谱元法应用于涡声传播问题的研究

包振忠; 秦国良; 耿艳辉; 和文强

doi:10.7652/xjtuxb201611017

您当前的位置：

首页 >

文章列表页 >

谱元法应用于涡声传播问题的研究

更新时间：2025-07-09

- 谱元法应用于涡声传播问题的研究
- Investigation of Vortex Sound Propagation Using Spectral Element Method
- 西安交通大学学报 2016年50卷第11期页码：110-114+120
- 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：
  
  : 2016-05-20。作者简介: 包振忠(1992—),男,博士生;秦国良(通信作者),男,教授,博士生导师。基金项目: 国家重点基础研究发展计划资助项目(2012CB026004)
- DOI：10.7652/xjtuxb201611017
  中图分类号： O121.8;G558
- 网络首发：2016-11-10，
  
  纸质出版：2016
- 稿件说明：
移动端阅览
包振忠, 秦国良, 耿艳辉, 等. 谱元法应用于涡声传播问题的研究[J]. 西安交通大学学报, 2016,50(11):110-114+120.

Investigation of Vortex Sound Propagation Using Spectral Element Method[J]. 2016, 50(11): 110-114+120.
包振忠, 秦国良, 耿艳辉, 等. 谱元法应用于涡声传播问题的研究[J]. 西安交通大学学报, 2016,50(11):110-114+120. DOI： 10.7652/xjtuxb201611017.

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.

关键词

Keywords

references

李晓东, 江旻, 高军辉, 等. 计算气动声学进展与展望 [J]. 中国科学: 物理学·力学·天文学, 2014(3): 234-248.

LI Xiaodong, JIANG Min, GAO Junhui, et al. Progress and prospective of computational aeroacoustics [J]. Science China: Physics, Mechanics & Astronomy, 2014(3): 234-248.

LELE S K, NICHOLS J W. A second golden age of aeroacoustics [J]. Philosophical Transactions of the Royal Society of London: A Mathematical, Physical and Engineering Sciences, 2014, 372(2022): 20130321.

GIVOLI D. High-order local non-reflecting boundary conditions: a review [J]. Wave Motion, 2004, 39(4): 319-326.

DAHL M D. Numerical solutions to the fourth and second computational aeroacoustics(CAA)workshop benchmark problems [C]∥The 4th Computational Aeroacoustics(CAA)Workshop on Benchmark Problems. Washington, DC, USA: NASA Glenn Research Center, 2004: 187-197.

徐康乐, 陈迎春, 陶俊, 等. 低马赫数条件下气动声场流场分裂求解方法研究 [J]. 复旦学报(自然科学版), 2014, 53(5): 636-644.

XU Kangle, CHEN Yingchun, TAO Jun, et al. A splitting simulation method for aeroacoustic at low Mach conditions [J]. Journal of Fudan University(Natural Science), 2014, 53(5): 636-644.

HÜPPE A, KALTENBACHER M. Spectral finite elements for computational aeroacoustics using acoustic perturbation equations [J]. Journal of Computational Acoustics, 2012, 20(2): 1240005.

ALI I, ESCOBAR M, KALTENBACHER M, et al. Time domain computation of flow induced sound [J]. Computers Fluids, 2008, 37(4): 349-359.

ZHU W J, SHEN W Z, SØRENSEN J N. High-order numerical simulations of flow-induced noise [J]. International Journal for Numerical Methods in Fluids, 2011, 66(1): 17-37.

HARDIN J, POPE D. An acoustic/viscous splitting technique for computational aeroacoustics [J]. Theoretical and Computational Fluid Dynamics, 1994, 6(5/6): 323-340.

FARSHCHI M, HANNANI S K, EBRAHIMI M. Linearized and nonlinear acoustic/viscous splitting techniques for low Mach number flows [J]. International Journal for Numerical Methods in Fluids, 2003, 42(10): 1059-1072.

EKATERINARIS J A. New formulation of Hardin-Pope equations for aeroacoustics [J]. AIAA Journal, 1999, 37(9): 1033-1039.

EKATERINARIS J A. An upwind scheme for the computation of acoustic field generated by incompressible flow [J]. AIAA Journal, 1997, 35(1): 14481455.

ZHU C, QIN G, ZHANG J. Implicit Chebyshev spectral element method for acoustics wave equations [J]. Finite Elements in Analysis and Design, 2011, 47(2): 184-194.

ZHANG R, QIN G, ZHU C. Spectral element method for acoustic propagation problems based on linearized Euler equations [J]. Journal of Computational Acoustics, 2009, 17(4): 383-402.

RIBNER H S. The generation of sound by turbulent jets [J]. Advances in Applied Mechanics, 1964, 8: 103182.

PAPAGEORGAKOPOULOS J, TSANGARIS S. A numerical method for predicting acoustical wave propagation in open spaces [J/OL]. [2016-04-06]. https:∥www.hindawi.com/journals/isrn/2011/174031/abs/.

CLAYTON R, ENGQUIST B. Absorbing boundary conditions for acoustic and elastic wave equations [J]. Bulletin of Seismological Society of America, 1977, 67(6): 1529-1540.

张荣欣, 秦国良. 用切比雪夫谱元方法求解均匀流场中的声传播问题 [J]. 西安交通大学学报, 2009, 43(7): 120-124.

ZHANG Rongxin, QIN Guoliang. Chebychev spectral elements method for acoustic propagation problem in a uniform mean flow [J]. Journal of Xi'an Jiaotong University, 2009, 43(7): 120-124.

LEE D J, KOO S O. Numerical study of sound generation due to a spinning vortex pair [J]. AIAA Journal, 1995, 33(1): 20-26.

朱昌允, 秦国良, 徐忠. 谱元方法求解波动方程及影响其数值精度的相关因素 [J]. 西安交通大学学报, 2008, 42(1): 56-59.

ZHU Changyun, QIN Guoliang, XU Zhong. Implicit spectral element method for wave equation and some factors influencing numerical accuracy [J]. Journal of Xi'an Jiaotong University, 2008, 42(1): 56-59.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

用切比雪夫谱元方法求解均匀流场中的声传播问题

Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播

局域共振弹性超材料梁禁带宽度的拓宽方法

谱元方法求解含吸收边界的声学问题

物理气相传输（PVT)法生长碳化硅的晶体形态热应力分析