Improved Wake Velocity Distribution Behind a Rising Bubble for Isothermal and Thermally Stratified Liquid Layers

Abstract

This paper aims at (a) improving the vertical velocity distribution in the wake of a rising isolated bubble for isothermal water layers and (b) evaluating the proposed distribution for thermally stratified therminol layers before and after the initiation of vortex shedding. To address these objectives, numerical investigations are performed, for the rise of an isolated bubble in isothermal and thermally stratified liquid layers, with a combination of the monotonic upwind scheme for conservation laws and pressure implicit with splitting of operators numerical scheme. The analysis revealed that the vertical velocity in the wake of a rising isolated bubble, for isothermal and thermally stratified liquid layers, differs remarkably from the Gaussian distribution. Based on the detailed investigations, region-wise wake velocity distribution comprising a linear superposition of Gaussian approximation with Burr distribution is proposed. Furthermore, this distribution is utilized to predict the rise velocity for a chain of bubbles having different frequencies of departure. Thus, the findings will be useful for the design of heat exchangers or cooling devices, which rely on the heat transfer augmentation with rising air bubbles from a heated surface for isothermal (buoyancy suppressed) and thermally stratified (buoyancy assisted) liquid layers.