Numerical Simulation Of Interference Effect Of Flow Around Multi-Circular-Cylinders Based On Spectral Element Method

Flow around multi-circular-cylinders is often encountered in practicalengineering. When flow past more than one cylinder the forces and the vortexshedding pattern are very different from those of an isolated cylinder, even at thesame Reynolds number.Spectral element method is a spectral method combined with the finite elementmethod.The solution region is divided into units, using isoparametric elements in eachunit with the N-order polynomial to approximate the variables, using Galerlkintechnology and Gauss quadrature, get the discretized equations. Spectral element is ahigh-order element combining the geometrical facility of the finite element methodand the high accuracy of the spectral method so that it can achieve a high convergenceand computing efficiency.This paper describes the basic theory of the spectral element method (SEM), andNavier-Stokes equation has been solved numerically by a three-step time splittingscheme. Flow around two circular cylinders in tandem and side-by-side array at aReynolds number of 200 with various spacing ratios is investigated numerically byusing SEM. The study focuses on the effect of spacing ratios (ratio of center-to-centerdistance to diameter) on flow characteristics to identify the critical spacing ration. Intandem array the critical spacing ratio is about 3.6. When the spacing ration is lessthan the critical spacing ratio, the upstream cylinder doesn't produce vortex shedding,and a symmetric recirculation zone is observed behind the upstream cylinder. Whenthe spacing ratio is larger than the critical spacing ratio, the upstream vortex sheddingcylinder produces, and the force statistics and the Strouhal number change a lot. Inside-by-side array, the critical spacing ratio is about 2.2. Different wake patterns areobserved, such as single bluff-body wake pattern (s=1.2), flip-flopping wake pattern(s=1.5), and in-phase synchronized or anti-phase synchronized wake pattern (s>2.2).Flow around four cylinders in in-line square and rotated square arrays at aReynolds number of 200 with various spacing ratios is also investigated numerically.When in in-line square array, three different wake patterns are observed, such asstable shielding flow pattern, wiggling shielding flow pattern and vortex sheddingflow pattern. When in rotated square array, different wake patterns are observed too. In this configuration, the wake patterns are more complex than the previous. Forspacing ratios between 2.5 and 3.5, the wake behind the upstream cylinder is unstable,and the force statistics and the Strouhal number of the downstream cylinders change alot. When the spacing ratio is large, the wake behind the cylinders is stable.