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BEST PRACTICES FOR THE MODELING AND SIMULATION OF FLUID FLOW AROUND MOTOR SPORT VEHICLES USING

HARPOON AND ANSYS FLUENT

Ştefan Bordei*, Florin Popescu†

Abstract

The present document is a result of different numerical experiments compared with wind

tunnel results to determine the best practice guidelines for vehicle flows. The smallest difference between numerical and physical experiment yielded the best practice guidelines for vehicle flows. Schemes for reducing preparation, discretization and simulation time are also presented.

1. INTRODUCTION The synergy between computational fluid dynamics (CFD) and wind tunnel testing has

increased the potential for optimization in external aerodynamic development of race cars. CFD in motor sport is often used to optimize car shapes for downforce and drag, correlations with wind tunnel tests and track tests.

In order to perform the optimization of the rear wing shape on the car we needed to converge towards a reliable method of simulation that would enable us to compare results for several alternative wing modifications.

The approach is always subject to constraints like available RAM and total CPU time. These constraints determine the modeling strategy used in terms of total number of grid points and the complexity of numerical models. The more resolution you have the better the accuracy, but the longer the total CPU time, so the really difficult part is finding the best compromise between the cost of the simulation and the accuracy.

The present paper is a capitalization of sixty one simulations we have made for this project. It is not intended to describe in detail all of them, but to highlight the best practices that resulted from our experience.

Detailed analysis of the full car (a personal creation based on a Ferrari F40 with simplified underbody and closed air inlets) yields strong coupling between various elements like the rear windshield angle with relation to the x axis, the B-pillar, the length of the rear trunk lid [1] and the performance of the rear wing. The quality of the flow towards the rear wing can be influenced even by the radius and the angle of the A-pillar. This means that studying the wing alone is not sufficiently relevant, due to the impossibility of replicating the complex interactions between the various car elements through the usage of simple Boundary Conditions.

For the calculation of airfoil characteristics the best method is actually the panel method (see figure 6) the next smallest error (absolute and relative) is the RSM model for angles of incidence α<100 but for higher ]1.22;10( the S-A model has the smallest error. All the simulations had the same structured quad grid. They were all compared to

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reference [7]. From this comparison the best practice for CFD is: the S-A model. It gives good results for low resources spent.

The simulations on the “Ahmed body” geometry [9] were done for the RKE, RSM, DES and LES turbulence models for two different grid resolutions: 500 k and 1.9 M.

The base level for the coarse grid (see figure 8 a) is 160 mm, reference surface length is 5 mm with 2.5 mm in areas of separation and the finest refinement zone was a 10 mm grid cell size.

The base level for the medium grid (see figure 8 b) is 160 mm, reference surface length is 1.25 mm and the finest refinement zone was a 10mm grid cell size.

The wake topology simulation results were compared with reference [8], see figure 7, for a slant angle of 25 0. Analysis of figure 7 and of the average relative error, leads to a hierarchy between the different methods. The smallest average relative error is achieved by the RKE, then by LES followed by the RSM and at last DES. Simulations done with the DES, shown in figure 10, prove that to reach grid convergence for a simplified car model you need a grid between 2M and 6M. Grid convergence for the simplified F40 with the RSM was possible with grids ranging from 11M to 15M. Future work on the Ahmed body geometry will focus on finer grids with the RSM and LES turbulence models to increase the accuracy of the simulations.

Mesh size and turbulence model Cd ∆ Cd Average y+

wind tunnel experiment 0.285 - -

coarse mesh (500 k) RKE 0.3018 5.89% 248

medium mesh (1.9M) RKE 0.3735 31.05% 112

coarse mesh (500 k) RSM 0.4098 43.79% 248

medium mesh (1.9M) RSM 0.2592 9.05% 104

coarse mesh (500 k) DES 0.2358 17.26% 206

medium mesh (1.9M) DES 0.3994 40.14% 112

coarse mesh (500 k) LES 0.3562 24.98% 229

medium mesh (1.9M) LES 0.2409 15.47% 92

2. MESHING

Complex geometry cleaning and meshing are the most repetitive and time consuming processes in CFD today.

HARPOON, developed by Sharc, is recommended for the automated surface and volume grid generation. It creates a high quality, unstructured, hexahedral dominant grid, but has some issues with boundary layer output.

There is no need for cleaning of the geometry and the software is very user friendly. You pass from days and weeks for the preparation of the model to hours and minutes. The recommended simulation domain is 40 m long, 8 m wide (for the half model) and

10 m high, with the center of the coordinate system at half wheel base and half width of the FIA (Fédération Internationale d’Automobile) GT (Grand Touring) car, on the ground.

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It can be effortlessly created by simply making use of the far-field option in HARPOON. The recommended reference surface length is 5 mm on the GT car [3].

In areas where flow separation was proven to occur, in the base CFD run (11 million cells RSM case from figure 5), a surface grid size of 2.5 mm is recommended.

On the rear wing we recommend 2 mm surface grid size. The first refinement zone around the rear wing is set to 5 mm. Refinement zones are what HARPOON uses for controlling the resolution of the cells in the volume. The next 2 refinement zones, for the rear wing, should have a grid size of 10 mm and 20 mm, respectively. All the simulations that gave good results converged towards 20 mm in the wake refinement zone. The wake usually accounts for about 60% of the total drag of the GT car and if we do not choose the right resolution in this area the computed drag coefficient could be inaccurate.

The proper resolution in the underbody area was found to be 10 mm. For the refinement zone of the heat exchangers the recommended resolution is: 5 mm

[4]. To avoid grid size varying too fast from very small to very large we recommend a

refinement zone around the whole FIA GT car of 40 mm cell size. At the far field, the coarsest zone is recommended to be set to 320 mm. The

recommended grid strategy can be observed in figure 1, 2, 3 and in table 1. The boundary layer is done after the whole domain is discretized, settings for the

Ahmed body boundary layer: initial cell height: 0.2 mm, number of layers: two (attempts with 5 and 10 failed) and constant expansion rate of 1.2.

There should not be any intersection between two or more reference zones of the same level or the discretization will fail.

The findings for the successful grid strategy agree also with reference [4] for the wake resolution for example.

3. SOLVING

3.1 Boundary Conditions It is crucially important to replicate as much as possible the experiment to which you

wish to compare the results [2]. A good simulation can be made invalid by a simple part that was not up to date (this,

of course, is true for wind tunnel tests also). Set up:

- Velocity inlet boundary condition with a figure 4 type profile that would gradually increase the velocity until final simulation velocity is reached. We must emphasize that this was proved to reduce the total number of iterations up to 65%! The first comparison was made between the iterations required to converge the residuals and the drag coefficient, Cd, of two transient cases on the same geometry with different resolutions. The first 6 million case took 87 300 iterations to converge with an S-A model and normal initialization with the final inlet velocity [3] and the second 15 million case took 30 000 iterations with a

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RSM model but we used the figure 4 type initialization. If we further compare other simulations done with the S-A model, on the same geometry, but similar resolution, than the gain is even higher: up to 76%. If, again, we further compare with a hexahedral dominant grid than the gain is 84%. The reason for which the initialization using a velocity value equal to 0.024*final (determined by trial and error) desired inlet velocity reduces computational effort is that this method provides the flow with a smooth transition to the desired inlet velocity and it avoids higher initial Cd values that would appear when initializing with zero velocity. As this first low speed (V∞≠0 m/s) case advances and iterates, it resolves the flow (for residuals 1e-3) and as the velocity is increased it serves as a good “guess” for the slightly higher speed. Another advantage is that the Cd value for the first iteration is better scaled, closer to the final one then an initialization with the final inlet velocity from the beginning which helps with the total number of iterations. This finding enabled us to carry out more high fidelity simulations in less time.

- Boundary layer suction, this is where the shear stresses will be set to zero, all modern wind tunnels have this feature;

- The dynamic mode: rotating wheels and moving ground (belt) can be replicated in ANSYS FLUENT via the Rotating Wall Boundary Condition for the tires, moving frame of reference (or moving mesh-> more expensive but probably more accurate, research in progress) for the spokes and Moving Wall Boundary Condition for the belt [6]. Without the moving ground BC the level of downforce of the vehicle will no doubt be false, making the impact of the rear wing on the vehicle total downforce impossible to evaluate;

- The exit of the virtual wind tunnel should be set up as Pressure Outlet Boundary Condition;

- Radiators, intercoolers, condensers and other heat exchangers can be set up as porous media fluid;

- The rest of the domain boundaries can be set up as Symmetry Boundary Condition.

3.2 Turbulence Modeling and transient calculation

Based on our experience, the most appropriate turbulence model, for motor sport external aerodynamics is the Reynolds Stress Model (RSM). It is the best turbulence model for capturing the separation lines, the strong vortices and wake physical structure.

The Realizable k-epsilon model predicts quite well the drag coefficient value, and is robust. We should keep in mind that it comes at less of a computational cost than the RSM, LES and DES.

The Spalart-Allmaras turbulence model is good for predicting the aerodynamic performance of the wing in a wide operating range, unfortunately for FIA GT car shapes

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it does not seem to accurately predict the drag. We compared the official Cd value of the F40 (Cd=0.34) and then substracted what we know to be the influence of the engine compartment and rough underbody, this was compared with the simulation results and found to be inaccurate.

As mentioned in ref [3], with the right resolution, the RSM model gives more accurate results than the k-e.

Begin the simulation with the RSM model (see figure 9). Recommended settings for the Reynolds Stress Model:

- Start with a steady solver - Initialize the flow field with a value 0.024*final inlet Velocity (fig. 4). Then

gradually increase the velocity by one meter per second every fifty iterations until you reach your desired simulation inlet velocity.

- Set Under Relaxation Factors for the RSM to: 0.65 for Pressure, 0.35 for Momentum and 0.50 for k and epsilon as in ref.[3]

- We recommend the firs 50 iterations with First Order Discretization then switch to Second Order, and increase the velocity by 1 m/s (fig.4)

- If convergence problems occur right at the beginning of the calculation, set Under Relaxation Factors for k and epsilon to 0.2 for 50 iterations, and then switch to 0.5 and after that switch to Second Order Discretization [3].

- The non-equilibrium wall functions are recommended. - An algebraic multi-grid (AMG) method is recommended, to accelerate solution

convergence. Solver Type: V cycle for all (pressure, momentum, k, ε, etc), AMG method: selective, stabilization method: BCGSTAB;

- The SIMPLEC algorithm, is advised for the pressure – velocity coupling. - After the convergence of the residuals (1e-6) and Cd (±1e-3) value check that the

average y+ value is between 30 and 300 (if the average y+ value is out of the desired range redo the grid with a different grid strategy).

- Switch to the transient solver. - The Large Eddy Simulation with WALE sub grid-scale model is recommended. - At the beginning of the transient calculation, start with a time step of 5e-5. - If the residuals or the Cd do not converge set the time step to 1e-6 and the AMG

from the V-cycle to the W-cycle. - We let the flow particle pass the length of the vehicle 5 times and that usually

results in converged drag values, but for some shapes it takes 12 times to see converged values.

- If still convergence issues then double the resolution (1/2*base level).

4. CONCLUSIONS The paper presents the latest advances and capabilities in external and internal

aerodynamic simulations with ANSYS FLUENT. It gives recommendations for geometry, grid, steady and transient case set-up. The focus is on high fidelity motor sport simulations but with as short as possible turnaround time.

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REFERENCES

[1] W.H. Hucho, “Aerodynamics of Road Vehicles”, 4th Edition, SAE International,

1998. [2] Rob Lewis & Philip Postle “CFD Validation for External Aerodynamics”, 1st

European Automotive CFD Conference 2003. [3] M. Lanfrit, “Best Practice Guidelines for Handling Automotive External

Aerodynamics with FLUENT”, Version 1.2, http://www.fluentusers.com, 2005. [4] Zenitha Chroneer “The CFD Process for Aerodynamics at Volvo Cars using

HARPOON-FLUENT”, 3rd European Automotive CFD Conference, 5-6 july 2007. [5] Harpoon User Guide version 3.6, Shark Ltd. [6] ANSYS FLUENT 12.0, User Guide and Tutorial Guide. [7] Robert M Pinkerton “Report No. 563 CALCULATED AND MEASURED

PRESSURE DISTRIBUTIONS OVER THE MIDSPAN SECTION OF THE N.A.C.A 4412 AIRFOIL”.

[8] H. Lienhart, C. Stoots, S. Becker “Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model)”

[9] Ahmed, S.R., Ramm G. “Some Salient Features of the Time-Averaged Ground Vehicle Wake”. SAE Technical Paper 840300, 1984.

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Figure 1. Side view of Harpoon hexcore mesh strategy

Figure 2. Side view detail of Harpoon hexcore mesh strategy

320 mm RF0

40 mm RF1

20 mm RF2

10 mm RF3

20mm RF2

10 mm RF 3

5 mm RF4

5mm RF4

20mm RF2

10 mm RF3

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Refinement zone level RF

Volume grid size

[mm]

Geometric size of the RF

Farfield 0 320 Around GT car 1 40

Wake car and rear wheel, around rear wing, wake

front wheel 2 20

Rear wing, A-pillar, mirror, Boundary Layer

RF 3 10

Rear wing, A and B-pillar 4 5

Size inspired from the base

CFD run (figure 5) type

surfaces.

Table 1.

Figure 3. Harpoon automatic, mixed, unstructured surface grid.

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Velocity Initialization

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25 30 35 40 45

V[m/s]

Itera

tions

Figure 4. The Velocity profile for the initialization Figure 5. Iso-surface of total pressure equal to zero as calculated in the base CFD

run (11M cells).

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Comparison between Cl CFD, PM and experiment TR 563

0

0.5

1

1.5

2

2.5

3

3.5

4

-5 0 5 10 15 20 25

alfa

Cl

exp TR 564 Fluent Inviscid Fluent rke Fluent S-AFluent RSM Visual Foil inviscid Visual Foil Thin Airfoil Theory Visual Foil PM BL thickness

Figure 6. Comparison between different numerical experiments and a reference physical one for a NACA 4412 airfoil at different angles of attack.

RKE coarse

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Figure 7 Comparison between different experiments for an “Ahmed body” with 25o slant angle [8].

RSM coarse LES coarse

DES coarse RKE medium

LES medium RSM medium

DES medium

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Figure 8.a) Coarse grid for the ahmed body” with 25o slant angle

Figure 8.b) Medium grid for the ahmed body” with 25o slant angle

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Figure 9. Road map for turbulence modeling and transient calculation

Pressure based steady solver

Turbulence model: RSM Non equilibrium wall

functions

Set up BC’s

Initialize with 0.024*final inlet velocity (fig. 4), and then

increase with 1 m/s every 50 iterations

Set under relaxation factors 0.65 for Pressure, 0.35 for Momentum and 0.50 for k and epsilon

Do 50 iterations with first order

(second point in fig.4)

Switch to second order

AMG V-cycle,

BCGSTAB for all

Pressure-Velocity coupling

SIMPLEC

Check avg. y+, convergence for residuals and Cd

Begin

Switch to the transient solver

Δt=5e-05

LES WALE

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Grid convergence for DES

0.639

0.437 0.438

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000

Number of elements

Cx

Figure 10. Grid convergence for DES and streamlines for simplified car geometry.

* Bordei Stefan is a PhD student at the University Dunărea de Jos of Galaţi, Faculty of Mechanics, Department of Thermotechnics, 47, Domneasca, str. 800008, Galaţi, Romania ( e-mail: Stefan.Bordei@ugal.ro).

† Florin Popescu is PhD, professor at the University Dunărea de Jos of Galaţi, Faculty of Mechanics, Department of Thermotechnics, 47, Domneasca, str., 800008, Galaţi, Romania (phone: +40-721-233-679, fax: +40-236-314-463; e-mail: florin.popescu@ugal.ro).