Numerical simulation of three-dimensional incompressible fluid in a box flow passage considering fluid–structure interaction by differential quadrature method

Abstract A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier–Stokes (N–S) equations by firstly taking fluid–structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow’s Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.

[1]  Stuart J. Price.  A Review of Theoretical Models for Fluidelastic Instability of Cylinder Arrays in Cross-Flow , 1995 .

[2]  A. Tijsseling,et al.  Fluid transients and fluid-structure interaction in flexible liquid-filled piping , 2001 .

[3]  Chang Shu,et al.  Numerical computation of three‐dimensional incompressible Navier–Stokes equations in primitive variable form by DQ method , 2003 .

[4]  C. Shu,et al.  Numerical simulation of natural convection between two elliptical cylinders using DQ method , 2004 .

[5]  Alexander Orellano,et al.  Numerical simulation (DNS and LES) of manipulated turbulent boundary layer flow over a surface-mounted fence , 2000 .

[6]  C. Meneveau,et al.  Scale-Invariance and Turbulence Models for Large-Eddy Simulation , 2000 .

[7]  Bo Yu,et al.  Effect of Weissenberg number on the flow structure: DNS study of drag-reducing flow with surfactant additives , 2003 .

[8]  C. Bert,et al.  Differential Quadrature Method in Computational Mechanics: A Review , 1996 .

[9]  J. Wissink.  DNS OF SEPARATING, LOW REYNOLDS NUMBER FLOW IN A TURBINE CASCADE WITH INCOMING WAKES , 2003 .

[10]  Chang Shu,et al.  FREE VIBRATION ANALYSIS OF COMPOSITE LAMINATED CONICAL SHELLS BY GENERALIZED DIFFERENTIAL QUADRATURE , 1996 .

[11]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

[12]  Chang Shu,et al.  Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates , 1999 .

[13]  Siu-Tong Choi,et al.  VIBRATION ANALYSIS OF NON-CIRCULAR CURVED PANELS BY THE DIFFERENTIAL QUADRATURE METHOD , 2003 .

[14]  C. Shu.  Differential Quadrature and Its Application in Engineering , 2000 .

[15]  On the performance of three iterative methods for solution of GDQ algebraic equations , 1998 .

[16]  N. Kasagi,et al.  DNS study of turbulence modification with streamwise-uniform sinusoidal wall-oscillation , 1998 .

[17]  Numerical simulation of natural convection in a square cavity by SIMPLE-generalized differential quadrature method , 2002 .

[18]  Samir Ziada,et al.  Flow-Induced Vibrations in Power and Process Plant Components—Progress and Prospects , 2000 .

[19]  Lixiang Zhang,et al.  Analytical Solution for Fluid-Structure Interaction in Liquid-Filled Pipes Subjected to Impact-Induced Water Hammer , 2003 .

[20]  Qiusheng Li,et al.  Longitudinal vibration analysis of multi-span liquid-filled pipelines with rigid constraints , 2004 .

[21]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[22]  Siu-Tong Choi,et al.  VIBRATION ANALYSIS OF ELASTICALLY SUPPORTED TURBOMACHINERY BLADES BY THE MODIFIED DIFFERENTIAL QUADRATURE METHOD , 2001 .

[23]  Nong Zhang,et al.  Frequency domain analysis of fluid–structure interaction in liquid-filled pipe systems by transfer matrix method , 2002 .

[24]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE: A TECHNIQUE FOR THE RAPID SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS , 1972 .

[25]  C. Shu,et al.  APPLICATION OF GENERALIZED DIFFERENTIAL QUADRATURE TO SOLVE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS , 1992 .

[26]  Lixiang Zhang,et al.  Fsi Analysis of Liquid-Filled Pipes , 1999 .

[27]  Seon Han.  Fluid-Induced Vibration , 2005 .

[28]  Georgi Kalitzin,et al.  DNS of fully turbulent flow in a LPT passage , 2003 .

[29]  M. P. Païdoussis,et al.  Fluid Coupling Characteristics and Vibration of Cylinder Cluster in Axial Flow. Part I: Theory , 1994 .