A comprehensive study of heat transfer characteristic and two-dimensional FIV for heated square-section cylinder with different damping ratios

The present study explores the effect of damping ratio and Reynolds number on the flow-induced vibration and heat transfer behavior of a heated square-section cylinder. To this end, fluid-structure interaction simulations based on the finite-volume method are conducted for five different damping ratios of zeta = 0, 0.01, 0.05, 0.1, 0.25 and 0.5 at four representative Reynolds numbers of Re = 80, 90, 220 and 250. By considering the square-section cylinder as a mass-spring-damper system, one can model its free vibration along transverse and streamwise directions due to lift and drag forces exerted from the fluid, in which the dynamic mesh technique is employed to couple the cylinder motion with the flow field. Owing to its sharp corners, the square-section cylinder first experiences the lock-in condition in which the vortex shedding frequency approaches the oscillator natural frequency. After surpassing the critical flow velocity, the square-section cylinder undergoes high-magnitude and low-frequency oscillations known as galloping. For a more comprehensive evaluation, the designated Reynolds numbers encompass all vibration regions of the square-section cylinder: out of lock-in and galloping (Re = 80), middle-point of lock-in region (Re = 90), middle-point of galloping (Re = 220) and the peak of galloping zone (Re = 250). The results show that at Re = 90, as the damping ratio increases from zeta = 0.01 to zeta = 0.05, the amplitude of cylinder oscillations significantly drops due to the de-synchronization type action. A notable reduction in the oscillation amplitude at Re = 220 and 250 occurs with increasing damping ratio from zeta = 0.1 to zeta = 0.25, attributed to the hidden frequency emersion phenomenon in which the fundamental frequency of cylinder transverse oscillations shifts to a secondary value. It is also shown that the heat transfer rate of the square cylinder with free vibration is more than that of a stationary cylinder. With increasing damping ratio, the heat transfer rate of the cylinder decreases compared to the undamped conditions.