Numerical simulation of interaction between laminar flow and elastic sheet

Abstract

A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.

Keywords

fluid-structure interaction (FSI) / numerical simulation / immersed boundary method / combined finitediscrete element method / three-dimensional flow

References

[1] Dowell E. H., Hall K. C. Modeling of fluid-structure interaction[J]. Annual Review of Fluid Mechanics, 2001, 33(1): 445-490.

[2] Jauvtis N., Williamson C. H. K. Vortex-induced vibration of a cylinder with two degrees of freedom[J]. Journal of Fluids and Structures, 2003, 17(7): 1035-1042.

[3] Feistauer M., Horáček J., Růžička M., et al. Numerical analysis of flow-induced nonlinear vibrations of an airfoil with three degrees of freedom[J]. Computers and Fluids, 2011, 49(1): 110-127.

[4] Liu Y. L., Liu W. K. Rheology of red blood cell aggregation by computer simulation[J]. Journal of Computational Physics, 2006, 220(1): 139 154

[5] Le Tallec P., Mouro J. Fluid structure interaction with large structural displacements [J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(24/25): 3039-3067.

[6] Cheng Y. G., Zhang H. Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow[J]. Computers and Fluids, 2010, 39(5): 871 881

[7] Chang K. S., Olbricht W. L. Experimental studies of the deformation of a synthetic capsule in extensional flow[J]. Journal of Fluid Mechanics, 1993, 250(5): 587-608.

[8] Gomes J. P., Yigit S., Lienhart H., et al. Experimental and numerical study on a laminar fluid-structure interaction reference test case[J]. Journal of Fluids and Structures, 2011, 27(1): 43-61.

[9] Degroote J., Bathe K. J., Vierendeels J. Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction[J]. Computers and Structures, 2009, 87(11/12): 793-801.

[10] Masud A., Bhanabhagvanwala M., Khurram R. A. An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction[J]. Computers and Fluids, 2007, 36(1): 77 91

[11] Baaijens F. P. T. A fictitious domain/mortar element method for fluid-structure interaction[J]. International Journal for Numerical Methods in Fluids, 2001, 35(7): 743 761

[12] Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows[J]. Journal of Computational Physics, 2005, 209(2): 448 476

[13] Thomas T. G., Williams J. J. R. Development of a parallel code to simulate skewed flow over a bluff body[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1997, 67/68(8): 155-167.

[14] Munjiza A. The Combined Finite-Discrete Element Method [M]. 2004, West Sussex, England: John Wiley & Sons.