Numerical investigation on the characteristics of underbody aerodynamic noise sources in electric vehicles

As the wind noise caused by the upper body is gradually controlled, the influence of high-speed underbody airflow on the interior noise of electric vehicles becomes increasingly prominent. The method involves the combined application of the Finite Volume Method (FVM) and Finite Element Analysis (FEA) to compute the aerodynamic noise inside a real vehicle model induced by high-speed airflow. A numerical simulation of the underbody wind noise in electric vehicles has been conducted to reveal the noise sources at the bottom of electric vehicles and cabin noise. Finally, the impact of side skirts and wind deflectors on chassis wind noise was evaluated.


Introduction
With the advancement of NVH (noise, vibration, and harshness) technology, the noise generated by powertrains and road surface excitations has continuously reduced.As a result, wind noise has emerged as the primary source of in-cabin noise in electric vehicles during high-speed travel [1] .Unlike traditional internal combustion engine vehicles, electric vehicles undergo changes in powertrains, leading to an increased separation of underbody airflow.This results in pronounced pressure fluctuations near the passenger cabin floor, which is the main contributor to chassis wind noise [2][3][4][5] .Consequently, optimizing the underbody design of electric vehicles can effectively enhance the in-cabin noise quality.
In the early years, research on chassis wind noise relied mainly on experimental testing due to limitations in computational resources.For instance, Kang et al. analyzed the contributions of wind noise sources from various chassis locations to in-cabin noise using acoustic holography [6] .Li et al. employed techniques such as beamforming, microphone arrays, and "Noise Vision" to measure noise sources both outside and inside vehicles, revealing that in-cabin low-frequency noise primarily originates from underbody wind noise [7] .They found that both ground movement and wheel rotation increased in-cabin sound pressure levels by 5 dB(A), primarily in the low-frequency range [9] .
In recent years, with the advancement of computer technology, numerical simulations have gradually become the primary method for studying chassis wind noise.Li et al. used numerical simulations to discover that the intensity of underbody noise sources is closely related to airflow disturbances in the underbody [7] .During the same period, Crouse et al. utilized the lattice Boltzmann method to numerically calculate wind noise sources in the underbody area of high-speed vehicles, noting that pressure fluctuations in the underbody region primarily occurred near 200 Hz [10] .Yang et al. used statistical energy analysis to compute the acoustic response of underbody wind noise transmitted through the floor panel to the interior.The simulation results closely matched the wind tunnel test results within the frequency range of 63-500 Hz [8] .Yasuhiko et al. achieved a 2 dB noise reduction by installing an engine undertray [11] .Moath optimized automotive wind noise by adjusting the position of the rearview mirrors [12] .Wang et al. used finite element methods to study the contribution of underbody wind noise to in-cabin noise in passenger cars.They found that low-frequency noise below 250 Hz primarily originates from underbody wind noise [13] .
The aforementioned research indicates that numerical simulations can now provide valuable guidance for optimizing and improving chassis wind noise.However, there has been relatively limited research on resolving chassis wind noise through the optimization of underbody airflow.This article conducts a numerical simulation of the vehicle's overall external flow field and inner acoustic field to investigate the chassis wind noise of a specific vehicle model.Finally, the study analyzes the influence of side skirts and front wheel wind deflectors on the chassis wind noise of this electric vehicle.

Methodology
This section describes the methodologies employed for computing the external airflow around the car and the interior acoustic field of the vehicle.

The governing equations for the computation of the airflow
In a large eddy simulation (LES), a numerical simulation is conducted to model the transient external flow field of the car, resulting in the temporal evolution of parameters such as pressure and velocity.Large eddy simulation is a turbulence modeling technique situated between direct numerical simulation (DNS) and the Reynolds-averaged Navier-Stokes (RANS) method.The fundamental idea is summarized as follows: the N-S equations are directly solved for large-scale eddies in turbulent flow, while small-scale eddies are computed using approximate models.The controlled equations for N-S equations, filtered in time and space, are as follows [14] : ( ) ( ) in the equation, ij τ is defined as the subgrid-scale stress (SGS):

Governing equations for wind noise simulations
The Ffowcs Williams-Hawkings (FW-H) equation is derived by Ffowcs Williams and Hawkings as an extension of the Curle equation [14] : in the equation,  = ( −  ) represents the density perturbation, which characterizes the intensity of sound.The value of  is zero on solid wall surfaces, and it is equal to the Lighthill tensor outside the surface.The FW-H equation provides a physical representation of the relationships between monopole sound sources, dipole sound sources, and quadrupole sound sources and their corresponding interactions with turbulence, fluctuating forces, and volume displacement.Due to the relatively low vehicle travel speeds and low Mach numbers, the noise generated by quadrupole sound sources is significantly smaller than that produced by dipole sound sources, and it can be safely neglected [15] .Therefore, this article primarily focuses on the study of dipole sound source noise in the context of wind noise.

CFD model
This article is based on calculations conducted using a specific electric sedan.Figure 1   The simulation domain for the vehicle is shown in Figure 2. The blockage ratio is less than 5%, meeting the needed criteria.To ensure the accuracy of the external flow field simulation, particular attention has been given to grid refinement in the chassis, wheel area, and grille region.The minimum grid cell size is 4 mm.Using hexahedral grids, the final grid count is approximately 53 million.The numerical simulation grid is depicted in Figure 3.The simulation boundary conditions are consistent with wind tunnel testing.The inlet wind speed is 33.33 m/s with a 0 yaw angle.The nonsteady simulation duration is set to 0.5 seconds.

Comparison of simulation and test results
In the simulation model, pressure monitoring points are positioned at the same locations as in the wind tunnel experiments, as depicted in Figure 5.After the transient calculations, a comparison of the simulation and experimental pressure spectrum curves at each monitoring point is shown in Figure 6.In the figure, within the calculated frequency range, there is a good match between the simulation and experimental spectrum curves at each monitoring point.As indicated in Table 3, the error between the experimental and simulated sound pressure levels is within a range of 5%, meeting the requirements for engineering applications.This suggests that the flow field simulation results are sufficiently accurate and can be used for subsequent acoustic calculations.

Acousticr results analysis
By applying flow field excitations to the passenger cabin floor, the acoustic source distribution on the floor's surface is obtained, as shown in Figure 7. From the figure, it is evident that the acoustic source intensity on the floor panel's surface increases with frequency, initially strengthens, and then weakens.

The impact of aerodynamic accessories on chassis wind noise performance
To control the interior wind noise caused by high-speed underbody airflow, it is common to add wind deflectors and side skirts to streamline the underbody airflow and reduce flow separation.As shown in Figure 9, these are the computational models for interior wind noise behind the aerodynamic accessories.The results are shown in Figure 10.In the figure, "case 0," "case 1," and "case 2" represent the original model, the model with the addition of a wind deflector, and the model with the addition of side skirts, respectively.The pressure fluctuation analysis at the exterior monitoring points indicates (Figure 10) that with the addition of the wind deflector, there is a significant improvement in the fluctuating pressure level at monitoring point 2 in the low-frequency range, resulting in an overall decrease of 11 dB in the total fluctuating pressure level.The improvement in the fluctuating pressure level at monitoring point 1 is less pronounced.After adding the side skirts, the fluctuating pressure levels at monitoring points 1 and 2 show significant improvement across various frequency ranges.

Conclusion
In the context of the trend toward electrification in the automotive industry, wind noise originating from the bottom of vehicles has become a significant component of automotive wind noise.Using the CFD+FEM simulation method, an investigation was carried out regarding wind noise generated by the vehicle's chassis, and the conclusions are as follows.
(1) The simulation of the actual vehicle was conducted using the CFD+FEM method.The frequency spectrum curves at the exterior monitoring points closely align with the experimental data, with errors of 5.6% and 5.4% in the pressure pulsation, demonstrating the reliability of the flow field simulation results.
(2) The interior noise caused by high-speed underbody airflow initially increases with frequency and then decreases, primarily concentrating in the mid-to-low-frequency range of 100 to 300 Hz.
(3) The wind deflector can effectively reduce the aerodynamic noise source intensity in the wheel area, but the improvement is not significant for the battery pack area.Installing side skirts at the bottom of the vehicle can effectively reduce the pressure pulsation in the battery pack.
displays the vehicle model used for simulation.The model has been reasonably simplified by removing geometric structures that have minimal impact on the flow field.The interior components have been treated with surface encapsulation, and the air intake grille is in the fully open position.

Figure 1 .
Figure 1.CFD Model of the vehicle.

Figure 2 .
Figure 2. Schematic of the computational domain.

Figure 3 .
Figure 3. Meshing for the external airflow around a car.

Figure 4
represents a simplified model for the internal acoustic field calculations.It primarily includes the driver, seat, steering wheel, dashboard, and so on.

Figure 4 .
Figure 4. Interior acoustic mesh.The floor of the passenger cabin functions as the main conduit for chassis wind noise to infiltrate the

Figure 6 .
Figure 6.The Comparison of Pressure Spectrum Curves at Monitoring Points in the External Flow Field.(a) Point 1 (b) Point 2.

Figure 7 .
Figure 7. Passenger Cabin Floor Sound Pressure Level Distribution Contour Map (a)125 Hz (b)250 Hz (c)375 Hz (d)500 Hz (e)625 Hz (f)750 Hz (g)875 Hz (h)1000 Hz.As shown in Figure 8, the sound pressure level frequency spectra at various interior cavity monitoring points are presented.It can be observed from the figure that the in-cabin noise caused by the airflow underneath the vehicle primarily concentrates in the low-frequency range of 100-200 Hz.Multiple peaks are evident within the frequency range of 100-200 Hz.As the frequency surpasses 200 Hz, the flowinduced in-cabin noise significantly decreases.

Figure 8 .
Figure 8. SPL Frequency Spectrum at the Driver's Left Ear Monitoring Point.

Figure 9 .
Figure 9.The CFD Model of the Vehicle with Added Aerodynamic Accessories (a) Wind Deflector (b) Side Skirt.

Table 1 .
The characteristics of the materials are detailed in Table1.Material Properties.Due to the complexity of the internal materials in the actual vehicle model, it is challenging to define each material property individually.Therefore, mixed boundary conditions are defined using the impedance boundary method for the vehicle's interior acoustics, as indicated in Table2.

Table 3 .
Comparison between Pressure Pulsation Experiments and Simulations.