Numerical Study on Aerodynamic Noise Reduction in Passenger Car with Fender Shape Optimization

Abstract

Despite the rapid development of vehicle intelligent technology, the aerodynamic noise problem of internal combustion engine vehicles and pure electric vehicles at high speed has always been a growing problem. In this study, the effects of the car body fender shape on the aerodynamic noises of the rearview mirror and wheel region were investigated, and a noise reduction method was also proposed by optimizing the fender shape. To realize the parametric modeling of the fender, five positional variables were selected to define the fender configuration; the free-form deformation (FFD) method was used to establish the response fender model according the DOE schemes, and computational fluid dynamics (CFD) simulations are used to obtain the noise results. Then, with the help of the radial basis function (RBF) model and the adaptive simulated annealing (ASA) algorithm, the aerodynamic shape of the fender was optimized to reduce aerodynamic noise. Comparative analysis was then employed to assess flow field characteristics of the optimized model against the original model and elucidate the fender configuration’s contribution to aerodynamic noise reduction and its realization mechanism.

1. Introduction

Under high-speed driving conditions, aerodynamic noise gradually becomes the predominant noise source inside the vehicle when the speed reaches or exceeds 100 km/h [1,2]. Currently, considerable progress has been made in reducing engine noise, vibration noise, and tire–road noise [3,4]. Consequently, aerodynamic noise has proven to be an increasingly significant component of vehicle noise at high speeds, thus becoming a crucial factor affecting ride comfort. The wheel area stands out as one of the foremost sources of aerodynamic noise during vehicle operation [5]. As air flows over the vehicle’s surface, the presence of the fender induces airflow stagnation and separation, while the wheels provoke complex flow instability phenomena such as body-wind flow-induced vortices, resulting in turbulence and energy dissipation in the wheel region. The presence of the fender alters the flow field characteristics in the wheel region, consequently indirectly influencing the flow fields at the bottom and sides of the vehicle body.

Li [6] focused on enhancing the wind noise performance of a car’s side mirrors through optimization. This optimization encompassed adjustments to the minimum distance between the mirrors and the triangular trim cover, the angle between the mirrors and the front side windows, and the shell slots of the mirrors. The simulation results indicated a reduction of 2.12 dB in the overall sound pressure level of the optimized vehicle. Additionally, Lian et al. [7] directed their attention towards the development and optimization of the skeleton spoiler. They employed the IDDES turbulence model for non-stationary simulation, reaching the best noise reduction effect through the optimization of the spoiler’s shape.

Automobile surfaces exhibit intricate geometries, giving rise to a plethora of complex flow phenomena. Turbulent regions induced by flow separation are ubiquitous across the car’s surface area. These separation zones encompass the airflow around the car’s rear, roof, and cavity, leading to pronounced pressure fluctuations that result in aerodynamic noise [8]. Owing to the intricate airflow structure, multiple sources of aerodynamic noise are present at the vehicle’s underbody. Wind tunnel experiments and simulations have revealed that underbody wind noise accounts for nearly 50% of the cabin noise level in certain scenarios, particularly in the low-frequency range below 630 Hz. In this frequency range, the chassis region predominantly generates low-frequency noise, with a significant contribution from the wheel region [9,10,11].

Hence, to ensure a tranquil environment inside the vehicle at high speeds, mitigating wind noise at the body’s bottom is imperative. Chen et al. [12] delved into the locations and shapes of airflow separation regions, identifying prominent separation regions primarily in the A-pillar and mirror areas, with larger ones situated in the fender and wheel regions. These separation regions serve as notable sources of aerodynamic noise. Moreover, prior wind tunnel experiments have revealed a significant aerodynamic noise source near the front wheels. Ringwal et al. [13] conducted a comparative analysis of four scenarios involving stationary and rotating wheels, as well as open and closed wheels. Their findings underscored the front wheels’ substantial contribution to noise generation. Wang et al. [14] employed phase microphone arrays, acoustic surface microphones, and an artificial head in conjunction with tape sealing to conduct sound pressure level tests on a passenger car’s aerodynamic noise performance. They analyzed wind noise sources, exterior surface noise levels, and the effect of sealing on interior noise levels to identify the main noise sources. At a wind speed of 140 km/h, the primary aerodynamic noise sources reside at the front and rear wheel areas of the vehicle, along with the rearview mirrors, with the predominant noise energy focused on the low- and mid-frequency ranges.

In automotive fender shape optimization, achieving the parameterization of numerous free-form surfaces is exceedingly challenging, and the process of recasting and remeshing them is both time-consuming and costly. To tackle these challenges, Sederberg et al. [15] introduced a mesh deformation-based free-form deformation (FFD) method, which involves placing control lattice points around the object to facilitate parameterization and economize on the costs associated with recasting and remeshing. Wang et al. [16] applied the free-form deformation method to a simplified prototype car, focusing on optimizing the entire vehicle, particularly the sedan’s front end and the rear’s lower section. Conversely, Castilla et al. [17] utilized the DrivAer automobile model as their research subject, employing the FFD method to alter the rear geometry of the model to decrease the vehicle’s drag coefficient. Through vehicle shape optimization, optimal aerodynamic characteristics can be achieved. To handle a multitude of geometric constraints, Wang et al. [18] proposed an effective approach for managing such constraints within the framework of surrogate-based optimization. They utilized a free-form deformation method for drag minimization and applied it to CRM wings, significantly improving the efficiency of aerodynamic shape optimization.

When confronting complex optimization problems, individually observing each entity within the entire ensemble is infeasible due to objective constraints. Hence, leveraging sample data to infer overall characteristics becomes imperative, necessitating the application of the design of experiments (DOE) method to select a representative sample set. Roshanian et al. [19] employed the Latin hypercube sampling (LHS) method for simulation runs, selecting sample values used to calculate constraints and reliability at each design point. In the actual optimization process, most relationships between input variables and outputs are uncertain and challenging to express analytically. Therefore, approximate modeling methods can be employed to establish explicit functional relationships between factors and outputs, facilitating quantitative analysis of these input–output relationships and enhancing optimization and design efficiency. Krzysztof et al. [20] conducted shape optimization of a car body during the early stages of automotive styling development using a parallel asynchronous surrogate modeling approach. By harnessing surrogate modeling approximation and asynchronous, parallel processing threads, they swiftly reduced the objective function value and substantially diminished processing time.

In this study, the CAERI Aero model developed by the China Automotive Engineering Research Institute was utilized to establish the computational domain and simulation analysis. We verified the accuracy of the modeling method by comparing the results with wind tunnel test data. To address the impact of the fender on the wheel region and the overall aerodynamic characteristics of the vehicle, as well as flow instability, we employed the free-form deformation technique to optimize the fender’s configuration parameters with the goal of reducing aerodynamic noise. Initially, we defined the region and range of design variables and devised an experimental program. Subsequently, we conducted simulation calculations founded on the experimental program and constructed an approximate model of the sound pressure level noise signal using of simulation results, checking out accuracy. Upon meeting the accuracy criteria, we employed an intelligent algorithm for optimization to obtain the optimal aerodynamic noise reduction scheme.

2. Simulation Methods

2.1. CFD Simulation Method

To investigate the flow characteristics of the fender region, this paper utilizes the CAERI Aero model from the China Automotive Engineering Research Institute. This model not only facilitates the optimization of aerodynamic design for traditional automobile standard models but also enables wind tunnel experiment alignment and calibration. In this study, a 1:1 scale model of the entire car was chosen as the research subject, with its dimensions of length, width, and height shown in Figure 1.

To ensure calculation accuracy and avoid impacting the flow characteristics around the vehicle, appropriate dimensions for the calculation domain were established. As depicted in Figure 2, the computational domain dimensions were set as follows: the front end length from the inlet is three times the vehicle length, the rear end length from the outlet is seven times the vehicle length, the width of the computational domain is eight times the vehicle width, and the height of the computational domain is five times the vehicle height. This configuration ensures that the blockage ratio of the computational domain is below 5%, meeting computational requirements [21].

The computational domain setup includes a velocity inlet and pressure outlet. The velocity inlet is configured to 120 km/h, consistent with the experimental wind speed, while the pressure outlet is set to 0 Pa. When the wheels are placed in the whole vehicle to be studied, the state of wheel motion is not the biggest factor affecting the aerodynamic characteristics of the wheel region [22]. The presence of the fender leads to airflow stagnation and separation, which affects the flow field characteristics in the wheel region and then indirectly affects the flow fields at the bottom and sides of the body [23]. Therefore, in the process of studying the fender configuration, the influence of the wheel moving state is not considered for the time being, and the wheel and the ground are set to be stationary. The upper top surface and sides serve as stationary slip walls, the ground surface acts as a fixed no-slip wall, and the body model surface is also designated as a fixed no-slip wall.

The aerodynamic drag coefficients of the whole vehicle are calculated using three different mesh schemes, and the results are shown in

Table 1. Calculation of domain mesh size.

Mesh	Body	Fender	Computational Domain	Cd
Coarse	15~30 mm	5~15 mm	30~200 mm	0.312
Medium	10~15 mm	1~5 mm	15~200 mm	0.245
Fine	5~10 mm	1~4 mm	10~200 mm	0.235

and Figure 3. With the increase in the number of iterations, the drag coefficients gradually converge, the medium mesh and the fine mesh are more effective, and the drag coefficients of the two are closer to each other. In order to ensure the calculation accuracy under the limited computing resources, the medium mesh is chosen as the basis for the subsequent meshing.

Medium mesh size is selected for simulation calculations. The meshing is performed in the computational domain, and the body mesh is generated using a cut body mesh with encrypted regions to improve the simulation accuracy in the complex flow region. As shown in Figure 4, in order to better capture the flow field characteristics near the surface of the body structure and to avoid abrupt changes in the mesh quality between different regions, mesh encryption zones are used, with different cell sizes set for different regions. Since at the vehicle surface, there is a near-wall boundary, where a large amount of drag is produced by air friction, in order to accurately characterize the effects at the body surface, prismatic layers were created to set up and control, as shown in Figure 5.

To validate the numerical method’s accuracy, wind tunnel experiments were conducted on the actual vehicle model at the China Automotive Technology Research Center, operating at a speed of 120 km/h. The aerodynamic drag of the test vehicle was measured using a wind tunnel aerodynamic sextuple balance output, and the aerodynamic drag coefficient was subsequently calculated. The wind tunnel experiment results are depicted in Figure 6. Comparing these experimental findings with the simulation results presented in

Table 2. Verification of simulation results.

Parameters	Projection Area/m2	Cd
Wind tunnel experiments	2.173	0.250
Numerical simulation	2.168	0.245
Errors/%	0.23	2.00

, the errors of the orthographic projected area and the drag coefficient fall within 3%.

Furthermore, a comparison between the numerical simulation and wind tunnel experimental results is conducted based on the measurement point pressure locations and numerical results outlined in the literature [24]. Figure 7a illustrates the distribution of the locations of the tail pressure measurement points, while Figure 7b shows the distribution of the pressure values at the tail simulation and experimental measurement points. As depicted in the figures, the pressure values at the measurement points are generally consistent, with fluctuations observed only at the edge of the rear glass at monitoring point 6. This observation serves to validate the reliability of the numerical simulation method employed in this study.

2.2. Aerodynamic Noise Analysis

Lighthill’s Equation (1) stands as one of the most fundamental equations in fluid acoustics research [25]. It delineates the correlation between acoustic wave propagation within a fluid and the parameters of the flow field. This equation holds pivotal importance in comprehending fluid acoustics and serves as a foundation for investigating phenomena such as fluid noise induced by solid boundaries and moving objects.

$$\frac{{\partial }^2{\rho }^{\prime }}{\partial t^2}-c_0^2{\nabla }^2{\rho }^{\prime }=\frac{{\partial }^2{T}_{ij}}{\partial x_i\partial x_j}$$

(1)

$$T_{ij}=\rho u_i{u}_i+(p-p_0){\delta }_{ij}-c_0^2(\rho -{\rho }_0){\delta }_{ij}$$

(2)

Here, $T_{ij}$ represents the Lighthill tensor, $(p-p_0)$ denotes the pressure pulsation in the flow field, $(\rho -{\rho }_0)$ signifies the fluctuation in fluid density, ${\delta }_{ij}$ stands for the unit tensor, and $c_0$ represents the speed of sound.

In vehicle noise computation, the direct assessment of aerodynamic noise is commonly known as the computational aeroacoustics approach (CAA) or direct noise computation [26]. In this method, the sound pressure pulsations are fully transient throughout the process of solving for the flow field. Both the sound source and the sound receiver reside within the computational domain, and by defining monitoring points, all acoustic information can be directly extracted from the computational fluid dynamics (CFD) results. The formula for computing the sound pressure level is depicted in Equation (3).

$$L_P=20\log \frac{P}{P_0}$$

(3)

Here, $L_P$ represents the sound pressure level, $P$ denotes the sound pressure, and $P_0$ signifies the reference sound pressure in air, where $P_0=2\times {10}^{-5}Pa$.

Considering the high cost of the direct calculation of aerodynamic noise in the external flow field of a car, this paper adopts a combination of steady-state and transient calculations. Firstly, the SST $k-\omega$ turbulence model is employed for the steady-state solution, and the calculation is iterated until the residual convergence demand is satisfied. Then, the steady-state calculation result file is used as the initial flow field for the unsteady-state calculation. In the unsteady-state calculation, the coupled pressure and velocity fields are used and the turbulence model is the LES model to calculate the aerodynamic noise. The discrete format is a second-order windward format with a time step of 1.25 × 10⁻⁴ s and five iterations in each unit time step. The total time for transient computation is 0.4 s. Two noise monitoring point regions are divided in the model; as shown in Figure 8, region I is the rearview mirror wake zone monitoring point, with the monitoring point number from 1 to 9, and region II is the wheel zone monitoring point, with the monitoring point number from 10 to 18.

The sound pressure level information of the monitoring points within the range of 0–4000 Hz is extracted, and the specific results are shown in Figure 9. In Figure 9, (a) illustrates the distribution of aerodynamic noise sound pressure levels at monitoring points 1~9 in the rearview mirror wake stream area, while (b) demonstrates the aerodynamic noise sound pressure level distribution at monitoring points 10~18 in the wheel area. The sound pressure level characteristics are observed in the frequency ranges of 500–2000 Hz, 500–4000 Hz, and 0–4000 Hz. Moreover, the evaluation of aerodynamic noise in reference [14] primarily focused on the rearview mirror wake region. In summary, monitoring point 5 and monitoring point 14, both located at the center, are selected as the evaluation indexes for aerodynamic noise in the subsequent collaborative optimization.

3. Optimization Methods

3.1. Optimization of Fender Configuration Based on FFD Method

Figure 10 depicts the flowchart detailing the optimization process for reducing aerodynamic noise in the automotive fender configuration. The optimization procedure for the fender configuration comprises five key steps. Firstly, the experimental design involves parameterizing the fender configuration to determine the variable range of control lattice points and employing the optimal Latin hypercube sampling method to generate the experimental scheme. Next, free-form deformation utilizes the experimental scheme to optimize the fender configuration using the free-form deformation method, resulting in the corresponding scheme model. Subsequently, the computational fluid dynamics (CFD) simulation of the car is conducted. This involves fluid simulation based on the scheme model, with steady-state calculation performed until convergence, followed by transient calculation based on the steady-state calculation to obtain noise information in the flow field. Following this, an approximate model is established using existing simulation results to construct a mathematical model approximating the relationship between input and response, enhancing computational efficiency by predicting the response value of unknown points. The accuracy of the approximate model is then verified. Finally, global optimization is pursued. Leveraging the mathematical model from the approximate model, the optimization algorithm is adopted to find the optimal solution iteratively. Variable values and predicted values of the optimal solution are obtained, and CFD calculations are performed based on the parameters of the optimal solution to obtain simulation value data. The error between the predicted value and the simulation value is compared to verify the accuracy of the method.

3.2. Parameterized Scheme for Fender Configuration

The optimization focus is chosen to be the wheel region of the fender due to its deflection effect, with the objective of optimizing aerodynamic performance by minimizing the aerodynamic noise of the CAERI Aero car model. This paper selects five control lattice point positions to define the fender’s shape parameters. Position 1 represents the front fender’s height from the ground, position 2 signifies the fender’s transverse width, position 3 indicates the fender’s height from the ground, position 4 denotes the longitudinal length of the front fender, and position 5 represents the longitudinal length of the fender. A configuration of 7 × 4 × 5 free-form deformation control lattice points is established, with the specific control body illustrated in Figure 11 below.

To achieve maximum deformation in the fender wheel area while maintaining an aesthetically pleasing body, this study selected five control lattice point positions within the variation range outlined in

Table 3. The range and direction of lattice point variations.

	Lower/m	Upper/m
1. The height of the front fender from the ground (FZ)32.33.182.184(z)	−0.35	0.35
2. The transverse width of the fender (WFY)69.92.96.102(y)	−0.15	0.15
3. The height of the fender from the ground (WFZ)74.158.75.160(z)	−0.05	0.05
4. The longitudinal length of the front fender (FX)92.90.141.142(x)	−0.1	0.1
5. The longitudinal length of the fender (WFX)80.164(x)	−0.05	0.05

.

3.3. Design of Experiments

Experimental design involves pre-defining experimental factors, research methods, and experimental procedures based on research objectives before conducting an experiment [27]. It is a method that considers the simultaneous effects of multiple input factors on the output. Reasonable sampling is a crucial step in addressing complex optimization problems.

According to

Table 4. Program sample points and their aerodynamic noise sound pressure levels.

No.	FZ/m	WFY/m	WFZ/m	FX/m	WFX/m	Sound Pressure Level/dB
						Point 5	Point 14
1	−0.018	0.134	−0.008	0.026	−0.05	99.87	105.07
2	−0.092	−0.103	0.029	−0.1	0.008	103.46	102.77
3	−0.276	0.087	−0.034	0.058	0.013	103.46	102.93
4	−0.239	−0.134	0.018	0.047	0.024	99.15	104.16
5	0.239	−0.055	0.045	0.005	0.034	96.83	100.7
6	−0.350	−0.024	0.002	−0.026	−0.034	97.35	100.87
7	0.350	0.008	0.008	0.079	−0.024	99.09	103.67
8	−0.055	−0.071	−0.040	0.068	−0.029	96.44	104.04
9	0.129	0.150	0.013	0.037	0.029	94.73	105.07
10	0.276	−0.150	−0.018	−0.016	0.002	109.68	105.87
11	−0.203	−0.087	−0.045	−0.047	0.018	101.54	105.32
12	−0.166	0.039	0.034	0.100	−0.013	98.64	104.22
13	−0.129	0.118	−0.029	−0.089	−0.008	97.41	102.24
14	−0.313	0.055	0.024	−0.037	0.040	97.53	101.35
15	0.166	0.024	−0.013	−0.068	0.050	98.32	104.7
16	0.203	−0.008	−0.003	−0.079	−0.045	124.07	104.35
17	0.092	−0.039	−0.024	0.089	0.045	97.75	105.19
18	0.018	0.103	0.050	−0.058	−0.018	96.28	102.9

, to control the variable range of lattice points, the optimal Latin hypercube sampling method was employed to obtain experimental data, which were then calculated using CFD simulation. The sound pressure level data at 5 monitoring points in the center of the window and 14 monitoring points in the center of the wheel area of the fender were taken as the target values. The detailed experimental scheme and corresponding aerodynamic noise values are presented in Table 4 below:

To investigate the impact of design variables on aerodynamic noise, a variance test was conducted to assess the functional relationship. The bar chart in Figure 12 illustrates the contribution of all terms in the quadratic polynomial to the response, encompassing single variables and quadratics with interaction terms, where the blue and red colors denote positive and negative effects, respectively.

In Figure 12a, monitoring point 5 is most affected by the interaction of fender clearance height (WFY) and front fender clearance height (FZ), contributing approximately 17.1%. Since FZ-WFZ, FX^2, WFZ^2, and FX^2 accounted for a larger proportion of the noise sound pressure level, which was 17.1%, 9.7%, and 9.1%, respectively, the interaction effect dominated the nonlinear effect of the interaction effect with a single design variable on the noise sound pressure level, and the factors that accounted for a proportion of more than 5% were all interaction terms with quadratic terms, indicating that the variables had a nonlinear relationship with the sound pressure level at monitoring point 5. In Figure 12b, monitoring point 14 is most affected by the square of the longitudinal length of the front fender (WFX), which contributes about 15.6%. Since WFX^2, FZ^2, WFZ^2, WFY^2, and FX^2 accounted for a larger proportion of the noise sound pressure level, which was 15.6%, 15.2%, 13.8%, 13.2%, and 11.9%, respectively, the nonlinear influence of a single design variable on the noise sound pressure level was dominant; the factors accounting for a proportion of more than 10% were all quadratic terms, indicating that the variables that had a nonlinear effect on the sound pressure level at monitoring point 14 are all nonlinear relationships, and the wheels are more sensitive to the variables. In Figure 12a, the blue color is dominant, and the sound pressure level at monitoring point 5 is mostly positively affected by the parameters of the fender; in Figure 12b, the red color is dominant, and the sound pressure level at monitoring point 14 is mostly negatively affected by the parameters of the fender.

3.4. Construction Approximate Models

An approximate model is a mathematical model constructed through interpolation or fitting based on limited experimental data to approximate the relationship between input and response in a real-world problem [28]. This enables the prediction of the response value at an unknown point. Compared to time-consuming finite element simulation models, approximate models offer explicit functional relationships. Consequently, leveraging approximate models in the optimization process can substantially reduce the complexity and computational time of optimization iterations, thereby enhancing computational efficiency. The mathematical relationship between the design variables and the target response in the approximate model is typically described using Equation (4).

$$y(x)=\tilde{y}(x)+\epsilon$$

(4)

where, $y(x)$, $\tilde{y}(x)$ are the true value and approximate value of the target response, $\epsilon$is the difference between the two, and $\epsilon ~N(0,{\sigma }^2)$.

The RBF neural network model comprises three layers of network structure: the input layer, the intermediate layer (hidden layer), and the output layer. Capable of solving nonlinear functions, the RBF model offers a straightforward computational process and features fast learning and efficient processing. Notably, Yao et al. [29] demonstrated that the RBF model significantly enhances the optimization efficiency of high-speed train heads, thereby shortening processing time, rendering it applicable for the aerodynamic optimization design of complex geometries. When constructing the approximate model, it is typical to divide the simulation data into training and test sets in an 8:2 ratio for model training and evaluation, respectively. Subsequently, the accuracy of the constructed model must be assessed, with the coefficient of determination ($R^2$) being one of the commonly used indices for evaluating prediction accuracy.

$$R^2=\frac{{\displaystyle \sum _{i=1}^N{\left(y_i-\overline{y}\right)}^2}}{{\displaystyle \sum _{i=1}^N{\left({\widehat{y}}_i-\overline{y}\right)}^2}}$$

(5)

In Equation (6), $y_i$ is the actual response value of the $i$th test point, ${\widehat{y}}_i$ is the response prediction value of the $i$th test point, $N$ is the number of test points in the test set, and $\overline{y}$ is the average of the actual response values of all test points.

In performing the compound correlation coefficient calculations, the accuracy of the approximate model is confirmed when the compound correlation coefficient is above 0.9.

$$\overline{y}=\frac{{\displaystyle \sum _{i=1}^N{y}_i}}{N}$$

(6)

In this paper, the RBF is utilized to establish the approximation model, and the test data generated by the optimal Latin hypercube test scheme are employed to verify the accuracy of the approximation model through the results of CFD simulation calculations, as depicted in Figure 13. The complex correlation coefficient of the aerodynamic noise at monitoring point 5 is 0.9801, and that of aerodynamic noise at monitoring point 14 is 0.9908. The simulated values and predicted values of the aerodynamic noise at monitoring points 5 and 14 are well fitted, indicating that the chosen approximation model exhibits high prediction accuracy and meets the requirements.

4. Results and Analysis

In order to obtain the optimal combination of design variables, an optimization algorithm was used to perform a global search of the RBF approximation model to arrive at the best solution for the aerodynamic noise SPLs at monitoring points 5 and 14. The optimal solution is then utilized to derive the optimal values for each parameter, which are used to generate the optimization scheme. Subsequent CFD calculations are conducted to obtain the data presented in

Table 5. Schemes and results of global optimization seeking.

No.	FZ/m	WFY/m	WFZ/m	FX/m	WFX/m	Sound Pressure Level/dB
						Point 5	Point 14
Original	0	0	0	0	0	98.57	104.82
Opti	−0.350	−0.031	0.003	−0.031	−0.035	94.85	102.01
Opti CFD	−0.350	−0.031	0.003	−0.031	−0.035	96.12	103.45
Errors/%	-	-	-	-	-	1.34	1.41

. In the optimized solution generated by the optimization algorithm and the optimized solution calculated by CFD, the errors of the sound pressure levels at aerodynamic noise monitoring points 5 and 14 are less than 2.0%, indicating accurate and acceptable results.

Figure 14 illustrates the comparison of the wheel area of the car before and after optimization. In the figure, gray represents the original model, while blue represents the optimized model (wheels remain unaffected by the deformation). Specifically, the front fender height off the ground at position 1 moves downward, the transverse width of the front fender plate at position 2 moves inward, the height of the front fender plate off the ground at position 3 moves upward, the longitudinal length of the front fender plate at position 4 moves forward, and the longitudinal length of the front fender plate at position 5 also moves forward.

4.1. SPL Characteristics

The time-domain pressure signal is Fourier transformed to obtain the frequency-domain signal. The computational aeroacoustics (CAA) method was utilized to convert the pulsating pressure signal into the sound pressure level signal. Figure 15 displays the aerodynamic noise sound pressure levels at frequencies for the nine monitoring points in the rearview mirror wake region. Comparing the aerodynamic noise simulation results, in the rearview mirror wake region, the original model and the optimized model essentially exhibit similar characteristics in the frequency range from 0 to 500 Hz. However, as the frequency increases, the optimized model’s rearview mirror wake generates a slightly lower sound pressure level than the original model’s rearview mirror near the frequency of 2000 Hz.

Figure 16 illustrates the aerodynamic noise sound pressure levels at the nine monitoring points in the front wheel center cross-section region across different frequencies. In the front wheel center cross-section region, within the frequency range of 0 to 500 Hz, both the original and optimized models exhibit similar characteristics. However, as the frequency increases, particularly in the range of 500 to 1500 Hz, notably around 1200 Hz, the optimized model demonstrates a more pronounced reduction in sound pressure levels near the wheels compared to the original model.

4.2. Velocity Vector Analysis

In order to analyze the variability of the flow field properties before and after the wing optimization, six cross sections were divided in the rearview mirror region and wheel region of the car. The specific cross-section locations are shown in Figure 17a. Figure 17b,c illustrates the velocity vector plot in the X = 1 m rearview mirror region. Attributed to the hindering effect of the rearview mirror, a symmetric vortex region appears in the rearview mirror wake region, which serves as one of the sources of aerodynamic noise. Compared with the original model, the optimized model shows a decrease in the value of the velocity vector, and this means that the air flow is in a relatively stable state. And the vortex in the optimized model near the side window region is improved. Thus, this will help to reduce the aerodynamic noise.

Figure 18 illustrates the velocity vector diagram of the rearview mirror region at Y = 0.9 m. The velocity vector distribution in the Y-direction cross section of the rearview mirror wake region reveals that the airflow passing through the mirror region is impeded by the obstructive effect of the mirror, resulting in the airflow being split into upper and lower flow separation regions, with vortices forming behind the rearview mirror. This pressure differential between the front and back contributes to the generation of aerodynamic noise. Upon comparing the wake velocity fields of the two mirrors in the Y direction, the optimized model exhibits a reduced value of the mirrors’ velocity vector field, resulting in a significant reduction in aerodynamic noise.

Figure 19 depicts the velocity vector diagram of the rearview mirror region at Z = 0.7 m. Observing the velocity vector distribution of the Z-direction cross section in the rearview mirror wake region, the hindering effect of the A-pillar causes airflow separation when passing through the automobile indentation. A portion of the airflow traverses the surface of the rearview mirror, while another portion passes through the area between the rearview mirror and the side window, where airflow velocity increases, and a pair of vortices with opposite directions of motion forms in the rearview mirror wake region. Consequently, significant aerodynamic noise is generated in the side window area. Comparing the airflow velocities between the mirrors and the side windows reveals that the new mirrors have smaller values for the velocity vector field, resulting in lower aerodynamic noise. Furthermore, compared to the wake flow of the original model mirrors, the wake flow of the optimized model mirrors exhibits two pronounced vortex divisions at the corresponding locations, reducing the interaction effect and further mitigating aerodynamic noise.

Figure 20 illustrates the velocity vector plot for the X = 0 m wheel region, depicting the distribution of velocity vectors in the X-direction cross section of the wheel region of the contrasting fender. The optimized model reveals a new vortex structure at the center of the body attributed to the downward movement of the front fender height above the ground. A comparison of airflow velocities at the X-direction cross section of the wheel indicates smaller values of the velocity vector field at the new wheel cross section, resulting in lower aerodynamic noise levels.

Figure 21 illustrates the velocity vector plot for the wheel region of Y = 0.76 m. From the figure, the velocity vector distribution in the Y-direction cross section of the wheel region of the contrasting fender is observed. The optimized model enhances the flow distribution in the wheel cavity due to the upward movement of the fender height above the ground, while the optimized longitudinal length of the fender moves forward, resulting in a reduced gap between the wheel and the wheel cavity. In the optimized model, the velocity flow between the ground and the car is smoother, and the velocity gradient of the streamlines is reduced. Consequently, the level of aerodynamic noise is reduced at the Y-direction cross section of the wheel region. Comparing the airflow velocity at the Y-direction cross section of the wheel, the value of the velocity vector field at the optimized wheel cross section is smaller, resulting in a corresponding reduction in the value of the aerodynamic noise.

Figure 22 illustrates the velocity vector plot for the Z = 0 m wheel region, comparing the velocity vector distributions in the Z-direction cross section of the fender plate wheel region. As the transverse width of the front fender plate is shifted inward, the optimized model exhibits a smoother flow at the inlet in the wheel region in front of the axle when gas flows through. The complex flow structure observed in the original model is no longer present. In the wheel cavity region, the original model shows two vortex phenomena at the top and bottom of the wheel cavity, whereas in the optimized model, the flow is no longer separated, and the two vortex structures are effectively suppressed.

To visually examine the flow field characteristics before and after fender optimization, Figure 23 presents 3D flow diagrams of the body surfaces of the original model and the optimized model. The speed streamlines are color-coded based on the X-direction speed, while the body surfaces are pressure colored. Fender configuration optimization reduces the airflow’s impact on the side of the flow, thereby improving interference with the wheel cavity surface. Additionally, airflow at the front of the body moves more backward along the bottom, resulting in a more concentrated and smoother airflow compared to the original model. This helps reduce vortex structure due to complex flow. Moreover, compared to the velocity vector plot of the wheel region at the Y = 0.76 m section in Figure 21, the airflow between the ground and the car is smoother, and the velocity gradient of the flow line is reduced. Overall, the optimized fender achieves aerodynamic noise reduction for the entire vehicle by enhancing flow field distribution in the wheel cavity region.

5. Conclusions

In this study, the car model developed by the CAERI was utilized, with a focus on optimizing the fender region to achieve the optimal aerodynamic shape using the free-form deformation technique.

(1) Initially, five positions of control lattice points were chosen to define the shape parameters of the region. An experimental design was employed to establish the experimental program, and the relationship between the response and the output of these five positions was determined through main effect plots and Pareto charts. It was found that FZ-WFZ, FX^2, WFZ^2, and FX^2 contributed significantly to aerodynamic noise at the monitoring points, with proportions of 17.1%, 12.9%, 9.7%, and 9.5%, respectively. Similarly, at the 14 monitoring points, WFX^2, FZ^2, WFZ^2, WFY^2, and FX^2 accounted for larger proportions of the noise sound pressure level, ranging from 11.9% to 15.6%, indicating the dominance of the nonlinear effect of a single design variable on the drag coefficient, particularly in the wheel area.

(2) Subsequently, the prediction of response values was conducted using the RBF, and model accuracy was evaluated based on the complex correlation coefficient. The fitting results of the simulated and predicted values of aerodynamic noise yielded a coefficient of 0.96, indicating a good fit. The approximate model results were utilized for global optimization, resulting in a 2.5% reduction in the sound pressure level of aerodynamic noise at monitoring point 5 and a 1.3% reduction at monitoring point 14 compared to the original model. Errors between predicted and simulated values were less than 2.0%, indicating accurate and acceptable results.

(3) Finally, a comparison and analysis of the differences in aerodynamic noise between the original and optimized models were conducted, focusing on the rearview mirror wake region and wheel region. Analysis was performed using three-dimensional cross-section velocity vector maps, body surface eddy current vector maps, and noise monitoring point data. Changes in the fender configuration resulted in fewer alterations in flow phenomena in the rearview mirror region, with optimized vector velocity values and slight enhancement in the frequency characteristics of noise sound pressure levels around the 2000 Hz range. Conversely, the flow phenomena in the wheel region improved significantly, with optimized vector velocity values and notable enhancement in the frequency characteristics of noise sound pressure levels around the 1200 Hz range.