A Computational Estimation of Velocity Distribution of Boundary Layer on a Spherical Bubble

Abstract

Abstract The aim of this study is to investigate a velocity distribution of velocity boundary layer on a spherical bubble using numerical simulation and to compare the results with the theoretical model. In this study, we calculated the axisymmetric flow around a spherical bubble, the Reynolds number ranged from 50–1000. We selected Navier-Stokes equations written in the vorticitystream function to capture small vorticity generated on the bubble surface. We described bubble surface with boundary-fitted coordinate system. As a preliminary test, we guaranteed the accuracy of calculation method adopted in this study. Previous study showed that it needs three calculation points in the theoretical boundary layer to describe the boundary layer with second order accuracy. Our study, however, shows that the it needs seven points to describe the boundary layer even if forth order accuracy. We compared the velocity distribution of numerical result to that of theoretical model. The velocity in the vicinity of bubble is divided into potential solution and perturbed velocity component. At bubble side, the absolute value of the perturbation velocity estimated by numerical result is slightly larger than that of the theoretical model in any Reynolds numbers. When we defined bubble boundary layer thickness as the region below to 99% velocity of the potential solution, we find that value of the boundary layer thickness proposed in this study is two to three times larger than that of theoretical model. In the vicinity of the rear stagnant region (i.e. in the wake of bubble), numerical and the theoretical velocity distribution does not match at all.