Secondary lock-in of vortex-induced vibration and energy transfer characteristics of a vibrating cylinder subject to cross buoyancy

Abstract

The hydrodynamic and thermal characteristics of a freely vibrating circular cylinder subject to cross buoyancy are numerically investigated at low Reynolds numbers. The structural responses and onset of vortex-induced vibration (VIV) are documented over a range of parameter space, 2.0≤ reduced velocity (Ur) ≤10.0, 0.7≤ Prandtl number (Pr) ≤10.0 and 0.5≤ Richardson number (Ri) ≤2.0. The fluid and structural coefficients are chosen as Reynolds number (Re)=100, mass ratio (m*)=10.0, and damping ratio (ζ)=0.01. A phenomenon of secondary VIV lock-in is found in the cases of Ri = 2.0 (the cross buoyancy effect becomes influential), Pr≲2.0 and Ur≳7.0. An extended VIV lock-in region is formed over a wide range of reduced velocity values together with a tremendous kinetic energy transfer between fluid and structure. This finding is significant for the research of hydropower harvesting. On the other hand, the influence of structural dynamics on heat convection over the surface of a heated circular cylinder is recorded and discussed as well. The significance and mutual influence between Prandtl and Richardson numbers on hydrodynamics, structural dynamics, and heat convection are discussed in detail. The temperature contours are found concentrating around the cylinder's surface in the cases of high Prandtl numbers, which are also associated with higher mean Nusselt number (Nu¯) values. The influence on heat convection over a cylinder's surface is quantified via the computation of Nu¯ and its fluctuation for different circumstances. The energy transfer coefficient is employed to quantify the kinetic energy transfer between the fluid and a heated structure in mixed convective flow. The phase angle difference between the transverse displacement and lift force is used to support the discussions of energy transfer in fluid.