CHARACTERISTICS OF WALL PRESSURE FLUCTUATIONS FOR A BOUNDARY LAYER AFFECTED BY FLOW OVER AN IDEAL SIDE MIRROR
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摘要: 钝体绕流引起的壁面压力脉动是气动/振动噪声的主要激励源. 钝体绕流引起的流动较为复杂, 无法直接采用基于平板边界层的模型直接模化壁面压力. 因此, 分析钝体绕流影响下的壁面压力在水下潜航器、汽车以及飞行器的自噪声和辐射噪声预测中具有重要意义. 文章以理想汽车后视镜绕流为例, 采用大涡模拟方法结合不同的亚格子湍流模型, 开展了后视镜下游壁面压力脉动时空性质的数值研究. 数值模拟中, 壁面压力相关统计量如压力系数和频率谱与文献中的数值和实验结果均相符. 藉由不同的相速度, 在时空能谱中分离了壁面压力脉动的3个特征流动: 对流、回流和声传播. 后视镜下游壁面压力脉动的空间谱, 相比于平板边界层, 出现等值线形状弯曲的现象. 通过基于泰勒冻结假设的统计分析, 得到了壁面压力脉动对流速度的空间分布. 根据对流速度, 壁面压力脉动在物理空间上可以分为: 回流区、稳定对流区和过渡区. 稳定对流区的壁面压力脉动的空间谱未出现弯曲现象, 而其空间关联半衰长度与频率倒数成正比, 表现出了经典平板边界层理论中的定量特性. 该工作表明, 钝体绕流使得边界层壁面压力传播方向发生偏转, 而壁面压力脉动在偏转后的稳定对流区依然保有平板边界层中的时空统计特性.Abstract: In low Mach number flows, wall pressure fluctuations induced by flows over a blunt body are the dominant source of aero- and vibroacoustic noise. Due to the complexity of flow patterns, their characteristics cannot be straightforwardly modeled with wall pressure models furnished by turbulent boundary layers (TBL). Therefore, studies on the flow over a blunt body and induced wall pressure play an essential role in predicting self- and radiated noises of underwater, automotive, and aerial vehicles. In this work, we employ large-eddy simulations (LES) with different sub-grid-scale (SGS) models to numerically investigate the flow over a generic side mirror of an automobile and space-time characteristics of the resulting wall pressure fluctuation. The statistical results from LES with both SGS models, including the pressure coefficient and frequency spectra, align well with published numerical and experimental results. In the spectral analysis, the downstream wall pressure fluctuation on the window is decomposed into three regimes in the wavenumber-frequency space via phase speed, including convection, recirculation, and acoustics. We observe that contours in the wavenumber spectrum of wall pressure in this work exhibit a bending effect compared to those in zero-pressure-gradient flat-plate TBLs. Based on the statistical analysis based on Taylor's hypothesis, we obtain the spatial distribution of the convection speed of wall pressure, which leads to three regions in physical space: recirculation, steady convection, and transition. The contours in the wavenumber spectra of wall pressure extracted from the steady convection region are free of bending effects. Moreover, the half-width of the spatial correlation function is proportional to the inverse of the corresponding frequency, which follows the attribute in the classical theory of TBL. This investigation indicates that the convection of wall pressure beneath a TBL deflects off the blunt body, while downstream wall pressure fluctuations in the steady-convection zone preserve the space-time characteristics of the TBL.
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Key words:
- blunt body /
- boundary layer /
- wall pressure /
- large-eddy simulation
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图 1 后视镜绕流几何配置: 理想汽车后视镜与平板 (单位: m)
Figure 1. Schematic diagram of the problem: a generic side mirror and a plate (unit: m)
图 3 后视镜绕流壁面压力脉动探测点: 后视镜表面(S1 ~ S8)和玻璃窗表面(S9 ~ S10)
Figure 3. Arrangement of pressure sensors: the side-mirror surface (S1 ~ S8) and the window surface (S9 ~ S10)
图 4 无量纲壁面压力脉动单边功率谱密度$\psi_{\rm{pp}}/(0.25\rho_\infty^2 U_\infty^3 D_{\rm{mr}})$. 实线为本文大涡模拟结果(WALE和SMA), 红色圆圈是实验结果[25], 三角和方块为文献中的数值结果[19-20]
Figure 4. Dimensionless PSD of wall pressure fluctuation $\psi_{\rm{pp}}/(0.25\rho_\infty^2 U_\infty^3 D_{\rm{mr}})$. Solid line (WALE and SMA in present work), red circles (experimental reference[25]), and triangles and squares (numerical reference[19-20])
图 5 大涡模拟时均流场流线(SMA模型): 蓝色为流经后视镜侧面的流线, 红色为流经后视镜顶部的流线
Figure 5. Streamlines of time-averaged flow fields in LES (SMA): blue are those passing around lateral sides, and red are those going over the top
图 7 玻璃窗口内无量纲壁面压力时空能谱(对流方向). 虚线对应的特征速度分别为: 红色($ \pm c_\infty+u_\infty $)、绿色($ u_\infty $)、紫色($ 0.3 u_\infty $)、黑色($ -0.15 u_\infty $)和蓝色($ -0.675 u_\infty $)
Figure 7. Wall pressure wavenumber-frequency spectrum $ \chi_C $. Phase speeds denoted by dashed lines are: red ($ \pm c_\infty+u_\infty $), green ($ u_\infty $), purple ($ 0.3 u_\infty $), black ($ -0.15 u_\infty $), and blue ($ -0.675 u_\infty $)
图 8 不同频率下玻璃窗口内无量纲压力波数谱: 频率范围$\omega_0/(2\text{π})\in[100,200,500]$ Hz (从左至右)
Figure 8. Dimensionless wavenumber spectra of wall pressure on the window at various frequencies: $\omega_0/(2\text{π})\in[100,200,500]$ Hz (from left to right)
图 9 玻璃窗口处的无量纲对流速度的流线分布和偏转角
Figure 9. Streamlines and the deflection angle of the convection speed on the window
图 10 稳定对流区内无量纲壁面压力脉动波数频率谱
Figure 10. Dimensionless wall pressure wavenumber-frequency spectrum in the steady-convection zone
图 11 不同频率下稳定对流区内无量纲化压力波数谱: 频率范围$\omega_0/(2\text{π})\in[100,200,500]$ Hz (从左至右)
Figure 11. Dimensionless wavenumber spectra of wall pressure in the steady-convection zone at various frequencies: $\omega_0/(2\text{π})\in[100,200,500]$ Hz (from left to right)
图 12 稳定对流区压力空间关联系数: 频率范围$\omega_0/(2\text{π})\in[100,200]$ Hz
Figure 12. Spatial correlation coefficients in the steady-convection zone: $\omega_0/(2\text{π})\in[100,200]$ Hz
图 13 空间关联半衰长度与频率倒数的线性拟合
Figure 13. Linear regression of the half-width of the spatial correlation and the inverse of the frequency
表 1 后视镜表面探测点坐标：S1 ~ S10 (坐标原点为后视镜底面前缘, 单位: m)
Table 1. Coordinates of pressure sensors: S1 ~ S10 (the origin of coordinate system rests in the front of the mirror's bottom, unit: m)
Coordinate S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 x 0.094 0 0.074 0 0.000 0 0.000 0 0.074 2 0.100 0 0.100 0 0.100 0 0.200 0 0.498 0 y 0.225 8 0.296 6 0.200 0 0.033 4 0.133 4 0.150 0 0.250 0 0.117 0 0.000 0 0.000 0 z −0.099 8 0.000 0 0.000 0 0.000 0 −0.096 6 −0.085 0 0.000 0 0.085 0 0.000 0 −0.142 0 
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表 2 后视镜表面探测点的时均压力系数：S1 ~ S7
Table 2. Time-averaged pressure coefficients at various locations on the side mirror: S1 ~ S7
Probes S1 S2 S3 S4 S5 S6 S7 experiment[25] −0.629 −0.725 0.886 0.991 −0.753 −0.507 −0.484 C-LES[20] −0.457 −0.592 0.879 0.991 −0.557 −0.498 −0.512 C-LES[21] −0.537 0.892 −0.925 −0.451 I-LES[19] −0.727 −0.898 0.898 0.1 −1.102 −0.477 −0.443 WALE (Eq.(7)) −0.718 −0.884 0.912 1.011 −1.105 −0.521 −0.496 SMA (Eq.(5)) −0.617 −0.911 0.920 1.023 −1.011 −0.556 −0.516
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