Effects of Pr and pool curvature on thermocapillary flow instabilities in annular pool

We linearly analyzed the effect of the Prandtl number (Pr) on the stability of thermocapillary flow in shallow annular pools with an aspect ratio Gamma = (R-o - R-i)/d = 20 and two radius ratios Gamma(R) = R-i/R-o= 0.50 and 0.98039, where d, R-o, and R-i are the liquid depth and the radii of the heated outer wall and the cooled inner wall, respectively. The results for Pr is an element of [0, 10(2)] show that the steady axisymmetric thermocapillary flows in these annular pools become unstable against oscillatory instability modes, OSC1, OSC2 and hydrothermal wave (HTW). Two co-dimension-two bifurcations occur at Pr-1* and Pr-2*. The critical mode for Pr <= Pr-1* is OSC2 with almost constant critical Reynolds number Re-c, large wave number and high frequency. OSC1 with smaller wave number and lower frequency is the critical mode for Pr-1* <= Pr <= Pr-2* and Re-c slightly decreases with increasing Pr. HTW is the critical mode for Pr >= Pr-2* and Re c decreases with increasing Pr. The values of (Pr-1*, Pr-2*) are (0.00953, 0.03054) for Gamma(R) = 0.50, and (0.01919, 0.01946) for Gamma(R) = 0.98039. Energy-budget analyses reveal that the instabilities in low-Pr range are caused by instabilities in the steady toroidal vortex (or vortices) near the cold wall. (C) 2019 Elsevier Ltd. All rights reserved.