Three-dimensional numerical simulation of thermocapillary flow of moderate Prandtl number fluid in an annular pool

Abstract

A series of unsteady three-dimensional numerical simulations were conducted for thermocapillary flow of 0.65 cSt silicone oil (Prandtl number Pr=6.7) in annular pools with different depths ( d=1–17 mm) heated from the outer wall (radius r o=40 mm) and cooled at the inner cylinder ( r i=20 mm) with an adiabatic solid bottom and adiabatic free surface. Simulation conditions corresponded to those in the microgravity experiments of Schwabe and Benz (Adv. Space Res. 29 (2002) 629). A temperature difference between the outer and inner walls (Δ T) generates roll-cell thermocapillary flow. Simulations with large Δ T predicted two types of oscillatory thermocapillary flows. One is the hydrothermal wave with curved spokes, which is dominant only in shallow pools ( d=1–3 mm). The second one is dominant in deep pools ( d>3 mm) and is characterized by traveling straight spoke patterns in the azimuthal direction. Critical conditions for the onset of the oscillatory flow in liquid pools of different depths were determined. Details of the flow and temperature fields were discussed. Oscillation frequencies were compared with the experimental results as functions of Δ T and pool depth d. Quantitative agreements were obtained for small Δ T and shallow pools.