Hysteresis phenomenon in the galloping oscillation of a square cylinder

Abstract

It is well known that a square cylinder with one side normal to a uniform stream will gallop when a critical flow velocity is exceeded. It is also quite well known that there is a hysteresis phenomenon in the variation of the cylinder's galloping amplitude with the flow velocity. However, little is known about the cause of this hysteresis phenomenon, and the objective of this paper is to study it more closely. In the present study, flow over a stationary square cylinder at different angle of attack (α) and at Reynolds number (Re) of 250 and 1000 was investigated numerically by using a 2-D hybrid vortex computation scheme. The study reveals that the well known point of inflection which exists in the side force (Cy) versus α plots at high Reynolds number only occurs at Re = 1000, α = 4° in the present numerical simulation. Nonlinear analysis further reveals that this point of inflection is the cause of the hysteresis phenomenon. By further analysing the computed flow field, it is noted that at Re = 1000, α = 4°, intermittent flow reattachment takes place at alternate vortex shedding cycle on one side of the cylinder. This results in larger side force fluctuation, and it is conjectured that such large side force fluctuation affects the increasing trend of the side force with angle of attack, resulting in the point of inflection reported earlier. The above-mentioned alternate cycle flow reattachment was much less prominent at α = 2° and 6° (Re = 1000), and was not observed at Re = 250. Finally, dye flow visualization was carried out in a recirculating water tunnel and the results at Re = 1000 confirms the existence of the intermittent flow reattachment. However, in the experiment, flow reattachment does not take place in a very regular alternate cycle manner as in the computation. Instead, it occurs intermittently, possibly due to three-dimensional effects in real flow. © 2003 Elsevier Ltd. All rights reserved.