Thermocapillary convection in cylindrical geometries.

摘要

Thermocapillary convection in three types of cylindrical geometries is studied by two- and three-dimensional numerical simulations: an open cylinder with a uniform heat flux, an open cylindrical annulus heated from the inside or outside wall, and a liquid bridge. The non-deformable free surface is either flat or curved as determined by the fluid volume, V, and the Young-Laplace equation. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number, Re, with either flat or curved surface. For the parameter ranges considered, it is found that only steady convection is possible at any Re in strictly axisymmetric computations, i.e. time-dependent thermocapillary convection with the wavenumber of 0 does not occur in cylindrical geometries. Transition to oscillatory three-dimensional motions occurs as Re increases beyond a critical value dependent on the aspect ratio (Ar), the Prandtl number (Pr ), and V. Good agreement with available experiments conducted in microgravity is achieved in all cases.; Two-lobed pulsating and three-lobed rotating waves are observed at the free surface in the open cylinder with a flat and a concave surface, respectively. The patterns remain unchanged with increasing Re beyond the critical value. While the critical Re, Re_c, increases with increasing Pr, it decreases with increasing V.; With an open annulus heated from the inside wall, two azimuthal waves are found rotating clockwise on the free surface near the onset of oscillations. These two rotating waves are replaced by two pulsating waves with increasing Re. Heat loss from the free surface is stabilizing; Re _c increases with increasing the Biot number, Bi. The heat loss can provide an explanation for the experimentally observed Re_c dependence on the container size at fixed aspect ratio.; Two kinds of waves are observed at the free surface in an open annulus heated from the outside wall: one is rotating and the other is pulsating. With Ar = 1, 2.5 and 3.33, we observe 5, 9 and 13 azimuthal wavetrains, respectively, traveling clockwise at the free surface near Re_c. With Ar = 8 and 16, there are substantially more, but pulsating waves near Re_c. A multi-roll structure appears beyond Re_c in shallow liquid layers with Ar = 3.33, 8 and 16. While Re_c decreases with increasing Ar in the case of azimuthally rotating waves, it increases in the case of azimuthally pulsating waves.; Rotating waves with the wavenumbers of 1 or 2 are observed in the liquid bridge. The critical wavenumber depends on Bi and V. With Bi = 1, it is found that two different branches exist in the stability diagram (V − Re _c), and between them there is a small range of volumes in which the flow is more stable.