Hydrothermal waves in differentially heated shallow annular pools of silicone oil

The characteristics of thermocapillary flow and hydrothermal waves (HTWs) in a shallow pool (r(i) = 20 mm, r(o) = 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, are investigated by numerical simulations. The critical Marangoni number (Ma(c)) for the incipience of HTWs is determined, using a very fine mesh system (202 x 603 x 16), to be Ma(c) = 3.36 x 10(5)(Delta T-c = 5.03 K) under a microgravity condition and Ma(c) = 3.94 x 10(5)(Delta T-c = 5.895 K) for normal gravity. These critical values are smaller than those determined by 2D simulations by a factor of 0.926 for 0 G, and 0.912 for 1 G. The wave number and angular velocity of HTWs vary with Ma. Under small Ma's, a single group of HTWs propagating in the azimuthal direction become dominant after a long calculation time. Numerical simulations with larger values of Ma show the coexistence of several groups of HTWs with different wave numbers and propagation directions. Analysis of motions of fluid elements indicates that the fluid elements exhibit small azimuthal displacements, although the HTW patterns are constantly traveling in the azimuthal direction. However, interference between different HTW groups causes a large displacement in the azimuthal direction. Numerical simulations reveal the mechanism of the large bending of the curved arms of HTW near the hot wall. Large values of Nusselt number appear at the top of the inner wall. Tempospatial variation of the Nusselt number appears on both walls corresponding to the propagation of HTW patterns. (c) 2006 Elsevier B.V. All rights reserved.