Analysis of Fully Coupled Flow-Induced Vibration of Structure Under Small Deformation With GMRES

ZHANG Li-xiang; GUO Ya-kun; ZHANG Hong-ming

doi:10.3879/j.issn.1000-0887.2010.01.009

Volume 31 Issue 1

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ZHANG Li-xiang, GUO Ya-kun, ZHANG Hong-ming. Analysis of Fully Coupled Flow-Induced Vibration of Structure Under Small Deformation With GMRES[J]. Applied Mathematics and Mechanics, 2010, 31(1): 81-90. doi: 10.3879/j.issn.1000-0887.2010.01.009

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Analysis of Fully Coupled Flow-Induced Vibration of Structure Under Small Deformation With GMRES

doi: 10.3879/j.issn.1000-0887.2010.01.009

Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650051, P. R. China;
School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK

Received Date: 2009-05-13
Rev Recd Date: 2009-11-09
Publish Date: 2010-01-15

Abstract

Abstract

Lagrangian-Eulerian formulations, based on a generalized variational principle of coupling fluid and solid dynamics, was established to describe flow-induced vibration of a structure under small deformation in incompressible viscous fluid flow. The spatial discretization of the formulations was on multi-linear interpolating functions using the finite element method for both the fluid and solid structure. The generalized trapezoidal rule was used to obtain apparently nonsymm etric linear equations in in cremental form for the variables of the flow and vibration. The nonlinear convective term and tmie factors were contained in nonsymmetric coefficient matrix of the equations. Generalized minimum residual method (GMRES) was used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark was developed to deal with flow-induced vibration with dynamical fluid-structure in teraction in complex geometry. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GMRES-Hughes-Newmark algorithm presented was suitable for dealing with the flowinduced vibration of structures under small deformation.
- flow-induced vibration,
- fluid-structure in teraction,
- generalized variational principle,
- numerical methods,
- GMRES

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References(33)

References

[1]	Weaver D S, Ziada S, Au-Yang M K, et al. Flow-induced vibration in power and process plants components- progress and prospects[J].ASME Journal of Pressure Vessel Technology, 2000, 122(3): 339-348. doi: 10.1115/1.556190
[2]	张立翔，杨柯. 流体结构互动理论及其应用[M]. 北京：科学出版社, 2004.
[3]	Wu X H, Durbin P A. Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage[J]. Journal of Fluid Mechanics, 2001, 446:199-228.
[4]	Wissink J G. DNS of separating, low Reynolds number flow in a turbine cascade with incoming wakes[J].International Journal of Heat and Fluid Flow, 2003,24(4): 626-635. doi: 10.1016/S0142-727X(03)00056-0
[5]	Rodi W. DNS and LES of some engineering flows[J]. Fluid Dynamics Research, 2006,38(2/3):145-173. doi: 10.1016/j.fluiddyn.2004.11.003
[6]	Moin P, Mahesh K. Direct numerical simulation: a tool in turbulence research[J]. Annual Review of Fluid Mechanics, 1998, 30: 539-578. doi: 10.1146/annurev.fluid.30.1.539
[7]	Wissink J G, Rodi W. Direct numerical simulation of flow and heat transfer in a turbine cascade with incoming wakes[J].Journal of Fluid Mechanics, 2006,569: 209-247. doi: 10.1017/S002211200600262X
[8]	Moin P. Advances in large eddy simulation methodology for complex flows[J]. International Journal of Heat and Fluid Flow,2002, 24(5): 710-720.
[9]	Manna M, Benocci C, Simons E. Large eddy simulation of turbulent flows via domain decomposition techniques—part 1: theory[J]. International Journal for Numerical Methods in Fluids, 2005, 48(4): 367-395. doi: 10.1002/fld.902
[10]	Benocci C, Giammanco R, Manna M, et al. Large eddy simulation of turbulent flows via domain decomposition techniques—part 2: applications[J]. International Journal for Numerical Methods in Fluids, 2005, 48(4): 397-422. doi: 10.1002/fld.903
[11]	Kjellgren P, Hyvrinen J. An arbitrary Lagrangian-Eulerian finite element method[J]. Computational Mechanics, 1998, 21(1):81-90. doi: 10.1007/s004660050285
[12]	Sarrate J, Huerta A, Donea J. Arbitrary Lagrangian-Eulerian formulation for fluid-rigid body interaction[J]. Computer Methods in Applied Mechanics and Engineering, 2001,190(24/25): 3171-3188. doi: 10.1016/S0045-7825(00)00387-X
[13]	Souli M, Ouahsine A, Lewin L. ALE formulation for fluid structure interaction problems[J]. Computer Methods in Applied Mechanics and Engineering, 2000,190(5/7): 659-675.
[14]	Peskin C S. Numerical analysis of blood flow in the heart[J]. Journal of Computational Physics, 1977, 25(3): 220-252. doi: 10.1016/0021-9991(77)90100-0
[15]	Kim J, Kim D, Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries[J]. Journal of Computational Physics, 2001, 171(1): 132-150. doi: 10.1006/jcph.2001.6778
[16]	Iaccarino G, Verzicco R. Immersed boundary technique for turbulent flow simulations[J]. Applied Mechanics Reviews, 2003, 56(30): 331-347. doi: 10.1115/1.1563627
[17]	Shin S, Bae S Y, Kim I C, et al. Computation of flow over a flexible plate using the hybrid Cartesian/immersed boundary method[J].International Journal for Numerical Methods in Fluids, 2007, 55(3):263-282. doi: 10.1002/fld.1459
[18]	Tezduyar T E. Computation of moving boundaries and interfaces and stabilizatation parameters[J]. International of Journal for Numerical Methods in Fluids, 2003, 43(5):555-575. doi: 10.1002/fld.505
[19]	Bayoumi H N, Gadala M S. A complete finite element treatment for the fully coupled implicit ALE formulation[J]. Computational Mechanics, 2004, 33(6): 435-452. doi: 10.1007/s00466-003-0544-y
[20]	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(41/43):5757-5779.
[21]	Tezduyar T E. Finite elements in fluids: stabilized formulations and moving bound aries and interfaces[J]. Computers and Fluids, 2007, 36(2):191-206. doi: 10.1016/j.compfluid.2005.02.011
[22]	Tezduyar T E. Finite elements in fluids: special methods and enhanced solution techniques[J]. Computers and Fluids, 2007, 36(2):207-223. doi: 10.1016/j.compfluid.2005.02.010
[23]	Tezduyar T E, Sathe S. Modelling of fluid-structure interactions with the space-time finite elements: solution techniques[J]. International of Journal for Numerical Methods in Fluids, 2007, 54(6/8):855-900. doi: 10.1002/fld.1430
[24]	Zhang L X, Guo Y, Wang W Q. Large eddy simulation of turbulent flow in a true 3D Francis hydro turbine passage with dynamical fluid-structure interaction[J]. International Journal for Numerical Methods in Fluids, 2007, 54(5): 517-541. doi: 10.1002/fld.1408
[25]	Zhang L X, Wang W Q, Guo Y. Numerical simulation of flow features and energy exchanging physics in near-wall region with fluid-structure interaction[J]. International Journal of Modern Physics B, 2008, 22(6): 651-669. doi: 10.1142/S0217979208038806
[26]	Liew K M, Wang W Q, Zhang L X, et al. A computational approach for predicting the hydroelasticity of flexible structures based on the pressure Poisson equation[J].International Journal for Numerical Methods in Engineering, 2007, 72(13):1560-1583. doi: 10.1002/nme.2120
[27]	Ishihara1 D, Yoshimura S. A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equation[J].International Journal for Numerical Methods in Engineering, 2005, 64(2):167-203. doi: 10.1002/nme.1348
[28]	Wang W Q, He X Q, Zhang L X, et al. Strongly coupled simulation of fluid-structure interaction in a Francis hydroturbine[J]. International Journal for Numerical Methods in Fluids, 2009, 60(5):515-538. doi: 10.1002/fld.1898
[29]	Teixeira P R F, Awruch A M. Numerical simulation of fluid-structure interaction using the finite element method[J]. Computers & Fluids, 2005, 34(2):249-273.
[30]	Heil M. An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(1/2): 1-23. doi: 10.1016/j.cma.2003.09.006
[31]	Saad Y, Schultz M H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems[J]. SIAM Journal on Scientific and Statistical Computing, 1986, 7(3):856-869. doi: 10.1137/0907058
[32]	Ayachour E H. A fast implementation for GMRES method[J]. Journal of Computational and Applied Mathematics, 2003, 15(2):269-283.
[33]	Zhang L X, Guo Y K, Wang W Q. FEM simulation of turbulent flow in a turbine blade passage with dynamical fluid-structure interaction[J].International Journal for Numerical Methods in Fluids, 2009,61(12):1299-1330. doi: 10.1002/fld.1996