Spectral Difference Solution of Incompressible Flow over an Inline Tube Bundle with Oscillating Cylinder

A high-order spectral difference (SD) method for solving the Navier-Stokes equations on moving, deformable unstructured grids has been developed [1]. In this paper, the SD method and the artificial compressibility method (ACM) are integrated with a dual time-stepping scheme to model unsteady incompressible viscous flow past an inline tube bundle of cylinders equally sized (diameter = d) and spaced (spacing = 2.1∗d) over an unstructured grid. Flow simulation results are obtained using a fourth-order space accurate SD method. Two forced oscillation cases are considered; (1) 1st cylinder oscillation and (2) 2nd cylinder oscillation. The Reynolds number used for both cases is 100 and the flow is laminar. Forced oscillation is performed in the tranverse direction, and the subsequent altering of the flow physics of the system is studied. The frequency of vortex shedding behind each cylinder is the same. Root mean square results show that the lift coefficient is greatest for the 4th inline cylinder in both cases. Furthermore, a reduction in both lift and drag coefficients is seen from case (1) to case (2). ∗PhD Student, [email protected]. †Assistant Professor, corresponding author, [email protected] ‡Professor, Department Chair, [email protected] INTRODUCTION The fluid dynamics across an array of multiple cylinders is rich indeed. Studies carried out for two cylinders [2] identify nine flow patterns that are dependent upon angle of incidence and tube spacing. Induced separation of flow, shear layer reattachment and vortex synchronization are just a few of the phenomena that have been observed. While flow around one or two cylinders has been greatly studied, fewer efforts have been devoted to studying a system involving many cylinders, commonly known as tube bundles. Tube bundles are widely used in power generation and oil industries (e.g. heat exchangers in nuclear reactors). Various tube bundle geometries exist; staggered symmetric, rotated square, normal triangle, parallel triangle, inline, etc. The focus of this paper is on the results of a study of two-dimensional incompressible flow past an inline tube bundle using the spectral difference method. Steady and unsteady incompressible flow about an inline stationary tube bundle has previously been studied [3]. In this paper, however, unsteady incompressible flow across six inline cylinders with one cylinder exhibiting tranverse oscillations will be studied within the context of the SD-ACM solver, which possesses the ability to move and deform the numerical grid such that the flow solution is properly computed as one of the cylinders oscillates.