A numerical analysis for the cooling module related
to automobile air-conditioning system
Hak Jun Kim
*, Charn-Jung Kim
School of Mechanical and Aerospace Engineering, Seoul National University, San 56-1, Shilim-dong, Gwanak-gu, Seoul 151-744, South Korea Received 19 September 2007; accepted 3 December 2007
Abstract
The main objective of this paper is to develop a 3D CFD program which can be used by the development engineer to analyze the performance of the vehicle cooling system.
There is a demand for new vehicles to be made in shorter product development cycles while continuously improving the vehicle’s performance and quality. These demands accelerate the use of Computer Aided Engineering (CAE) tools for vehicle test simulations. For engine cooling, it is very important to use CFD tools for the prediction of front end airflow pattern. However, the geometry of a vehicle’s front end and underbody region are extremely complex. From this study, the performance of the automotive cooling system can be predicted and also compared with experimental data. That is, a method to predict the coolant inlet temperature of the radiator is presented. This method includes predicting the coolant and air flow patterns in front of the condenser and radiator in a real vehicle model. This method employed the SIMPLE and SIP numerical methods to solve the Navier–Stokes equations for incompressible and three-dimensional fluid motion. The standard k–e turbulence model was applied and the law of wall was applied to the wall boundary. For the validation of the developed method, numerous simulations were completed in accordance with various conditions and the results were compared with existing experimental data.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Vehicle cooling system; SIP; Validation; Coolant inlet temperature; CFD
1. Introduction
Within the automotive industry, the subject of vehicle design is moving rapidly into the use of newer and state-of-the-art techniques. The purpose of a vehicle cooling sys-tem is to ensure that the engine is maintained at its most efficient practical operating temperature.
The trend for today’s product development process is to continuously reduce the time-to-delivery and the number of physical tests. The goal of using CAE is to accurately pre-dict the vehicle cooling system before the component/sys-tem are built.
The cooling airflow in today’s vehicle engine cooling systems is generated by a ram effect resulting from the vehicle’s motion and suction produced by fan operation. This airflow passes through the grille, condenser, radiator, cooling fan, and other components, removing the rejected heat to the surrounding environment. It is well known, both theoretically and experimentally, that the flow rate and temperature of the air in front of the radiator have a strong influence on the heat dissipation capacity of the radiator and on the performance of the cooling system. Therefore, the airflow is an essential factor affect-ing the engine coolaffect-ing system performance and has always been of primary concern in the engine cooling system design.
Due to the complex flow pattern and the interactive fac-tors that influence the flow behavior, the analytical and experimental study of cooling airflow is challenging.
1359-4311/$ - see front matterÓ 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2007.12.002
*
Corresponding author. Tel.: +82 2 880 1656; fax: +82 2 883 0179. E-mail addresses: hjkim99@snu.ac.kr (H.J. Kim), kimcj@snu.ac.kr
(C.-J. Kim).
www.elsevier.com/locate/apthermeng Applied Thermal Engineering xxx (2008) xxx–xxx
Fig. 1shows the air coming through grille and into the cooling system. There are corresponding pressure drops and rises as the air progresses through each component. Ideally, the predicted ram air effect would be computed using a commercial CFD program instead of experimental test. Of course, the validation of the CFD results should be done before using the commercial CFD program.
A number of CFD vendors provide the capability for front end simulations coupled with one-dimensional cool-ing performance. Some one-dimensional coolcool-ing perfor-mance codes, such as KULI, can also be used to integrate three-dimensional CFD. With KULI-CFD, the integration is possible using the non-uniform air flow dis-tribution on heat exchangers while utilizing the cooling air velocity distribution on the heat exchanger calculated by the CFD analysis. The results of the CFD are trans-ferred to KULI, and it calculates the coolant inlet temper-ature [1]. In a similar study, Bernhard’s results show the heat exchanger program can be directly coupled with an under hood flow simulation by using a user defined subrou-tine in Star-CD[2].
Another paper showed that the coolant inlet tempera-ture of the radiator obtained with CFD was within
±4°C of the experimental data, the differences being
dependent on the car speed.[3]. But these methods required engineers to have substantial experience using the commer-cial CFD codes and the meshing software.
Sakai showed one example of cooling system optimized by utilizing computer simulation in the early development stage. A numerical simulation was conducted to obtain the airflow rate through the engine compartment room by the software ‘‘STREAM”. The optimization of this sys-tem was conducted utilizing a design of experiment study for cost saving and weight reduction. The test value corre-lated well with the calcucorre-lated one and the CAE was con-firmed to be very helpful for saving prototype cost and time[4].
Also Moffat introduced a method to couple 1D and 3D CFD models for the prediction of transient hydraulics in engine cooling circuits[5].
In general, the solution of automotive cooling hydraulic networks required the construction of two separate models. Initially, a 3D CFD model was required to predict airflow patterns through the bumper apertures. The results were then fed into 1D hydraulic model. The 1D model was then used to predict engine coolant temperatures using either measured or predicted results for heat exchanger perfor-mance and calculated radiator coolant flow rates. Predict-ing transient temperature and flow rates within a circuit for a single drive cycle, vehicle speed and engine load con-tinuously changing, can become extremely time consuming. This study described a technique for coupling the two methodologies in a manner that eliminated the need for repeatedly calculating 3D solutions for every vehicle oper-ating condition. The modeling approach was easily extend-able to predict the effects of variations in any of the cooling system component strategies.
Jansen showed another method of using the Lattice-Boltzmann method to solve the engine cooling system. Lat-tice-Boltzmann equation (LBE) solvers represented an alternative to the Navier–Stokes solvers. They did not need any special iterative procedures to satisfy mass, momen-tum, and energy conservation. This paper showed the LBE solvers are numerically very efficient and robust. The increased numerical efficiency allowed handling of matrices with a very large number of elements and the properties of the Boltzmann equation allowed an improved treatment of the fluid flow interaction with the wall surface. Also presented were cooling airflow and external aerody-namic simulations of a Land Rover LR3 and Ford Mon-deo under several driving conditions[6].
Nicolas Francois showed the Fluent CFD software to be a fast and cost effective tool and increasingly utilized at dif-ferent stages of heat exchanger design optimization. A few highlighted examples showed CFD analysis improving the design of radiator, condenser and cooling system perfor-mance in the vehicle’s underhood region but did not dis-close the detail of the simulation or the test data[7].
The method presented in this study aids automotive engineers in the design of cooling module with a reliable CFD data. The method is simple and only requires
Fig. 1. (a) The schematic configuration of cooling module and the air flow pattern in the engine room of vehicle. (b) The pressure drop and up depend on the function of each component.
combining the computational domain with a specially developed automotive cooling module to calculate the CFD solution.
2. Mathematical method, modeling and solving 2.1. Governing equations
To solve the complicated physical phenomena corre-sponding to the complex geometry of the vehicle and cool-ing system model, there are necessary requirements. A simple coordinate system for stable solving is needed. Additionally, a special method defining the relation of the computational domain to the simple coordinate system and the complex geometry is also necessary.
Generally, the testing of the engine cooling module is completed when the coolant inlet temperature of the radi-ator varies little over the time of test. Therefore, this study used the steady state continuity, momentum equations as follows because it was unnecessary to solve the transient equations: – continuity equation oðquiÞ oxi ¼ 0 ð1Þ – x, y, z momentum equations oðqukujÞ oxk ¼ op oxj þ o oxi louj oxi þ Sj ð2Þ
In the above equations, the stress tensor term split so that a portion of the normal stress appears in the diffusion term, and the rest is contained in Sj
Sj¼ fjþ o oxj l oui oxi 2 3 o oxj louk oxk þ Ssource ð3Þ
– energy (temperature) equation oðqukTÞ oxk ¼ o oxj j Cp oT oxj þ ST ð4Þ
2.2. Turbulence model and wall function
When the flow is turbulent the solution variables may be divided into a time averaged value and its instantaneous component. For example the instantaneous velocity may be represented as U + u0, its mean and fluctuating values
respectively. However as we are usually interested in the mean values rather than a fluctuating value.
For most engineering purposes, it is unnecessary to resolve the details of the turbulent fluctuations. Therefore, the standard two equation k–e model was applied to the study. lt¼ qCl k2 e oðqukkÞ oxk ¼ o oxj lt rk ok oxj þ G qe ð5Þ oðqukeÞ oxk ¼ o oxj le re oe oxj þ ðC1eG C2eqeÞ e k ð6Þ Cl¼ 0:09; rk ¼ 1:00; re¼ 1:30; C1e¼ 1:44; C2e¼ 1:92
A basic wall function equation for the velocity parallel to the wall was applied. The ‘‘logarithmic law of the wall” equation is given as
uþ¼1 jlnðEy
þÞ ð7Þ
In this formula, j is von Karman’s constant (0.4187) and E is an integration constant that depends on the roughness of the wall. For smooth walls with constant shear stress, E has a value of 9.0.
2.3. The computational domain and complex geometry
Fig. 2shows the vehicle model used in this study. The
model was created considering the real vehicle shape (the
Fig. 2. Vehicle model used in the simulation and the front view showing the carrier, bumper frame, condenser, radiator and fan.
overall length of vehicle: 4800 mm, the full width of vehicle: 1830 mm, the overall height of vehicle: 1475 mm) and con-sists of the exterior of the vehicle, engine block, engine environmental block, carrier part, wheels, radiator, con-denser and fan. The grille opening area was the same as the vehicle. The heat exchangers (i.e. condenser and radia-tor) also had the same dimension as the real components. The process for preparing the data input related to the geometries for calculation was as follows:
Step (1) Prepare the complex vehicle geometry from CAD or other special in-house geometry program and make the tetra mesh using Hypermesh or another pre-processing tool.
Step (2) Make the computational domain with non-uni-form orthogonal grids well matched with the range of all complex geometries.Fig. 3shows the computational domain merged with the tetra geometry of the vehicle model. Each cell in the domain that is intersected by tetra surfaces will have the available area occupied by the air calcu-lated by the in-house program.
Step (3) Each grid cell is intersected by the tetra mesh of geometry. The in-house first program developed through this study calculates the surface number and connectivity for each cell and sorts the unique surface numbers and saves the result. That is, through using a special in-house algorithm, each cell surface which is in contact with the tetra sur-faces is determined.
Step (4) The in-house second program automatically cal-culates the open area of each cell with the above result data, refer toFig. 4.
It takes approximately 1 h to calculate the open area of all cells using an HP C8000 machine (4G RAM). In this study, the computational domain consisted of approxi-mately 5 million cells and 140,000 total surfaces.
The number of computational cells depends on the detailed surface information. If the tetra surface is small, the number of computational cells will be greater. Engi-neers decide the number of total cells by reviewing the size of each cell and the tetra mesh of the surfaces. Attention to how accurately the geometry detail reflects reality is always considered.
2.4. The modeling of heat exchanger and fan 2.4.1. Heat exchanger model
The condenser and radiator cores were modeled as rect-angular fluid domains with empirical correlations for the airside pressure drop. Two porous zones were defined: one for the condenser and the other for the radiator. The resistance coefficients were determined from the pressure drop curve provided by the component calorimeter test. In the momentum equation, this pressure drop was treated as a source term. The heat transfer between the ambient air
and the coolant was modeled using e NTU. The
effective-ness of the heat exchanger is defined as the ratio of the actual heat transfer rate to the maximum possible heat
transfer rate. With applicable correlations of e NTU,
which can be found for any standard heat exchanger, the effectiveness eeffof the radiator was obtained.
The total heat transfer rate can be calculated as shown below
_qrad¼ _mcaeeffðTw;i Ta;iÞ ð8Þ
Eq. (8) shows that the higher the core effectiveness the
higher the radiator capacity is for a given temperature
difference between two fluids. The table of eeff from an
experimental data is the function of air velocity and cool-ant flow rate. The changes of eeff, caand Ta,iare small under
normal operating conditions. Therefore, the supply coolant inlet temperature Tw,iis the parameter that dominates the
capacity for a given airflow rate. The engine heat into coolant was measured by a test or was estimated by a
vehi-Fig. 3. Geometry of vehicle model connected with computational domain.
cle laboratory. In the program, the heat capacity of the radiator was treated as a heat source in the energy equa-tion. The engine heat into coolant was a given value. If there is a deviation, the program automatically iterates and adjusts the coolant inlet temperature. The employed heat exchanger model computes both the total heat rejec-tion of the core and the coolant inlet temperature of the radiator in accordance with operating ambient conditions. In the engine’s part-load operating range, a conven-tional cooling system has to remove an excessive amount of heat and considerably lower the component tempera-ture.Fig. 5shows the heat balance in part-load road going operation. ‘‘Q_Engine_In” is the energy supplied to the engine, ‘‘Pe” is the effective engine power and ‘‘Q_exhaust” is the waste heat to surrounding atmosphere. Q_water, the engine heat into coolant, is about 20% of the energy sup-plied to the engine[8]and should be used as the heat rejec-tion, which should be cooled by the radiator in the analysis of the cooling system.
2.4.2. Fan model
The fan pressure rise over the blades was obtained from experimental data and was treated as a source term in the momentum equation. The pressure rise curve from experi-mentally obtained data was modeled with dimensionless fan function like /, w
/¼ Q_ AfanUtip ð9Þ w¼DP1 static 2qU 2 tip ð10Þ Since the fan characteristics depend on the air density in the fan blade region, the dimensionless function was corre-lated to the air temperature at the estimated working con-dition in the vehicle.
2.5. Others
To accurately calculate cooling airflow rates, the energy equation has to be solved simultaneously with the
momen-tum equations using variable fluid properties for density and viscosity. These fluid properties vary with temperature. Density was modeled using an incompressible ideal gas law and viscosity was modeled using a polynomial function. The turbulence model used was standard k–e with standard wall functions. The calculation was carried out in continu-ous steps: the momentum and the turbulence equations were solved and the energy equations were solved simulta-neously with the heat exchanger model activated.
A system of linear equations was solved by using the SIP Solver [9,10]. A Strongly-Implicit-Procedure (SIP Solver) according to Stone is suitable for solving systems of linear equations resulting from a discretisation of partial differen-tial equations.
3. Results and discussion 3.1. Test experiment
The radiator instrumentation packages consisted of 15 vane anemometers mounted to the front face of the core, refer toFig. 6a. The system was calibrated on a flow stand over a wide range of flow rates with fan–motor–shroud assembly installed. The accuracy of the corrected flow rate measurements on the flow stand was about 2%.
Fig. 5. Thermal balance of an engine during part-load.
Fig. 6. (a) Fifteen anemometers which were installed on the frontal surface of radiator. (b) The distribution of air velocity obtained by experimental test.
The laboratory calibration on the flow stand was neces-sary to improve the quality of experimental data by remov-ing some of the uncertainties in the measurement system. These uncertainties were; (a) the circular anemometers did not completely cover the rectangle radiators, (b) the ram air induced airflow caused the anemometers to mea-sure an inaccurate airflow, and (c) the shroud and fan imposed non-uniform velocity gradients across the radiator [11]. In the real vehicle test, the front end configurations imposed additional velocity gradients across the radiator as shown inFig. 6b.
Fig. 7 shows the deviation between measurement and
simulation. Of particular note is that the deviation is greater at high speed. The reason is that the ram air induced airflow caused the anemometers to measure an inaccurate airflow as mentioned previously. The measured air velocity of test was an average of 15 anemometer read-ings. Similarly, the air velocity in the simulation was a cal-culated average corresponding to the air velocity readings at locations matching the test setup, refer toFig. 6.
To measure the coolant flow rate, turbine type flow meters were installed in the inlet part of the radiator to measure the exact coolant flow rate in the real vehicle sys-tem. Thermocouples were used to measure the coolant inlet and outlet temperatures. An estimate of the exact heat rejection of the radiator was then calculated. It was assumed that this calculated heat rejection was the same with the engine heat into the coolant, which was used as an input for the program. A calculated coolant inlet tem-perature will be compared with simulation result to vali-date the developed program through this study.
Fig. 7. Comparison between test and simulation in the averaged air velocity based on the position of 15 anemometers before radiator.
Table 1
Test and simulation condition (variation based on the condition of 50 km/h)
Vehicle speed Coolant flow rate
Engine heat into coolant
Condenser heat rejection
50 km/h (8% G/L) Base Base Base
100 km/h (6% G/L) 49.0%" 27.7%" 33.3%" 140 km/h 42.5%" 16.6%" 50.0%" All test data come from the experimental measurement.
Fig. 8. The layout of fan used in test, simulation and the radiator of (a)– (c) type is radiator ‘‘A”: (a) center position fan, (b) partial displacement fan, (c) partial displacement fan containing 3 holes (the area of each hole: 0.00304 m2) on the shroud.
3.2. Test and simulation conditions
The vehicle model used through this study was ‘‘C class” in the classification of vehicle grade. Test and simulation were done with various conditions of each vehicle speed
as described inTable 1. Additionally, both test and simula-tion were done in accordance with changing the layout of the fan, radiator and fan power. The results were compared with each other in the view point of relative comparison. 3.3. The discussion
3.3.1. The effect of fan layout
Fig. 8a–c shows the layout of the fan used in the test and simulation. The radiator used in this study is radiator ‘‘A”, refer to Table 2. The performance of the fan is generally not affected by the shroud type on the airflow stand. How-ever, in a case where heat exchangers interfere with a fan,
Table 2
The specification of radiator ‘‘A” and radiator ‘‘B”
Type of radiator Width (mm) Height (mm) Fin density (FPDM)
Radiator ‘‘A” 636.0 460.0 70
Radiator ‘‘B” 636.0 460.0 90
The depth of all radiators is 18.5 mm.
Fig. 9. Simulation result showing the distribution of air velocity before radiator and the coolant temperature in the tube of radiator ‘‘A” in accordance with the layout of fan at 50 km/h; (a) center position fan, (b) partial displacement fan, (c) partial displacement fan containing 3 holes on the shroud.
this interference does affect the airflow pattern and airflow rate through heat exchangers and fan. Normally, the non-uniform airflow due to the shroud type makes the per-formance of the heat exchanger worse. Therefore, it is nec-essary to make the flow uniform before the heat exchanger as much as possible.Fig. 9shows the result in accordance with the fan type. If the fan type is a partial displacement fan (Fig. 9b), this increases the resistance of fan shroud and makes the airflow pattern more non-uniform. This then reduces the airflow rate through heat exchanger. To reduce the effect of a partial displacement fan, installation of holes on the surface of the fan shroud were created to reduce the resistance. This increases the airflow rate pro-portional to vehicle speed. These holes on the shroud play a primary role at high vehicle speed (above 100 km/h). The reason is that the ram air has little effect on airflow rate at low speed. In this case, the fan performance dominates the airflow rate through the heat exchanger. However at high speed, the airflow rate is dominated by the ram air and the holes in the shroud have the effect of reducing the resis-tance of the shroud.
Fig. 9c is nearly the same airflow pattern withFig. 9b as mentioned above. However, observe the airflow through these holes when the vehicle speed is over 100 km/h.
Sometimes the use of a partial displacement fan is needed because of engine packaging and to avoid interfer-ing with other components. In this case, these holes on the shroud help to increase the airflow.
Fig. 10a shows the difference of coolant inlet
tempera-ture at each vehicle speed according to the fan type. The maximum deviation between test and simulation is
1.1°C. The effect of holes on the shroud is large at 100
and 140 km/h, refer toFig. 10b. 3.3.2. The effect of radiator performance
Fig. 11a shows that the performance of radiator ‘‘B” is
much better than that of radiator ‘‘A”, specifications of these radiators are in Table 2. The airside pressure drop of radiator ‘‘B” is also higher than that of radiator ‘‘A”. Ref. [3] shows that if the engine heat into the coolant is increased by about 2%, the coolant inlet temperature of the radiator is decreased by 1.4°C. Both the heat rejection into the coolant and the performance of the radiator had a greater effect on the coolant inlet temperature than other factors such as airflow.
In this study, we observe that the coolant temperature decreased from 4.2 to 5.8°C in the case of changing radia-tor ‘‘A” into radiaradia-tor ‘‘B”. The airflow rate also was reduced, but test data showed a lesser effect than simula-tion did (Fig. 10a). The test data contains uncertainty of measurement and invisible error because theoretically the result of simulation is right.
3.3.3. The effect of fan power
When increasing the motor power of the fan from A
power to B power with the same base fan,Fig. 11b shows
the gap of fan P–Q curves decreased as airflow rate
increased. With this phenomenon, it can be estimated that the airflow rate will be close to each other at the high speed of vehicle. The test and simulation showed the results to be as expected. That is, the coolant inlet temper-ature has a larger difference for a vehicle at low speed as compared with a vehicle at high speed.Fig. 12b shows that the higher the vehicle speed the lower the effect of the fan is.
Through this study, good information was obtained. If the coolant inlet temperature has a high value, there is lit-tle gained by increasing the fan power. One needs to increase the performance of the radiator to avoid the overheating.
Fig. 10. (a) The difference between partial displacement fan and center position fan in relative comparison (the result of partial displacement fan – that of center position fan). (b) The difference between partial displace-ment fan having 3 holes on the shroud and partial displacedisplace-ment fan in relative comparison (the result of partial displacement fan having 3 holes – that of partial displacement fan).
3.3.4. The effect of heat rejection into coolant
As a parametric study, a simulation of the coolant inlet temperature while changing the heat rejection into the coolant was completed. The study assumes a 5%, 10% and 20% increase to the heat rejection into the coolant.
Table 3a shows the coolant inlet temperature and the
line-arity in accordance with increased heat rejection. It is very important to measure or get the exact heat rejection from test or the automobile maker.
3.3.5. The effect of ambient air temperature
With changing the ambient temperature, the prediction of coolant inlet temperature is also linear with the ambient temperature as seen inTable 3b. The variation of coolant
temperature is proportional to the ambient temperature because the ITD (Inlet Temperature Difference = coolant inlet temperature – inlet air temperature) should affect the heat performance of the radiator. The coolant inlet
Fig. 12. (a) The relative comparison when changing radiator ‘‘A” into radiator ‘‘B” (the result of using radiator ‘‘B” – that of using radiator ‘‘A”). (b) The relative comparison when changing A fan power into B fan power (the result of using B power fan – that of using A power fan) in this case of using radiator ‘‘A”.
Table 3
(a) The variation of coolant inlet temperature according to the engine heat into coolant at 50 km/h. (b) The variation of coolant inlet temperature according to the ambient temperature at 50 km/h
(a) Engine heat into coolant 5.00%" 10.0%" 20.0%" dT of coolant inlet temperature 2.88°C " 5.76°C " 11.6°C " (b) Ambient temperature 10.0°C " 20.0°C " –
dT of coolant inlet temperature 11.9°C " 23.8°C " – Fig. 11. (a) The thermal performance of radiator ‘‘A” and ‘‘B”. (b) Fan
temperature has to be increased in proportion to the increased inlet air temperature before the radiator due to the ambient temperature increased to meet the engine heat into coolant.
4. Conclusion
Through this study, a 3D CFD program to predict the performance of the engine cooling module under various operating conditions was accomplished. Validation of this
program with experimental data was completed. Fig. 13
show results obtained from this program as output exam-ples including contour velocity plots and air particle traces. (1) The predicted air velocity before the radiator was well matched with test data within a maximum deviation of 7.9%.
(2) The partial displacement fan has little gain in the coolant inlet temperature and the maximum devia-tion between test and simuladevia-tion is 1.1°C.
(3) The holes in the shroud had the effect of reducing the resistance of the shroud at high vehicle speeds by increasing the air flow rate.
(4) The radiator performance with ambient temperature and engine heat into coolant had a linear relation with the coolant inlet temperature.
(5) There is no performance improvement by increasing the fan power at high speeds to reduce the coolant inlet temperature.
References
[1] Magna Powertrain, KULI Tutorial Manual, version 7.0, pp. 163–181. [2] Bernhard Uhl, Fredrich Brotz, Jurgen Fauser, Uwe Kruger, Devel-opment of Engine Cooling Systems by Coupling CFD Simulations and Heat Exchanger Analysis Programs, SAE Paper 2001-01-1695. [3] Andres Jerhamre, Andres Jonson, Development and Validation of
Coolant Temperature and Cooling Air Flow CFD Simulations at Volvo Cars, SAE Paper 2004-01-0051.
[4] Tetsuya Sakai, Shinichi Ishiguro, Yoshifusa Sudoh, The Optimum Design of Engine Cooling System by Computer Simulation, SAE Paper 942270.
[5] John Moffat, Coupling of 1D and 3D CFD Models to Predict Transient Hydraulics in an Engine Cooling Circuit, SAE Paper 2002-01-1285.
[6] Wilko Jason, Ales Alajbegovic, Bing Xu, Alex Konstantinov, Joe Amodeo, Simulation of Cooling Airflow under Different Driving Conditions, SAE Paper 2007-01-0766.
[7] Nicolas Francois, Using CFD for heat exchanger development and thermal management, in: 2nd European Automotive CFD Confer-ence, pp. 185–196.
[8] Wolf-Heinrich Hucho, Aerodynamics of Road Vehicles, fourth ed., p. 536.
[9] H.L. Stone, Iterative solution of implicit approximations of multidi-mensional partial differential equations, SIAM Journal of Numerical Analysis 5 (1968) 530–558.
[10] C.-J. Kim, Computational Fluid Dynamics, second ed., pp. 395–400. [11] Jack Williams, Guru Vemaganti, CFD Quality – A Calibration Study for Front-End Cooling Airflow, SAE Paper 980039, 1998, 133–147. Fig. 13. (a) The contour of air velocity in the vehicle model. (b) The air