 95 km/h

Ambient air temperature 31.3 C Size [MFe (V/S)] 8.2/7.7

Charge Air Cooler (CAC) mcoolant=0.097kg/s Tcharge inlet=195 C Radiator mcoolant=1.77kg/s Heat input=65.2kW

Condenser Heat input=12.0kW Fan 2440 RPM

Table 1. Set-up parameters.



Figure 2. Details of the simulation preparation: a.) front grille geometry, b.) heat exchangers, and c.) fan

geometry.

The front grille geometry is shown in Figure 2a. The grille geometry has dominant influence on the amount of airflow entering the underhood area. After the grille, the air proceeds towards the heat exchangers. The heat exchanger cores are represented by the rectangular boxes shown in Figure 2b. The fan is placed right behind the heat exchangers as shown in Figure 2c. Used is detailed fan geometry and the flow in the fan is modeled using the multiple-reference-frame (MRF) approach. The implemented MRF model has been validated extensively and the predicted fan performance curves were well within 5% with respect to the measured data. High air velocity of the upstream air is limiting the fan influence on the airflow. The detailed configuration of the heat exchangers from the side view is shown in Figure 3. The charge-air-cooler (CAC) is placed beneath the condenser and the radiator.

The heat exchangers are modeled as porous media. The resistance of the heat exchangers is imposed from the measured relation between the air velocity and the pressure drop through the heat exchanger. The obtained data is correlated using Darcys law [21].

Heat transfer between the airflow and coolant in the heat exchanger is modeled with the 1D-tool [22]. The 1D-tool does not model all the internal details of the heat exchanger. It models the heat flow that propagates in the heat exchanger in the flow direction. The heat transfer coefficients used in the calculation of the heat transfer between the coolant and air flow is obtained in a calorimeter. The measurement error in heat transfer coefficients was about 5% for the majority of the data points. The measured heat transfer coefficients as a function of the coolant and air mass flow rates are shown in Figure 4. The measured data is interpolated using the sandwich formula and the interpolation curves are shown in red. Sandwich formula is represented by the following function:

1

1 1a h c

a c

Htc

K D Km m

= + + & &

(12)

where am& is air mass flow rate, cm& is coolant mass flow rate, and aK , cK , hD , , are the interpolation coefficients that need to be calculated. It can be seen that the interpolation is quite good for the CAC, but not as good for the radiator. Therefore, the calculated interpolation is used only for the CAC. Bi-linear interpolation is used for the calculation of the heat transfer in the radiator. Condenser is not modeled with the 1D-tool. The known condenser heat rejection is uniformly distributed through the condenser volume. This approach proved to provide very good results while allowing to avoid dealing with the complexity of the condenser physics.

Figure 3. Configuration of the underhood geometry.



Figure 4. Heat transfer coefficients at different coolant mass flow rates for a.) the radiator and b.) the charge-

air-cooler.

RESULTS

The simulation was performed on a 64 processor Linux cluster. The simulation was run for 30,000 time steps before starting the coupling with the 1D-tool. This time interval is needed for the flow to settle. After that, the coupling between the 1D-tool and the LBE solver was done every 4,000 time steps. The entire simulation time was 66 hours, resulting in 4224 CPU hours.

The evolution of the coolant inlet temperature (TTT), inlet and outlet air temperatures, and air mass flow rates through the radiator and CAC as a function of the coupling iteration is shown in Figure 5. The calculated values cannot be shown due to the confidentiality issues.

It can be observed that the steady state is achieved after only six (6) coupling iterations. Consequently, the simulation didnt need to run as long as it did and could be stopped approximately after 2,500 CPU hours. Of course, the other option to reduce calculation times is to increase number of processors. The LBE solvers are linearly scalable with the number of processors.

Figure 5. Evolution of the air mass flow rate, coolant entry temperature (TTT), inlet and outlet air

temperatures as a function of coupling iteration with the 1D-tool for a.) radiator and b.) charge-air-cooler.

The most important calculated parameter of interest was the coolant temperature at the inlet into the radiator also known as the top tank temperature. In this case, the calculated value was exactly 1C higher than the measurement. The overall temperature difference between the inlet and outlet coolant temperature in radiator was around 10C. Such accuracy is not uncommon for the presented simulation methodology using the LBE solver, even for much higher heat rejections. High level of geometry resolution allows accurate predictions of the airflow through the vehicle underhood area and consequently accurate predictions of the air mass flow rates through the heat exchangers. Correct prediction of the air mass flow rate is paramount for the correct prediction of the coolant inlet temperature.

It is interesting to observe flow structure and temperature field in the underhood area. The two fields are shown both on the centerline and horizontal planes in Figure 6. Flow accelerates through the grille openings and enters the condenser and CAC. Flow heats up in the condenser and continues through the radiator with further increase in temperature. Even larger heating



rates can be observed in the CAC. The flow is complex, but doesnt show any recirculation patterns that could result in the feedback between the exit and inlet temperatures into the heat exchangers.

One of the important features of the presented method is the ability to resolve both underhood and external aerodynamics flows simultaneously as shown in Figure 7. Observed can be typical characteristics of the external air flow over the vehicle body. In this particular case the set-up didnt use the placement of variable resolution (VR) regions that would be necessary for the detailed resolution of the external flow features. The reason for this was to simulation focus on the flow in the underhood area. However, joint resolution of the exterior and underhood flows is possible and only increases the case size and simulation times. At the same time, the need to prepare only one case significantly reduces geometry and case preparation times.

Figure 6. Velocity and temperature fields on centerline and horizontal planes through the underhood.

Figure 7. Details of the external flow aerodynamics.

CONCLUSION

Performed was the simulation of the airflow over the Land Rover LR3 with complete geometry details of the external body and the underhood area. The employed simulation method doesnt require geometry simplifications. The generation of the simulation lattice (flow domain discretization) is entirely automatic and doesnt require any user intervention. The interaction between the airflow and heat exchangers was simulated using the 1D-tool. Special attention in the calculation was placed in the resolution of the underhood flow. The predicted inlet coolant temperature (top tank temperature) was exactly 1C higher than in the experiment.



REFERENCES

1. K. Srinivasan, Z.J. Wang, W. Yuan, R. Sun, Vehicle thermal management simulation using a rapid omni-tree based adaptive Cartesian mesh generation methodology, HT-FED2004-56748, 204 ASME Heat Transfer/Fluids Engineering Summer Conference, July 11-15, Charlotte, North Carolina, USA.

2. B. Uhl, F. Brotz, J. Fauser, U. Krueger, Development of engine cooling systems by coupling CFD simulation and heat exchanger analysis programs, SAE 2001-01-1695.

3. G. Seider, F. Bet, T. Heid, U. Hess, T. Klein, and J. Sauer, A numerical simulation strategy for complex automotive cooling systems, SAE 2001-01-1722.

4. H. Knaus, C. Ottosson, F. Brotz, W. Kuehnel, Cooling module performance investigation by means of underhood simulation, SAE 2005-01-2013.

5. T.P. Nobel, S.K. Jain, A multidimensional approach to truck underhood thermal management, SAE 2001-02-2785.

6. C.L.R.Siqueira, P. Vatavuk, M. Jokuszies, M.R. Lima, Numerical simulation of a truck underhood flow, SAE 2002-01-3453.

7. E.A. Costa, CFD approach on underhood thermal management of passenger cars and trucks, SAE 2003-01-3577.

8. F. Fortunato, F. Damiano, L. Di Matteo, P.Oliva, Underhood cooling simulation for development of new vehicles, SAE 2005-01-2046.

9. U. Frisch, B. Hasslacher, and Y. Pomeneau, Lattice gas automata for the Navier-Stokes equation, Physical Review Letters, 56:1505-1508, 1986.

10. S. Chen and G. D. Doolen, Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics, 30:329-364, 1998.

11. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Series Numerical Mathematics and Scientific Computation, Clarendon Press, Oxford, 2001.

12. D. dHumieres, P. Lallemand and Y. H. Quian, Lattice BGK models for Navier-Stokes equations, Europhysics Letters, 17(6):479-484, 1992.

13. V. Yakhot, and S.A., Orszag, Renormalization Group Analysis of Turbulence. I. Basic Theory J. Sci. Comput., 1(2), 3-51, 1986.

14. V. Yakhot, V., S.A. Orszag, S. Thangam, T. Gatski, and C. Speziale, Development of turbulence models for shear flows by a double expansion technique, Phys. Fluids A, 4 (7), 1510-1520, 1992.

15. H. Chen, S.A. Orszag, I. Staroselsky, and S. Succi, Expanded Analogy between Boltzmann Kinetic Theory of Fluid and Turbulence, J. Fluid Mech., 519: 307-314, 2004.

16. H. Chen, H-theorem and generalized semi-detailed balance conditions for lattice gas systems, J. Stat. Phys. 81:347-359, 1995.

17. H. Chen and C. Teixeira, H-Theorem and origins of instability in thermal lattice Boltzmann models, Comp. Phys. Communication, 129:21-31, 2000.

18. H. Chen and R. Zhang, Lattice Boltzmann method for simulations of liquid-vapor thermal flows, Phys. Rev. E67(6): Art. no. 066711 Part 2, 2003.

19. C. M. Teixeira, Incorporating turbulence models into the lattice-Boltzmann method,. Int. J. Modern Physics C, 9(8):1159-1175, 1998.

20. PowerFLOW Users Guide, Release 4.0, Exa Corporation, Boston, Massachusetts, 2006.

21. D.M. Freed, Lattice Boltzmann method for macroscopic porous media modeling,. Int. J. Modern Physics C, 9(8):1491-1504, 1998.

22. PowerCOOL Users Guide, Release 4.0, Exa Corporation, Boston, Massachusetts, 2006.

CONTACT

Ales Alajbegovic Exa Corporation 17177 N. Laurel Park Drive Livonia, MI 48152 email: [email protected]



2006 Cooling Airflow Simulation for Passenger Cars Using Detailed Underhood Geometry

Documents

Transcript of 2006 Cooling Airflow Simulation for Passenger Cars Using Detailed Underhood Geometry