A Comparison of Experimental Investigations and Numerical Simulations around Two-box form Models Sylvain Parpais (+), Jean Farce (++), Olivier Bailly (+), Herve Genty (*) Technocentre Renault, La Ruche, 4e etage, 1 Avenue du Golf, F-78288 Guyancourt Cedex, France + Technocentre Renault, ++ Formerly Technocentre Renault, now Renault F1, * Renault Wind tunnel team Swapan Mallick, Alain Belanger, Satheesh Kandasamy Exa Corporation, 450 Bedford Street, Lexington, MA 02420 Synopsis The effect of back-end and underbody geometry variations on lift and drag for two-box form shapes has been investigated using Renaults test suite models. For these geometries, detailed new experimental data has been obtained including centreline pressure data, off-centreline pressure data, and extensive wake visualisations, as well as aerodynamic lift and drag. Further, numerical simulations of these geometries have been performed using the Digital Physics based software PowerFLOW. The objective of this study is to present the results of experimental investigations and to assess the ability of PowerFLOW to predict the flow-field around two-box form cars. The effects of geometry variations on both experiment and numerical simulation are discussed and compared. It is concluded that good agreement between experiment and PowerFLOW is observed. Some deviations from the wind tunnel investigations are noted and discussed. 1. Introduction The equations of fluid flow are recovered using the Lattice Boltzmann Method [1]. Further, the recovery of isolated flow field structures in simple geometries and a demonstration of the recovery of interacting three dimensional aerodynamic structures were demonstrated by comparing predicted drag for 30 vehicles with experiment [2]. Additionally, these vehicles were subdivided into classes to demonstrate the prediction of rank ordering. An extensive validation of aerodynamic prediction of the class of stylised three-box form geometries has been previously demonstrated [3,4]. In this paper, we specifically consider two-box form models, and consider two types of geometric changes: modifications of backlight angle (where the flow regime

changes between 25 degrees and 37 degrees), and modifications to underbody geometry. In general, decreasing complexity of underbody design leads to a reduction in drag, as a result of reduced protrusion drag. Whilst this is not always the case, in the series of test cases presented, drag does indeed follow this trend. More importantly the effect on lift can be quite dramatic since small changes in geometry can have a marked effect on the underbody lifting surface. Comparisons between numerical and experimental flow structures are presented. 2. Mathematical Models The underlying computational method, Digital Physics is based on the Lattice Boltzmann Method. Details of this method have been given in a number of sources including [1, 5]. A description of the modeling strategy employed for both wall and turbulence models have also been previously described [6]. A number of sophisticated improvements to both the wall and turbulence models have been recently incorporated in PowerFLOW, which have improved predictions of transient flow structures [7]. These have been shown to maintain good aerodynamic predictions [3] whilst facilitating sophisticated aero-acoustics predictions via spectral filtering of aerodynamic noise sources [8]. 3. Test cases 3.1 Changing backlight angle The effect of changing the backlight angle may be considered in terms of competing two-dimensional and three-dimensional separation. Two-dimensional separation occurs when flow separates on edges perpendicular to the flow direction, leading to vortices with axis lines perpendicular to the flow. These may either reattach on the vehicle itself such as for leading edge hood vortices, vortices on the edges of the bumpers, vortices in the stagnation zone at the base of the windshield, or subtle separations in adverse pressure gradients on the backlight. Or they may separate without reattachment at points where the flow is subject to a local expansion such as at the end of the roof, or the end of the vehicle - this leads to a dead water region [9]. Three-dimensional separation occurs at edges, which are partially parallel to the flow direction: flow separates from the edges rolling up to form highly energetic, free, trailing vortices fed directly from the kinetic energy of the free-stream flow - they are conical in shape and are similar to those which occur on delta wings. Well-defined vortex lines in horseshoe pattern may be defined when these separations are symmetric about the centerline, and are typically observed on A and C-pillars. Both types of separations may be characterised for the three basic car shapes: fastback, notchback and squareback [10]. Squarebacks may be considered the limiting geometry of a fastback shape, and two box form models are of either fastback or squareback configuration. In general, squarebacks simply have two-dimensional separations. However, for fastbacks there is an interplay between the C-pillar vortices and the two-dimensional roof separations from the end of the roof dependent on backlight angle.

For shallow backlight angles, there may be a short roof separation, which reattaches on the slant edge, and a pair of weak C-pillar vortices. As the angle is increased, the reattachment point of the roof separation moves downstream, reducing the pressure within the confined recirculation zone. The C-pillar vortices also become stronger since the free-stream flow feeds directly onto the vortex more easily. Additionally, the change in recirculation pressure also causes the C-pillar vortices to be drawn inward, also contributing to an overall reduction in base pressure [10]. This leads to an increase in drag. At some critical angle, the roof separation is no longer able to reattach on the length of the slant, and the C-pillar vortices burst, leading to a sudden increase in base pressure and a marked reduction in drag. At this point, the wake is essentially two-dimensional with no C-pillar vortices observed, and looks much like a squareback wake. These two flow regimes, high drag and low drag, have been well documented for axi-symmetric bodies with a slanted backlight (with no ground) [11], where the critical angle is between 50 and 70 degrees, and simplistic vehicle shapes (with ground present), where the critical angle is 30 degrees [11,12]. Both papers show backlight pressure distributions corresponding to each flow regime. In the Morel body, there is as much as 0.4 difference in Cp between the flow regimes, along the centreline. The characterisation of this phenomenon on realistic car shapes has also been reported, with a critical angle at 28 degrees, which is quite close to the critical angle reported by Morel for simplistic geometries. 3.1.1 Vehicle geometries Figure 1 shows the baseline geometry. The models have some degree of complexity with detailed wheels and wheel housings. Four geometries are used: modules 7, 1, 9 and 5 which correspond respectively to backlight angles, , of 0, 16, 25 and 37 degrees (measured from horizontal). Wake surveys are captured at three positions, 0.010m, 0.280m and 0.560m downstream of geometry. Pressure taps cover the full backlight on one side. 3.1.2 Experimental results The experimental results have been obtained using a two fifth scale model. Figure 2 shows backlight pressures for module 9 (=25) and module 5 (=37), showing the difference between the attached and separated flow regimes. Module 9 (=25) shows fully attached pressure recovery, on the full span of the backlight. On the far outboard sides of the backlight, the presence of C-pillar vortices is marked by a significant reduction on pressure. Module 5 (=37) shows fully separated flow across the span of the backlight. Oil streamlines are shown in Figure 3, for modules 1 (=16), 9 (=25) and 5 (=37). Fully attached flow is shown for module 1 (=16) and 9 (=25). There appears to be large region of slow moving, attached fluid in module 9 (=25) which is not picked up by the visualisation technique). Module 5 (=37) shows a fully separated flow pattern. Figures 4-7 show wake surveys of total pressure deficit of each configuration, at the locations marked in Figure 1. In Figure 4, the squareback shape of the module

7 (=0) shows a plane of two-dimensional separation from the roof and upper sides, which recovers downstream. In Figure 5, when a backlight angle is introduced in module 1 (=16) the presence of a pair C-pillar vortices is shown this is barely noticeable at position (a), but becomes increasingly pronounced downstream. The downwash created in the middle of these vortices drags the wake down from the roofline this can be seen by comparing Figure 4(c) with Figure 5(c). The centre of the vortices stays approximately the same height above the ground in the wake. In Figure 6, (module 9, =25), as the backlight angle is increased, the lobes resulting from the C-pillar vortices are much more pronounced, dominating most of the wake flow. However, in Figure 7 (module 5, =37), we see the flow fully separate with a very weak C-pillar vortex signature present. This is quite similar to the wake flow of the squareback, module 7 (=0), in that the wake largely consists of one flow profile in the upper section compare for example, Figure 4(c) with Figure 7(c). There is an asymmetry in the flow field, which is evident in Figure 7(c) it is not clear if this is coming from the incoming flow or the geometry itself it can also be seen in Figure 5(c). Figure 8 shows measured forces. The squareback shows a considerably higher drag than any of the other configurations. As backlight angle increase, from modules 1 (=16) to module 9 (=25) drag increases this is comparable with the drag increase observed in stylised geometries in a high drag flow regime as backlight angle increases. Once separation occurs, in module 5 (=37), drag drops indicating a change in flow regime. The change in drag is quite subtle, but the effect of the change in flow regime is pronounced in lift. From module 7 (=0) to module 1(=16), there is an increase in lift caused by the large area on the upper surface with low pressure which is created by the presence of an angled backlight. As backlight angle increases, base pressure drops along the slant, giving an increase in lift as well as a drag increase. For the module 5 (=37), the base pressure increases leading to a drop in lift. 3.1.3 Numerical analysis The PowerFLOW cases were set up to match experiment. Surface meshes were created for each geometry from CAD data, which are then imported into the wind tunnel template provided with PowerFLOW. This template contains a series of nested grid regions that are automatically defined. These are used during the calculation to generate automatically a volumetric grid of cubic cells - the length of each cubic cell changes by a factor of two across each grid region, permitting rapid changes in cell size. Additional resolution requirements are added to the geometry so that each local resolution is increased using a consistent case setup methodology. 3.1.4 Comparisons PowerFLOWs results are shown in Figures 2-8. The pressure profiles of the attached and separated flow regimes of module 9 (=25) and module 5 (=37) respectively is correctly predicted. This is also shown in the oil streamlines in Figure 3. The C-pillar vortices for module 9 (=25) are captured but the details of

the structure would require increased resolution. Separated flow is clear for the module 5 (=37), and the separation line appears to be correct. Good comparisons with wake flow structure can be seen in Figures 4-7, showing total pressure deficit at three wake locations shown in Figure 1. In Figure 4, the squareback shape of module 7 (=0) separates cleanly along the upper sides and roof at position (a). The position of the wheel wakes matches, and there is good agreement in the underbody flow, as evidenced by the envelope of low total pressure deficit. As the wake develops the signature of the hip profile of the geometry is seen both numerically and in experiment this is very pronounced in Figure 4(c). When a backlight angle is introduced in module 1 (=16), C-pillar vortices form. In Figure 5(b), there is a very slight difference in the strength of these vortices comparing the simulation to experiment. This is more pronounced in Figure 5(c), however the general shape matches experiment well. Additionally, the development of the wheel wake from Figure 5(a) to 5(c) shows good agreement. As the backlight angle increases, in module 9 (=25), the interaction between the roof separation and the C-pillar vortices increases. This is shown in Figure 6(b), where the upper lobes of the C-pillar vortices are just slightly apart, distanced by the roof separation. In Figure 6(c) the downwash from the C-pillar vortices reduces the signature of the roof separation. In module 5 (=37), two-dimension separation but the separation from the outboard edges can still be seen, in Figure 7(a), (b). The yaw from experiment is not captured in the flow field predicted numerically, since this was not accounted for in the simulation. Predicted lift and drag are compared with experiment in Figure 8. Both qualitative and quantitative values match well. 3.2 Modifications to underbody detail We now consider the effect of modifying the underbody for a fixed upperbody two-box form model. In the model selected, the backlight angle is high and two-dimensional separation occurs from both the roof and C-pillars. The benefit of optimising the underbody during aerodynamic development can be significant, allowing for potential savings of, perhaps 20-30 counts (i.e. 0.020-0.030 in drag coefficient). Additionally, the underbody can have a significant effect on the lift profile. However, since obtaining detailed experimental flow structure information in the underbody region can be awkward, CFD can be of great assistance in understanding these local flow structures, and in determining what changes might be considered to meet design criteria. 3.2.1 Vehicle geometries The underbody model variants are for the Renault CLIO with production level complexity, including wing mirrors, inset glass, detailed bumpers and body styling. Figure 9 shows the baseline geometry and the variations in underbody for each of the models, ranging from highly detailed to completely smooth. Clio A has the most realistic geometry with detailed wheels and suspension, wheel housings, a full

exhaust line, fuel tank and spare tyre. Clio B has flat underbody panels that do not cover the exhaust line, and Clio C has the smoothest underbody geometry. 3.2.2 Experimental results The experimental results have been obtained using a two fifth scale model. Figure 10 shows smoke visualisations of Clio A. Clear separation is shown on the upper surface, and a clean separation line might be expected on the backlight at this angle, as is demonstrated in the CFD visualisation. Figure 11 shows experimental drag and lift. A clear drop in drag is observed as underbody complexity is reduced suggesting little change in upper body flow structure due to the differing underbody designs. Changes in the lift are more pronounced. However, Clio Bs lift is lower than Clio A, due to reduced rear axle lift caused by the smoother geometry around the rear axles. Clio C has the lowest lift of and this is again due to the smoother surface reducing underbody pressures. 3.2.3 Comparisons to CFD All three Clios configurations have been simulated using PowerFLOW. Figure 11 shows the comparison of experiment with prediction. The trend in both drag and lift is correctly captured. Numerical analysis shows that despite the close absolute values of drag for Clio B and Clio C, the force integration plot of Figure 12 shows that Clio B has significant differences from Clio C in the way in which the total drag of the vehicle is created. Initially, flow stagnates on the nose of the geometries, leading to a sudden large increase in drag; this can be observed between x=-1.5 and x=-1.4. At the point of flow acceleration around the leading edge of the bonnet, extremely low pressures lead to a suction which causes the integrated drag to fall. At the point of the front wheels, geometry differences in the wheel housing of Clio B lead to a significantly higher drag than the smooth underbody geometry of Clio C. More detailed analysis of this section of the flow would lead to potential design changes which could reduce the overall drag. For example, rounding the wheel housings would reduce separations immediately downstream of the wheel. The extra drag caused by the wheel housings is marked as a constant difference between the cumulative drag of Clio B and Clio C along much of the remaining body length, till x=0.75. A few features may be noted in this section. Firstly, cumulative drag drops at the top of the windscreen, again because of pressure suction from accelerated flow. Additionally, cumulative drag increases only slightly between x=-0.25 and x=0.75, even though Clio B has some considerably complex geometry in this region. This indicates, perhaps counter-intuitively, that design modifications in this section are likely to be of little benefit. At x=0.75, the pressure recovery begins. A significant discontinuity occurs just upstream of the rear wheel, at x=0, which is possibly caused by end of the exhaust channel where flow is stagnating. This has a downstream effect which, though minimised, appears to lead to the increased drag in Clio B compared with Clio C. The lift of Clio A is considerably different to that of Clio B and Clio C. The force integration plot in Figure 12(b) indicates that the difference comes purely from the

backend at x=1.0. At this point Clio A has a fuel tank, which has a guard immediately upstream of it. It appears that flow is stagnating on this guard and generating considerable lift. 4 Conclusions Good agreement is shown between experiment and PowerFLOW. The bulk flow characteristics in the flow field of two-box models in Renaults test suite are captured well, across a range of different backlight angles. PowerFLOW is seen to capture the balance between relative strength of C-pillar vortices with the strength of the roof separation. Additionally drag and lift trends for changes in underbody detail are predicted. 5 Acknowledgements Exa would like to thank SGI for their assistance in the preparation of this paper. References [1] Chen, .H., Teixeira, C. and Molvig, K., Digital Physics Approach to Computational Fluid Dynamics: Some Basic Theoretical Features. International Journal of Modern Physics C, (1994), 8, 4, 675-684. [2] Mallick, S., Remondi, S., Chen, H., Pervaiz, M., Developing CFD through Validation of Turbulence Models, MIRA Vehicle Aerodynamics Conference (2000). [3] Lietz, R., Mallick, S., Kandasamy, S., and Chen, H., Exterior Airflow Simulations Using a Lattice Boltzmann Approach, SAE 01-0596 (2002). [4] Lietz, R., Pien, W. and Remondi, S., A CFD Validation Study for Automotive Aerodynamics, SAE 00PC-229, (2000). [5] Chen, H., Teixeira C., Molvig, K., Realization of Fluid Boundary Conditions via Boltzmann Dynamics, Int. J. Mod. Phys. C, (1998), 9, 8, 1281-1292. [6] Teixiera, C.M., Pervaiz M.M., Two Equation Turbulence Modeling with the Lattice Boltzmann Method, Proc. ASME PVP Division Conf., 2nd Int. Symp. Computational Techniques for Fluid/Thermal/Chemical Systems with Industrial Applications, Aug 1-5, 1999 Boston, MA, USA. [7] Yakhot, V., et al, A New Approach to Modelling Strongly Non-Equilibrium, Time-Dependent Turbulent Flows (Internal Document). [8] Duncan, B.D., Sengupta, R., Mallick, S., Shock, R., Sim-Williams, D.B., Numerical Simulation and Spectral Analysis of Pressure Fluctuations in Vehicle Aerodynamic Noise Generation, SAE 01-0597 (2002). [9] Hucho W.H., Aerodynamics of Road Vehicles, 4th ed., Butterworth & Co., 1987. [10] Ahmed, S.R., Ramm, G., Faltin, G., Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE 840300, (1984). [11] Morel T., Aerodynamic Drag of Bluff Body Shapes Characteristic of Hatch-Back Cars, SAE 780267 (1978). [12] Bearman, P.W., Near Wake Flows Behind Two-Dinemsional and Three-Dimensional Bluff Bodies, J. Wind. Eng. 69-71 pp33-54, (1997).

Figure 1: Baseline geometry (with wake survey locations at 0.010m, 0.280m and 0.560m downstream of geometry). The four angles tested are shown. Positions of experimental probes are also shown.

Figure 2: Experimental and computational Cp results for module 9 (=25, left) and 5 (=37, right). C-pillar vortices in left image are indicated by drop in outboard pressure. Fully separated flow in right image shows little variation across span.

(a) (c) (b)

Figure 3: Oil streamlines for modules 1 (=16, top), 9 (=25, middle) and 5 (=37, bottom). Top and middle images show fully attached flow. Bottom image shows full separation.

Figure 4: Module 7 (=0) wake survey, at three positions.

(a) (b)

0.1 1.0

(c)

Note: Three sets of images are shown for each position (a), (b), and (c) as defined in Figure 1. Each set of images shows experiment (upper) and PowerFLOW (lower). This squareback geometry shows separations (on the upper body) which are relatively clean. The influence of the hip is evident at position (c).

Figure 5: Module 1 (=16) wake survey

(a) (b)

1.0

(c) (c)

Note: For a small backlight angle, a weak C-pillar vortex forms. This is shown at position (b) and there is a good match between computation and experiment. There is a slight difference between the strength of the vortex in experiment and computationally, evident at position (c).

0.1

Figure 6: Module 9 (=25) wake survey

(a) (b)

1.0 0.1

Note: Interaction between roof separation and C-pillar vortices is stronger for the module 9 (=25) than the module 1 (=16). This is evident at position (b), where the upper lobes of the C-pillar vortices are slightly apart. There is good match between numerical and experimental wake surveys.

Figure 7: Module 5 (=37) wake survey

(b)

1.0

(c) (c)

(a)

0.1

Note: The backlight angle is now past the critical angle, and the flow fully separates. The yaw found in experiment is not captured in the computation solution, since this was not modelled.

Figure 8: Modules Forces comparisons between experiment and PowerFLOW. Drag factor comparison is in left image, lift factor comparison is on the right.

Figure 9: Clio baseline geometry and underbody configurations. Clio A has the most detailed underbody, and Clio C is the least detailed.

Figure 10: Upper body flow field of Clio

Clio A Clio B Clio C

0.64

6

0.54

5

0.59

1

0.58

1

0.61

3

0.54

8 0.62

6

0.62

1

0.3

0.4

0.5

0.6

Mod 7 Mod 1 Mod 9 Mod 5

Geometry

AC

d ACd (Expt-new)ACd (3.4)

0.09

9

0.50

2 0.68

0.30

2

-0.0

73

0.28

1 0.5

1

0.29

4

-0.2

0

0.2

0.4

0.6

0.8

Mod 7 Mod 1 Mod 9 Mod 5

Geometry

AC

l ACl (Expt-new)ACl (3.4)

Figure 11: Force comparisons for Clio. Drag factor is in left image, lift factor is on right.

Figure 12: Forces integration for Clio configurations. Left image shows the integration of drag factor for the three cases. Clio B and C have similar total drag factor, but this is generated from different mechanisms. Right image shows integration of lift factor. Clio A has a very different lift to that of Clio B or C. This comes from a component located at x=0.8, which turns out to be a guard for the fuel tank.

0.63

2

0.57

7

0.55

50.62

5

0.60

0

0.58

8

0.300

0.400

0.500

0.600

0.700

Clio A Clio B Clio C

Geometry

AC

d ACd (Expt-new)ACd (3.4)

029

8

0.18

7

0.12

7

038

5

0.16

0

0.09

0

0.0000.1000.2000.3000.4000.500

Clio A Clio B Clio C

Geometry

AC

l ACl (Expt-new)ACl (3.4)

(a) (b)