Numerical simulation for a co-rotating vortex pair&rsquo;s sounding

PDF(1866 KB)

Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (13) : 43-48.

Numerical simulation for a co-rotating vortex pair’s sounding

BAO Zhenzhong, QIN Guoliang, HE Wenqiang, WANG Yazhou, MU Yiwei

Author information +

History +

Abstract

To investigate the theory of flow-induced sounding deeply, the dilatation theory proposed by Ribner and Meecham was extended to a case with background flow field existing. A co-rotating vortex pair’s sounding was numerically simulated in both stationary medium and mean flow. The spectral element method was applied in space discretization, and the implicit Newmark method in time domain. Then, Eliane-Dan-Thomas absorbing boundary condition was adopted for external boundary. The numerical results were compared with those of the analytical solution obtained using the matched asymptotic expansion (MAE) method, both of them agreed well. Moreover, sounding statuses of a co-rotating vortex pair were simulated and analyzed under different rotating Mach numbers, uniform flows and shear mean flows. The components of their frequency spectra were also analyzed. The study showed that the spectral element method combined with the dilatation theory can be used to solve aero-acoustic problems induced by incompressible flows; using the absorbing boundary condition can effectively reduce acoustic wave reflection at the boundary; with increase in rotating Mach number, wavelengths of sound wave decrease, sound source intensity increases and the peak value frequency increases; the sound field produced by a co-rotating vortex pair reveals typical Doppler effects under the action of mean flow and shear flow.

Key words

computational aero-acoustics / spectral element method / acoustic analogy theory / dilatation theory / absorbing boundary condition / co-rotating vortex pair

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

BAO Zhenzhong, QIN Guoliang, HE Wenqiang, WANG Yazhou, MU Yiwei. Numerical simulation for a co-rotating vortex pair’s sounding[J]. Journal of Vibration and Shock, 2018, 37(13): 43-48

References

[1]LIGHTHILL MJ. On sound generated aerodynamically. I. General theory[J]. Proceedings of the Royal Society of London, SeriesA:MathematicalandPhysicalSciences, 1952,211: 564-587.
[2]RIBNER HS. The generation of sound by turbulent jets[J]. Advances in Applied Mechanics, 1964, 8: 103-182.
[3]RIBNER H S. Aerodynamic sound from fluid dilatations: a theory of the sound from jets and other flows[R].AFOSR, TN 3430, 1962.
[4]MEECHAM W. Discussion of the pressure-source aerosonic theory and of Doak’s criticism[J]. The Journal of the Acoustical Society of America, 1981, 69 (3): 643-646.
[5]HARDIN J, POPE D. An acoustic/viscous splitting technique
for computational aeroacoustics[J]. Theoretical and Computational Fluid Dynamics, 1994, 6 (5-6): 323-340.
[6]FLEMMING F, SADIKI A, JANICKA J. Investigation of combustion noise using a LES/CAA hybrid approach[J]. Proceedings of the Combustion Institute, 2007, 31 (2): 3189-3196.
[7]HIRAMOTO R, TOYODA K, SATO K. Study on mechanism of aerodynamic sound generation by flow visualization and fluctuating static pressure measurements[J]. Journal of Fluid Science and Technology, 2010, 5 (1): 45-55.
[8] ESCOBAR M, ALI I, KALTENBACHER M, et al. Investigation of vortex sound propagation using a FE implementation[C]// 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference). Cambridge, Massachusetts:AIAA, 2006:2518.
[9]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, (03): 234-248.
LI Xiaodong, JIANG Min, GAO Junhui, et al. Progress and Prospective of Computational Aeroacoustics(in Chinese)[J].Sci Sin-Phys Mech Astron, 2014, (03): 234-248.
[10]WANG M, FREUND JB, LELE SK. Computational prediction of flow-generated sound[J]. Annu Rev Fluid Mech, 2006, 38: 483-512.
[11] PATERA AT. A spectral element method for fluid dynamics: laminar flow in a channel expansion[J]. Journal of Computational Physics, 1984, 54 (3): 468-488.
[12] CANUTO C, HUSSAINI MY, QUARTERONI AM, et al. Spectral methods in fluid dynamics[M]: Springer Science & Business Media, 2012.
[13] SERIANI G, PRIOLO E. Spectral element method for acoustic wave simulation in heterogeneous media[J]. Finite Elements in Analysis and Design, 1994, 16 (3): 337-348.
[14]HASBESTAN JJ, NEWMAN J, ARABSHAHI A. Least squares spectral element method for laminar compressible flows[C]// 54th AIAA Aerospace Sciences Meeting. San Diego, California, USA: AIAA, 2016: 1075.
[15]耿艳辉，秦国良. Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播[J]. 西安交通大学学报, 2012, (03): 100-106.
GENG Yanhui, QIN Guoliang. Chebyshev spectral elements method for 2-dimensional acoustic propagation problem in a uniform mean flow with absorbing boundary condition[J].Journal of Xi’an Jiaotong University,2012, (03): 100-106.
[16] GENG Yanhui, QIN Guoliang,WANG Yang, et al. The research of space-time coupled spectral element method for acoustic wave equations[J]. Chinese Journal of Acoustics, 2016, (01): 29-47.
[17] 张荣欣，秦国良，许丽娜. 管道声传播问题的一种高精度数值模拟[J]. 振动与冲击，2010,29 (8): 115-119.
ZHANG Rongxin,QIN Guoliang,XU Lina.A high-accurate numerical simulation of acoustic propagation problemin pipe[J].Journal of Vibration and Shock,2010,29 (8): 115-119.
[18] 林伟军. 弹性波传播模拟的 Chebyshev 谱元法[J]. 声学学报, 2007, 32 (6): 525-533.
LIN Weijun. A chebyshev spectral element method for elastic wave modeling[J].ACTA Acoustic, 2007, 32 (6): 525-533.
[19]BÉCACHEE, GIVOLI D, HAGSTROM T. High-order absorbing boundary conditions for anisotropic and convective wave equations[J].Journal of Computational Physics, 2010, 229 (4): 1099-1129.
[20] 王勖成. 有限单元法[M]. 北京：清华大学出版社，2003.
Wang, Xucheng. Finite element method[M]. Beijing: Press of Tsinghua University, 2003.
[21]KÜCHEMANN D. Report on the IUTAM symposium on concentrated vortex motions in fluids[J]. Journal of Fluid Mechanics, 1965, 21 (01): 1-20.
[22]MÜLLER EA, OBERMEIER F. Vortex sound[J]. Fluid Dynamics Research, 1988, 3 (1-4): 43-51.
[23] ZHU Weijun, SHEN Wenzhong, SØRENSEN JN. High-order numerical simulations of flowinduced noise[J]. International Journal for Numerical Methods in Fluids, 2011, 66 (1): 17-37.
[24] LEE DJ, KOO SO. Numerical study of sound generation due to a spinning vortex pair[J]. AIAA Journal, 1995, 33 (1): 20-26.
[25] 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, (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.
[26] 刘聪尉, 许万顺, 李环, 等. 不可压缩旋转涡对的流噪声计算研究[J]. 水动力学研究与进展A辑, 2016, (03): 269-276.
LIU Congwei, XU Wanshun, LI Huan, et al. Numerical study of flow noise from anincompressible co-rotating vortex pair[J].Chinese Journal of Hydrodynamcis,2016, (03): 269-276.
[27] 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, (11): 1-6.
BAO Zhenzhong,QIN Guoliang,GENG Yanhui, et al.Investigation of vortex sound propagation using spectral element method[J].Journal of Xi’an Jiaotong University,2016,(11): 1-6