Three-Dimensional Numerical Simulation on Thermocapillary Convection of Moderate Prandtl Number Fluid in an Annular Shallow Pool with Surface Heat Dissipation

Abstract

In order to understand the effect of surface heat dissipation on thermocapillary convection of moderate Prandtl number fluid in an annular shallow pool, we performed a series of three-dimensional numerical simulations by using the finite volume method. An annular shallow pool is full of 0.65cSt silicone oil with Prandtl number of 6.7. The radius ratio and the aspect ratio of the pool are respectively fixed at 0.5 and 0.1. Surface heat dissipation Biot number is varied from 0 to 50. Results indicate that the critical Marangoni number of flow destabilization mainly depends on the coupling effect of the thermocapillary force and surface heat dissipation on the free surface, which decreases first, and then increases gradually. When Biot number is small, the steady axisymmetric flow after the flow destabilization will bifurcate to the hydrothermal wave. With the increase of Marangoni number, the flow pattern evolution at a small Biot number is similar to that of an adiabatic free surface, and the fundamental oscillatory frequency increases gradually. With the increase of Biot number, the radial roll cells near the outer cylindrical wall gradually extend to the inner wall, and eventually occupy the whole liquid pool. When Biot number is large, the flow pattern after the flow destabilization is a radial rolling cell pattern with alternating azimuthal direction. Then it gradually evolves into azimuthal waves, and the fundamental oscillatory frequency has a slight decrease.