Force Acting on a Spherical Bubble Rising through a Quiescent Liquid

Abstract

The direct numerical simulation is performed on the spherical bubble unsteadily rising through a quiescent liquid. The method is based on a finite-volume solution of the equations on an orthogonal curvilinear coordinate system. The calculations are performed for a bubble rising through a clean liquid and contaminated one. Following the former experimental results, the tangential stress free condition is given for a clean bubble, and no-slip condition for contaminated one. The numerical results are compared with those of the model equation of the translational motion of the bubble, which is often used in numerical models of a bubbly flow. The steady drag, added mass and history terms are checked up by the comparison. It is revealed that the history force effect is negligible for a bubble rising through the clean liquid beyond Re=O (50). From the numerical point of view, the fact that the history force is negligible is quite important, because it reduces the calculation time and memory for a bubbly flow model. For a contaminated bubble, history force effect is not negligible even though the Reynolds number is high enough. It is found that the expression of the history force by Basset kernel gives an over-estimation of the history force for the bubble rising at moderate Reynolds number. This error becomes larger with increasing Reynolds number and it reduces the accuracy to calculate the bubble motion by the model equation.