Vol.28 No.1(1) [2006]

Thermocapillary convection in a shallow annular pool of silicone oil

Wanyuan Shi and Nobuyuki Imaishi


Thermocapillary flow in a shallow annular pool (Ri=20 mm, Ro=40 mm and depth d=1.0 mm) of silicone oil (0.65 cSt, Pr=6.7), heated from the outer wall and cooled at the inner wall, is investigated by numerical simulation. Numerical results clarified details of pattern formation and oscillatory behavior of hydrothermal waves (HTW) as well as the critical conditions for their incipience. In non-rotating pool, the critical Marangoni number Mac for the incipience of the HTW is 8.396×10^3(ΔTc=5.03K). The critical azimuthal wave number mc is 27. At slightly super critical conditions, a single group of HTW propagating in the azimuthal direction is dominant after a long calculation time. Further increase in Ma causes coexistence of several groups of HTW with different wave numbers and propagation directions. Effect of a slow rotation of the pool around its central axis destabilizes the basic steady axisymmetric flow against HTW. At Ta=0.322 (corresponding to a rotation rate of 2 r.p.m.), the Mac was determined as 8.096×10^3(ΔTc=4.85K) with mc=30. Over a range of Ma from 8.76×10^3 to 2.0×10^4, numerical simulations indicate that the HTW propagates azimuthally opposite to the direction of the pool rotation in a rotating coordinate. This phenomenon, i.e. a selection of propagation direction, is caused by the azimuthal velocity component in the basic flow field induced by the Coriolis force. At Ma=1.34×10^4, the azimuthal wave number m increases up to 54 accompanied by an appearance of finger-shaped patterns. At Ma=2.0×10^4, two groups of HTW with greatly different wave numbers (m=48 and m=5) coexist and propagate in the opposite azimuthal directions.