NUMERICAL SIMULATION OF FLOW FIELD IN WHEELHOUSE OF CARS

Transcription

1 Journal of Computational and Applied Mechanics, Vol. 5, Num. 2, (2004), pp. 1-8 NUMERICAL SIMULATION OF FLOW FIELD IN WHEELHOUSE OF CARS Tamás Régert (1) and Dr. Tamás Lajos (2) (1) Ph.D. student; (2) Professor Department of Fluid Mechanics Faculty of Mechanical Engineering Budapest University of Technology and Economics H-1111 Budapest Bertalan L. u. 4-6, Hungary [Received: ] Abstract: The paper reports the results of the investigation of the flow field inside the wheelhouses of passenger cars by means of Computational Fluid Dynamics (CFD). The numerical model developed has been validated by comparing the calculated pressure distribution around an isolated rotating wheel to the measured one. Numerical simulations of flow past simplified vehicle models for which measurement results are available in literature were carried out, including the detailed analyses of flow past wheels rotating in a wheelhouse. Parameter study was carried out regarding the wheelhouse geometry and the results are compared to those from the corresponding literature. Reasonable agreement was found between the calculated and measured drag and lift coefficients. Mathematical Subject Classification: none Keywords: vehicle aerodynamics, wheel, wheelhouse, aerodynamic lift and drag, separation 1. Introduction The field of road vehicle aerodynamics is reaching its limits in terms of designing optimal body shapes. Basic low-drag body shapes have been developed during the last few decades (Hucho [7]). The effect of the rotating wheels exposed the free stream, or being partially covered by the wheelhouse of the car, leads to a dramatic increase in drag coefficient through a mechanism that is still an open question. The contribution of the wheels and wheelhouses to the total aerodynamic drag of a modern car is around 30%, so the car industry puts significant effort into researching this flow field. Experiments have already been carried out within the past decade to investigate full-scale cars [15], scale-model passenger cars [4], and idealized car models [5, 14]. For realistic car models, it has been concluded in all cases that the rear wheels have a dramatic effect on the drag, i.e. 20% of the above-mentioned 30% contribution to the total drag is caused by the rear wheels [15, 4]. On the basis of the experimental work, some assumptions have been made about the flow mechanisms, but a detailed structure of the flow

2 field in this region has still not been published. Elofsson et al. [4] made a parameter study on a scale-model Volvo passenger car by means of experiments, changing the geometry of the rear spoiler and the fender behind the rear wheel. They observed significant changes in drag that showed the importance of the interaction between the wake of the wheel and flow in the wheelhouse, as well as the wake of the body. The first parameter study of wheels in wheelhouses was made by Cogotti [3] who used a streamlined egg -shaped body with only one pair of wheels (one axis and two wheels) with wheelhouses in a fixed ground wind tunnel (there was a small ground clearance between the wheels and the ground plane). The geometry of the wheelhouses was variable. Another parameter study was made by Fabijanic [5] on the effect of wheelhouse geometry on the forces acting on the vehicle, using a body that also had only one pair of wheels with one axis. Fabijanic s model was not streamlined, it was more vehicle-shaped and had a large wake behind its base. Due to the complexity of the flow, only a few measured quantities are appropriate for comparison to the CFD results. Such parameters are usually the integral parameters: the lift and drag coefficients. These parameters are not enough to give a full insight into the flow characteristics and the mechanisms governing them. Road vehicles are bluff bodies, characterized by large regions of flow field influenced by boundary layer separation. Due to the characteristics of the geometry of the wheel and wheelhouse, the separation forms mainly shear layers characterized by an unsteady rollup of vortices that leads to an unsteady and extremely complex 3D flow field that cannot be simplified to a 2D problem. The Reynolds number is in the range of 8 x 10 5 so the flow is far into the turbulent regime. The fluid can be regarded as incompressible, isothermal, single-phase and nonreactive, so there is no need for an energy equation in the simulation. 2. Methods of investigation The present problem includes flow separation, the presence of high-energy vortices and large separation bubbles. Most of the single-point type experimental methods (hotwire, pressure probes, Laser Doppler Velocimetry) fail in exploring the characteristics of such flow fields. The measurement of pressure using pressure taps is reported to be relatively accurate but Fabijanic [5] reported strong fluctuations and large uncertainties when using it for wheelhouse flow. The only one-field measurement technique is Particle Image Velocimetry (PIV), which is restricted to a 2D plane and thus is not capable of producing 3D fields. The other problem is the lack of optical accessibility that usually causes serious problems when investigating the flow in a wheelhouse. The other method that can be applied for exploring the flow characteristics is numerical simulation. This is the solution process of the system of partial differential equations of fluid flow (Navier-Stokes and continuity equations since no thermal effects are included). As the flow is unsteady and turbulent, one might think of solving the governing equations directly (Direct Numerical Simulation DNS). However, this cannot be carried out due to the given Reynolds number range (see [8, 10]). Large Eddy Simulation (LES) unfortunately requires a large computational facility and a computational time of order of several years, too, thus its application has to be rejected for the moment. Due to the complex geometry there are severe convergence problems with the use of Reynolds Stress Modelling, so only the isotropic eddy viscosity models seem to provide a suitable approach (k-ε, k-ω). The problem of anisotropy is

3 mainly concentrated in the region of boundary layers, thus these regions are handled by either logarithmic wall functions or by a two-layer model. Two layer models are prescribing linear velocity profile in the viscous sub-layer of the turbulent boundary layers and apply a Wolfstein [16] one equation low-reynolds-number turbulence model. This turbulence model is applied within the logarithmic region and the outer regions until a given wall-reynolds number ( Re y = 200 ) is reached. This Reynolds number is defined as follows: Re y v p y = ν where v p [m/s] is the velocity in point P, ν [m 2 /s] is the kinematical viscosity and y[m] is the wall-normal coordinate. To determine the appropriate turbulence model for the present problem, validation was carried out for the case of an isolated rotating road wheel [11]. Concerning the integral parameters (lift and drag coefficients) and the pressure distribution on the surface of the wheel, the steady computations using eddy viscosity models performed reasonably well. Pressure distributions and steady flow field details showed low dependence on turbulence model and grid refinement. For numerical simulation of the flow, the commercial software packages FLUENT 5.5 and FLUENT 6.1 were used. 3. Description of computations Three different computational domains and body geometries were studied. Parameter study was carried out on one of the geometries shown in Fig. 1-A). For each geometry, grid independence was checked using refinements. To see the dependence on the physical model, several eddy viscosity turbulence models were used. The size of computational domain was also checked in regard to its effect on the results. Boundary conditions were prescribed: total pressure at the inlet surface, static pressure at the outlet face, and no-slip boundary condition on the walls. All investigations were made in a reference frame fixed to the vehicle body. The Reynolds number based on the freestream velocity and the diameter of the wheel varied in the range of 5 x x The geometries investigated are shown in Fig. 1. Fig. 1-A) has a fore-body which is different from that of the other two cases. This test serves for the determination of the effect of the shape of the fore-body on the flow in wheelhouses. Fig. 1-B) and C) have a similar fore-body shape but the distance between the wheel and the front of the vehicle is smaller in the case of Fig. 1-C) than in the case of Fig. 1-B), so a comparison of the results indicates the effect of the growing yaw angle of the wheel-approaching-flow on the flow field in the wheelhouse. The diameter of the wheels for the cases Fig. 1-A), C) is 0.5 m, while for B) it is m according to the experiments of Fabijanic[5]. 4. Validation and verification Validation of the simulation model applied was carried out on an isolated wheel of varying profile shape and aspect ratio, rolling on a moving road. Computations were carried out using a combination of different near-wall treatment approaches, turbulence models and mesh structures to analyze the structure of the flow field. The typical validation references were: integral

4 quantities (lift and drag coefficients) and pressure distribution in the central plane of the wheel, which were measured by Fackrell [6] and Skea et al. [13]. The computational results are compared to the results of the experiments in Fig. 2. The agreement is quite good for almost all parts of the wheel periphery except for the top region between degrees. Here the experimental results are also in disagreement. This discrepancy is assigned to a boundary layer separation that occurs in Fackrell s case but does not occur in Skea s case. The agreement in the wake region of the wheel is remarkably good, so the problematic point is similarly to the experiments - the prediction of pressure in the region of boundary layer separation. The CFD results indicate the presence of a depression maximum in good agreement with the corresponding literature [1, 8, 13]. A) B) Y Z X Fig. 1: Body geometries for investigation of flow in wheelhouses C) The pressure distribution on the whole surface of the wheel is validated also via its integral leading to drag and lift coefficients. For the stationary wheel the measured value of drag coefficient was C D =0.76±15% [1, 6, 8, 14], and of lift coefficient was C L =0.77±15%, where the ranges in coefficients indicate unsteady flow characteristics. For rotating wheels the measured values were typically C D =0.58±15% and C L =0.44±15% [1, 6, 8, 14]. For the stationary wheel numerical simulation resulted in a prediction of lift and drag coefficient within 10-15% and ±10% range around the measured mean values, respectively. In the case of a rotating wheel the lift and drag coefficients were estimated within 8%-10% and 15-20% of the mean of the measured lift and drag values, respectively. A qualitative comparison of the flow structures was made based on the experiments of Schiefer [12] and good agreement was found. After validation of the isolated road wheel, flow past the wheel in a wheelhouse was simulated. Two validation tests based on the measurements of Axon et al. [2] and Fabijanic [5] were made to determine integral quantities. The models of Axon et al. [2] and Fabijanic [5] are shown in Fig. 3 and Fig. 1-B), respectively.

5 Exp-Fackrell Exp-Skea CFD-'real.' k-eps CFD-k-omeg(SST) Cp [-] fi [ ] Fig. 2: Pressure coefficient distribution over the periphery of an isolated rotating wheel in its vertical symmetry plane A) B) Fig. 3: Validation case for wheelhouse (partially covered wheel). Geometry based on Axon et al Table 1: Experimental and CFD values of drag and lift coefficients of Axon s model. Subscript s indicates body, w indicates wheel, t indicates body and wheel C Ls C Ds C Dw C Dt Experimental CFD (authors ) Difference ( C) (90%) 0.01(-3.3 %) 0.01(-7.9 %) 0.04(-9.24%) The measured integral quantities published by Axon et al. [2] are compared in with results of CFD computations carried out by the authors. The coefficients are related to the projection of the total area of the vehicle in the streamwise direction and the free stream velocity. The differences between measured and computed lift and drag coefficients are in the range of

6 (see ). The drag coefficients were in an agreement within 10% of the experimental case. Since the exact details of the experimental set-up are not available, the relatively large difference in lift force ( C Ls =0.07, 90%) can be the result of the numerical model. It was observed that a slight change in the pitch angle caused abrupt decrease in lift coefficient. Differences of physical and numerical model causes, e.g., change in pitch angle in front of the wheels. As another validation case, the numerical simulation of the Fabijanic [5] model gave good agreement with the experiments (see ). Table 2: Experimental and CFD values of drag and lift coefficients for Fabijanic s vehicle model (Figure 1-B) C Lw C Dw Experiment 0.02± ±0.008 CFD (authors ) 0.007± ±0.001 Difference C(%) ~ (-65%) ~ (-11%) In the lift and drag coefficients were also related to the stream-wise projection of the front surface of the whole vehicle and to the freestream velocity. The large difference between the corresponding values of and is due to the huge difference in the front surface. In CFD computations under-predicted both values. The discrepancy in lift coefficients is presumably not due to wrong computations. During the experiments [5], the wheels were not connected to the body but they were supported from outside by long struts. The struts passed across the undisturbed flow domain and thus it was excited by vortex shedding which led to vibration due to its circular shape (confirmed by Fabijanic [5]), disturbing the measurement of lift and drag on the rotating wheel. To prevent vibration, the strut was covered by an envelope with a symmetrical airfoil cross-section. The computational model did not contain the struts, neither did the covering envelope. The approximate numerical model might explain the discrepancy in the lift coefficients. 5. Parameter study Numerical parameter studies were carried out by changing the main parameters influencing the flow: the depth (B) and diameter (D) of the wheelhouse related to the width (b) and diameter (d) of the wheel, respectively (see Fig. 4). The basic topological features of the bodies used for the CFD investigations were similar to those used in the experiments: there was only one pair of wheels and the surface of the underbody was smooth.

7 Fig. 4: Parameter test for wheelhouse geometry CD 0.16 CFD 0.14 Experiment D/d A) CFD Experiment C L B/b CD CFD Experiment B) C) Fig. 5: Comparison of numerical parameter studies with experimental ones (Fabijanic [5] & Cogotti [3]) The simulation results were compared to the experimental results of Fabijanic [5] (also in good agreement with Cogotti [3]). In Fig. 5 the geometries of the vehicle bodies are different from each other (see Fig. 1-A) and Fig. 1-B)) but the flow characteristics are similar: attached flow to the surface of the vehicle upstream from the wheel. Here, changes in the drag and lift coefficients are plotted vs. the relative diameter (D/d) or width (B/b) of the wheelhouses. C values indicate differences of coefficients belonging to vehicle-model configurations with wheel and wheelhouse and configurations with no-wheel and no-wheelhouse. The agreement is good in both the tendency and the quantitative values. A linear trend-line was fitted to the CFD data. B/b

8 Deviation of the CFD values from this line is very close to that of the experimental values. 6. Conclusions This work summarizes the results of numerical investigation of complex 3D flow past simplified vehicle models with wheels and wheelhouses present. Numerical simulation was carried out using FLUENT software. The modelling method was validated first based on the published results of experiments into the flow past isolated rotating wheels and moving ground. As the agreement between the computational and experimental results was acceptable, the numerical model was applied for computing the flow field within a wheelhouse cavity. Grid independence and effects of turbulence models were investigated. Validation of the results of computations of flow past vehicle models with wheels and wheelhouses using drag and lift data published by Axon et al. [2] and Fabijanic [5] showed relatively good agreement. Parameter studies concerning the geometry of the wheelhouse were also carried out. The results of the studies showed good agreement with the experiments of Cogotti [3] and Fabijanic [5]. Since the numerical model developed seems to describe the flow properly, further analysis of the flow field topology is possible. REFERENCES 1. Axon, L., Garry, K., Howell, J.: An Evaluation of CFD for Modelling the Flow Around Stationary and Rotating Isolated Wheels. Society of Automotive Engineers Paper , Detroit, pp , Axon, L., Garry, K., Howell, J.: The Influence of Ground Condition on the Flow Around a Wheel Located Within a Wheelhouse Cavity. Society of Automotive Engineers, Inc , pp , Cogotti, A.: Aerodynamic characteristics of car wheel. Impact of Aerodynamics on Vehicle Design. Int. Journal of Vehicle Design, SP3, pp , Eloffson, P., Bannister, M.: Drag reduction mechanisms due to moving ground and wheel rotation in passenger cars. SAE paper, pp , 2002, Fabijanic, J.: An experimental investigation on wheel-well flows. Society of Automotive Engineers paper, pp , 1996, Fackrell, J. E., Harvey, J. K.: The flow field and pressure distribution of an isolated road wheel. Advances in Road Vehicle Aerodynamics, pp Hucho, W. H.: Aerodynamics of Road Vehicles. Butterworth and Co. Publishing, Boston, Lajos, T.: Az áramlástan alapjai. Műegyetemi könyvkiadó, Mears, A. P., Dominy, R. G., Sims-Williams, D. B.: The air flow about an exposed racing wheel. Society of Automotive Engineers paper, pp , 2002, S.B. Pope: Turbulent flows. Cambridge University Press Régert, T., Lajos, T.: Numerical simulation of flow field past road vehicle wheel. Proceedings of Gépészet 2002 conference, BME, Schiefer, U.: Zur Simulation des freistehenden Fahrzeugrades im Windkanal. Dissertation am IVK, Universität Stuttgart Skea, A. F., Bullen, P. R., Qiao, J.: The use of CFD to predict air flow around a rotating wheel. 31st. Int. Symposium on Automotive Technology and Automation, Düsseldorf, pp Skea, A. F., Bullen, P. R., Qiao, J.: CFD simulations and experimental measurements of the flow over a

9 rotating wheel in a wheel arch. Society of Automotive Engineers paper, pp , 2000, Wickern, G., Zwicker, K.: Zum Einfluß von Rädern und Reifen auf den aerodynamischen Widerstand von Fahrzeugen. Tagung Aerodynamik des Kraftfahrzeugs, Haus der Technik e. V., Essen, pp , Wilcox, D. C.: Turbulence modeling for CFD. DCW Industries Inc., 2000