FEDSM-ICNMM 2010-30577 FLOW INDUCED CYLINDER OSCILLATION AND ITS CONTROL WITH HIGH ORDER SPECTRAL DIFFERENCE METHOD ON DEFORMABLE MESH

In the recent work by the authors, high order spectral difference (SD) method has been formulated in a framework with dynamic deformable meshes, and been demonstrated to preser ve the design accuracy of the underlying high order temporal an d spatial discretization methods. In this study, the current SD method has been extended to solve fluid structure interactio n problems on deforming meshes. The SD method with collocated solution and flux points is used as the spatial discretization method, while the expl icit fourth order five-stage Runge-Kutta is used to advance the flo w in time. The solid structure, which is the cylinder, is model led as a spring-mass system. The movement of the solid cylinder i s handled with a dynamic deforming mesh using an algebraic hig h order blending polynomial. The present work has focused on flow induced cylinder oscillation, bluff body wake and cylinder interaction, and co ntrol of flow induced oscillation through mechanism of counter-rota ting cylinders. Numerical experiment for flow over counter-rota ting cylinder pair shows that significant drag reduction and wake suppression can be obtained. Numerical calculation for a fr eestream flow over a free-floating cylinder shows that the wake symmetry of a cylinder can not be maintained. The resultant wake instability propels the cylinder in the cross-flow dire ction, but the cylinder was found to eventually locked in a flow induc ed self-oscillation at an equilibrium position. Active contr ol of the cylinder vibration through the mechanism of counter-rotat ion of ∗Address all correspondence to this author. solid bodies is finally investigated. INTRODUCTION Current CFD research has seen high order methods emerging as promising and competitive tools for solving both stea dy and unsteady fluid dynamic problems. Extensions of high orde r methods to dynamic deforming meshes and fluid structural interaction problems are areas of ongoing research. The abili ty to handle mesh deformation and fluid structure dynamic allow us to expand the application of CFD into a wider field of engineer ing, and this study is an attempt to demonstrate both capabil ities using a high order accurate CFD method. In addition to flow analysis, we are also exploring ways to actively control the flow so that undesirable effects such as excessive drag and vibra tion can be alleviated or even suppressed. The paper is organized as such: we will first present the details of the high order spectral difference method; next, th e extension of the spectral difference method to deal with movin g deforming boundary problem, as well as the method to deform and blend mesh, are discussed; this is followed by sections o n structure model and fluid structure coupling; finally, we pre sent numerical results to examine the fluid structure interactio n dynamics, active flow control mechanism, as well as the performance of high order method and deforming mesh technique. 1 Copyright c © 2010 by ASME NUMERICAL METHOD FOR FLUID SOLVER For the fluid solver, we use the high order spectral differenc e method [1–5] . The SD method, like Discontinuous Galerkin [6–11], is element-wise discontinuous. Within each indivi ual element, collocated solution and flux points are used to stor e fl w solution and flow flux information. With these solution and flu x points, one solution polynomial and one flux polynomial can b e constructed to represent the flow solution and flux in the loca l domain spanned by the element. The flux polynomial is one order higher than the solution polynomial such that when it is diff erentiated the flux divergence is of the same order as the soluti on polynomial. Therefore, the number of flux points is one more than that of solution points. At the element interface, wher e two sets of local solution meet each other, the flux across the int erface is discontinuous. A method to enforce continuity is to u se a Riemann solver, which was developed to handle discontinui ty across interface. Such a Riemann solver for enforcing flux co ntinuity includes Roe [13] flux or Rusanov [14] flux. Details of the SD formulation are outlined in the subsequent section. T he standard SD method, which follows the work by Sun etc [12], is presented first. This is then followed by its extension to r otating/sliding boundary problem, and, later, moving defor ming mesh problem. Spatial Discretization with Spectral Difference Method Consider the unsteady 2D conservation law of the form ∂Q ∂ t + ∂F ∂x + ∂G ∂y = 0 (1) whereQ is the vector of conserved variables; F andG are the total fluxes including both inviscid and viscous flux vectors . The conservative variables Q and Cartesian components of the in viscid flux vectorFinv(Q) are given by