流体力学与飞行力学

基于改进虚拟单元浸没边界法的椭圆气动噪声问题

  • 张阳 ,
  • 罗佳奇 ,
  • 曾先
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  • 浙江大学 航空航天学院,杭州 310027
.E-mail: jiaqil@zju.edu.cn

收稿日期: 2022-12-21

  修回日期: 2023-02-06

  录用日期: 2023-02-23

  网络出版日期: 2023-03-10

基金资助

国家自然科学基金(12202383);国家科技重大专项(2017-II-0006-0020);浙江省自然科学基金(LXR22E060001)

Elliptic flow noise by improved ghost⁃cell immersed boundary method

  • Yang ZHANG ,
  • Jiaqi LUO ,
  • Xian ZENG
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  • School of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China
E-mail: jiaqil@zju.edu.cn

Received date: 2022-12-21

  Revised date: 2023-02-06

  Accepted date: 2023-02-23

  Online published: 2023-03-10

Supported by

National Natural Science Foundation of China(12202383);National Science and Technology Major Project(2017-II-0006-0020);Natural Science Foundation of Zhejiang Province(LXR22E060001)

摘要

气动噪声的准确数值模拟对于研究航空发动机中叶片绕流噪声和涡声共振现象具有重要的意义。提出了一种基于局部边界加密的改进虚拟单元浸没边界法,将其与高精度有限差分算法相结合,成功实现了对低雷诺数气动声场问题的直接数值求解。该浸没边界法的改进之处在于通过在虚拟点之间构造多个中间节点,并依据边界条件建立流体域内镜像点与固体域内中间点之间的关系,使得固壁边界的离散程度相比原来大为增加,这样起到对固壁边界局部加密的作用,从而使得边界的描述更为准确。通过对低雷诺数下圆柱绕流气动噪声问题的数值验证,表明所提出方法得到的升阻力特性、尾迹脱落涡演化以及近远场噪声传播特性与文献结果吻合较好,气动声场的计算精度得到了提高。对比研究了不同纵横比对椭圆绕流气动声源产生和噪声传播规律的影响,发现尾迹脱落涡交替排列并向下游演化,所形成的噪声场关于长轴线呈对称分布,其流动模式和声场特征与圆柱绕流类似,但其升阻力脉动以及噪声强度明显小于圆柱算例。进一步地,通过声压分解发现偶极子声源对整体噪声强度的贡献比重随着纵横比减小而下降,进而尾迹中单极子和四极子声源的贡献比重上升,直接导致了噪声传播方向向上游偏转。

本文引用格式

张阳 , 罗佳奇 , 曾先 . 基于改进虚拟单元浸没边界法的椭圆气动噪声问题[J]. 航空学报, 2023 , 44(19) : 128418 -128418 . DOI: 10.7527/S1000-6893.2023.28418

Abstract

Accurate numerical simulation of aerodynamic noise is of great significance for the study on flow-induced noise and vortex-acoustic resonance of aeroengine blades. This paper proposes an improved ghost-cell immersed boundary method based on local boundary refinement, which is combined with the high-precision finite difference method to successfully solve the fluid-solid coupling aeroacoustic problem at a low Reynolds number. The improvement in the current immersed boundary method includes the construction of a large number of intermediate nodes between the ghost points, and the establishment of relationship between the mirror image points in the fluid domain and the intermediate points in the solid domain according to the boundary conditions. Compared with the previous method, the dispersion of the solid wall boundary is significantly increased, thereby playing a role in local mesh refinement and leading to more accurate boundary description. Verification of the aerodynamic noise problem in the flow around a cylinder at a low Reynolds number shows that the characteristics of lift and drag, the evolution of wake shedding vortex and the near-field and far-field noise propagation characteristics obtained by the proposed method are in good agreement with the results in the literature. The numerical accuracy of the aerodynamic sound field is improved. The effects of different aspect ratios on the generation of aerodynamic sound sources and the propagation of noise in the elliptical flow are also studied. It is found that the wake shedding vortices are alternately arranged and evolve downstream. The noise field formed is symmetrically distributed about the long axis. Its flow pattern and noise characteristics are similar to those in the flow around a cylinder, but with significantly smaller lift drag fluctuation and noise intensity. Furthermore, through sound pressure decomposition, it is revealed that the contribution proportion of the dipole sound source to the overall sound intensity decreases with the decrease of the aspect ratio, while that of the monopole and quadrupole sound sources in the wake increases, directly causing the noise propagation direction to deflect upstream.

参考文献

1 乔渭阳. 航空发动机气动声学[M]. 北京: 北京航空航天大学出版社, 2010.
  QIAO W Y. Aeroacoustics of aeroengine[M]. Beijing: Beihang University Press, 2010 (in Chinese).
2 李志彬, 王晓宇, 孙晓峰, 等. 单级低速轴流压气机噪声特性实验研究[J]. 推进技术201839(6): 1275-1282.
  LI Z B, WANG X Y, SUN X F, et al. Experimental research on noise of single-stage low-speed axial compressor[J]. Journal of Propulsion Technology201839(6): 1275-1282 (in Chinese).
3 BROOKS T F, POPE D S, MARCOLINI M A. Airfoil self-noise and prediction: No. L-16528[R]. Washington, D.C.: NASA, 1989.
4 同航, 黎霖, 卯鲁秦, 等. 波浪前缘静子叶片对高速轴流风扇单音噪声的影响[J]. 航空学报202041(10): 123565.
  TONG H, LI L, MAO L Q, et al. Tonal noise reduction of a high-speed single axial fan with wavy leading-edge stator[J]. Acta Aeronautica et Astronautica Sinica202041(10): 123565 (in Chinese).
5 HOLZINGER F, WARTZEK F, SCHIFFER H P, et al. Self-excited blade vibration experimentally investigated in transonic compressors: Acoustic resonance[J]. Journal of Turbomachinery2016138(4): 041001.
6 HOURIGAN K, THOMPSON M C, TAN B T. Self-sustained oscillations in flows around long blunt plates[J]. Journal of Fluids and Structures200115(3-4): 387-398.
7 TAN B T, THOMPSON M C, HOURIGAN K. Sources of acoustic resonance generated by flow around a long rectangular plate in a duct[J]. Journal of Fluids and Structures200318(6): 729-740.
8 HELLMICH B, SEUME J R. Causes of acoustic resonance in a high-speed axial compressor[J]. Journal of Turbomachinery2008130(3): 031003.
9 洪志亮, 赵国昌, 杨明绥, 等. 航空发动机压气机内部流体诱发声共振研究进展[J]. 航空学报201940(11): 023139.
  HONG Z L, ZHAO G C, YANG M S, et al. Development of flow-induced acoustic resonance in aeroengine compressors[J]. Acta Aeronautica et Astronautica Sinica201940(11): 023139 (in Chinese).
10 BROOKS T F, HODGSON T H. Trailing edge noise prediction from measured surface pressures[J]. Journal of Sound and Vibration198178(1): 69-117.
11 ZHU W J, SHEN W Z, S?RENSEN J N, et al. Improvement of airfoil trailing edge bluntness noise model[J]. Advances in Mechanical Engineering20168(2): 1-12.
12 COX J S, BRENTNER K S, RUMSEY C L. Computation of vortex shedding and radiated sound for a circular cylinder: Subcritical to transcritical Reynolds numbers[J]. Theoretical and Computational Fluid Dynamics199812(4): 233-253.
13 LIGHTHILL M J. On sound generated aerodynamically I. General theory[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences1952211(1107): 564-587.
14 INOUE O, MORI M, HATAKEYAMA N. Aeolian tones radiated from flow past two square cylinders in tandem[J]. Physics of Fluids200618(4): 046101.
15 INASAWA A, ASAI M, NAKANO T. Sound generation in the flow behind a rectangular cylinder of various aspect ratios at low Mach numbers[J]. Computers & Fluids201382: 148-157.
16 JOHNSON S A, THOMPSON M C, HOURIGAN K. Predicted low frequency structures in the wake of elliptical cylinders[J]. European Journal of Mechanics - B/Fluids200423(1): 229-239.
17 VIJAY K, SRINIL N, ZHU H B, et al. Flow-induced transverse vibration of an elliptical cylinder with different aspect ratios[J]. Ocean Engineering2020214: 107831.
18 MAHATO B, GANTA N, BHUMKAR Y G. Numerical investigation of sound generation due to laminar flow past elliptic cylinders[J]. Numerical Mathematics: Theory, Methods and Applications202013(1): 27-62.
19 傅德薰, 马延文, 李新亮. 可压缩湍流直接数值模拟[M]. 北京: 科学出版社, 2010.
  FU D X, MA Y W, LI X L. Direct numerical simulation of compressible turbulence[M]. Beijing: Science Press, 2010 (in Chinese).
20 LI X L, FU D X, MA Y W, et al. Direct numerical simulation of shock/turbulent boundary layer interaction in a supersonic compression ramp[J]. Science China Physics, Mechanics and Astronomy201053(9): 1651-1658.
21 SEO J H, MITTAL R. A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries[J]. Journal of Computational Physics2011230(4): 1000-1019.
22 XIE F, QU Y, ISLAM M A, et al. A sharp-interface Cartesian grid method for time-domain acoustic scattering from complex geometries[J]. Computers & Fluids2020202: 104498.
23 ZHANG Y, FANG X, ZOU J, et al. Numerical simulations of shock/obstacle interactions using an improved ghost-cell immersed boundary method[J]. Computers & Fluids2019182: 128-43.
24 张阳, 邹建锋, 郑耀. 改进虚拟边界算法在超声速流动问题求解中的应用[J]. 力学学报201850(3): 538-552.
  ZHANG Y, ZOU J F, ZHENG Y. An improved ghost-cell immersed boundary method for solving supersonic flow problems[J]. Chinese Journal of Theoretical and Applied Mechanics201850(3): 538-552 (in Chinese).
25 CHAUDHURI A, HADJADJ A, CHINNAYYA A. On the use of immersed boundary methods for shock/obstacle interactions[J]. Journal of Computational Physics2011230(5): 1731-1748.
26 CHAUDHURI A, HADJADJ A, SADOT O, et al. Computational study of shock-wave interaction with solid obstacles using immersed boundary methods[J]. International Journal for Numerical Methods in Engineering201289(8): 975-990.
27 FRANKE R. Scattered data interpolation: Tests of some methods[J]. Mathematics of Computation198238(157): 181-200.
28 TSENG Y H, FERZIGER J H. A ghost-cell immersed boundary method for flow in complex geometry[J]. Journal of Computational Physics2003192(2): 593-623.
29 QU Y G, SHI R C, BATRA R C. An immersed boundary formulation for simulating high-speed compressible viscous flows with moving solids[J]. Journal of Computational Physics2018354: 672-691.
30 DE TULLIO M D, DE PALMA P, IACCARINO G, et al. An immersed boundary method for compressible flows using local grid refinement[J]. Journal of Computational Physics2007225(2): 2098-2117.
31 EHSAN KHALILI M, LARSSON M, MüLLER B. Immersed boundary method for viscous compressible flows around moving bodies[J]. Computers & Fluids2018170: 77-92.
32 CHI C, ABDELSAMIE A, THéVENIN D. A directional ghost-cell immersed boundary method for incompressible flows[J]. Journal of Computational Physics2020404: 109122.
33 BOUKHARFANE R, EUGêNIO RIBEIRO F H, BOUALI Z, et al. A combined ghost-point-forcing/direct-forcing immersed boundary method (IBM) for compressible flow simulations[J]. Computers & Fluids2018162: 91-112.
34 LUO K, MAO C L, ZHUANG Z Y, et al. A ghost-cell immersed boundary method for the simulations of heat transfer in compressible flows under different boundary conditions Part-II: Complex geometries[J]. International Journal of Heat and Mass Transfer2017104: 98-111.
35 CIMBALA J M, NAGIB H M, ROSHKO A. Large structure in the far wakes of two-dimensional bluff bodies[J]. Journal of Fluid Mechanics1988190: 265-298.
36 POINSOT T J, LELEF S K. Boundary conditions for direct simulations of compressible viscous flows[J]. Journal of Computational Physics1992101(1): 104-129.
37 INOUE O, HATAKEYAMA N. Sound generation by a two-dimensional circular cylinder in a uniform flow[J]. Journal of Fluid Mechanics2002471: 285-314.
38 KWON K, CHOI H. Control of laminar vortex shedding behind a circular cylinder using splitter plates[J]. Physics of Fluids19968(2): 479-486.
39 WILLIAMSON C H K. Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers[J]. Journal of Fluid Mechanics1989206: 579-627.
40 FEY U, K?NIG M, ECKELMANN H. A new Strouhal?Reynolds-number relationship for the circular cylinder in the range 47<Re<2×105 [J]. Physics of Fluids199810(7): 1547-1549.
41 CICATELLI G, SIEVERDING C H. The effect of vortex shedding on the unsteady pressure distribution around the trailing edge of a turbine blade[J]. Journal of Turbomachinery1997119(4): 810-819.
42 MA R X, LIU Z S, ZHANG G H, et al. Control of Aeolian tones from a circular cylinder using forced oscillation[J]. Aerospace Science and Technology201994: 105370.
43 LANDAU L D, LIFSHITZ E M. Fluid mechanics[M]. 2nd ed. Oxford: Pergamon Press, 1987.
44 GOLDSTEIN M E. Aeroacoustics of turbulent shear flows[J]. Annual Review of Fluid Mechanics198416: 263-285.
45 CURLE N. The influence of solid boundaries upon aerodynamic sound[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences1955231(1187): 505-514.
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