A computational study of vortex rings interacting with a constant-temperature heated wall

Abstract

This study is motivated by understanding the connections between the vortical structures in impinging jets and the wall heat transfer. Of particular interest are: (1) examining how the stage of evolution of vortex pairing in the jet might influence the wall heat transfer, and (2) establishing correlations between the vortex characteristics and the Nusselt number (Nu) distribution. To this end, CFD simulations are conducted of three simplified model problems involving the interaction of isolated axisymmetric vortex rings with a flat, constant-temperature, heated wall. The cases represent three scenarios of vortex-wall interaction: before (Case I), during (Case II) and after (Case III) pairing. The results show that when two vortices concurrently interact with the wall and undergo pairing (Case II), a significant instantaneous enhancement in Nu is attained in comparison to that associated with a single vortex interacting with the wall (Cases I and III). However, Case II also leads to the largest subsequent decay in Nu enhancement due to the formation of a particularly strong secondary vortex. In all cases, a deterioration in Nu, relative to unsteady diffusion, is observed simultaneously with the enhancement. Notwithstanding this deterioration, the net effect of vortex-wall interaction on the heat transfer remains positive with Case II producing the highest heat transfer rate. An analysis is conducted to establish the connection between the instantaneous maximum and minimum Nu, the circulation and the radial and the wall-normal location of the core-centers of the vortices, the thermal boundary layer thickness, the boundary layer separation location and the wall shear stress.