NUMERICAL SIMULATION OF THERMOCAPILLARY BUBBLE MIGRATION UNDER MICROGRAVITY FOR LARGE REYNOLDS AND MARANGONI NUMBERS

Abstract

Thermocapilktry migration of a spherical bubble under microgravity in an infinite medium with a linear temperature distribution is investigated. The two-dimensional Navier-Stokes equations for axisymmetric flow around the bubble are discretized in polar coordinates on a ring around the bubble. The grid has equally spaced mesh lengths Δr in the r direction and Δθ in the θ direction. Velocities and temperature are calculated at the vertices of the quadrilateral cells of this grid. Pressure is calculated at the cell centers. The energy equation and the two momentum equations are discretized by standard three-point second-order central differences centered at the cell vertices. The continuity equation is discretized by two-point second-order central differences around the centers of the cells. The resulting nonlinear system of algebraic equations for velocities, temperature, pressure, and the terminal steady-state velocity of the bubble are solved by an iterative procedure that uses the Newton and secant methods. The banded linear systems that occur are solved by a direct solver. Computations have been carried out for Reynolds numbers from 10⁻⁷ to 2000 and Marangoni numbers from 10⁻⁷ to 1000. For these ranges, the scaled bubble velocities vary by less than one order of magnitude. The bubble velocity is influenced more by the Marangoni number than by the Reynolds number.