Transverse Harmonic Oscillation of Rectangular Container With Viscous Fluid: a Lattice BoltzmannImmersed Boundary Approach
-
摘要: 将三维格子Boltzmann法(LBM)与浸没边界法(IBM)相结合,研究弹性矩形容器中黏性流体的横波谐振所引起的流动物理特性.提出了一个半微观表达式来计算边界节点处的流体受力.基于薄板弹性变形理论,使用解析变形解法来计算边界所经历的位移.基于该方法的数值模拟结果与固定边界的理论预测结果一致.采用振荡边界模拟展现了与理论预期相符合的流动模式.
-
关键词:
- 格子Boltzmann法 /
- 浸没边界法 /
- 谐波振荡
Abstract: We combined the 3D lattice Boltzmann method (LBM) with the immersed boundary method (IBM) to study the flow physics induced by an elastic rectangular container undergoing harmonic oscillations surrounding a viscous fluid. We propose a semi-microscopic expression for the drag force to compute the hydrodynamic forces at the boundary nodes. An analytical deformation solution is used based on a thin plate elastic deformation theory to calculate the displacement experienced by the boundary. The numerical simulation result(All the results on figure axes, in this article, are displayed in lattice units.) based on the proposed method agreed with the theoretical predictions for channel flow with stationary boundary. The oscillating boundary simulation exhibits the expected flow pattern in line with theory.-
Key words:
- lattice boltzmann method /
- immersed boundary method /
- harmonic oscillation
-
[1] KOZLOV V, KOZLOV N, SCHIPITSYN V. Steady flows in an oscillating deformable container: effect of the dimensionless frequency[J]. Physical Review Fluids, 2017,2(9): 094501. [2] MIRAS T, SCHOTTE J-S, OHAYON R. Liquid sloshing damping in an elastic container[J]. Journal of Applied Mechanics,2012,79(1): 010902. [3] LOPEZ D, GUAZZELLI E. Inertial effects on fibers settling in a vortical flow[J]. Physical Review Fluids,2017,2(2): 024306. [4] SAURET A, CEBRON D, LE BARS M, et al. Fluid flows in a librating cylinder[J]. Physics of Fluids,2012,24(2): 026603. [5] HABTE M A, WU Chuijie. Influence of wall motion on particle sedimentation using hybrid LB-IBM scheme[J]. Science China : Physics, Mechanics & Astronomy,2017,60(3): 034711. [6] J KAY J M, NEDDERMAN R M. Fluid Mechanics and Transfer Processes [M]. Cambridge, New York: Cambridge University Press, 1985. [7] SCHLICHTING H, GERSTEN K, KRAUSE E, et al. Boundary-Layer Theory [M]. Vol7. Springer, 1955. [8] BUXTON G A, VERBERG R, JASNOW D, et al. Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models[J]. Physical Review E,2005,71(5): 056707. [9] WU Z, MA X. Dynamic analysis of submerged microscale plates: the effects of acoustic radiation and viscous dissipation[J]. Proceedings: Mathematical, Physical, and Engineering Sciences,2016,472(2187): 20150728. [10] AURELI M, PORFIRI M. Low frequency and large amplitude oscillations of cantilevers in viscous fluids[J]. Applied Physics Letters,2010,96(16): 164102. [11] FANG H, WANG Z, LIN Z, et al. Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels[J]. Physical Review E,2002,65(5): 051925. [12] DESCOVICH X, PONTRELLI G, MELCHIONNA S, et al. Modeling fluid flows in distensible tubes for applications in hemodynamics[J]. International Journal of Modern Physics C,2013,24(5): 1350030. [13] DOCTORS G M. Towards patient-specific modelling of cerebral blood flow using lattice-Boltzmann methods[D]. Ph D Thesis. University of London, 2011. [14] MOUNTRAKIS L, LORENZ E, HOEKSTRA A. Revisiting the use of the immersed-boundary lattice-Boltzmann method for simulations of suspended particles[J]. Physical Review E,2017,96(1): 013302. [15] YAN G, LI T, YIN X. Lattice Boltzmann model for elastic thin plate with small deflection[J]. Computers & Mathematics With Applications,2012,63(8): 1305-1318. [16] ARENAS J P. On the vibration analysis of rectangular clamped plates using the virtual work principle[J]. Journal of Sound and Vibration,2003,266(4): 912-918. [17] GORMAN D. Free-vibration analysis of rectangular plates with clamped-simply supported edge conditions by the method of superposition[J].Journal of Applied Mechanics,1977,44(4): 743-749. [18] SUNG C-C, JAN C. Active control of structurally radiated sound from plates[J]. The Journal of the Acoustical Society of America,1997,102(1): 370-381. [19] LADD A, VERBERG R. Lattice-Boltzmann simulations of particle-fluid suspensions[J]. Journal of Statistical Physics,2001,104(5/6): 1191-1251. [20] LADD A J. Numerical simulations of particulate suspensions via a discretized Boltzmann equation, part 1: theoretical foundation[J]. Journal of Fluid Mechanics,1994,271: 285-309. [21] QIAN Y, D'HUMIRES D, LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Letters,1992,17(6): 479. [22] LADD A J. Lattice-Boltzmann methods for suspensions of solid particles[J]. Molecular Physics ,2015,113(17/18): 2531-2537. [23] LADD A J. Numerical simulations of particulate suspensions via a discretized Boltzmann equation,part 2: numerical results[J]. Journal of Fluid Mechanics,1994,271: 311-339. [24] NIU X, SHU C, CHEW Y, et al. A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows[J].Physics Letters A,2006,354(3): 173-182. [25] SQUIRES K D, EATON J K. Particle response and turbulence modification in isotropic turbulence[J]. Physics of Fluids A: Fluid Dynamics,1990,2(7): 1191-1203. [26] CAI S-G, OUAHSINE A, FAVIER J, et al. Moving immersed boundary method[J]. International Journal for Numerical Methods in Fluids,2017,85(5): 288-323. [27] DI FELICE R. The voidage function for fluid-particle interaction systems[J]. International Journal of Multiphase Flow,1994,20(1): 153-159. [28] BROWN P P, LAWLER D F. Sphere drag and settling velocity revisited[J]. Journal of Environmental Engineering,2003,129(3): 222-231. [29] ESTEGHAMATIAN A, RAHMANI M, WACHS A. Numerical models for fluid-grains interactions: opportunities and limitations[C]// European Physical Journal Web of Conferences.Vol140. 2017: 09013. [30] SUNGKORN R, DERKSEN J. Simulations of dilute sedimenting suspensions at finite-particle reynolds numbers[J]. Physics of Fluids,2012,24(12): 123303. [31] REIDER M B, STERLING J D. Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations[J].Computers & Fluids,1995,24(4): 459-467. [32] MAIER R S, BERNARD R S, GRUNAU D W. Boundary conditions for the lattice Boltzmann method[J]. Physics of Fluids,1996,8(7): 1788-1801. [33] ZHANG W, SHI B, WANG Y. 14-velocity and 18-velocity multiple-relaxation-time lattice Boltzmann models for three-dimensional incompressible flows[J]. Computers & Mathematics With Applications,2015,69(9): 997-1019. [34] HOFEMEIER P, SZNITMAN J. Revisiting pulmonary acinar particle transport: convection, sedimentation, diffusion and their interplay[J].Journal of Applied Physiology,2015,118(11): 1375-1385. [35] SHI Y, SADER J E. Lattice Boltzmann method for oscillatory stokes flow with applications to micro-and nanodevices[J]. Physical Review E,2010,81(3): 036706. [36] SON S W, YOON H S, JEONG H K, et al. Discrete lattice effect of various forcing methods of body force on immersed boundary-lattice Boltzmann method[J].Journal of Mechanical Science and Technology,2013,27(2): 429-441. [37] LIBERSKY L D, PETSCHEK A G, CARNEY T C, et al. High strain Lagrangian hydrodynamics: a three dimensional SPH code for dynamic material response[J]. Journal of Computational Physics,1993,109(1): 67-75.
点击查看大图
计量
- 文章访问数: 1146
- HTML全文浏览量: 141
- PDF下载量: 697
- 被引次数: 0