Abstract
This paper is concerned with numerical simulations of flow fields around a deformable gas bubble rising through an incompressible viscous fluid in a pipe. In the present analysis, an orthogonal boundary-fitted coordinate system proposed by Ryskin and Leal was applied for the grid generation around a deformable gas bubble. The simulations were performed using the MAC-type solution method to solve afinite differencing approximation of the Navier-Stokes equations governing an incompressible viscous fluid flow. It is assumed that the boundary geometry and flow fields are both axisymmetric and steady owing to the fact that the Reynolds number used here is comparatively low.(Re≤60).
The steady solutions obtained by the mathematical model have been compared with the previous experimental data for the bubble shape and the drag coefficient. It has been shown that a fairly good agreement is obtained between them. It has been clarified by the numerical results that the drag coefficient of the bubble strongly depends upon the ratio of the pipe radius to the bubble radius, but there is no effect of the ratio on the drag coefficient when the ratio exceeds five on condition that Re=20.
