MARANGONI CONVECTION WITH TWO FREE SURFACES

Abstract

A numerical model is presented for a two-dimensional surface-tension-driven flow with two free surfaces, as is the case for a stationary full-penetration weld. Focus is on the flow patterns with the presence of two free surfaces and how they differ from those with one free surface. A standard splitting scheme is used to numerically solve the governing equations with primitive variables u, v, p, T and the locations of the free surfaces. Results for several combinations of Reynolds number, capillary number, Bond number, and external pressure are presented. It is found that with low Reynolds number, thermocapillary flows with two free surfaces have stronger secondary vortex than those with one free surface. For two-free-surface flows with high Reynolds number, thermocapillary forces at the bottom free surface are strong enough to generate a secondary vortex that is comparable to the primary vortex generated by the thermocapillary forces at the top free surface. Furthermore, two-free-smface flows are more flexible than one-free-surface flows; therefore, under the same conditions, the former oscillate with a higher frequency than the later. This is consistent with prior experimental observation and analytical investigation.