Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method

A hybrid Cartesian/immersed boundary code is developed and applied to interactions between a flexible plate and a surrounding fluid. The velocities at the immersed boundary (IB) nodes are reconstructed by interpolations along local normal lines to an interface. A new criterion is suggested to distribute the IB nodes near an interface. The suggested criterion guarantees a closed fluid domain by a set of the IB nodes and it is applicable to a zero-thickness body. To eliminate the pressure interpolation at the IB nodes, the hybrid staggered/non-staggered grid method is adapted. The developed code is validated by comparisons with other experimental and computational results of flow around an in-line oscillating cylinder. Good agreements are achieved for velocity profiles and vorticity and pressure contours. As applications to the fluid–structure interaction, oscillations of flexible plate in a resting fluid and flow over a flexible plate are simulated. The elastic deformations of the flexible plate are modelled based on the equations of motion for plates considering the fluid pressure as the external load on the plate. Two non-dimensional parameters are identified and their effects on the damping of the plate motion are examined. Grid convergence tests are carried out for both cases. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Sharon R. Lubkin,et al.  Numerical analysis of interfacial two‐dimensional Stokes flow with discontinuous viscosity and variable surface tension , 2001 .

[2]  Sangmook Shin,et al.  Internal wave computations using the ghost fluid method on unstructured grids , 2005 .

[3]  Tibor S. Balint,et al.  Instability of a cantilevered flexible plate in viscous channel flow , 2005 .

[4]  Rainald Löhner,et al.  On the computation of multi-material flows using ALE formulation , 2004 .

[5]  E. Balaras,et al.  A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids , 2003 .

[6]  C. Peskin,et al.  Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method , 2002 .

[7]  Ernst Rank,et al.  Computation of wind-induced vibrations of flexible shells and membranous structures , 2003 .

[8]  Randall J. LeVeque,et al.  An Immersed Interface Method for Incompressible Navier-Stokes Equations , 2003, SIAM J. Sci. Comput..

[9]  Boyce E. Griffith,et al.  On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems , 2005 .

[10]  S. Y. Lee,et al.  Dynamic analysis of baffled fuel‐storage tanks using the ALE finite element method , 2003 .

[11]  F. Durst,et al.  Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers , 1998, Journal of Fluid Mechanics.

[12]  K. Bai,et al.  Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid , 2004 .

[13]  Julius Miklowitz,et al.  Dynamics of elastic systems , 1963 .

[14]  C. Peskin.  Flow patterns around heart valves: A numerical method , 1972 .

[15]  H. S. Udaykumar,et al.  A Sharp Interface Cartesian Grid Methodfor Simulating Flows with ComplexMoving Boundaries , 2001 .

[16]  E. Kuhl,et al.  An arbitrary Lagrangian Eulerian finite‐element approach for fluid–structure interaction phenomena , 2003 .

[17]  Michael Griebel,et al.  Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems , 2006 .

[18]  K. Namkoong,et al.  Computation of dynamic fluid-structure interaction in two-dimensional laminar flows using combined formulation , 2005 .

[19]  Clive L. Dym,et al.  Energy and Finite Element Methods In Structural Mechanics : SI Units , 2017 .

[20]  Haecheon Choi,et al.  Immersed boundary method for flow around an arbitrarily moving body , 2006, J. Comput. Phys..

[21]  S. Armfield,et al.  A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid , 2003 .

[22]  W. Shyy,et al.  Elafint: a Mixed Eulerian-Lagrangian Method for Fluid Flows with Complex and Moving Boundaries , 1996 .

[23]  Elias Balaras,et al.  An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries , 2006, J. Comput. Phys..

[24]  Keiji Kawachi,et al.  Regular Article: A Numerical Study of Undulatory Swimming , 1999 .

[25]  Dartzi Pan,et al.  An immersed boundary method for incompressible flows using volume of body function , 2006 .

[26]  F. Sotiropoulos,et al.  A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies , 2005 .

[27]  H. Fasel,et al.  A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains , 2005 .