Vortex induced vibration for mixed convective flow past a square cylinder

In this work, a comprehensive numerical investigation of the combined effect of buoyancy and flow approach angle ( alpha) on vortex-induced vibration of an elastically mounted square cylinder at a fixed Reynolds number, Re = 100, Prandtl number (Pr = 7.1) and mass ratio (M red ) of 2 is conducted. Extensive numerical experiments were carried out for different flow approach angles ( alpha = 0 degrees-90 degrees) and for various reduced velocities (U red = 3-25) at Richardson number, Ri = 0, 0.25 and 0.50. The Arbitrary Lagrangian-Euler (ALE) approach models the solid-fluid interaction. The coupled fluid-structure interaction problem in two-degree-of-freedom (2-DOF) was solved using a high-fidelity finite difference-based solver. The Lock-in regime was found to be fixed, between U red = 5 and 6, for all flow approach angles irrespective of Ri. For all flows other than transverse flow, the reduced frequency is found to be equal in both directions ( f x = f y ) but in the transverse situation, ( alpha= 90 degrees), reduced frequency in the x-direction is twice that of the y-direction for all reduced velocities (U red ). Different vortex shedding modes 2S, 2S *, P + S and 2P are also observed in the study. The average coefficient of drag ( C over bar D ) and Nusselt number ( N over bar u ) was found to peak at alpha = 45 degrees for all U red . It was also found that as alpha is increased, C over bar D and N over bar u increases due to larger heated surface area exposure to the fluid particles. When Ri increases, C over bar D and N over bar u increases at a alpha due to the higher heat transfer rate. Highest value of N over bar u is observed for U red = 6, alpha = 45 degrees at Ri = 0.5.