Numerical Simulation of Flow Induced Vibration Based on Fully Coupled Fluid-Structural Interactions

Abstract

A fully coupled numerical methodology is developed for calculating the flow-structure interaction problems. The Roe scheme is extended to moving grid and used with the finite-volume method. The unsteady solutions march in time by using a dual-time stepping implicit unfactored line Gauss-Seidel iteration. The unsteady Navier-Stokes equations and the linear structural equations are fully coupled implicitly via successive iteration with pseudo time stepping. The moving mesh and mesh deformation strategy is based on two mesh zones, a fine mesh zone surrounding the solid body without mesh deformation and a coarse mesh zone surrounding the fine mesh zone and deforms with the solid object. This mesh deformation strategy can maintain the orthogonality of the mesh near the wall and save CPU time for re-meshing. The study cases presented include a vortex-induced oscillating cylinder, a forced pitching airfoil, and an elastically mounted transonic airfoil. For the elastic transonic airfoil, the flutter boundary is calculated. Other phenomena captured include the limit cycle oscillation (LCO) and the steady state flow conditions, under which the aerodynamic forces and moments are balanced by the structure. The computational results agree well with the experiments and the computed results of other researchers. The methodology is demonstrated to be accurate, robust and efficient.

Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes

“…In their scheme, both the flow and structure solution methods use dual time-stepping. More recently, Chen et al [19] applied a dual time-stepping scheme to achieve strong coupling by updating the structure solution after each iteration of their line Gauss-Seidel method used for the flow solution.…”

“…(19) denotes the number of edges connected to node i, DS j is the area of the node-dual boundary associated with the jth edge, and V i (Q) is the final contribution of the viscous fluxes to the controlvolume around node i. …”

“…A different approach followed by others is the ALE formulation with a moving mesh source term [17][18][19]. Even though such a formulation has produced reasonable results in moving mesh simulations, there was neither a clear derivation of the source term, nor detailed discussion of its significance.…”

High order conservative differencing for viscous terms and the application to vortex-induced vibration flows

“…The LES is also carried out by using a finite element method [36] and the standard second-order finite difference scheme [19,37]. Chen and Zha [38,39] developed a fully coupled fluid-structural interaction method, in which the 3rd order MUSCL differencing for inviscid fluxes and 2nd-order central differencing for viscous terms are used. Except the spectral methods, the finite differencing schemes in the aforementioned research work are all at 2nd-order accuracy.…”

“…Since there are no shock discontinuities in the cylinder flows, the WENO scheme is fixed to its optimal weights to achieve minimum dissipation. The fully coupled fluid-structural interaction strategy developed by Chen and Zha [38,39] is employed.…”