Numerical calculations are carried out to simulate the flow field and the noise for arrays of circular cylinders in various arrangements. The finite element method based on hybrid quadrilateral grids is used for solution of the incompressible Navier-Stokes equations. The consistent streamline upwind/Petrov-Galerkin (SUPG) method is used for the upwind weighted formulation and the pressure-implicit with splitting of operators (PISO) scheme with the equal-order bilinear element is adopted as a segregated velocity-pressure formulation. The dipole formula for predicting the noise signal of circular cylinders in a uniform field is used. The basic assumption made in deriving this formulation is that sound radiation from a circular cylinder in uniform flow is primarily due to the fluctuating pressure exerted on the cylinder surface. In an effort to avoid shortcoming in geometries, hybrid grids for the SUPG finite element method are presented, here structured rectangular elements cover the viscous region close to the surface of each body, while unstructured quadrilateral elements are created elsewhere. Hence, the hybrid grid approach is to contain the capability of unstructured grid in handling complex geometries, the efficiency of structured grid in resolving viscous terms and the consistency of quadrilateral elements in applying SUPG to all computational domains.
The accuracy of the present approach is compared with the solutions of the well-known benchmark problem for flow past a circular cylinder at Re = 100 and 200. The numerical method is then applied to flow past two circular cylinders and three circular cylinders in various arrangements. The solutions obtained show good agreement with the results of other studies, including the critical spacing in which the forces on the cylinders are drastically reduced. In addition, through the use of hybrid quadrilateral grids, our analysis can be further extended into the region in much closer proximity of two cylinders, including in contact. The critical spacing is found to decrease inversely to the Reynolds numbers up to 300. The effects of distance between the two cylinders are shown on the Strouhal number as well as the lift coefficient.
