赵东旭, 王垿桁, 宋亚辉, 等. FW-H方程在声学速度预测中的拓展[J]. 空气动力学学报, 2021, 39(s): 1−11. DOI: 10.7638/kqdlxxb-2024.0089
引用本文: 赵东旭, 王垿桁, 宋亚辉, 等. FW-H方程在声学速度预测中的拓展[J]. 空气动力学学报, 2021, 39(s): 1−11. DOI: 10.7638/kqdlxxb-2024.0089
ZHAO D X, WANG X H, SONG Y H, et al. Extension of the FW-H equation for acoustic velocity prediction[J]. Acta Aerodynamica Sinica, 2021, 39(s): 1−11. DOI: 10.7638/kqdlxxb-2024.0089
Citation: ZHAO D X, WANG X H, SONG Y H, et al. Extension of the FW-H equation for acoustic velocity prediction[J]. Acta Aerodynamica Sinica, 2021, 39(s): 1−11. DOI: 10.7638/kqdlxxb-2024.0089

FW-H方程在声学速度预测中的拓展

Extension of the FW-H equation for acoustic velocity prediction

  • 摘要: 声学速度矢量在声场特征描述和流声模态分解方面具有独特优势。经典FW-H方程广泛应用于远场声压外推,但没有对声学速度3个分量的计算做出规定,因而不能直接用于远场声学速度预测。考虑均匀流中点源辐射声场,利用对流格林函数和线化动量方程建立了远场声学速度与声压的频域显式物理关联表达式,进而基于FW-H积分方程,提出了声学速度频域解析公式FV3A-M。利用均匀流中单极子和偶极子声辐射典型测试算例,证明了公式FV3A-M及其实施的有效性。通过数值方法评估了圆柱-翼型流动产生的噪声,并与实验数据进行比较。DDES方法的湍流模拟和FW-H方程的声压外推结果均与实验数据吻合。在观察平面内,声学速度 u'_1 分量的主峰值指向性形如典型四极子声压场特征,而 u'_2 和 u'_3 分量的分布则呈现偶极子声压场特性。依据公式FV3A-M预测远场声学速度仅是FW-H方程外推声压的积分过程副产品,有力地拓展了FW-H方程的应用场景。

     

    Abstract: Acoustic velocity vector offers unique advantages in characterizing the acoustic field and flow sound decomposition. However, despite its wide application in extrapolating the far-field acoustic pressure, the classical FW-H equation cannot be directly used to predict the far-field acoustic velocity. Based the acoustic radiation from a point source in uniform flows, we established an explicit physical correlation in the frequency domain between the far-field acoustic velocity and pressure, leveraging the convective Green's function and the linearized momentum equation. Consequently, a novel analytical formulation for acoustic velocity in the frequency domain, FV3A-M, is proposed in this paper. The validity of FV3A-M is demonstrated by its successful application to benchmark cases involving a monopole and a dipole radiating in a uniform flow. Furthermore, The noise generated by a low-Mach-number turbulent flow past the rod-airfoil configuration is numerically obtained by DDES and the acoustic pressure extrapolated with the FW-H equation agree well with the experimental data. In the observation plane, the directivity of the streamwise component of acoustic velocity at the primary frequency resembles the characteristics of typical quadrupole acoustic pressure fields, whereas the distributions of the remaining two components exhibit characteristics of dipole acoustic pressure fields. Notably, the prediction of far-field acoustic velocity through FV3A-M is only a by-product of the integration process of FW-H equation's acoustic pressure extrapolation, significantly broadening the application scenarios of the FW-H equation.

     

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