LARGE-EDDY SIMULATION OF UNSTEADY VEHICLE AERODYNAMICS …

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 Vehicle Aerodynamics, Large-Eddy Simulation, Running Stability, Vortical Structure, Passenger Sedan.

1 INTRODUCTION

Regarding safety and passengers’ comfort, running stability is one of the most important characteristics of a vehicle. For the vehicle stability, the aerodynamic force and its stability is a considerable factor as well as the suspension control, especially in a highway condition. In these days, a weight of vehicle has been reduced for fuel economy and it also makes the aero-dynamics more important in the aspect of vehicle stability. Within the last two or three dec-ades, both wind tunnel experiment and computational fluid dynamics (CFD) technologies have improved vehicle aerodynamics in steady state. However, to achieve more sophisticated aerodynamic design for the aerodynamic stability, it is expected to consider unsteady flow characteristics and interactions between the flow and the vehicle motion. Large Eddy Simula-tion (LES) has been expected as a better and more precise turbulence model for prediction of unsteady vehicle aerodynamics. 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 unsteady flow simulations.

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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

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

relating to the running stability. The LES prediction method is constructed and validated on the ASMO model [2], which is designed for a study of vehicle aerodynamics. In the valida-tion of the LES, the comparisons with the conventional RANS models with the same compu-tational grid systems are conducted. Based on the validation, we conduct the LES on two simplified vehicle geometries, which are modeling 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 vortical 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. The standard Smagorinsky model is adopted to estimate the SGS eddy viscosity. The Smagorinsky constant is given as Cs=0.15 and the Van-Driest type damping function is adopted for near-wall region.

The governing equations are discretized based on the cell-centered unstructured finite vol-ume 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 the numerical stability. The second order Adams-Bash 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 [4] on the 1/5 scale ASMO model shown in figure 1. Three computational grid systems are applied and they consist of 1.3M, 5.5M and 24M elements, respectively. The RANS simu-lations using standard k-ε model are also conducted on the same grid systems, though the dis-cretization 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 fully developed turbulent boundary layer.

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 Figure 2. They are caused by the insufficient spatial resolu-tion at the corners and the central difference scheme for the convective term in the LES.

Fig.1 ASMO

B:290

H: 270

L:810

model Fig.2 Base pressure profiles on ASMO model

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

2.3 Modification of numerical treatment To eliminate the problem in the LES, numerical treatments in the near-wall region are in-

vestigated. Two additional grid systems that are different in the near-wall region are applied and compared to the middle size grid system with 5.5M elements. The time-averaged pressure distributions in each case are shown in figure 3. It is found that the tetrahedral grids clustered around the corners of the body reduce numerical oscillation, while those with the prism layer mesh inserted on the surface of the vehicle body perform better reduction of the oscillation.

Fig.3 Base pressure distributions (Left) and profiles (Right) on the modified computational grid systems

3 APPLICATION IN SIMPLIFIED VEHICLE MODEL Based on the validation, we conduct the LES predictions of the aerodynamics of two sim-

plified vehicle geometries, which are about 1/20 scale model. Their differences are mainly appeared in the curvatures of front and rear pillars as shown in figure 4. The original passen-ger sedans of these model geometries have different running stabilities in the in-vehicle re-search [3] because the pressures on the trunk deck respond differently to the pitch motion of the vehicle. The model geometries also have the same tendency in the experiment [5].

The present simulations are conducted with the same numerical methods mentioned above. Figures 5 show time-averaged flow structures around the models visualized by streamlines. The angular pillars generate clear longitudinal vortexes in each model. In the model B, the front pillar vortex influences the flow over the rear pillar and it enhances the inward flow from the side onto the trunk deck. On the contrary, in the model A, the smooth front pillars generate no vortex and a rear pillar vortex behind the rear pillar does not enhance but prevent the inward flow onto the trunk deck. Thus, the differences of the pillar geometries appear not only in the flow around the pillars but also in the flow structures over the trunk deck.

Model A Model B

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

Fig. 5 Time-averaged streamlines (Left: Model A, Right: Model B)

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Uniform(5.5M) Clustered Clustered and Prism

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

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Regarding to the unsteady flow characteristics, Figures 6 show the time-series results pre-dicted over the trunk deck. The left graph shows time-series of pressure at a point on the trunk deck. The intensive peaks are predicted only in the model A, and this tendency is also ob-served in the steady state experiment [5]. This quantitative agreement of the unsteady feature indicates the possibility of the present LES to investigate the unsteady vehicle aerodynamics. The right figures show the instantaneous vortical structures visualized by iso-surfaces of pres-sure Laplacian ∆p. In the model A, the large hairpin like vortex (arrowed) is produced inter-mittently, while, in the model B, small vortexes are produced continuously. The intensive pressure peak mentioned above appears after the large vortex goes over the trunk deck. This difference of flow unsteadiness in each model may respond to unsteady vehicle motion differ-ently. In that case, the different responses would cause the different running stability.

Fig.6 Time-series of pressure on the trunk deck (Left) and Instantaneous vortical structures over the deck (Right)

4 CONCLUSIONS

In the present study, the numerical prediction method for vehicle aerodynamics using LES is constructed and validated. In the comparisons with the conventional RANS models with the same computational grid system, the LES showed better results than the RANS.

Based on the validation, we conduct the LES on two simplified vehicle model that have different running stability in the experiment. The LES can reproduce the same characteristics of pressure fluctuations observed in the experiment. The predicted flows around the model vehicles are compared and discussed in an aspect of steady flow structures and unsteady vor-tical structures behind the vehicle. Unsteadiness of the vehicle with regard to flow structures behind the vehicle, especially over the trunk deck, will be mentioned in the final paper.

ACKNOWLEDGEMENTS A part of this work was supported by NEDO. Authors deeply thank their supports.

REFERENCES [1] M. Tsubokura et al., SAE Paper, No.2007-01-0106, 2007.

[2] D. Aronson et al., SAE Paper, No. 2000-01-0485, 2000.

[3] Y. Okada et al., Proceedings of JSME-FED-2007, Paper No.211 ,2007.(In Japanese).

[4] M.Tsubokura et al., FISITA Transactions 2006, Paper No. F2006M111T, 2007.

[5] Ichimiya et al., Proceedings of JSME-FED-2007, Paper No.212 ,2007.(In Japanese).

Model A

Model B