Extension of the FW-H equation for acoustic velocity prediction

ZHAO Dongxu; WANG Xuheng; SONG Yahui; LIU Qiuhong

doi:10.7638/kqdlxxb-2024.0089

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Extension of the FW-H equation for acoustic velocity prediction

更新时间：2026-05-28

- Extension of the FW-H equation for acoustic velocity prediction
- Vol. 43, Issue 7, Pages: 52-62(2025)
- 作者机构：
  
  西北工业大学飞行器基础布局全国重点实验室,西安,710072
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2024.0089
  CLC： V211.3
- Published：2025
- 稿件说明：
移动端阅览
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, 2025, 43(7): 52−62.

ZHAO Dongxu, WANG Xuheng, SONG Yahui, et al. Extension of the FW-H equation for acoustic velocity prediction[J]. 2025, 43(7): 52-62.
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, 2025, 43(7): 52−62. DOI： 10.7638/kqdlxxb-2024.0089

ZHAO Dongxu, WANG Xuheng, SONG Yahui, et al. Extension of the FW-H equation for acoustic velocity prediction[J]. 2025, 43(7): 52-62. DOI： 10.7638/kqdlxxb-2024.0089.

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，结果显示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，声学速度分量$ {u'_1} $的主峰值指向性符合典型四极子声压场特征，而分量$ {u'_2} $和$ {u'_3} $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 on 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

was proposed in this paper. The validity of FV3A-M was 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 was numerically obtained by DDES and the acoustic pressure extrapolated with the FW-H equation agreed well with the experimental data. In the observation plane

the directivity of the streamwise component of acoustic velocity at the primary frequency resembled the characteristics of typical quadrupole acoustic pressure fields

whereas the distributions of the remaining two components exhibited 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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references

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