Flow past rectangular cylinders: receptivity to transverse forcing

Abstract

The flow at low Reynolds number around rectangular cylinders of varying chord-tothickness ratios under transverse periodic forcing is studied numerically. Although of relatively low amplitude, the forcing locks the shedding from both the leading and trailing edges to the applied frequency. The base suction, and the lift and the drag on the cylinders are found to be complex functions of the forcing frequency. At low Reynolds numbers and without applied forcing, the flow is controlled by a global instability with the leading-and trailing-edge shedding locked; moreover, the reduced frequency of shedding varies in a stepwise manner with the chord-tothickness ratio. This global instability is still evident in the flows under external forcing examined in this paper. While previous researchers have conjectured that the trailing-edge shedding plays a dominant role in the preferred frequency selection in the natural shedding case, the important role of trailing-edge shedding when the flow is forced is confirmed in the present study. In particular, the individual contributions from leading-and trailing-edge vortices on the perturbation to the leading-edge shear layer are examined. In addition, it is shown that the base suction is maximum when the forcing frequency is close to the global instability frequency observed in unforced flows, thereby strengthening the argument that the unforced, forced, and duct resonant cases are strongly influenced by the same global instability. The variations of the lift, drag and formation length with chord-to-thickness ratio are quantified.

Features of the turbulent flow around symmetric elongated bluff bodies

“…For the triangular-edged model, the vortices travel along the body at about 0.8U N , and then speed up as they approach the trailing edge. It should be noted that for the low Reynolds number simulations of rectangular cylinders, similar speed-up behaviour is observed (Tan et al, 2004).…”

“…However, in their experiments at Re = 3.11 Â 10 4 , Parker and Welsh (1983) found that there is a large regime based on these elongation ratios where there is no dominant frequency in the wake, indicating an absence of periodic vortex shedding at higher Reynolds numbers. Several studies have shown that the shedding activity is highly susceptible to external forcing at the expected shedding frequency both at low Reynolds numbers (e.g., Mills et al, 2003;Tan et al, 2004) and at high Reynolds numbers where the ILEV instability is suppressed for unforced flows (e.g., Parker and Welsh, 1983;Mills et al, 2002).…”

3D flow around a rectangular cylinder: A computational study

“…On one hand, the lowReynolds number flow around rectangular cylinders has been clarified in both its 2D and 3D features by several studies (e.g. [3,4,5]. On the other hand, the high-Reynolds number flow (i.e.…”

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

“…A number of authors have examined the locking of leading-edge shedding through a feedback loop involving the upstream pressure pulse as released vortices pass the trailing edge of the plate (e.g. Nakamura, Ohya & Tsurata 1991;Ohya et al 1992;Hourigan, Thompson & Tan 2001;Mills, Sheridan & Hourigan 2003;Tan, Thompson & Hourigan 2004).…”