summary
In a wind tunnel, the effect of wind on the aerodynamic characteristics of a vehicle is simulated by vehicle yawing, where the wind speed remains constant at altitude. But in reality, natural wind is a laminar flow, there is shear between layers, and the wind speed changes with height. In this paper, CFD simulations are performed to compare the aerodynamic characteristics of fast-back and square-back DrivAer models when subjected to crosswinds, where yaw simulations are performed at a yaw angle of 10°. The results show that when the mass flow of the crosswind at the height of the car is similar, the car is subjected to almost the same force and torque in both cases.
1. Introduction
The aerodynamic characteristics of a car when subjected to crosswind can only be approximated in experimental or virtual simulations, mainly because steady-state techniques are used to study transient events in nature. In a wind tunnel, the effect of crosswinds is expressed by setting the yaw angle of the vehicle to the airflow, and CFDs also typically simulate this arrangement. Both methods simulate a car driving on an open road with crosswinds, where the wind speed does not change with altitude. But in reality, vehicles traveling in crosswinds are located in the lowest region of the Earth's atmospheric boundary layer, and in this shear flow, the velocity is zero on the ground and increases with the increase in altitude from the ground, so both the local yaw angle and the synthetic velocity increase as the height of the car increases.
Wind tunnel and CFD simulations also employ stable, low turbulence wind inputs, whereas natural winds can be highly unstable and may include significant turbulence levels, as shown in Figure 1. In this article, only the shear flow shown in the middle of Figure 1 is studied.
However, information on the natural wind characteristics of the height above ground (i.e. less than 2 m) associated with the car is extremely limited, and the available data is inferred from data obtained from higher (generally 10 m) buildings and wind turbines, and the relationship between the natural wind speed Uz and the ground height z is as follows:
（1）
In the formula, U10 is the wind speed at 10m, the exponential α depends on the terrain, and Table 1 gives the typical α values for different terrains. (ZG is the depth of the atmospheric boundary layer for each terrain)
2. Mesh and boundary conditions
The DrivAer model has a range of interchangeable rear-end geometries, so the effect of shear on fast-back and square-back vehicle types was studied, with the main dimensions of the model shown in Table 2 and the use of a smooth bottom and a closed engine compartment to reduce computational costs.
The model is placed in the calculation domain of 5 L (Length=4.613m) and 6L from the primary and secondary inlets, the size of the computed domain is x=18L, y=13L, z=3L, and the bottom surface is set to slip, as shown in Figure 2. Most of the body surfaces use mesh elements with a size of 0.001L, but in some locations a smaller grid element of size 0.0001L is required to guarantee the quality of the surface of curved parts such as A-pillar and C-pillar. Therefore, the total number of face meshes for the fast-back and square-back models is 2.7M and 2.8M, respectively. The total thickness of the boundary layer is 0.001L, and the number of layers is 8. The dimensionless proximity spacing value y+ on the entire surface
The mesh size near the body surface is 0.002L, and this area extends 0.5L under the body and 0.3L to the leeward side of the body to capture yaw wake. The outer encryption domain extends 2.7 L to the underside of the body and 1 L to the body leeward surface, the maximum size of the body mesh unit is 0.14L, and the total number of body meshes of the two sets of meshes is about 69M. The body mesh is shown in Figures 3 and 4.
At the two inlets, the velocity component Uv is fixed at 27.8m/s, and for non-shear simulations, the Uw velocity component is valued at 4.9 m/s, in the positive direction of the Y axis, resulting in a yaw angle of about 10° and a synthesis velocity of Ur=28.23 m/s. For the shear simulation, the Uw velocity component takes the curve shown in Figure 5 (which is calculated from Equation 1) and assumes that the mass flow at the height of the vehicle is the same as the mass flow rate in the unheared situation. The exponential α =0.16 indicates open, smooth terrain (see Table 1).
It is also possible to calculate the average speed UWM at a certain height:
where UWH is the wind speed at height H, and the height z at which this speed appears on the shear profile is given by the following equation:
Thus, it can be found that the speed without shear is 0.862 times the maximum speed (roof speed) at the time of shear, that is, the speed at 39.5% of the height of the car.
3. Simulation method
A pressure-based finite volume solver based on the non-compressive semi-implicit separation flow was chosen, and all simulations used a mixed second-order windward/bounded center differential convection solution using the IDDES turbulence model. The second-order time scheme reduces the numerical dissipation of the velocity; the time step of 1×10-4s ensures that the number of kurans in the LES region is less than 1; and five internal iterations per time step ensure consistent convergence of the residuals. All CFD simulations are performed using CD-Adapco's Star-CCM+ software v10.04.009.
All simulations are initialized using a steady-state RANS solver before calculating the stabilization period of 1 second or 6 convection units using the DES method. The simulation then runs for 2 seconds (12 convection flow units), during which the convection field is averaged. Ideally, this average interval should be longer, but the number of simulations in this study is large and computational resources are limited. It takes about fifty-eight hours to run three seconds in parallel on the 320 cores of the HPC-Midland device in the UK.
4. Results
Table 3(a) and Table 3(b) show the force coefficient results for the fast and square backs, respectively, and compare them with data at 0° yaw (i.e., no crosswind input).
At a 10° yaw angle, the force coefficient with and without shear except the lift coefficient does not change much in all cases, but there is no obvious trend of change, in the shear flow, the resistance and lateral force of the fast back car increase slightly, while the square back car is the opposite. Figures 6, 7 and 8 show the distribution of drag coefficients, lateral force coefficients and lift coefficients on fast and square back vehicles, respectively.
The drag distribution is shown at the height of the body, while the lateral force and lift distribution are shown on the body length. Comparing the drag and lift data at yaw with the zero yaw situation shows that although the resistance fluctuates greatly, the trend of the distribution remains the same regardless of yaw or not; the same is true of the lift distribution.
In all cases, the local load difference between shear and unhear crossflows is negligible. Since lateral forces are similarly distributed along the X axis in uniform or shear flow, the yaw moment is essentially the same in both cases.
5. Discussion
5.1 Average resistance
Aerodynamic resistance is strongly dependent on the yaw angle, which is affected by the size and direction of the wind speed. In order to calculate the mean wind resistance coefficient, assuming that the crosswind direction is the same, the velocity profile is given by Equation (1), so that the ratio of the height to the total height at the same mass flow rate and the equivalent average flow rate is a certain value. For the shear flow studied here, the α = 0.16 and the height ratio is 0.395, as shown in Figure 5. Increase the α to 0.40 and the height ratio to only 0.431. This result shows that the velocity at about 40% vehicle height is equivalent to the average velocity of the shear flow, which is about 0.55 to 0.75 m, generally 0.6 m.
5.2 Resistance distribution
The resistance distributions in Figures 6(a) and 6(b) show that the shear and non-shear distributions at yaw are essentially the same, as is the overall drag coefficient. Drag is created at the front of the car, but creates local negative pressure zones at the rear of the hood and the front edge of the roof. Figures 9(a) and 9(b) show the front and rear resistance distributions of fast-back and square-back bodies, respectively. The solid line is the front-end resistance, and the dashed line is the back-end resistance.
Comparing Figure 9 and Figure 6, it can be seen that most of the local drag changes that occur at the height of the body are on the front end. In contrast, the posterior resistance coefficients are relatively evenly distributed. The front end resistance curve shape of both bodies is almost the same, as this is a common front end shape, but interestingly, yaw is the same as the yaw-free situation. This suggests that the increased drag at low yaw angles is primarily due to increased back-end drag.
5.3 Lift and lateral force distribution
The lift distribution shown in Figure 7 indicates that lift increases during yawning, mainly at the rear of the hood and roof, especially above the rear edge of the roof and rear tailgate, where windward edges may experience higher speeds. Table 3 shows that lift is the aerodynamic characteristic most affected by shear, and the lift coefficient at the rear axle of the vehicle increases by more than 0.02, of course, the impact of this amplitude on the driver is negligible.
The lateral force distribution in Figure 8 shows that the lateral force is mainly generated at the front of the vehicle and at the windshield, and there is little difference between different operating conditions.
5.4 Load similarity
Figure 10 shows the cross-flow velocity contour in a cross-section of the fast-back vehicle in both shear and uniform crosswind situations, with the cross-flow velocity contour at the top of the windshield, where local lateral forces and lift are high. Comparing Figures 10(a) and 10(b) shows that the surface velocity distribution is almost the same, while the velocity distribution away from the body surface is very different. The similarity of the surface velocity distribution of the body leads to the similarity of the surface pressure distribution.
For both cases shown in Figure 11, in the same longitudinal position (x = 2.0 m), the body is affected by suction, and the yaw is slightly increased on the windward side, but the roof is basically unchanged, while a very large increase in suction is generated at the A column on the leeward side. The pressure distribution is similar at higher local loads, which explains why the rotational moments for shear and unshetched conditions in Table 3 are almost the same.
5.5 Research Limitations and Future Work
The data provided seem to indicate that when the mass flow in the crosswind is the same at the vehicle height, the forces and moments on the vehicle in the shear crosswind are essentially equal to the uniform flow. However, this conclusion is still not rigorous enough, as results were obtained only on two vehicles of the same height, the simulated car had no internal cooling airflow, the underbody was smooth, and the data were obtained only in one yaw angle and one example of shear flow.
It can be expected that higher SUV type vehicles will show the same characteristics as square-backed vehicles, but it is impossible to infer its impact on MPV models, as MPV models have different front shapes.
This limited study shows that for the two vehicles considered, the effect of shear is small or small. In the future, the effects of arbitrary yaw angles or ranges associated with the car, as well as different shear flow fields, should also be studied; different models and more realistic body shapes should also be studied.
6. Conclusion
CFD simulation compares the aerodynamic characteristics of fast-back and square-backEd DivAer models when subjected to shear and uniform crosswinds.
The results show that when the mass flow in the crosswind above the height of the car is similar, the car is subjected to almost the same force and torque in both cases, and this similarity of aerodynamic characteristics stems from the fact that the shear cross-flow becomes more uniform when approaching the body.
文章来源：Howell, J., Forbes, D., Passmore, M., and Page, G., "The Effect of a Sheared Crosswind Flow on Car Aerodynamics," SAE Int.J. Passeng. Cars - Mech. Syst. 10(1):2017, doi:10.4271/2017-01-1536.