Investigation of Vortex Sound Propagation Using Spectral Element Method

doi:10.7652/xjtuxb201611017

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Investigation of Vortex Sound Propagation Using Spectral Element Method

更新时间：2025-07-09

- Investigation of Vortex Sound Propagation Using Spectral Element Method
- Vol. 50, Issue 11, Pages: 110-114+120(2016)
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201611017
  CLC： O121.8;G558
- Online First：10 November 2016，
  
  Published：2016
- 稿件说明：
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Investigation of Vortex Sound Propagation Using Spectral Element Method[J]. 2016, 50(11): 110-114+120.
DOI：

Investigation of Vortex Sound Propagation Using Spectral Element Method[J]. 2016, 50(11): 110-114+120. DOI： 10.7652/xjtuxb201611017.

摘要

为了满足计算气动声学对低色散、低耗散高精度数值离散格式的需求

将高精度谱元法结合声比拟理论应用于求解气动声学问题。以伪声压的时间二阶导数作为非齐次波动方程的声源项

空间离散采用谱元法

时间离散应用隐式Newmark法

并在外边界采用C-E-M吸收边界条件

求解了由两个相距为2r

的等环量点涡组成的同向旋转涡对的发声问题。旋转涡对的不可压缩流场通过复位势理论获得

声源由流场量计算得来

并将数值结果与应用多级匹配展开法得到的解析解进行比较

可得数值解与分析解吻合较好。研究结果表明:应用高精度谱元法进行空间离散时

每波长的网格数为11时可达到很高的精度; 网格数一定的情况下

时间步长越小得到的数值解与分析解之间的误差就越小; 另外

证明了将伪声压对时间的二阶导数作为声源项

能够高精度求解不可压缩流动引起的气动声学问题。

Abstract

In order to meet the requirements of low dispersive and low dissipative numerical discretization schemes in computational aero-acoustics

the spectral element method combined with Lighthill's acoustic analogy theory for the simulation of aeroacoustic problems is investigated. Taking the second temporal derivative of pseudopressure as the source of the inhomogeneous wave equation

and space discretization using spectral element method time discretization using implicit Newmark method

under the C-E-M absorbing boundary condition the acoustic field generated by a co-rotating spinning vortex pair is solved. This co-rotating vortex pair consists of two point vortices separated by a fixed distance of 2r

with a circulation intensity Γ. The incom

pressible flow field is obtained using the complex potential theory

and the acoustic source terms are computed using these hydrodynamic quantities. The acoustic pressure results are evaluated by comparing them with the analytical solution obtained from the matched asymptotic expansion(MAE)method The numerical solutions are in good agreement with the analytical solutions. The results show that the spectral element method can obtain high accuracy using only eleven grids in one wavelength. In the case of the same number of grids

the smaller the time step

the smaller the error between numerical solution and analytical solution. Finally

it is proved that the aero-acoustic problems induced by incompressible flows can be solved with high accuracy by using the second temporal derivative of the pseudopressure as the acoustic source.

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references

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