Numerical Study on Vortex Induced Vibration of a Flexible Plate Behind Square Cylinder with Various Flow Velocities

doi:10.1007/s12204-014-1529-z

摘要/Abstract

摘要： The vortex induced vibration (VIV) of a flexible plate behind the square head with various flow velocities is simulated. The closely coupling approach is used to model this fluid-structure interaction problem. The fluid governed by the incompressible Navier-Stokes equations is solved in arbitrary Lagrangian-Eulerian (ALE) frame by the finite volume method. The structure described by the equations of the elastodynamics in Lagrangian representation is discretized by the finite element approach. The numerical results show that the resonance occurs when the frequency of vortex shedding from square head coincides with the natural frequency of plate. And the amplitude of both the structure motion and the fluid load keeps increasing with the time. Furthermore, it is also found that in particular range of flow velocity the vibration of the plate would reach a periodical state. The amplitude of plate oscillating increases with the growth of velocity, while the frequency is locked.

关键词: fluid-structure interaction, closely coupling approach, vortex induced vibration (VIV), resonance

Abstract: The vortex induced vibration (VIV) of a flexible plate behind the square head with various flow velocities is simulated. The closely coupling approach is used to model this fluid-structure interaction problem. The fluid governed by the incompressible Navier-Stokes equations is solved in arbitrary Lagrangian-Eulerian (ALE) frame by the finite volume method. The structure described by the equations of the elastodynamics in Lagrangian representation is discretized by the finite element approach. The numerical results show that the resonance occurs when the frequency of vortex shedding from square head coincides with the natural frequency of plate. And the amplitude of both the structure motion and the fluid load keeps increasing with the time. Furthermore, it is also found that in particular range of flow velocity the vibration of the plate would reach a periodical state. The amplitude of plate oscillating increases with the growth of velocity, while the frequency is locked.

Key words: fluid-structure interaction, closely coupling approach, vortex induced vibration (VIV), resonance

中图分类号:

TK 124

HU Shi-lianga* (胡世良), LU Chuan-jinga,b (鲁传敬), HE You-shenga,b (何友声). Numerical Study on Vortex Induced Vibration of a Flexible Plate Behind Square Cylinder with Various Flow Velocities[J]. 上海交通大学学报（英文版）, 2014, 19(4): 488-494.

HU Shi-lianga* (胡世良), LU Chuan-jinga,b (鲁传敬), HE You-shenga,b (何友声). Numerical Study on Vortex Induced Vibration of a Flexible Plate Behind Square Cylinder with Various Flow Velocities[J]. Journal of shanghai Jiaotong University (Science), 2014, 19(4): 488-494.

参考文献

[1] Hou G, Wang J, Layton A. Numerical method for fluid-structure interaction: A review [J]. Communications in Computational Physics, 2012, 12(2): 337-377.
[2] Cebral J R. Loose coupling algorithms for fluidstructure interaction [D]. Virginia, USA: Institute for Computational Science and Informatics, George Mason University, 1996.
[3] Blom F J. A monolithical fluid-structure interaction algorithm applied to the piston problem [J]. Computer Methods in Applied Mechanics and Engineering, 1998,167(3): 369-391.
[4] Lian Y, Shyy W, Ifju P, et al. A computational model for coupled membrane-fluid dynamics [C]//Proceedings of 32nd AIAA Fluid Dynamics Conference and Exhibit. Missouri, USA: AIAA, 2002:2492-2494.
[5] Bearman P W. Circular cylinder wakes and vortexinduced vibrations [J]. Journal of Fluids and Structures,2011, 27(5): 648-658.
[6] Gabbai R D, Benaroya H. An overview of modeling and experiments of vortex-induced vibration of circular cylinders [J]. Journal of Sound and Vibration, 2005,282(3): 575-616.
[7] Turek S, Hron J. Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow [C]//Lecture Notes in Computational Science and Engineering,Fluid-Structure Interaction. Berlin, Germany:Springer-Verlag, 2006: 371-385.
[8] van Zuijlen A H, Bijl H. Multi-level accelerated subiterations for fluid-structure interaction [C]//Lecture Notes in Computational Science and Engineering,Fluid Structure Interaction II. Berlin, Germany:Springer-Verlag, 2010: 1-25.
[9] Rannacher R, Richter T. An adaptive finite element method for fluid-structure interaction problems based on a fully Eulerian formulation [C]//Lecture Notes in Computational Science and Engineering,Fluid Structure Interaction II. Berlin, Germany:Springer-Verlag, 2010: 159-191.
[10] Bungartz H J, Benk J, Gatzhammer B, et al.Partitioned simulation of fluid-structure interaction on Cartesian grids [C]//Lecture Notes in Computational Science and Engineering, Fluid Structure Interaction II. Berlin, Germany: Springer-Verlag, 2010: 255-284.
[11] Wall W A, Ramm E, Fluid-structure interaction base upon a stabilized (ALE) finite element method[C]//Proceedings of 4th World Congress on Computational Mechanics. Barcelona, Spain: CIMNE, 1998:1-20.
[12] Hubner B, Walhorn E, Dinkler D. A monolithic approach to fluid-structure interaction using spacetime finite element [J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(23): 2087-2104.
[13] Dettmer W, Peri′c D. A computational framework for fluid-structure interaction: Finite element formulation and applications [J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(41): 5754-5779.
[14] Wang W Q, Yan Y. Strongly coupling of partitioned fluid-solid interaction solvers using reduced-order models[J]. Applied Mathematical Modelling, 2010, 34(12):3817-3830.
[15] Kassiotis C, Ibrahimbegovic A, Niekamp R, et al.Nonlinear fluid-structure interaction problem. Part II.Space discretization, implementation aspects, nested parallelization and application examples [J]. Computational Mechanics, 2011, 47(3): 335-357.
[16] Oxtoby O F, Malan A G. A matrix-free, implicit,incompressible fractional-step algorithm for fluid-structure interaction applications [J]. Journal of Computational Physics, 2012, 231(16): 5389-5405.
[17] Malan A G, Oxtoby O F. An accelerated,fully-coupled, parallel 3D hybrid finite-volume fluidstructure interaction scheme [J]. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 426-438.
[18] Bathe K J. Finite element procedures [M]. New Jersey,USA: Prentice-Hall, 1996.
[19] Jansen K, Shakib F, Hughes T J R. Fast projection algorithm for unstructured meshes [C]//Computational Nonlinear Mechanics in Aerospace Engineering. Reston, VA, USA: AIAA,1992: 175-204.