1. School of Aerospace Engineering, Xiamen University, Xiamen 361102, China 2. Key Laboratory of Aerodynamic Noise Control, China Aerodynamics Research and Development Center, Mianyang 621000, China
The generalized form of interpolation-supplemented lattice Boltzmann method (GILBM) was proposed for aeroacoustics simulation on non-uniform meshes. The correctness of GILBM code was validated by simulating the lid-driven cavity flow and the low Reynolds number cylinder flow. On this basis, this method was applied to simulate the Gaussian pulse propagation, acoustic periodic point sources and aerodynamic noise of two-dimensional cylinder flow. Results show that the propagation process of Gaussian pulse and acoustic periodic point sources can be well simulated on non-uniform meshes by GILBM, and the simulation results are in good agreement with the analytical solution. Also, the generation and propagation of the aerodynamic noise produced by the vortex shedding generated by a cylinder can be simulated on non-uniform body-fitted mesh by GILBM, and the sound pressure propagation in the near field and the far field can be well captured. The aerodynamic noise characteristics of flow around a cylinder show a dipole pattern. Results present a good agreement with the references, which confirms the correctness and the feasibility of GILBM in simulating sound propagation problems and aerodynamic noise on non-uniform meshes.
Wan-hong LIU,Rong-qian CHEN,Ruo-fan QIU,Wei LIN,Yan-cheng YOU. Generalized form of interpolation-supplemented lattice Boltzmann method for computational aeroacoustics. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1637-1644.
Fig.2Dimensionless velocity profiles along centrelines
Fig.3Schematic diagram and computational grid of cylinder model
Fig.4Pressure distribution coefficient of cylinder surface for different Reynolds numbers
Fig.5Computational model and computational grid of 2D Gaussian pulse
Fig.6Contours and curves of density for different horizontal velocities at $t = 0.4$
Fig.7Contour and cross-profile of density fluctuation at $t = 75$
Fig.8Time-averaged pressure distribution of cylinder surface for Re of 150
Fig.9Lift coefficient of cylinder and acoustic pressure fluctuation of monitor
Fig.10Aerodynamic noise characteristics of flow around a cylinder
[1]
MARIé S, RICOT D, SAGAUT P Comparison between lattice Boltzmann method and Navier–Stokes high order schemes for computational aeroacoustics[J]. Journal of Computational Physics, 2009, 228 (4): 1056- 1070
doi: 10.1016/j.jcp.2008.10.021
[2]
KAM E W S, LEUNG R C K, SO R M C, et al A lattice Boltzmann method for computation of aeroacoustic interaction[J]. International Journal of Modern Physics C, 2007, 18 (4): 463- 472
doi: 10.1142/S0129183107010693
[3]
VIGGEN E M. The lattice Boltzmann methods with applications in acoustics [D]. Trondheim: Norwegian University of Science and Technology, 2009.
[4]
VIGGEN E M Acoustic multipole sources for the lattice Boltzmann method[J]. Physical Review E, 2013, 87 (2): 023306
doi: 10.1103/PhysRevE.87.023306
[5]
王勇, 何雅玲, 刘迎文, 等 声波衰减的格子-Boltzmann 方法模拟[J]. 西安交通大学学报, 2007, 41 (1): 5- 8 WANG Yong, HE Ya-ling, LIU Ying-wen, et al Simulation on attenuation of sound waves with lattice-Boltzmann method[J]. Journal of Xi’an Jiaotong University, 2007, 41 (1): 5- 8
doi: 10.3321/j.issn:0253-987X.2007.01.002
[6]
司海青, 石岩, 王兵, 等 基于格子Boltzmann方法的气动声学计算[J]. 南京航空航天大学学报, 2013, 45 (5): 616- 620 SI Hai-qing, SHI Yan, WANG Bing, et al Computational aeroacoustics based on lattice Boltzmann method[J]. Journal of Nanjing University of Aeronautics and Astronautics, 2013, 45 (5): 616- 620
doi: 10.3969/j.issn.1005-2615.2013.05.007
[7]
SI H Q, WANG B, SHI Y, et al. Aero-acoustics computations of square cylinder using the latticeBoltzmann method [J]. Applied Mechanics and Materials. 2014, 444-445: 400-405.
[8]
邵卫东, 李军 计算气动声学中的伽辽金玻尔兹曼方法研究[J]. 西安交通大学学报, 2016, 50 (3): 134- 140 SHAO Wei-dong, LI Jun Study on the Galerkin Boltzmann method for computational aeroacoustics[J]. Journal of Xi’an Jiaotong University, 2016, 50 (3): 134- 140
[9]
李凯. 可压缩格子Boltzmann 方法研究[D]. 西安: 西北工业大学, 2016. LI Kai. Study on the compressible lattice Boltzmann method [D]. Xi’an: Northwestern Polytechnical University, 2016.
[10]
江茂强, 张瑞, 柳朝晖 求解复杂边界的直接力浸入边界-格子Boltzmann耦合方法[J]. 工程热物理学报, 2018, 39 (12): 139- 144 JIANG Mao-qiang, ZHANG Rui, LIU Zhao-hui Direct forcing immersed boundary-lattice Boltzmann coupling method for solving fluid structure interaction with complex boundary[J]. Journal of Engineering Thermophysics, 2018, 39 (12): 139- 144
doi: 10.1007/s10765-018-2458-0
[11]
CHEN L, YU Y, LU J, et al A comparative study of lattice Boltzmann methods using bounce: back schemes and immersed boundary ones for flow acoustic problems[J]. International Journal for Numerical Methods in Fluids, 2014, 74 (6): 439- 467
doi: 10.1002/fld.3858
[12]
周昊, 芮淼, 岑可法 多孔介质内流体流动的大涡格子Boltzmann方法研究[J]. 浙江大学学报: 工学版, 2012, 46 (9): 1660- 1665 ZHOU Hao, RUI Miao, CEN Ke-fa Study of flow in proous media by LES-LBM coupling method[J]. Journal of Zhejiang University: Engineering Science, 2012, 46 (9): 1660- 1665
[13]
IMAMURA T, SUZUKI K, NAKAMURA T, et al Acceleration of steady-state lattice Boltzmann simulations on non-uniform mesh using local time step method[J]. Journal of Computational Physics, 2005, 202 (2): 645- 663
doi: 10.1016/j.jcp.2004.08.001
[14]
李维仲, 冯玉静, 董波, 等 直角和贴体坐标系下两种格子Boltzmann方法的比较研究[J]. 计算力学学报, 2014, (3): 357- 362 LI Wei-zhong, FENGN Yu-jing, DONG Bo, et al Comparison of two lattice Boltzmann Schemes in Cartesian coordinate and body-fitted coordinate system[J]. Chinese Journal of Computational Mechanics, 2014, (3): 357- 362
doi: 10.7511/jslx201403013
HE X, DOOLEN G Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder[J]. Journal of Computational Physics, 1997, 134 (2): 306- 315
doi: 10.1006/jcph.1997.5709
[17]
GHIA U, GHIA K N, SHIN C T High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method [J]. Journal of Computational Physics, 1982, 48 (3): 387- 411
doi: 10.1016/0021-9991(82)90058-4
[18]
XU H, SAGAUT P Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics[J]. Journal of Computational Physics, 2011, 230 (13): 5353- 5382
doi: 10.1016/j.jcp.2011.03.040
[19]
INOUE O, HATAKEYAMA N Sound generation by a two-dimensional circular cylinder in a uniform flow[J]. Journal of Fluid Mechanics, 2002, 471: 285- 314
doi: 10.1017/S0022112002002124
[20]
LAFITTE A, PEROT F. Investigation of the noise generated by cylinder flows using a direct lattice-Boltzmann approach [C] // 30th AIAA Aeroacoustics Conference. Miami: AIAA, 2009: 3268.
