Impact of a single bubble rising near a wall on the wall-to-liquid heat flux

Abstract

This paper presents a numerical study of the heat transfer improvement around a bubble rising near a wall in a shear flow. The Navier Stokes equations and energy equation are solved in a frame of reference following the bubble to examine the dependence of the wall to liquid heat transfer on flow patterns around the bubble. The front tracking method is used to track the interface of non-condensable gas bubbles, and the finite volume method is used to solve for temperature and momentum. Our simulations show an enhancement and a diminishment of heat transfer in the downstream and upstream regions of the bubble, respectively. The enhancement and reduction of heat transfer are attributed to the reversal of flow that occurs near the wall due to the presence of a bubble. The heat transfer rate non-monotonically varies with the dimensionless shear rate γ̇‾=γ̇dg. In the range of 0.3⩽γ̇‾≤2.25, the heat transfer rate first increases, attains a maximum value and then decreases. The optimum γ̇‾ increases as the Archimedes number is increased. The heat transfer rate is found to decrease as the Laplace number is increased. The flow reversal near the wall is characterized by two parameters, namely the ‘reversal height’ and ‘reversal width’. A control volume analysis is performed for a simplified 2D version of the problem in order to relate heat transfer enhancement to the reversal height and width. The functional dependence of heat transfer enhancement on reversal height and width from our 3D simulations match the result of the control volume analysis. The analytical solution of an inviscid shear flow over a cylinder is used for qualitative insights into flow reversal mechanism. Our simulations of transient heat transfer showed that the fractional improvement in heat transfer compared to a single phase flow attains a constant value after a certain amount of time. Finally, we report the results of heat transfer enhancement due of an array of bubbles rising near a wall.