Surface Heat Dissipation Dependence of Thermocapillary Convection of Moderate Prandtl Number Fluid in an Annular Pool

Abstract

In order to understand surface heat dissipation dependence of thermocapillary convection for moderate Prandtl number fluid in a deep annular pool, a series of three-dimensional numerical simulations have been carried out by using the finite volume method. The radius ratio and the aspect ratio of an annular pool are fixed at 0.5 and 1.0, respectively. The working fluid is 0.65cSt silicone oil with Prandtl number of 6.7. Surface heat dissipation Biot (Bi) number is varied from 0 to 50. Results indicate that with the increase of Biot number, the radial temperature gradient near the inner cylindrical wall decreases, and near the outer cylindrical wall it increases, so the flow is enhanced. When 0 < Bi < 10, with the increase of Marangoni number, the axisymmetric steady flow first transits to the standing wave, and then to the azimuthal waves. The standing wave should be attributed to Marangoni-Benard instability. However, the azimuthal waves should be corresponded to hydraulic instability, which is mainly driven by the azimuthal motion of temperature fluctuation from the sudden change of flow direction near the bottom and the inner cylindrical wall. When Bi ≥ 10, when the flow destabilizes, the axisymmetric steady flow transits directly to the azimuthal waves. With the increase of Biot number, the critical Marangoni number of the flow destabilization increases. Furthermore, the fundamental frequency and the wave number of three-dimensional oscillatory flow increase gradually with the increase of Biot number.