Flow around an Oscillating Cylinder at Low Reynolds Number with Forced Convection: Effect of Corner Radius and Reynolds Number

Abstract

This numerical study investigated the flow-induced vibration (FIV) on non-heated and heated cylinders with different normalized corner radii (r*) at different Reynolds numbers (Re). Four different values of r* were considered (i.e., 0 (square cylinder), 0.5, 0.75, and 1.0 (circular cylinder)) at three different Re: 100, 150, and 200 within the laminar regime. The cylinder constrained in the axial direction and oscillated transversally was considered for a fixed nondimensional cylinder mass (m*)  of 10 and a reduced velocity (Ur) of 4.92. The effect of r* and Re could be seen in the vibration modes of cylinders. The two-dimensional incompressible Navier–Stokes and energy equations were solved together with Newton’s Second Law governing the motion of the cylinder with the help of a computational solver. Four different modes were observed in this study: Mode-I characterized by exceptionally low amplitude; Mode-II characterized by fluctuating amplitude known as hysteresis (beating); Mode-III characterized by high amplitude due to synchronization or lock-in; and Mode-IV characterized by the monotonic oscillation of fixed amplitude. For r* = 1, synchronization phenomenon/lock-in was observed. For the heated cylinder cases, due to the change in the normalized corner radius, a notable change in nondimensional vibrational amplitude A/D and the average Nusselt number Nuavg was seen. It was observed that A/D was higher when lock-in occurred (at Re = 100 and r* = 1), leading to a rise in Nuavg by 47.9% compared to Re = 100 and r* = 0. Due to the change in r*, a shifting phenomenon was observed at Re = 150, r* = 0.75 and Re = 200, r* = 1. A major change in Nuavg was observed from the circular cylinder to square cylinder at different Re. The beating phenomenon was observed at Re = 100 for r* = 0.75, which was similar to that occurring at Re = 150 and r* = 0.5, and those at Re = 200 and r* = 0. Heat transfer and wake structure parameters were found to be dependent on r* and Re.