﻿ 基于LBM的方柱流固耦合数值研究
 舰船科学技术  2022, Vol. 44 Issue (15): 37-40    DOI: 10.3404/j.issn.1672-7649.2022.15.008 PDF

Numerical study on fluid-structure interaction of square cylinder based on Lattice Boltzmann method
XIE Zhen-wu, YANG Yi-ni, ZOU Ming-song
China Ship Scientific Research Center, Wuxi 214082, China
Abstract: In this paper, Immersed boundary-lattice Boltzmann method (IB-LBM) is used to simulate the vibration of a rectangular square cylinder with elastic support based on Fortran and OpenMP parallel algorithm. The lift and drag coefficient of flow around stationary square cylinder and the flow field are calculated and compared with the previous literature. The vibration of square cylinder with elastic support is numerically simulated, and the simulation results are compared with those of Fluent. Then, the fluid-structure interaction vibration of a square cylinder with elastic support at low Reynolds number (Re=100) is studied. By analyzing the amplitude and lift coefficient of the square cylinder, the vibration response of the square cylinder with the reduced velocity (Ur), the flow patterns of the surrounding flow field are discussed.
Key words: lattice Boltzmann method     immersed boundary method     rigid square cylinder     fluid-structure interaction
0 引　言

1 数值方法 1.1 流体控制方程

 $\begin{split}& {f_\alpha }\left( {{{\boldsymbol{r}}_i} + {{\boldsymbol{e}}_\alpha }{\delta _t},t + {\delta _t}} \right) = {f_\alpha }\left( {{{\boldsymbol{r}}_i},t} \right) - \frac{1}{\tau }\left[ {f_\alpha }\left( {{{\boldsymbol{r}}_i},t} \right) - \right.\\&\left.f_\alpha ^{eq}\left( {{{\boldsymbol{r}}_i},t} \right) \right] + \quad {\delta _t}F\left( {{{\boldsymbol{r}}_i},t} \right) 。\end{split}$ (1)

 $\dot X(t) = \int {{d^3}x{\boldsymbol{u}}({\boldsymbol{x}},t){{\Delta }}({\boldsymbol{x}} - {\boldsymbol{X}}(t))} ，$ (2)

 ${\boldsymbol{f}}({\boldsymbol{x}},t) = \int {{d^2}X{\boldsymbol{F}}({\boldsymbol{X}}(t),t)\delta ({\boldsymbol{x}} - {\boldsymbol{X}}(t))} 。$ (3)
1.2 固体控制方程

 图 1 计算模型 Fig. 1 Calculation model
 $m\dfrac{{{\partial ^2}Y}}{{\partial {t^2}}} + kY = {F_y} 。$ (4)

2 网格无关性验证及程序考核 2.1 网格无关性验证

2.2 程序考核

 图 2 方柱振动位移曲线对比 Fig. 2 Comparison of vibration displacement curves of square column

3 静止方柱绕流

 图 3 静止方柱绕流涡量图 Fig. 3 Vorticity of flow around stationary square column

 图 4 升阻力系数曲线图 Fig. 4 Curve of lift and drag coefficient
 ${C_L} = {F_y}/\left( {0.5\rho {U^2}D} \right),{C_D} = {F_x}/\left( {0.5\rho {U^2}D} \right) 。$ (5)

 图 5 升力系数频谱 Fig. 5 Spectrum of lift coefficient
4 结果讨论 4.1 振幅及升阻力分析

 图 6 不同折减速度Ur下方柱的振幅比和频率比 Fig. 6 Amplitude and frequency ratios of square cylinder under different Ur

 图 7 位移/升力系数时程曲线 Fig. 7 Displacement and lift coefficient time history curve
4.2 漩涡发放

 图 8 弹性支撑方柱涡量图 Fig. 8 Vortex pattern in wake of elastic cylinder
5 结　语

 [1] GELLER S, KRAFCZYK M, TÖLKE J, et al. Benchmark computations based on Lattice-Boltzmann, finite element and finite volume methods for laminar flows[J]. Computers & Fluids, 2006, 35(8): 888-897. [2] SOHANKAR A, NORBERG C, DAVIDSON L. Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition[J]. International Journal for Numerical Methods in Fluids, 1998, 26(1): 39-56. DOI:10.1002/(SICI)1097-0363(19980115)26:1<39::AID-FLD623>3.0.CO;2-P [3] PERUMA D A, KUMAR G, DASS A K. Numerical Simulation of Viscous Flow over a Square Cylinder Using Lattice Boltzmann Method[J]. ISRN Mathematical Physics, 2012, 2012: 1-16. [4] REGULSKI W, SZUMBARSKI J. Numerical simulation of confined flows past obstacles–the comparative study of Lattice Boltzmann and Spectral Element Methods[J]. Archives of Mechanics, 2012, 64(4): 423-456. [5] INAMURO T, ADACHI T, SAKATA H. Simulation of aerodynamic instability of bluff body[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1993, 46: 611-618. [6] KHALAK A, WILLIAMSON C. Dynamics of a hydroelastic cylinder with very low mass and damping[J]. Journal of Fluids and Structures, 1996, 10(5): 455-472. DOI:10.1006/jfls.1996.0031 [7] OKAJIMA A. Strouhal numbers of rectangular cylinders[J]. Journal of Fluid Mechanics, 2006, 123: 379-398. [8] 杨旖旎. 基于进入边界-格子玻尔兹曼方法的水下二维结构流固耦合计算研究[D]. 中国舰船研究院, 2021. [9] DAVIS R W, MOORE E F A. numerical study of vortex shedding from rectangles[J]. Journal of Fluid Mechanics, 1982, 116: 475-506. DOI:10.1017/S0022112082000561