Study on the Influence of Rolling Wheels on Car External Flow Field and Aerodynamic Noise

Abstract: In order to illustrate the external flow field and aerodynamic noise of cars with the influence of rolling wheels, the investigation is conducted through numerical simulation in this paper. Wheel rolling is modeled by using a rotating wall. Combined with Realizable k – ε and LES, the flow field and aerodynamic noise of the rolling wheels and the stationary wheels are simulated, respectively. Then the related monitoring points are set to provide the basis for further evaluation. The transient calculation is carried out with two typical cases. Furthermore, air fluctuating pressure and sound pressure level spectrum of the monitoring points in wheel cavity is obtained. The results show that rolling wheels have distinctive influence on vortex formation and car aerodynamic characteristics.


Introduction
Aerodynamic noise caused by the automobile is one of the focuses in automotive engineering.With the increasing of vehicle speed and car ownership, car noise problem becomes important sharply [1].Vehicle external flow field is a kind of complex disturbed flow motion, the rolling of wheels makes car external flow field more complex and it results car aerodynamic noise.Previous study on automobile wheels is simplified and does not consider the effect of rolling wheels.Although the results have certain significance, there are still large gaps compared with real cars.The latest studies involve the rolling wheels, but they do not conduct a detailed analysis and discussion of car flow field and aerodynamic noise near the rolling wheel.Literature [2] shows that wheels noise was relatively loud through the study of aerodynamic noise contribution quantity of car body parts.
In this paper, the simulation research of flow field characteristics and aerodynamic noise distribution of the wheel in both rolling and static conditions are conducted through numerical simulation.

Numerical model for vehicle external flow field 2.1 Description of Vehicle Model
In this paper, a vehicle model including the key features of vehicle body such as rear view mirror, wheel and side window is established.Due to wheel spokes and wheel brake disc disturb the airflow motion when rolling, which will change the flow fields, car wheel is no longer depicted by a simple cylinder, but a wheel model including spokes, tread grooves and brake disc, as shown in Figure 1.The front of the computational domain is 3 times of car length, the rear for 7 times of car length, one side is 3 times of car width, height is 5 times of car height [3], as shown in Figure 2.

Mesh for Vehicle Model
This paper uses tetrahedral and triangular prism grid to mesh the computational domain.The mesh size of the computational domain is controlled between 3mm and 40mm by integral control method.In the vicinity of the surface of car body, in order to capture the turbulent situation around the body as far as possible, a region surrounding car body is established and the grid is encrypted.The unit length of encryption area is set to 10mm.Additional, to improve the accuracy of the calculation, the inflation grid is adopted in near wall of the body, tires and wheel cover, the inflation layer of the body is 5 and the wheel is 3 [4].The total number of meshes is 12 million.The mesh is shown in Figure 3.

Boundary Conditions and Solving Settings
Vehicle motion belongs to the incompressible flow in low speed and the solution of this study is based on pressure based solver [6].First, the steady state calculation is carried out by the Realizable ε − k model, and then the transient calculation is carried out by the large eddy simulation method.
(1) Inlet boundary: a velocity inlet boundary is set.The vehicle speed is 27.8m/s.
(2) Outlet boundary: outlet boundary is set as pressure boundary.
(3) Wheel and the ground: For rolling wheel, rotating wall is used to simulate wheel rolling with a radius of 0.315m and an angular velocity of 88.2rad/s.The mobile wall is applied to simulate the movement of the ground and the speed of the movement is the same as that of the inlet velocity.For static wheel, car wheels are set to the static wall and the ground is still moving wall.
The frequency domain is generally determined by the time step.In the study, the maximum frequency is 5000Hz.Due to the maximum frequency of fast Fourier transform (FFT) of a time series is 1/(2Δt), the calculation time step is set to 0.0001s.The time steps are set to 2000, 20 iterations per time step [5].So the total computation time is 0.2 seconds.

Simulation results and analysis
The pressure distribution around car will affect the aerodynamic noise around car surface directly.To analyze car aerodynamic noise, this paper analyzes the pressure on the surface of car body firstly.Figure 4 presents the static pressure contours of car body surface and wheel.It can be seen that the contour of the wheel is denser, the pressure gradient is larger, which indicates that the pressure fluctuation of the wheel is intense.This paper will focus on the analysis of the characteristics of the aerodynamic noise of the wheel cavity and the far field.Due to wheel rolling motion driving airflow attached to tread counterclockwise, the two phase flow between tire tread and the wheel cover are encountered mutually.This causes many vortices with different sizes and different directions formed between tire tread and wheel cover.When wheels are rolling, there are three obvious vortices at the top left of the front wheel as shown in Figure 5 (1) marked with 1,2,3.Compared with the rolling wheel, there is only one vortex in the stationary front wheel as shown in Figure 5 (2) marked with 1.
Figure 6 gives the velocity vector diagram of wheel cavity of the front rolling wheel at different times.It can be seen that vortex is in a constantly changing process.In 0.05 seconds, vortex is not obvious.In 0.1 second, three obvious vortices can be seen.After which, vortices are broken away.Then they are reformed.The formation of vortex in the whole time is in the process of formation, development, disappearance and reformation, with the dissipation of energy.It cause the change of the pneumatic pressure around car wheel and then lead to the increasing of drag and lift force of the whole vehicle in rolling condition.Because the airflow movement of the rear wheel is affected by the front wheel, the rear wheels of the two working conditions have no obvious vortex.From simulation results, it is found that the fluctuating pressure of each monitoring point is changed with time in 0-0.2 seconds.The distribution of sound pressure level spectrum is similar to the change.In the low frequency region sound pressure level drops, and later, with the increase of frequency, the sound pressure level keep stable in a certain range.Figure 7 presents the fluctuating pressure of vehicle front wheel monitoring point 1 in the rolling situation.The sound pressure level spectrum of the rolling front wheel monitoring point 1 is shown in Figure 8.To superimpose the sound pressure level at each frequency, the total sound pressure level of each monitoring point is obtained [7].The total sound pressure level of the front and rear wheel of the rolling wheel and the static wheels are shown in Figure 9 and 10.The results show that the value of most monitoring points is 100 dB or so.From points 4, 5, 6, 7 corresponding to the velocity vector map, it is shown that these places have a large number of vortices, due to the vortex's constantly formation, constantly shedding, make air pressure fluctuating.These lead to the increasing of sound pressure level.In addition, it can be seen that the value of sound pressure level at monitoring point 9 is all the monitoring point of minimum.This is because the special position of the point, when the airflow flowed through the bottom of body and met the wheel, the airflow is obstructed, and most of the airflow gathered here, led to the accumulation of a large amount of air, the airflow velocity get slower, and therefore smaller sound pressure level numerical.The numerical value of the front wheel of the stationary case is not the same as the rolling wheel, because the vortex generated by the static condition is less, the sound pressure level of the upper part of the wheel cavity is smaller than the rolling condition.Similarly, monitoring 9 in static situation, sound pressure level is smaller.
In analyzing the sound pressure level of the various monitoring points of rear wheel cavity, it is shown that the distribution is not the same as front wheel, the rear wheel cavity is not as the same as front wheel to produce more obvious vortices.The sound pressure level of the upper part of the rear wheel cavity is lower than that of the front wheel due to the absence of intense vortex motion.By using the center of car to establish a half arc with a radius of 5 meters and an interval of 18 degrees, 11 receiving points with a height of 1.2 m above ground are set to study the impact of wheel rolling on the outside car noise.The layout of the monitoring points is shown in Figure 11.It is shown in Figure 12 that the sound pressure level of rolling wheel at each monitoring point in the far field is higher than static wheel.It is shown in the left that the amount of change is small and the sound pressure level at monitoring points 1, 2, 3 changes are less than 1 dB, which indicates that the wheel rolling has little noise impact on the front of the car.But the change of sound pressure level is relatively large in the middle body central and the rear car body.It indicates that when the wheel in the rolling, it disturbs air flow motion in the middle and rear which led to the change of the aerodynamic noise around the body.The sound propagates outward and outside and car noise increases in far field.

Conclusion
This paper takes into account wheel rolling on the influence of car aerodynamic noise.The influence on flow field characteristics and the far field noise is studied through numerical simulation system under the condition of rolling and static wheels.From the simulation results, the following conclusions can be drawn: 1.The effect of rolling wheels on car aerodynamic noise is illustrated through the present research.It not only qualitatively explains the significance of rolling wheel, but also gives the quantitive effect at the cavity and the far field of car aerodynamic noise.2. The results also illustrate the flow field characteristics of wheel cavity quantitively.
It gives the causes producing the change of car noise.The generating process of vortices is investigated in detail in the paper.The generating process of vortices accompanies with air pressure fluctuating.It is useful for further research on ameliorate car aerodynamic noise.

Figure 4 .
Figure 4. Air Pressure distribution of body and wheel surface

Figure 5
Figure5and 6 give the velocity vector diagram of longitudinal symmetric cross section of rolling wheel and static wheel.Due to wheel rolling motion driving airflow attached to tread counterclockwise, the two phase flow between tire tread and the wheel cover are encountered mutually.This causes many vortices with different sizes and different directions formed between tire tread and wheel cover.When wheels are rolling, there are three obvious vortices at the top left of the front wheel as shown in Figure5(1) marked with 1,2,3.Compared with the rolling wheel, there is only one vortex in the stationary front wheel as shown in Figure5(2) marked with 1.Figure6gives the velocity vector diagram of wheel cavity of the front rolling wheel at different times.It can be seen that vortex is in a constantly changing process.In 0.05 seconds, vortex is not obvious.In 0.1 second, three obvious vortices can be seen.After which, vortices are broken away.Then they are reformed.The formation of vortex in the whole time is in the process of formation, development, disappearance and reformation, with the dissipation of energy.It cause the change of the pneumatic pressure around car wheel and then lead to the increasing of drag and lift force of the whole vehicle in rolling condition.Because the airflow movement of the rear wheel is affected by the front wheel, the rear wheels of the two working conditions have no obvious vortex.

Figure 7 .
Figure 7. Fluctuating pressure in time domain

Figure 7 .
Figure 7. Fluctuating pressure in time domain

Figure 7 .
Figure 7. Fluctuating pressure in time domain