Numerical Analysis and Optimization of the Front Window Visor for Vehicle Wind Buffeting Noise Reduction Based on Zonal SAS k- ε Method

: Numerical investigations were conducted to determine the effectiveness of the front window visor for wind buffeting noise reduction. An unsteady ﬂow simulation was carried out using a zonal Scale Adaptive Simulation (SAS) k- ε turbulence model. Firstly, the accuracy of the simulation method was validated based on a benchmark problem. The benchmark results, frequency, and sound pressure levels of feedback and resonance modes all matched well with the experimental data. The effect of the front window on the buffeting noise reduction was numerically investigated based on three different front side window openings. The analysis focused on the suppression effect of the front window visor. The results show that the front window visor changed the A-pillar vortex shedding trajectory and thus reduced the driver’s ear pressure ﬂuctuation. On this basis, an optimization algorithm was employed to optimize the shape of the front window visor. The main design goal was to decrease the sound pressure level ( SPL ) values of the driver’s left ear. Simulation results showed that the monitoring point’s SPL of buffeting noise after the visor optimization was reduced by 12.6%, compared with that of the original visor.


Introduction
In recent years, a significant amount of research has been carried out on mechanical noise (such as engine noise, transmission noise, etc.), and effective noise control methods have been proposed; wind buffeting noise is becoming more and more prominent with the continuous increase in the practical speed of vehicles. Wind buffeting noise is caused by the coupling of flow instability of the shear layer and the air in the vehicle cabin while driving a vehicle with a sunroof or window open, and is a type of aerodynamic noise. Wind buffeting noise has the features of high strength and low frequency. It not only affects the vehicle ride comfort but also affects driving safety. Therefore, to improve the quality of automobile products, it is very important for automotive manufacturers to predict and analyze the wind buffeting noise at the designing stage.
The characteristics of sunroof buffeting noise and its control methods have been extensively studied [1][2][3][4][5][6][7][8][9][10]. However, there are few research findings on the characteristics and the control methods of buffeting noise caused by opening the side window. Yang et al. conducted road tests on the buffeting noise of a sedan caused by different side window openings [11]. The results showed that there exist discrepancies in the characteristics of wind buffeting noise. When a single rear window opens, or two rear windows open at

Computational Schemes
Scale adaptive simulation (SAS) is an improved URANS formulation based on introducing the von Karman scale into the turbulence scale equation [20]. The information provided by the von Karman length-scale allows SAS models to dynamically adjust to resolved structures in a URANS simulation, which results in a LES-like behavior in unsteady regions of the flow field. At the same time, the model provides standard RANS capabilities in stable flow regions. The computational resources consumed by scale adaptive simulation are only half that of the large eddy simulation [20], which is very suitable for engineering applications. However, under the condition of low Mach number flow, SAS cannot trigger the LES-like behavior in the flow region far from the wall due to the flow instabilities loss. In the flow region near the wall, it cannot show the scale resolution ability due to the defects of the RANS equation [21].
Given the advantages and disadvantages of the SAS turbulence model, combined with the widely used standard k − ε turbulence model in engineering, according to the literature [22], the SAS equation can be rewritten as follows: where k is the turbulence kinetic energy, ε is the dissipation rate, µ t is the turbulent viscosity, G k represents the generation of turbulence kinetic energy, G k = −ρu i u j

∂(ρε) ∂t
is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, M T = √ k/a 2 is the turbulent Mach number, and a is the speed of sound. This compressibility modification is available when the compressible form of the ideal gas law is used. The model constants c 1ε , δ k , and σ ε have the following default values: c 1ε = 1.44, c u = 0.09, σ k = 1.0, σ ε = 1.3. In Equation (2), the user-defined source term is: The von Karman length-scale is redefined as: where κ = 0.41 is the von Karman constant. The first velocity derivative ∂U ∂y is represented in L vκ by U , which is equal to S ij , a scalar invariant of the strain rate tensor S: ). The second velocity derivative, U , is generalized to 3D using the magnitude of the velocity Laplacian: The model also provides direct control of the high wave number damping. This is realized by a lower constraint on the value of L vk in the following way: To describe the two flow regions, a blending function for the ε equation across the interface is used at the interface to describe both flow regions with the turbulence models of the same representation level. In the present study, the interface is placed at Y + = 80. According to the literature [23], two different values are adopted in the present approach: c 2ε = 1.92 < 2 is adopted in the near-wall region (low Reynolds number region), and c 2ε = 2.36 > 2 is adopted in the area away from the wall (high Reynolds number area).

Methodology and Validity of CFD Simulations
Yang et al. conducted road tests on the buffeting noise of a sedan caused by different side window openings [11]. The results showed that Helmholtz resonance plays an important role. Flow over an open side window in a vehicle exhibits similar characteristics to the flow over an open deep cavity. They all present the phenomenon of flow-excited Helmholtz resonance. A deep cavity as a benchmark problem for the validity of the CFD simulations is shown in Figure 1.
Yang et al. conducted road tests on the buffeting noise of a sedan caused by different side window openings [11]. The results showed that Helmholtz resonance plays an important role. Flow over an open side window in a vehicle exhibits similar characteristics to the flow over an open deep cavity. They all present the phenomenon of flow-excited Helmholtz resonance. A deep cavity as a benchmark problem for the validity of the CFD simulations is shown in Figure 1. The dimensions are similar to those used in wind tunnel experiments. The methodology for obtaining these experimental results has been described in the literature [4,17]. Flow is fully turbulent over the cavity with an inlet-free stream velocity of 25 m/s. One receiver point, at the center of the cavity bottom, is considered to validate the frequency spectrum with experimental results. To ensure an accurate resolution of the shear layer dynamics, more meshes are allocated over the opening of the cavity. The minimum grid spacing around the cavity corners is set to 0.1 mm. The total number of node points is approximately 2.576352 × 10 6 , and the number of hexahedral cells is 2.504167 × 10 6 . The total number of elements is 2.647365 × 10 6 . Partial grids along the longitudinal symmetry plane and prism layer are shown in Figure 2. To assess the reliability of the numerical solution, a grid dependence study was carried out, as shown in Table 1. The mean pressure coefficient and the peak values of the second monitor point's pressure fluctuation have been extracted from the simulation results for the three different mesh refinements. From Table 1, the discrepancies for the re- The dimensions are similar to those used in wind tunnel experiments. The methodology for obtaining these experimental results has been described in the literature [4,17]. Flow is fully turbulent over the cavity with an inlet-free stream velocity of 25 m/s. One receiver point, at the center of the cavity bottom, is considered to validate the frequency spectrum with experimental results. To ensure an accurate resolution of the shear layer dynamics, more meshes are allocated over the opening of the cavity. The minimum grid spacing around the cavity corners is set to 0.1 mm. The total number of node points is approximately 2.576352 × 10 6 , and the number of hexahedral cells is 2.504167 × 10 6 . The total number of elements is 2.647365 × 10 6 . Partial grids along the longitudinal symmetry plane and prism layer are shown in Figure 2.
Yang et al. conducted road tests on the buffeting noise of a sedan caused by different side window openings [11]. The results showed that Helmholtz resonance plays an important role. Flow over an open side window in a vehicle exhibits similar characteristics to the flow over an open deep cavity. They all present the phenomenon of flow-excited Helmholtz resonance. A deep cavity as a benchmark problem for the validity of the CFD simulations is shown in Figure 1. The dimensions are similar to those used in wind tunnel experiments. The methodology for obtaining these experimental results has been described in the literature [4,17]. Flow is fully turbulent over the cavity with an inlet-free stream velocity of 25 m/s. One receiver point, at the center of the cavity bottom, is considered to validate the frequency spectrum with experimental results. To ensure an accurate resolution of the shear layer dynamics, more meshes are allocated over the opening of the cavity. The minimum grid spacing around the cavity corners is set to 0.1 mm. The total number of node points is approximately 2.576352 × 10 6 , and the number of hexahedral cells is 2.504167 × 10 6 . The total number of elements is 2.647365 × 10 6 . Partial grids along the longitudinal symmetry plane and prism layer are shown in Figure 2. To assess the reliability of the numerical solution, a grid dependence study was carried out, as shown in Table 1. The mean pressure coefficient and the peak values of the second monitor point's pressure fluctuation have been extracted from the simulation results for the three different mesh refinements. From Table 1, the discrepancies for the re- To assess the reliability of the numerical solution, a grid dependence study was carried out, as shown in Table 1. The mean pressure coefficient and the peak values of the second monitor point's pressure fluctuation have been extracted from the simulation results for the three different mesh refinements. From Table 1, the discrepancies for the receiver location's mean pressure coefficient are very small. Furthermore, the difference between the peak pressure fluctuation for the fine and medium mesh is not large. Therefore, a fine mesh was used in this study. Five monitoring lines were selected in the flow direction (x) of the opening area of the cavity; the height of each line is 0.9 m, and the distances from the front edge of the opening of the cavity are 0.01 m, 0.03 m, 0.05 m, 0.07 m, and 0.09 m. The streamwise direction length of the opening of the cavity (l c = 0.1 m) is used for dimensionless treatment. In the simulation, the mean streamwise velocity of the monitoring point is obtained through calculation. The comparison between the wind tunnel test results and the simulation results is shown in Figure 3. The abscissa adopts the ratio of the mean velocity (U mean-x ) to inlet velocity (U 0 = 25 m/s) for dimensionless treatment, and the ordinate takes the ratio of height (z) in the vertical direction to the opening height of the cavity (10h c = 0.15 m) for dimensionless treatment. It can be seen from Figure 3 that the trend of simulated values is consistent with the experimental values at different locations, and the shape of the mean velocity curve approximately matches with the inverse hyperbolic tangent function distribution, which is consistent with the literature [24]. This proves that the zonal SAS k-ε turbulence model can accurately capture the flow characteristics. Five monitoring lines were selected in the flow direction (x) of the opening a the cavity; the height of each line is 0.9 m, and the distances from the front edge opening of the cavity are 0.01 m, 0.03 m, 0.05 m, 0.07 m, and 0.09 m. The streamwi rection length of the opening of the cavity (lc = 0.1 m) is used for dimensionless treat In the simulation, the mean streamwise velocity of the monitoring point is obt through calculation. The comparison between the wind tunnel test results and the lation results is shown in Figure 3. The abscissa adopts the ratio of the mean ve (Umean-x) to inlet velocity (U0 = 25 m/s) for dimensionless treatment, and the ordinate the ratio of height (z) in the vertical direction to the opening height of the cavity ( 0.15 m) for dimensionless treatment. It can be seen from Figure 3 that the trend of lated values is consistent with the experimental values at different locations, and the of the mean velocity curve approximately matches with the inverse hyperbolic ta function distribution, which is consistent with the literature [24]. This proves th zonal SAS k-ε turbulence model can accurately capture the flow characteristics.
x/l=0.9 x/l=0.7  Based on the time histories of the fluctuating pressure, it is possible to convert the computed data to the frequency-domain results by a standard fast Fourier transform (FFT) routine. The sound pressure level (SPL) was finally converted to dB units using the formula: where p is the fluctuating pressure and p re f is the sound pressure for reference:  Figure 3. The first resonant peak is the fundamental frequency of the flow instability over the cavity. For the frequency of the first peak SPL, there is no significant difference between the experimental results and the simulation results; the difference is less than 2 Hz. The frequency of the second peak SPL captured differs from the experimental value by 2 Hz, within acceptable ranges. Both the frequencies of the third peak SPL and the fourth peak SPL are further and further away from the test values. The overall trend of the SPL spectra captured by the zonal SAS k − ε turbulence model almost perfectly matches with the experimental values. The present model underestimates the amplitude of the high-order resonance and overestimates the frequency of the high-order resonance, which may be explained by the following. First, these were caused by the difference between the numerical simulations and the experimental measurements. It is very important to note in our numerical simulations that a uniform velocity profile with a turbulent intensity of 0.5% was assumed at the inlet boundary of the flow field. However, the turbulent boundary expected in the experimental measurements was generally not available. Second, the computation model used in the present study did not include the simulation of the background noise. Third, this might be due to the fact that the higher-order modes cause relatively weak oscillation in the present simulation.   Figure 3. The first resonant peak is the fundamental frequency of the flow instability over the cavity. For the frequency of the first peak SPL, there is no significant difference between the experimental results and the simulation results; the difference is less than 2 Hz. The frequency of the second peak SPL captured differs from the experimental value by 2 Hz, within acceptable ranges. Both the frequencies of the third peak SPL and the fourth peak SPL are further and further away from the test values. The overall trend of the SPL spectra captured by the zonal SAS k ε − turbulence model almost perfectly matches with the experimental values. The present model underestimates the amplitude of the high-order resonance and overestimates the frequency of the high-order resonance, which may be explained by the following. First, these were caused by the difference between the numerical simulations and the experimental measurements. It is very important to note in our numerical simulations that a uniform velocity profile with a turbulent intensity of 0.5% was assumed at the inlet boundary of the flow field. However, the turbulent boundary expected in the experimental measurements was generally not available. Second, the computation model used in the present study did not include the simulation of the background noise. Third, this might be due to the fact that the higher-order modes cause relatively weak oscillation in the present simulation.
In general, the agreement between the compared results is very satisfactory, showing the ability of the zonal SAS k ε − model to predict the cavity noise. It indicates that this model can be used for window buffeting noise predictions at earlier stages of the program and verification of the design of the buffeting fix.

Effects of the Rain Visor on the Reduction of the Window Buffeting Noise
The numerical simulation model of the sedan refers to the literature [17]. The meshing scheme is adopted from the best practices of Scale Resolved Simulation (SRS) [25]. The numerical simulation model of the sedan is appropriately simplified for reducing the calculation, and the external flow field of the screen wiper, door handles, and other accessories are ignored. The unstructured computational grids used in the simulations were constructed with ICEM CFD 16.2. The total size of the mesh for the computational domain is In general, the agreement between the compared results is very satisfactory, showing the ability of the zonal SAS k − ε model to predict the cavity noise. It indicates that this model can be used for window buffeting noise predictions at earlier stages of the program and verification of the design of the buffeting fix.

Effects of the Rain Visor on the Reduction of the Window Buffeting Noise
The numerical simulation model of the sedan refers to the literature [17]. The meshing scheme is adopted from the best practices of Scale Resolved Simulation (SRS) [25]. The numerical simulation model of the sedan is appropriately simplified for reducing the calculation, and the external flow field of the screen wiper, door handles, and other accessories are ignored. The unstructured computational grids used in the simulations were constructed with ICEM CFD 16.2. The total size of the mesh for the computational domain is 8.484437 × 10 6 . Installing the rain visor on the A-pillar, the surface meshes of the left front window are shown in Figure 5. As shown in Figure 6, when the left front window is fully open, there are two vorticity lines in the shear layer of the horizontal tangential plane through the driver's ear. The outer side vortex is shedding from the upper edge of the rearview mirror, and the inner side vortex is from the A-pillar. When the A-pillar is installed with the visor, the trajectory of the vortex from the A-pillar is changed, and the amount of vorticity invading the cabin is reduced. Therefore, the fluctuation pressure beside the driver's left ear is reduced, as shown in Figure 7a. of the vortex from the A-pillar is changed, and the amount of vorticity invading the cabin is reduced. Therefore, the fluctuation pressure beside the driver's left ear is reduced, as shown in Figure 7a. As shown in Figure 6, when the left front window is fully open, there are two vorticity lines in the shear layer of the horizontal tangential plane through the driver's ear. The outer side vortex is shedding from the upper edge of the rearview mirror, and the inner side vortex is from the A-pillar. When the A-pillar is installed with the visor, the trajectory of the vortex from the A-pillar is changed, and the amount of vorticity invading the cabin is reduced. Therefore, the fluctuation pressure beside the driver's left ear is reduced, as shown in Figure 7a. In the case of no visor, the peak SPL of the driver's left ear is 118 dB; the peak SPL is reduced by 6 dB after installation of the visor, and the corresponding frequency is shifted from 19.25 Hz to 20.29 Hz, as shown in Figure 7b. Therefore, the rain visor can effectively reduce the wind buffeting noise when the front window is fully opened.  outer side vortex is shedding from the upper edge of the rearview mirror, and the inn side vortex is from the A-pillar. When the A-pillar is installed with the visor, the trajecto of the vortex from the A-pillar is changed, and the amount of vorticity invading the cab is reduced. Therefore, the fluctuation pressure beside the driver's left ear is reduced, shown in Figure 7a. In the case of no visor, the peak SPL of the driver's left ear is 118 dB; the peak SPL reduced by 6 dB after installation of the visor, and the corresponding frequency is shift from 19.25 Hz to 20.29 Hz, as shown in Figure 7b. Therefore, the rain visor can effective reduce the wind buffeting noise when the front window is fully opened.  In the case of no visor, the peak SPL of the driver's left ear is 118 dB; the peak SPL is reduced by 6 dB after installation of the visor, and the corresponding frequency is shifted from 19.25 Hz to 20.29 Hz, as shown in Figure 7b. Therefore, the rain visor can effectively reduce the wind buffeting noise when the front window is fully opened. Therefore, the wind buffeting noise caused by the front window opening can be effectively suppressed by adding a rain visor to the A-pillar.

Design Variables and Constraints
In this research, the front rain visor of a sedan is selected as the optimization object, and the optimization parameters are shown in Figure 8. Therefore, the wind buffeting noise caused by the front window opening can be effectively suppressed by adding a rain visor to the A-pillar.

Design Variables and Constraints
In this research, the front rain visor of a sedan is selected as the optimization object, and the optimization parameters are shown in Figure 8. According to the modelling features of the rain visor, the following parameters were selected as design variables without affecting the driver's field of vision: (1) The design variable L1: Take the midpoint of the upper and lower sides of the front window and make the midline on the window's curved surface. Make the intersec- According to the modelling features of the rain visor, the following parameters were selected as design variables without affecting the driver's field of vision: (1) The design variable L 1 : Take the midpoint of the upper and lower sides of the front window and make the midline on the window's curved surface. Make the intersection midline of the two endpoints of the rain visor on the window's curve at one point, then the curve will be regarded as the edge line of the rain visor, and the intersection point is the radiant point of the rain visor's edge. Considering the rain shielding effect of the rain visor and the range of visual field of the driver, two points, A and B, are taken as the limit position of the intersection, and the curve between them is L 1 . Make the position of point B zero, and then the value range of L 1 is [0~39 mm]. Restricted by the short edge of the visor, the value range of R is set as [0~15 mm].
According to the previous analysis, the front visor can change the trajectory of the vortex in the shear layer separated from the A-pillar. Therefore, when the left front window is fully open and the inlet velocity is 30 m/s, the peak value of the sound pressure level at the driver's left ear is taken as the objective function, P, and the objective function value cannot exceed 116 dB.

Approximate Agent Model
According to the value range of design variables, four design variables were selected, including the upper and lower edges' midline L 1 of the window, the distance, W, between the lower edge of the rain visor and the window, the long edge, L 2 , of the visor, and the radius, R, of the visor. Ten groups of sample points are designed using the optimal Latin hypercube sampling method. The design scheme is shown in Table 2. According to ten groups of sample points in Table 2, CAD modelling was performed, the mesh was built, and ten groups of response values were obtained by CFD simulation calculation. The sound pressure level spectrums of the driver's left ear are shown in Figure 9. The sound pressure levels at the monitoring points of the driver's left ear have different degrees of decline. The fifth group of sample points is the best, with the lowest peak sound pressure level, as shown in Figure 9e. Figure 10 shows the main effect of each design variable on the objective function value, P. It can be seen from the slope of different curves in Figure 10 that the peak value of the Appl. Sci. 2022, 12, 6906 9 of 13 wind buffeting noise inside the vehicle cabin decreases with the increase in L 1 and W. In comparison, the slope of L 1 is greater than W, so P changes more significantly with L 1 . Meanwhile, as R and L 2 increase, P increases and then decreases.
The kriging model can reduce the computational cost of performing optimization [26]. According to the optimal Latin hypercube design of experiments in Table 2 and the CFD results in Figure 9, the kriging model was used to establish an approximation model of the response relationship between the design variables and the optimization objective. To verify the accuracy of the approximation model, any two test points outside the scheme of the design of the experiment are selected in the design space for CFD simulation, compared with the results obtained by the approximation model. The comparison results are shown in Table 3. It can be seen from Table 3  According to ten groups of sample points in Table 2, CAD modelling was performed, the mesh was built, and ten groups of response values were obtained by CFD simulation calculation. The sound pressure level spectrums of the driver's left ear are shown in Figure  9. The sound pressure levels at the monitoring points of the driver's left ear have different degrees of decline. The fifth group of sample points is the best, with the lowest peak sound pressure level, as shown in Figure 9e.  Figure 10 shows the main effect of each design variable on the objective function value, P. It can be seen from the slope of different curves in Figure 10 that the peak value of the wind buffeting noise inside the vehicle cabin decreases with the increase in L1 and W. In comparison, the slope of L1 is greater than W, so P changes more significantly with L1. Meanwhile, as R and L2 increase, P increases and then decreases.   The kriging model can reduce the computational cost of performing optimization [26]. According to the optimal Latin hypercube design of experiments in Table 2 and the CFD results in Figure 9, the kriging model was used to establish an approximation model of the response relationship between the design variables and the optimization objective. To verify the accuracy of the approximation model, any two test points outside the scheme of the design of the experiment are selected in the design space for CFD simulation, compared with the results obtained by the approximation model. The comparison results are shown in Table 3. It can be seen from Table 3 that the results calculated by using the approximation model are quite close to those obtained by CFD simulation. The results show that the established approximation model can well describe the relationship between design variables and response. The established approximation model has high precision and can directly replace CFD simulation.

Global Optimization
Based on the approximation model, the multi-island genetic algorithm is applied to the global optimization design. The subgroup size is set to 20, the total population size is 50, and the total evolutionary algebra is 20 generations. The optimal solution is validated by CFD simulation. The comparison results are shown in Table 4. The noise reduction effect of the optimized visor is shown in Figure 11. It can be seen from Figure 11 that the vorticity invading the cabin is very small, and the peak sound pressure level at the driver's left ear is 102 dB. Compared with that without the visor of the front window, the noise value at the driver's left ear is reduced by approximately 14 dB, and the noise reduction range is 12.4%.

Global Optimization
Based on the approximation model, the multi-island genetic algorithm is applied to the global optimization design. The subgroup size is set to 20, the total population size is 50, and the total evolutionary algebra is 20 generations. The optimal solution is validated by CFD simulation. The comparison results are shown in Table 4. The noise reduction effect of the optimized visor is shown in Figure 11. It can be seen from Figure 11 that the vorticity invading the cabin is very small, and the peak sound pressure level at the driver's left ear is 102 dB. Compared with that without the visor of the front window, the noise value at the driver's left ear is reduced by approximately 14 dB, and the noise reduction range is 12.4%.

Conclusions
The phenomenon of the window buffeting noise caused by opening the front left window was analyzed by CFD. The results obtained are summarized as follows: (1) A zonal formulation of the SAS k ε − approach was employed in this study. A deep cavity as a benchmark problem was used to validate the approach. The results show that the CFD method can be used for side window buffeting noise predictions at earlier stages of the program.

Conclusions
The phenomenon of the window buffeting noise caused by opening the front left window was analyzed by CFD. The results obtained are summarized as follows: (1) A zonal formulation of the SAS k − ε approach was employed in this study. A deep cavity as a benchmark problem was used to validate the approach. The results show that the CFD method can be used for side window buffeting noise predictions at earlier stages of the program. (2) Aiming at the problem of the wind buffeting noise of the front side window, the CFD numerical simulation of the front side window fully opened was carried out. The results show that the front window visor changes the path of vortex shedding from the A-pillar, and thus reduces the vortex invading the cabin. The fluctuation pressure at the driver's ear is reduced, so the wind buffeting noise is better suppressed. (3) The optimization algorithm is used to optimize the shape of the front rain visor.
Compared with the case without the visor, the CFD results show that the optimized visor reduces the peak sound pressure level of the driver's left ear by 14.5 dB.
In future, validation of the reduction noise effect of the visor is needed via wind tunnel experiments and road tests.  Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: All the data produced in this study is contained in the manuscript text.