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BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20-24 2008

LARGE-EDDY SIMULATION OF UNSTEADY VEHICLE AERODYNAMICS AND FLOW STRUCTURES

Takuji Nakashima , Makoto Tsubokura†, Takahide Nouzawa , Takaki Nakamura , Huilai Zhang††, and Nobuyuki Oshima†

Department of Social and Environmental Engineering Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan

e-mail: [email protected], Phone and Fax: +81-82-424-7771

† Division of Mechanical and Space Engineering Hokkaido University N13, W8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan

e-mails: [email protected], [email protected]

Mazda Motor Corporation, 3-1 Shinchi, Fuchu-cho, Aki-gun, Hiroshima 730-8670, Japan

e-mail: [email protected], [email protected]

††Advancesoft Corporation, 1-9-20 Akasaka, Minato-Ku, Tokyo 107-0052, Japan

e-mails: [email protected]

Keywords: Unsteady Aerodynamics, Vehicle Aerodynamics, Large-Eddy Simulation, Run-ning Stability, Vortex Structure, Road Vehicle, Passenger Sedan.

Abstract. The purpose of the present study is an investigation of a vehicle running stability from viewpoints of steady and unsteady flow characteristics, such as vortex structures and their motion, around the vehicle. For this purpose, a numerical method for unsteady vehicle aerodynamics using Large-Eddy Simulation (LES) is constructed and validated. Special focus is on a pitching stability, which relates to the passengers’ comfort and safety, and influences of the forced pitching motion on the vehicle aerodynamics are investigated. Two simplified vehicle models, which represent real passenger sedans with different running stability in past road tests, are adopted as the objects. First, the simplified models are tested in the stationary condition to see whether the same characteristic pressure fluctuations as observed in the real sedans are reproduced. Then, aerodynamic characteristics and its relationships with flow structures in quasi- and non-stationary conditions are investigated. Particular emphasis is on the aerodynamic forces acting on the trunk deck, which are expected to be strongly related to the stability of the pitch motion, and they are studied by relating to the steady and unsteady wake structures of the vehicle. The result indicates that consideration of the unsteady aerody-namic characteristics based on the flow structures around the vehicle is important to evaluate the vehicle stability as well as the conventional evaluation based on steady aerodynamics. Thus, the availability of LES is expected for the evaluation of vehicle aerodynamic stability.

T. Nakashima, M. Tsubokura, T. Nouzawa, T. Nakamura, H. Zhang and N. Oshima

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1 INTRODUCTION With regard to safety and passengers’ comfort, running stability is one of the most impor-

tant characteristics of a road vehicle. While the vehicle stability in the normal running condi-tion is mainly discussed in terms of the suspension control, more attention is to be paid to the aerodynamic forces and its relation to the vehicle stability is going to be discussed especially in high-speed running condition, together with recent tendency of body weight reduction for fuel economy. Within the last two or three decades, both wind tunnel experiment and compu-tational fluid dynamics (CFD) technologies have improved vehicle aerodynamics in steady state. However, to achieve more sophisticated aerodynamic design for the aerodynamic stabil-ity, it is expected to consider unsteady flow characteristics and interactions between the flow and the vehicle motion. Large Eddy Simulation (LES) has been expected as a better and more precise turbulence model for prediction of unsteady vehicle aerodynamics[1]. Because LES simulates large and coherent flow structures directly in three-dimensional space with time marching, it can reduce the model dependency compared to RANS and be suitable for the un-steady flow simulations.

The purposes of the present study are to construct a numerical prediction method for un-steady vehicle aerodynamics and to investigate unsteady flow characteristics around a vehicle relating to the running stability. The LES method constructed is first validated on the ASMO model [2], of which reliable wind-tunnel experimental data are available. The conventional RANS models with the same computational grid systems are conducted to see the validity of LES. Based on the validation, the LES on two simplified vehicle geometries are then con-ducted. The models are constructed based on the real passenger sedans with different running stability in the in-vehicle research [3]. The unsteady flow characteristics around the models in the stationary state are investigated toward a study of interaction between the vehicle motion and unsteady flow around the vehicle. The predicted flows around the two models are com-pared and discussed from the viewpoints of flow features, such as vortex structures.

2 NUMERICAL METHOD

2.1 Governing Equations and Discretization The governing equations adopted in the present LES method for a vehicle aerodynamics

prediction are the spatially filtered continuity and Navier-Stokes equations as follows;

0i

i

ux

(1)

SGS2ii j ij

j i j

u Pu u St x x x

(2)

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i jij

j i

u uSx x

(3)

/ / 3i ii iP p u u u u . (4)

Here, ui, p, , and mean flow velocity in i-direction, pressure, density, and dynamic viscosi-ty of the fluid, respectively. An over-bar ( ) means the spatial filtered value of the physical value.


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Sub-Grid Scale(SGS) eddy viscosity SGS appeared in Eq. (2) must be modeled by a turbu-lent model. The standard Smagorinsky model [4] is adopted to estimate SGS as follows;

2SGS 2 ij ijS dC f S S (5)

Here, means the spatial filter width that is evaluated by a cubic root of cell volume. Cs is the Smagorinsky constant and is given as 0.15, which is the standard value for external flow simulations. To represent a damping of SGS eddy viscosity in near-wall region, the Van-Driest type damping function fd in Eq. (5) is introduced as follows;

1 exp / 25df y , (6)

where y+ is the wall unit. These governing equations are discretized based on the vertex-centered unstructured finite

volume method and SMAC algorism. The central finite difference scheme with the second order accuracy is adopted for the spatial discretization except for the convective term in which 5% of the first order upwind component is blended for a numerical stability. The second order Adams-Bashforth scheme is adopted for the time integration.

2.2 Validations of LES for vehicle aerodynamics The ability of the LES for vehicle aerodynamics prediction had been investigated and vali-

dated [5] on the 1/5 scale ASMO model [2] shown in Fig. (1). Three computational grid sys-tems are applied and they consist of 1.3M, 5.5M and 24M tetrahedral elements, respectively. The RANS simulations using standard k- model (i.e. [6]) are also conducted on the same grid systems, though the discretization of a convective term is the third order TVD scheme and is different from the LES. The boundaries of floor and body surface are treated artificially, and the surface shear stress is estimated with the logarithmic law assuming a fully developed tur-bulent boundary layer.

Fig.1 ASMO model

In the comparisons with the RANS, the LES results agreed well with the experiment. Fig-ure (2) shows the base pressure profiles predicted in the simulations. The pressure recovery on the base is well predicted in the LES (left graph), though the RANS results cannot reproduce the recovery and it conserved to the lower pressure in high spatial resolution case. The prob-lem in the LES results is the spatial pressure oscillation at the corners of the body, which are shown at Z/H= 0.82 and 0.22 in Fig. (2). They are caused by the insufficient spatial resolution at the corners and the central difference scheme for the convective term in the LES.

B:290 L:810

H: 270


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Fig.2 Base pressure profiles on ASMO model

However, the additional simulations for the validation showed that non-uniform computa-tional grids clustered to the corner could reduce the spatial pressure oscillation sufficiently. The prism layer mesh on the body was also effective for the reduction of the oscillations. Fi-nally, it was confirmed that the problem of the spatial pressure oscillation around the corner could be eliminated by these technique of grid generation.

3 NUMERICAL SIMULATION OF VEHICLE’S AERODYNAMIC STABILITY Based on the validation, we conduct the LES predictions of the aerodynamics of two sim-

plified vehicle geometries in order to investigate an aerodynamic stability of a vehicle in a pitch motion.

3.1 Vehicle aerodynamic stability on the pitching motion In the Ref. [2], Okada et al. investigated running stability of two sedan-type vehicles in

cruising condition. Although their steady or mean aerodynamic characteristics such as a drug and a lift coefficients, Cd and Cl, are similar, their running stabilities in a highway condition were found to be quite different. In the study, the stability was represented by the difference of the dynamic pitch motion measured as a rear ride-height and its stability. Thus, they fo-cused on the pressure distributions on the trunk decks of the vehicles, and found out a specific difference between them.

For more essential study, Ichimiya et al. [5] constructed the two simplified vehicle models and they conducted wind-tunnel experiments. The two models seemingly resemble each other and the specific difference appears only in the geometrical shape of front and rear pillars, which typically represents the original real sedans. The validity of the simplified models for the study of aerodynamic pitching stability was demonstrated in the wind-tunnel measure-ments by reproducing the specific pressure fluctuation on the trunk decks observed in the real vehicles. Thus, it is expected that the essential flow features around the original sedan, which relate to the unsteady flow characteristics, are reproduced by these simplified models.

Considering these experimental studies, the difference of flow structures around the ve-hicle, which is caused by the tiny geometrical difference of a pillar curvature, can be expected to influence the stability of the vehicle pitch motion and thus the running stability. In this study, the simplified models are more intensively studied in the context of flow structures and their relationships with the aerodynamic pitching stability. The special focus is over the trunk deck where the different flow characteristics were measured in the experiments.


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3.2 Simplified vehicle model The target models are about 1/20 scale of the original passenger sedan. The body size is

210mm length (L), 80mm width (W), and 65mm height (H). Their differences are mainly ap-pearing in the curvatures of front and rear pillars as shown in Fig. (4). As previously de-scribed, the original passenger sedans of these models have different running stabilities in the in-vehicle research and these simplified geometries also have the same tendency in the expe-riment. The vehicle model, which has high stability of the pitch motion in the experiments, is shown in a left figure of Fig. (4) and it is called as “Model A” in this paper. The other model, which has low stability, is shown in a right of Fig. (4) and is called as “Model B”.

Fig.4 Schematic view of the simplified model geometries (Left: Model A, Right: Model B)

In the present numerical simulations, the simplified model is set into the rectangular duct as shown in a left figure of Fig. (5). Clearance under model’s floor is 0.23H. At an inlet boun-dary, uniform and constant flow velocity U0 = 16.7m/s is assumed. Reynolds number, based on a vehicle length and an inlet velocity, is about 2.3 x 105.

Regarding the boundary conditions, the vehicle body and a part of floor, which is yellow-colored in the left of Fig. (5), are treated by the wall-model same as the validation on ASMO. The green-colored floor, which is treated as free-slip wall boundary, represents a suction of a boundary layer developed on the floor. The vehicle model is located 0.14L downstream from this suction. The side and top walls are also treated as free-slip boundary.

The origin and direction of the pitch motion are defined as a right figure of Fig. (5). They are based on the experimental geometry in Ref. [6], where cylindrical struts support the mod-els at the positions of front and rear wheels and the rear struts pushes up the models for the pitch motion. Here, the origin is defined at the position of the front strut in the experiment.

Fig.5 Schematic view of the computational domain (Left) and the objective geometries (Right).

(side view)


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The computational domain is divided to about seven million elements and 1.5 million nodes in each case. The computational grids on the model surfaces are shown in Fig. (6). The minimum distance between the nodes on the surface is 0.5mm on the edges. Eight layers of prism mesh are inserted on the vehicle body and thickness of the first layer is about 0.1 mm. The other region is divided by tetrahedral meshes except for the prism-layer on the outlet boundary.

Fig.6 Computational grids on the model surfaces (Left: Model A, Right: Model B)

3.3 Large-Eddy Simulation in a stationary condition First, the LES of flows around the models in a stationary condition is conducted. Pitch an-

gle is set be zero and the steady and unsteady flow characteristics around the models are in-vestigated.

Figures (7) show time-averaged flow structures around the models visualized by flow rib-bons. In both cases, the angular pillars generate clear longitudinal vortexes. Thus, in the mod-el A, the approaching flow goes around the smooth front pillar and the angular rear pillar generates a clear longitudinal vortex on the side of the trunk deck. On the other hand, in the model B with an angular front pillar, the front pillar vortex is generated and goes onto the rear shield. The vortex is paired with the other vortex generated from the rear pillar.

These features of the pillar vortexes are also clearly shown in Fig.(8), which visualize the time-averaged vortex structures as iso-surfaces of vorticity magnitude. The front pillar vor-texes are observed only in the model B having angular front pillar.

Fig. 7 Time-averaged streamlines (Left: Model A, Right: Model B).

Fig. 8 Iso-surfaces of time-averaged vorticity magnitude ( =1.5x103[1/s], Left: Model A, Right: Model B).


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Figures (9) show time-averaged vorticity and in-plane velocity distributions on the cut-plane over the trunk deck. As a result of the strong interactions among each flow structures generated front and rear pillars, the slight geometrical difference causes significant difference of flow structures especially over the trunk deck.

Fig. 9 Time-averaged vorticity distribution and in-plane velocity vectors on the cut-plane over the trunk deck

(Left: Model A, Right: Model B).

Regarding the unsteady flow characteristics, a graph in Fig. (10) shows the time-series of aerodynamic force acting on the trunk deck in the vertical direction. Here, the positive lift force means the upward force. The unsteady fluctuations are predicted in both models. The intensity of the fluctuation is stronger in the model A than in the model B and intensive peaks such as observed around 2.1 sec are observed only in the model A.

Fig.10 Time-series of aerodynamic lift force acting on the trunk deck

Such unsteady fluctuations of aerodynamic force are also identified on the pressure signal on the trunk deck. In the Fig. (11), two graphs show time-series of pressure coefficient Cp at points on the trunk deck shown in the figures added above. The Cp is defined as follows;

20 0 2pC p p U . (7)

At both points 1 and 2, the intensive peaks of pressure are predicted in Model A, and no such strong fluctuation is predicted in Model B. This tendency of pressure fluctuation corres-ponds to the measurements in the steady state experiment. This qualitative agreement of the unsteady feature indicates the possibility of the present LES to investigate the unsteady ve-hicle aerodynamics.


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(a) Point 1 (b) Point2

Fig.11 Time-series of pressure coefficient at the probe points on the trunk deck

From the other viewpoint, the unsteady characteristics of the flow are compared based on the instantaneous vortex motions. The flow over the roof of the model separates from a front end of a rear shield and this separation generates vortex shedding over the rear shield and the trunk deck.

Figures (12) show the instantaneous vortex structures in the model A visualized by iso-surfaces of pressure Laplacian p. Vortex shedding of a typical hairpin like vortex (indicated by arrow A) occurs intermittently. Simultaneously, the vortexes from the rear pillars are bro-ken (indicated by arrow B). These vortex motions of model A disturb overall flow structures above the trunk deck intermittently following the hairpin-like vortex shedding frequency, which will cause the intermittent pressure oscillation. Thus, the intensive pressure peaks of the aerodynamic force shown in Fig. (10) and (11) are expected to appear after the hairpin vortex goes over the trunk deck and the rear pillar vortexes are broken.

On the other hand, in the model B shown in Fig. (13), vortexes are more continuously pro-duced, which will cause less pressure oscillation with less intensive peak over the trunk deck as shown in Fig. 11.

From the LES in the stationary condition at fixed pitching angle of 0 degree, it was demon-strated that slight geometrical difference of front and rear shapes results in drastic difference of entire flow structures around the vehicle. The flow characteristics of the stable model A is found to be more intermittent involving hairpin-like vortex shedding over the rear shield and succeeding trailing-vortex break down. These differences of flow unsteadiness may respond to the difference of aerodynamic unsteadiness observed in the dynamic pitching motion.

3.4 Large-Eddy Simulation in quasi-stationary condition Secondly, the aerodynamic stability of the simplified vehicle models is investigated in the

quasi-stationary manner. The LES of the flow around the simplified vehicle models with fixed pitch angle of 4.0 degree is conducted and the results are compared with the case of zero pitch angle. The changes of steady and unsteady flow characteristics around the models are dis-cussed in this part. The pitch angle of 4.0 deg is the same order as the experiment with a pitch motion in Ref. [3].


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Fig. 12 Time-series of instantaneous vortical structures over the trunk deck in model A

(Visualized as iso-surfaces of p)

Fig. 13 Time-series of instantaneous vortical structures over the trunk deck in model B

(Visualized as iso-surfaces of p)

Fig. (14) shows the visualization of steady vortex structures around the vehicle models

based on the iso-surfaces of time-averaged vorticity magnitude. The longitudinal vortices from the rear pillars in the both models are slightly weakened, because the pitch angle de-

A

B


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creases the angle between the main stream and the rear shield. In the model A, the weakened vortex from the rear pillar decreases the prevention of the inward flow from the vehicle side onto the trunk deck. On the other hand, in the model B, the vortexes from the front pillars are enhanced by the increased flow angle around the rear pillars. The inward flow onto the trunk deck is rather enhanced because the pair vortices from the front and rear pillars come close to each other and then their interaction, which enhances the inward flow, is also enhanced. These change of the vortex structures, and accordingly alternation of each vortex magnitude, cause different responses of flow structures to the pitch angle change.

(a) Model A

(b) Model B

Fig.14 Comparisons of time-averaged vortical structures in quasi-stationary simulation of the pitch motion. (Visualized as iso-surfaces of vorticity magnitude =1.5x103[1/s],

Left: without pitch angle pitch=0.0 deg., Right: with pitch angle pitch=4.0 deg.)

The distributions of the time-averaged pressure coefficient Cp on the trunk deck in the both

cases with 0 and 4 degree pitch angles are visualized in Fig. (15) and (16), respectively. The pressure distribution of the model A is more uniform in the spanwise direction than the model B. This tendency generated by the difference of the inward flows onto the trunk deck and the vortex structures from the pillars. The changes of the pitch angle increase the time-averaged pressure on the rear shield and the side of the trunk deck in both models A and B. At the side region of the trunk deck, the model A generate larger high pressure region than the model B with some pitch angle. This difference is caused by the difference of the flow structures gen-erated by the pillars, though the rear shield pressure is influence by the change of angle be-tween the shield and the main flow over the roof.

For a quantitative comparison, the aerodynamic forces acting on the trunk deck in both models are shown in Fig. (17). In this graph, time-series of lift force is shown and its negative value means a down force acting on the trunk deck. Although intensive peaks of the force in the model A are reduced at the pitching angle of 4 degree compared with 0 degree, the lift force acting on the trunk deck becomes lower level. The fluctuation period and intensity still differ from another model. Considering the time-averaged forces, the aerodynamic down force in model A increase 13.5%, though the down force on the deck in model B increase only 3.7% from the case with no pitch angle. This means that the aerodynamic force acting on the trunk deck in the model A works more effectively to reduce the pitch motion than in the mod-el B.


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Fig. 15 Time-averaged pressure coefficient distribution on the trank deck without pitch angle pitch=0.0 deg.

(Left: Model A, Right: Model B)

Fig. 16 Time-averaged pressure coefficient distribution on the trank deck with pitch angle pitch=4.0 deg.

(Left: Model A, Right: Model B)

Fig.17 Time-series of aerodynamic lift force acting on the trunk deck in the quasi-stationary condition

3.5 Large-Eddy Simulation in non-stationary condition Finally, the aerodynamic stability of the vehicle is investigated in the non-stationary man-

ner by introducing a pseudo moving boundary condition. The boundary condition for the ve-hicle body with pitch motion is given as a mass flux by considering the relative moving velocity to the fixed ground. The mass flux Q through a cell surface on the boundary is de-termined from the assumed motion and a surface area of each cell surface. The Q can be cal-culated as,


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SnrQ rrr )( . (8)

Here, nr is an unit normal vector of the cell surface and S is an area of the surface. rr is the position vector of a center of the cell surface. r is an angular velocity vector based on the assumed pitch motion. The motion is given as the sinusoidal function of a pitch angle pitch, as follows;

Tttpitch

2cos1)( max . (9)

Here, T is a period of the pitch motion and max is a maximum pitch angle, which is set to be 0.4 degree in the present non-stationary condition.

Applying the artificial condition, the LES of flow around the vehicles with a forced pitch motion are conducted. In the pitch motion, Strouhal number St is set to 0.13, where the fre-quency of the sinusoidal pitch motion is 10.0 Hz. This Strouhal number is similar to the in-vehicle measurement, though the wind-tunnel measurement using the same simplified model was conducted in a frequency and also a Strouhal number one order-of-magnitude less than the present condition.

Figure (18) shows the comparisons of aerodynamic forces acting on the trunk deck in the stationary, the quasi-stationary, and the non-stationary conditions. In the non-stationary con-dition, the pseudo moving boundary condition is applied from 0.24 sec. In this condition, both models A and B show the lower down-force than the other conditions. These changes are ex-pected to be caused by slow periodic fluctuation of the force, which synchronize with the pitch motion. This slow fluctuation can be considered as an adaptive mass of the pitch motion.

Regarding to the other fluctuation, its intensity is still larger in model A than in model B and this tendency indicates again the different responses of the flow structures to the pitch motion in both models.

Fig.18 Time-series of aerodynamic lift force acting on the trunk deck in the non-stationary condition


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4 CONCLUSIONS In the present study, the numerical prediction method for vehicle aerodynamics using LES

was constructed. The LES was validated on the simplified car model ASMO by comparing the surface pressure distributions with reliable wind-tunnel data, as well as the conventional RANS model with exactly the same grid resolution as LES. The LES generally showed better results than the RANS, and good agreement with the experimental data was achieved.

Based on the validation, we conducted the LES on two simplified vehicle models that have different running stability in the experiments. The predicted flows around the models were compared and discussed;

The slight geometrical differences of front and rear pillars between the two simplified vehicle models cause the drastic difference of the steady flow structures around the ve-hicle, especially over their trunk decks.

Only in the vehicle model A, which has high running stability, the time-series of pressure acting on its trunk deck show intensive peaks. The present LES can reproduce the same characteristics of pressure fluctuations having observed in the previous experiments.

In the model A, the flow behind the vehicle has some intermittency, such as the large vortex shedding. This flow feature may relate to the characteristics of pressure fluctua-tion on the trunk deck. On the other hand, the other model B, which has low running sta-bility, shows less intermittent flow structures and definite pressure peaks is not observed..

As mentioned above, the differences of steady and unsteady flow structures around the ve-hicle are specifically represented in the stationary condition, while they are generated by the small differences of the pillars’ shape.

To investigate the influences of vehicle pitch position on the flow characteristics in terms of the quasi-steady analysis, we also conducted the LES for the same vehicle models with a different pitch angle. The numerical result showed;

The steady flow structures and their interactions, such as an interaction of vortexes from the pillars, are changed with the pitch angle.

In the model A, the change of pitch angle generates the change of aerodynamic force act-ing on the trunk deck. The force acts to stabilize the pitch motion. However, in the other model B, the notable change of the aerodynamic force is not predicted.

With regard to the unsteady flow characteristics, the intermittency of the flow, such as the vortex shedding from the rear shield, does not change significantly. While, the inten-sive peaks of the pressure on the trunk deck are suppressed by the change of the pitch angle in the model A.

Based on the investigation in quasi-stationary manner, the numerical result indicates that the model A is aerodynamically more stable, against the pitch motion of the vehicle.

Finally, in order to represent the change of aerodynamic characteristics in non-stationary condition, we conduct the LES with a pseudo moving boundary condition, which control the mass flux on the vehicle body. In the both vehicle models A and B, reduction of aerodynamic down-force acting on the trunk deck is predicted and it can be considered as an acceleration effect of the motion, such as an additive mass.


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ACKNOWLEDGEMENTS This work was supported by Industrial Technology Research Grant Program in 2007 from

New Energy and Industrial Technology Development Organization (NEDO) of Japan. Devel-opment of the base software FFR was supported by the projects of FSIS and “Revolutionary Simulation Software (RSS21)” sponsored by MEXT, Japan. The wind tunnel data on ASMO provided by Volvo Car Corporation. Authors deeply thank their supports.

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[3] Y. Okada, T. Nouzawa, T. Nakamura and S. Okamoto. Influence of unsteady pressure caused by boundary-layer structure on the automobile trunk deck. Proceedings of JSME-FED-2007, Paper No.211 ,2007.(In Japanese).

[4] J. Smagorinsky. General Circulation Experiments with Primitive Equations. Monthly Weather Rex. . Vol. 91, No. 3, pp. 99-164, 1963.

[5] B. E. Launder and D. B. Spalding. The Numerical Computation of Turbulence Flow. Computer Methods in Applied Mechanics and Engineering, 3, 260-89, 1974.

[6] M. Tsubokura, K. Kitoh, N. Oshima, T. Tominaga, H. Zhang, K. Onishi, T. Kobayashi and S. Sebben. High Performance LES on Earth Simulator: A Challenge for Vehicle Aerodynamics. FISITA Transactions 2006, Paper No. F2006M111T, 2007.

[7] M. Ichimiya and Y. Akiyama. Pressure Fluctuation on the Vibrating Vehicle Model. Proceedings of JSME-FED-2007, Paper No.212 ,2007.(In Japanese).

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