27th AIAA Applied Aerodynamics Conference 22-25 June 2009, San Antonio, Texas AIAA 2009-3505 On the Unsteady Aerodynamic Forces Acting on a Formula Car in a Wind Gust Makoto Tsubokura 1 Hokkaido University, Sapporo-shi, Hokkaido, 060-8628, Japan Takuji Nakashima 2 Hiroshima University, Higashi Hiroshima-shi, Hiroshima, 739-8527, Japan Yoshihiro Sasaki 3 AdvanceSoft Co.,Ltd, Minato-ku, Tokyo, 107-0052, Japan and Kozo Kitoh 4 Kozo Kitoh Technology, Inc., Shibuya-ku, Tokyo, 150-0022, Japan A numerical method specially designed to predict unsteady aerodynamics of road vehicle has been developed based on unstructured Large-Eddy Simulation (LES) technique. The code was intensively optimized on the Earth Simulator in Japan to deal with the excessive computational resources required for LES, and could treat numerical meshes of up to around 120 million elements. The method was applied to a formula car subjected to a wind gust and unsteady aerodynamic forces acting on the vehicle was estimated. Two types of gust were considered: one is the sudden crosswind and the other is the streamwise gust with continuous acceleration and deceleration. It was found that some components of the aerodynamic forces overshoot or undershoot during the processes. The nonlinear behavior of the transient forces is difficult to estimate in the conventional wind tunnel measurements, and the validity of the LES was demonstrated. Nomenclature C p = pressure normalized by the dynamic pressure ρu 2 /2 Cs = Smagorinsky constant for the SGS turbulent model f = spatially filtered value of f l + = distance from the solid wall in wall unit p = static pressure t = time u i = flow velocity in i-direction U = mean inlet velocity x i = coordinate in i-direction ρ = fluid density ν = kinetic viscosity ν SGS = SGS turbulent viscosity Δ = width of a spatial filter 1 Associate Professor, Division of Mechanical and Space Eng., N13, W8, Kita-ku, Member AIAA. 2 Assistant Professor, Department of Social Eng. And Environmental Eng., 1-4-1 Kagamiyama, Member AIAA. 3 Engineer, Analysis Group, Akasaka 1-9-20, Non-member AIAA. 4 Researcher/CEO, 2-17-25 Hiroo, Non-member AIAA. 1 Copyright 2009 by the, Inc. All rights reserved.
I. Introduction hile it is widely acknowledged that a gust of wind strongly influences the total vehicle aerodynamic Wperformance 1,2, unsteady aerodynamic forces acting on a vehicle in such conditions are difficult to measure or estimate in a conventional wind tunnel test 3,4,5 and alternative methods of investigation would be desirable in order to close the gap between the wind-tunnel and track-test data. The fact is more serious in motorsports community, because most of the aerodynamic tuning still has been done in wind tunnel facility. Computational Fluid Dynamics (CFD) is an attractive approach as it allows to reproduce the conditions typical of crosswind gusts at a fraction of the cost of a full experimental setup. Moreover, CFD can provide a large amount of data and detailed information on the flow field, that can help in turn to understand the mechanisms by which unsteady aerodynamic forces act on vehicles. Over the past decade attempts have been made to employ both the overset grid approach and the Arbitrary Lagrangian Eulerian (ALE) method 6,7 to the study of flow in crosswind gusts with limited success. Previous investigations mostly adopted Reynolds-averaged Navier-Stokes (RANS) turbulence models, the accuracy of which is questionable for the transient aerodynamic response caused by the higher wave-number turbulence typical of flow in crosswind gusts. Large Eddy Simulation (LES), on the other hand, holds great promise because it can reproduce unsteady turbulence characteristics with high accuracy. However, the disadvantage of LES is its higher computational cost required, so that only few attempts have been made so far to apply LES to the investigation of transient vehicle aerodynamics. In a previous study, the authors have developed an unstructured Finite Volume CFD code, FrontFlow/red, especially designed for LES and optimized for execution on the Earth Simulator using High Performance Computing (HPC) techniques. Vector and parallel efficiencies as high as 95% and 99% respectively were achieved in a simulation of flow around a formula car in a steady condition, which is conducted on 800 parallel processors 8. In the present study, an innovative numerical technique is presented, which is capable of reproducing conditions of wind gust, and is applied to the flow around the formula car in a gusty condition. II. Numerical Methods A. Governing Equations In Large Eddy Simulation the equations of motion (continuity and momentum) are spatially filtered. These read, in tensor notation:, (1), (2) in which over-bar denotes the spatially filtered quantity;,, and are the -th velocity component, the kinetic viscosity, and fluid density, respectively. The strain rate tensor and the filtered pressure in eq. (2) are, (3). (4) The effect of subgrid-scale (SGS) turbulence on the grid-scale turbulence motion is represented by the SGS eddy viscosity, which is modeled following Smagorinsky 9 :, (5) 2
Figure 1. Target geometry (left) and the computational domain (right). Figure 2. Grid resolutions around the vehicle. where is the volume of the generic numerical element, and the model coefficient is given as 0.15, which is typically used in simulations of flow around a rectangular cylinder. The eddy viscosity is damped in the vicinity of solid using a Van-Driest-like function:, where is the distance from the wall in wall coordinates. 3 (6)
B. Discretization The governing equations are discretized in space by a vertex-centered unstructured finite volume method. Second-order central differences are applied for the spatial derivative, blended with a first-order upwind scheme for the convective term in the Navier-Stokes to avoid the excessive numerical oscillation appearing at coarse tetrahedral elements. It should be noted here that use of first-order upwind should be avoided, whenever possible, in LES due to the excessive amount of numerical dissipation introduced. On the other hand the dissipation properties of upwind schemes may be desirable to a certain extent for engineering applications of LES on unstructured meshes such as those adopted here. As a compromise, the contribution of the upwind discretisation to the convective fluxes is set to be as low as 5%. In LES, first-order explicit Euler scheme should not be used for the time marching method, because of its absolute instability. On the other hand, fully implicit schemes often used for conventional engineering LES hopefully should be avoided because longer time increment permitted by the fully implicit scheme happens to damp higher wave-number turbulence. Thus, the second-order Adams-Bashforth scheme is adopted for time discretisation in this study. The SMAC (Simplified Marker and Cell) method is employed to maintain coupling between the pressure and the velocity. C. Software and Hardware The computational code adopted in the present study was originally developed in the "Frontier Simulation Software for Industrial Science" project 10. The project started in 2002 as an IT research program, sponsored by Ministry of Education, Culture, Sport, Science and Technology in Japan. The code was intensively optimized by the authors on the Earth Simulator (40 Tflops/10TB memory) for LES applications under the subsequent IT project Revolutionary Simulation Software (RSS21) 11, and parallel and vector efficiency as high as 96% and 99% respectively were achieved in simulations performed on 100PNs/800CPUs. This allowed completion of LES calculations of flow around a formula car with complex geometry (LOLA B03/51 used 2006 Japanese championship Formula Nippon) in about 120 hours 5. The computational meshes adopted counted up to 120 million cells with a typical memory usage of more than 500 GB, also including data storage for the calculation of time-averaging turbulence statistics. The code has been optimized for unsteady vehicle aerodynamics simulations in the context of a project supported by an Industrial Technology Research Grant Program in 2007 from New Energy and Industrial Technology Development Organization (NEDO) 12 of Japan. D. Gusty Wind Models Natural wind gusts observed in the real world are diverse and strongly depending on the geographic conditions of land surface, atmospheric stratification, as well as the traffic conditions itself. Recently Wordley and Saunders 13 conducted on-road measurements at different terrains and traffic conditions using a real road vehicle at 100km/h velocity with velocimeters mounted on the front, and obtained that the turbulence length scale derived by the von Karman spectrum versus turbulence intensity. According to their results, the length scale reaches about 10m maximum at city canyon while its turbulence intensity is relatively small (around 2 to 3%). On the other hand, at freeway traffic, wide range of turbulence intensity up to 16% is observed while its length scale is found to be less than 3m. In any case, it is not reasonable to define universal wind gust for the reproduction in CFD. Another difficulty of reproducing such wind gust in terms of CFD lies in the fact that its length scale is large comparable to vehicle size. Thus conventional turbulence generator or driver utilized in CFD of engineering inner flow or geophysical flow is difficult to adopt here to avoid excessively large analysis region. Accordingly wind gust is simplified in this study, and is modeled in two ways: one is a stepwise cross flow which suddenly changes relative yaw angle of incoming wind with respect to the vehicle center line; the other is a monotonic acceleration and deceleration of incoming flow. It should be noted that by combining these two methods by utilizing existing on-road measurement data, more complicated and realistic wind gust can be generated. As shown in Fig. 1(right), the sudden crosswind is generated by imposing the stepwise lateral velocity on the side wall of the numerical domain, then the interface of the lateral velocity on the side boundary is convected downstream at the same velocity as the inlet velocity. As a result, the rectangular crosswind region approaches and passes through the vehicle fixed on the floor of the domain. Corresponding experiments have been proposed and conducted by Dominy & Ryan 5. Uniform velocity of 45.0m/s is imposed at the inlet and cross wind velocity of 22.5m/s inlets at the side wall. As a result, the relative yaw angle of the incoming flow with respect to vehicle center line rapidly changes 0 to 27 degrees when the crosswind region reaches the vehicle. The monotonic acceleration and deceleration of the incoming flow is generated by imposing the uniform streamwise pressure gradient on entire flow domain as an external force of the momentum equations. In this study, 10% of the incoming flow or equivalently supposed vehicle velocity is imposed as wind gust with its length scale of 4
Figure 3. Time history of the aerodynamic forces (left) and moments (right) during the sudden crosswind condition. The axis origin for the moments is on the center plane at the mid point between front and rear wheel axis. The downforce and moments do not include the contribution of wheels. about the half of the vehicle length. Accordingly sinusoidal perturbation with the amplitude of 4.5m/s and the frequency of 45Hz is uniformly imposed on the streamwise velocity of 45.0m/s when the vehicle length is set to 2.26m (as shown in Fig. 1) E. Numerical Conditions Figure 1 illustrates the target geometry (length x width x height=2.26m x 0.89m x 0.48m) and the boundary conditions adopted in the study. Uniform velocity (45.0m/s) is imposed at the inlet, while free outlet condition with pressure fixed is given at the exit of the analysis domain. Free-slip boundary condition is adopted on the surface of the ceiling and floor to avoid excessive boundary layer development. On the surface of the vehicle body, a solid wall condition is adopted. The assumed log-law profile is directly applied to the instantaneous velocity field, and the surface friction obtained from the log-law profile is imposed on the solid surface as a boundary condition. The typical wall distance of the first nearest grid point measured from the numerical result come out to be around 100 in wall unit, which are located within the logarithmic region of the supposed mean velocity profile. On the floor around the vehicle, moving floor condition with the velocity 45.0m/s is imposed. The rotation of wheels are modeled by imposing corresponding rotation speed on the surface of the wheel. The total of around 45 million tetrahedral elements with 8 million nodes is utilized to reproduce the complicated geometry of the vehicle (the grid resolution on the surface is less than 7mm), as well as to fill in the entire flow region (see Fig. 2 for the geometry of grid allocation). III. Validation on the steady case The method is validated by comparing the results with the wind tunnel data provided. For the validation simple uniform flow without gust inlets and averaged drag and lift are measured. For the experimental reason, the provided lift coefficient does not include the effect of wheels. Agreement of the lift coefficient between the LES (-1.93) and experiment (-1.95) is excellent and our LES estimates the value only about 1% larger than the wind tunnel data, while the disagreement of the drag coefficient is relatively larger but still it is less than 10% (1.00 by LES and 0.91 by experiment). For the detail of the validation, refer to Tsubokura et al. 8 IV. Unsteady Aerodynamics A. Sudden crosswind condition Figure 3 (left) illustrates the time history of the aerodynamic forces acting on the vehicle. The crosswind region reaches the front edge of the vehicle at T=0.144sec, and the entire body is subjected to crosswind at T=0.194sec. Owing to the transient yawing-angle change from 0- to 27-degrees with the increase of the flow rate from 45 to 5
Figure 4. Snapshots of the velocity magnitude on the plane z=0.20m (left) and the surface pressure coefficient Cp on the vehicle (right): T=0.136sec. right before the crosswind, T=0.176sec. the nose subjected to crosswind, T=0.196sec. the tail running through the crosswind, and T=0.296sec. entire body subjected to the crosswind. 6
Figure 5. Time history of the aerodynamic forces (left) and moments (right) during the condition of continuous streamwise acceleration and deceleration. The axis origin for the moments is on the center plane at the mid point between front and rear wheel axis. The downforce and moments do not include the contribution of wheels. about 50m/s, relatively large increase in side forces are identified. It is interesting to note that there seems to be time lag for the increase of side forces or the decrease of downforces, both of which overshoot or down shoot at the final stage of the transient process. Unsteady aerodynamic feature is more clearly observed in the moments, as shown in Fig. 3 (rigtht). Generally the roll and yaw moments decrease, and the pitch moment increases in the crosswind condition, while remarkable undershoot is identified on the yaw moment. The roll moment also shows a slight overshoot. The time delay for the increase of the pitch moment, compared with other two components, is also interesting. Figure 4 shows the snapshots of the magnitude of velocity and surface pressure distribution on the formula car during the process of rushing into the crosswind region. At T=0.136sec. right before the crosswind, the wake structure of the vehicle is almost symmetric with respect to the vehicle centerline. At T=0.176sec., about 0.02sec. after the nose rushing into the crosswind, asymmetric pressure distribution is observed on the front wing, while the wake of the front wheel remains its symmetry. At T=0.196 just after the entire body is subjected to the crosswind, the wake of the front wheel declines to about 30 degrees against the vehicle centerline, while the vehicle wake is not strongly affected by the crosswind, which loses its symmetry around T=0.296sec. The coexistence of the declined wake created by the front wheels and the wake along x direction by the rear wheels are especially remarkable at T=0.196sec., which will contribute to non-linear transient aerodynamics forces during this process. B. Continuous streamwise acceleration and deceleration Figure 5 indicates time history of the aerodynamic forces (left) and moments (right) when the vehicle is subjected to sinusoidal streamwise perturbation. The inlet flow has been steady until 0.1sec., then the spatially uniform 10% perturbation is imposed on the streamwise velocity. For references, the incoming velocity is also shown in the figure. The notable feature on the transient forces is their synchronized trend on the sinusoidal velocity, which is especially remarkable on the drag, downforce and pitch moment. The amplitude of the drag amounts to about 40% of its mean value, which is larger than the assumed 20% under the quasi-steady assumption when the velocity amplitude is set to 10%. Considering the fact that the phase of the transient drag shifts about π/2 behind that of the transient velocity, the unsteady contribution to the drag seems to be caused by the additional mass effect as a result of the acceleration of the approaching flow. While the amplitude of the downforce also shows slightly larger value than 20%, it is more notable that its peak value varies rather drastically at each local maximum and minimum points. However the reason of the unstable peaks of the downforce is not clear at the moment, one possible explanation is the unstable separation and reattachment of flow on the surface of the front and rear wings caused by the acceleration and deceleration of flow. In Fig.6, the snapshots of the magnitude of velocity and surface pressure distribution on the vehicle at four consecutive moments are shown. Around T=0.1335sec., incoming flow reaches minimum value. The acceleration of 7
Figure 6. Snapshots of the velocity magnitude on the plane z=0.20m (left) and the surface pressure coefficient Cp on the vehicle (right): T=0.1335sec., u~40.5m/s at minimum; T=0.1395sec., u~45m/s; T=0.1455sec., u~49.5m/s; T=0.1500sec., u~45m/s. 8
the flow become maximum around T=0.1395sec. and reaches maximum velocity at T=0.1455sec. The deceleration become maximum around T=0.1500sec. The difference of T=0.1395sec. (during acceleration) and T=0.1500sec. (during deceleration) under the same incoming velocity of 45m/s is remarkable, which express the contribution to the fully unsteady aerodynamics. V. Conclusion Unsteady aerodynamic forces and moments acting on a formula car under gusty wind conditions were estimated using LES based on High Performance Computing (HPC) techniques. The wind gusts were simplified and modeled as (1)the stepwise crosswind velocity profile and (2)continuous streamwise acceleration and deceleration. In the cross wind case, remarkable overshoot or undershoot was identified in yaw and pitch moments, as well as the side force. In the acceleration and deceleration cases, the drag, lift and pitch moment shows synchronized trend on the sinusoidal incoming perturbation. It was supposed that the unsteady feature of the drag is mainly caused by the additional mass effect, while other two components do not show significant phase shifting to the incoming velocity perturbation. The coupling method of unsteady flow and the vehicle motion caused by the unsteady aerodynamic forces are now underway. Acknowledgments This research was done in "Research and Development of Innovative Simulation Software" project supported by Research and Development for Next-generation Information Technology of Ministry of Education, Culture, Sports, Science and Technology (MEXT). The computer resources offered by the Earth Simulator Center under the collaboration project, and the vehicle data provided by Japan Race Promotion Co., Ltd and LOLA Cars International Ltd are also greatly acknowledged. The gust wind model was developed under the project supported by Industrial Technology Research Grant Program in 2007 from New Energy and Industrial Technology Development Organization (NEDO) of Japan. References 1 Cooper, K. R., and Watkins, S., The Unsteady Wind Environment of Road Vehicles, Part One: A Review of the On-road Turbulent Wind Environment, SAE Technical Paper Series 2007-01-1236, 2007 2 Watkins, S., and Cooper, K. R., The Unsteady Wind Environment of Road Vehicles, Part Two: Effects on Vehicle Development and Simulation of Turbulence, SAE Technical Paper Series 2007-01-1237, 2007 3 Carlino, G., Cardano, D., and Cogotti, A., A New Technique to Measure the Aerodynamic Response of Passenger Cars by a Continuous Flow Yawing, SAE Technical Paper Series 2007-01-0902, 2007 4 Macklin, A. R., Garry, K. P., and Howell, J. P., Comparing Static and Dynamic Testing Techniques for the Crosswind Sensitivity of Road Vehicles, SAE Technical Paper Series 960674, 1996 5 Dominy, R. G., and Ryan, A., An Improved Wind Tunnel Configuration for the Investigation of Aerodynamic Cross Wind Gust Response, SAE Technical Paper Series 1999-01-0808, 1999 6 Okumura, K., and Kuriyama, T., Transient Aerodynamic Simulation in Crosswind and Passing an Automobile, SAE Technical Paper Series 970404, 1997 7 Guilmineau, E., and Chometon, F., Numerical and Experimental Analysis of Unsteady Separated Flow behind an Oscillating Car Model, SAE Technical Paper Series 2008-01-0738, 2008 8 Tsubokura, M., Kitoh, K., Oshima, N., Nakashima, T., Zhang, H., Onishi, K., and Kobayashi, T., Large Eddy Simulation of Unsteady Flow around a Formula Car on Earth Simulator, SAE 2007 Trans. J. of Passenger Cars Mechanical Systems, 2007-01-0106, 2007 9 Smagorinsky, J., General Circulation Experiments with the Primitive Equations, I. The Basic Experiment, Monthly Weather Rev., vol.91, Num. 3, pp.99-164, 1963 10 Frontier Simulation Software for Industrial Science (FSIS), http://www.ciss.iis.u-tokyo.ac.jp/fsis/en/index.html 11 Revolutionary Simulation Software (RSS), http://www.ciss.iis.u-tokyo.ac.jp/rss21/en/index.html 12 New Energy and Industrial Technology Development Organization, http://www.nedo.go.jp/english/index.html 13 Wordley, S., and Saunders, J., On-road Turbulence: Part2, SAE Technical Paper Series 2009-01-0002, 2009 9