Source-like patterns of flow past a circular cylinder of finite span at low Reynolds numbers

Abstract

This article is to report results of a joint numerical and experimental investigation of vortex structures of flow past a circular cylinder of diameter D and finite span L in a range of low Reynolds numbers. The aspect ratio (AR) (= L/D) of the cylinder varies from 1.5 to 5, and the Reynolds number Re varies from 10 to 150. Given Re = 80, we study the various cases of AR, and given AR = 5, we study the various cases of Reynolds numbers Re. In a regime of parameters, the flow is found to be steady, separated, and doubly symmetric. Beyond this regime, the present study also covers a range of unsteady flow with vortex shedding in the wake behind the cylinder. This study is focused on the streamline patterns on the two planes of symmetry: the middle cross section plane (MCP) of the circular cylinder as well as on the bisectional cross section plane (BCP) on the circular cylinder. The exclusive phenomenon discovered is the occurrence, in a range of flow conditions, of a point-like or line-like source pattern of streamlines in the wake on the MCP. The center of the singular source is denoted by the center of the source (CS). In the cases of steady flow, there is always a pair of recirculating eddies on the BCP, which forms a saddle point (SP) structure at their far end from the cylinder. At the occurrence of source-like flow patterns, CS coincides with SP, signifying that the source-like points concentrate in a small neighborhood of CS (or SP). The SP is characterized by normalizing the location of the source Ds from the cylinder center. It is given a definition of the strength of the source (SS), determined by normalizing the two-dimensional divergence ∇2·v on the MCP. Moreover, the flow patterns with or without a singular source are classified into four categories on the Re–AR parameter plane. In particular, a criterion on SS is found for the occurrence of a source-like pattern. The formation of the source-like wake flow and variations of the source locations and the source strength with Re and AR are given full physical explanations. The interesting trends of the drag coefficients with AR are explained on the relative importance of the surface friction and the pressure (form) drag.