Vortex shedding suppression of vibrating square cylinder in mixed convection regime

In the present work, vortex shedding suppression of a vibrating square cylinder is numerically studied at Reynolds number, Re = 100, and Prandtl number, Pr = 7.1, in a mixed convection regime. Navier–Stokes equations with Boussinesq approximation are solved using a finite difference method by transforming it into a body-fitted coordinate system. The relationship between fluid flow and a vibrating square cylinder is captured using an Arbitrary Lagrangian Euler method. Numerical simulations are conducted for reduced velocities, Ured = 3–8 keeping the reduced mass (Mred) = 2 and damping coefficient, ξ′ = 0. The role of baroclinic vorticity is studied on the vortex shedding suppression for an elastically mounted free vibrating heated square cylinder. The critical Richardson number, Ric (Richardson number at which vortex shedding becomes suppressed) is determined by increasing the Richardson number (Ri) and observing the vortex shedding pattern. For every Ured = 3–8, a Ric is obtained. It is found that critical Richardson number (Ric) for the lock-in regime (Ured = 6) is 0.395 whereas for the initial branch (Ured = 3) and lower branch (Ured = 8) it is 0.17 and 0.18, respectively. Baroclinic vorticity generation for the lock-in regime, initial branch, and lower branch is also investigated comprehensively. The Ric for the initial and lower branch is close to Ric for the stationary cylinder. The Ric for the stationary cylinder (SC) is 0.165.