A quadrupole correction model to suppress spurious sound with moving permeable integral surfaces
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摘要: Ffowcs Williams-Hawkings（FW–H）方程是Lighthill声比拟方程在运动边界问题中的推广，但在FW–H方程中使用运动可渗透积分面时，常因涡结构穿过可渗透积分面引起虚假噪声。本文利用可渗透积分面上Lighthill应力张量的通量估计涡结构对远场噪声的贡献，并消去其所导致的虚假噪声。在频域Lighthill应力张量通量四极子修正模型基础上，本文考虑了运动积分面对四极子修正模型的影响，提出了适用于运动可渗透积分面的四极子修正模型。该模型基于冻结流假设与格林函数的远场近似特性，通过求解关于四极子体积分项的代数方程，在被积函数中包含了运动积分面的速度。圆柱绕流和对流涡远场噪声预测验证了本文所提出修正模型的有效性。Abstract: Ffowcs Williams–Hawkings (FW–H) equation is the extension of the Lighthill’s acoustic analogy equation for sound prediction with moving boundaries. However, the spurious sound often arises from vortex structures crossing through permeable FW–H surfaces. This work aims to approximate the contribution of the vortex structures to far-field sound using the Lighthill stress tensor flux and subtract the resulting spurious sound. Based on the frequency-domain Lighthill stress tensor quadrupole correction model, a quadrupole correction model is proposed to account for the effect of a moving integral surface on the spurious sound. Based on the frozen flow assumption and far-field approximation of the FW–H equation’s Green’s function, the proposed model incorporates the FW–H surface’s velocity into the integrand of the quadru-pole correction model by solving an algebraic equation of the quadrupole volume integral term. The proposed model is validated by the far-field sound prediction of flows over a circular cylinder and a convecting vortex.
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图 1 二维圆柱绕流涡量分布云图和FW–H积分面位置示意图
Figure 1. Diagram of vorticity distribution of flows around a circular cylinder and the location of the FW–H integration surface
图 2 不同出口面修正前后的远场噪声计算结果对比
Figure 2. Comparison of far-field sound predicted by using formulations with and without quadrupole correction model
图 3 二维对流涡压力分布及坐标系定义示意图
Figure 3. Diagram of the pressure distribution of a convecting vortex
图 4 二维对流涡算例FW–H积分面位置及运动示意图
Figure 4. Diagram of position and motion of the FW–H surface
图 5 来流马赫数0.1的对流涡算例中，四极子项相反数与单极子项、偶极子项之和的对比
Figure 5. Comparison between the negative quadrupole correction model and the summary of the monopole and dipole terms at the freestream Mach number 0.1
图 6 来流马赫数0.3的对流涡算例中，四极子项相反数与单极子项、偶极子项之和的对比
Figure 6. Comparison between the negative quadrupole correction model and the summary of the monopole and dipole terms at the freestream Mach number 0.3
图 7 来流马赫数0.5的对流涡算例中，四极子项相反数与单极子项、偶极子项之和的对比
Figure 7. Comparison between the negative quadrupole correction model and the summary of the monopole and dipole terms at the freestream Mach number 0.5
图 8 来流马赫数0.3的对流涡算例中，四极子项相反数与单极子项、偶极子项之和的对比
Figure 8. Comparison between the negative quadrupole correction model and the summary of the monopole and dipole terms at the freestream Mach number 0.3
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