Thermocapillary flow driven by the surface tension gradient has received much attention because of its importance in fundamental study and engineering applications. Many researches on thermocapillary flow instability have been carried out. However, the existing experiments and numerical simulations mostly focus on the thermocapillary flow in an annular pool heated from its outer wall. There are few researches on the annular pool heated from the inner wall. This paper presented a set of direct numerical simulations on the thermocapillary flow of moderate-Prandtl number fluid in annular pools with a heated inner cylinder. The working fluid is 2cSt silicone oil with Pr=28.01. The radius ratio of the annular pools is fixed at 0.2 and the aspect ratios are 0.375 and 0.75, respectively. On the basis of the numerical simulation results, we can obtain the following conclusions: (1) As the surface tension gradient acts on the free surface, the center of the thermocapillary flow cell is close to the free surface. Because Prandtl number of the fluid is large, the radial temperature drop mainly occurs in the boundary layer near the inner cylinder. In contrast, the temperature variation in the middle of the free surface is very small. With the decrease of the aspect ratio, the flow is weakened and the center of the flow cell moves toward the inner cylinder, but the temperature distribution has only a slight change. (2) With the increase of Marangoni number, the flow is enhanced. When Marangoni number is higher than the critical value, two-dimensional axisymmetric steady flow destabilizes and bifurcates to oscillatory flows. The critical Marangoni number of flow destabilization decreases with the increase of the aspect ratio. (3) When the aspect ratio is 0.75, the basic flow bifurcates into azimuthal waves propagating in an anticlockwise direction. With the increase of Marangoni number, the surface temperature fluctuation patterns remain similar, but the wave number decreases. The maximum amplitude of the temperature fluctuation on the free surface is always located in the middle region. As Marangoni number increases further, the flow is enhanced. The maximum temperature fluctuation location moves toward the inner cylinder gradually. But, the flow pattern remains as azimuthal waves and the wave number is also 3. However, the azimuthal distribution of the surface temperature fluctuation becomes no longer uniform. (4) When the aspect ratio is decreased to 0.375, the flow bifurcates at first to a two-dimensional oscillatory flow. In this case, the temperature fluctuation moves back and forth along the radial direction. Different from the temperature fluctuation of the azimuthal wave, the temperature fluctuation on the free surface is axisymmetric. Therefore, the azimuthal wave number is m=0. When Marangoni number is more than about 1.3×105, a non-uniform azimuthal temperature fluctuation pattern appears, whose wave number is m=5. These temperature fluctuations emerge and vanish at the fixed azimuthal positions, and do not propagate along the azimuthal direction. In this case, the axial symmetry of the temperature fluctuation distribution is broken. This flow pattern can be considered as a coexistence of an oscillatory fluctuation of m=0 and a standing wave type fluctuation caused by the two azimuthal waves of m=5 propagating in the opposite azimuthal directions. With the further increase of Marangoni number, this combination flow pattern evolves into azimuthal waves which propagate along a clockwise direction.

Thermocapillary Flow of a Moderate-Prandtl Number Fluid in Annular Pools With a Heat Inner Cylinder

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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