Hydrodynamic and heat transfer characteristics of vortex- induced vibration of square cylinder with various flow approach angle

Abstract

In this work, the effect of flow approach angle (α) on forced convective heat transfer from an elastically mounted vibrating rigid square cylinder is studied numerically. The Navier-Stokes equations along with the two-dimensional equation of motion of elastically mounted rigid square cylinder are solved using finite difference method. An Arbitrary Lagrangian Euler (ALE) method is used to capture the relation between fluid flow and vibrating cylinder. Numerical simulations are conducted for different Reynolds number ∈ [60–100], reduced velocity (Ured∈[3−8]) and flow approach angle (α∈[0o−45o]). Prandtl number (Pr) = 7.1 and Reduced mass (Mred) = 2 are kept constant and damping coefficient, ξ' = 0. The detailed kinematics of the flow and temperature fields is visualized in terms of instantaneous vorticity and isotherm contours. Examining the distribution of local Nusselt number (Nu) along the faces of the heated square develops further detailed insights. Overall gross characteristics are reported in terms of the time average drag coefficient and Nusselt number. Average Nusselt number (Nu‾) scales linearly with Reynolds number (Re) while both Ured and α has quadratic relationship. Different vortex shedding modes viz; 2S, 2S* and P + S have also been observed for different flow approach angle. At α =30o, the average Nusselt number (Nu‾) is maximum for Ured = 6, 8 and at all Reynolds numbers as the flow shows 2S* mode of vortex shedding.