Chun-Mei Wu

Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

In order to understand the characteristics of the complex flow driven by the combined thermocapillary-buoyancy effect and differential rotation of a cylindrical pool and a disk on the free surface, a series of unsteady three-dimensional numerical simulations were performed. Results indicate that the flow is axisymmetric and steady at a small temperature difference and low rotation rates. The basic meridional flow structures are composed of toroidal circulations. With an increase of the rotation rate and/or temperature difference, the basic flow transits to a three-dimensional oscillatory flow. Without rotation, the unstable thermocapillary-buoyancy flow is characterized by pulsating spoke patterns with the periodic growth and decay of temperature and velocity oscillations. When the disk and/or cylinder rotate, the oscillatory flow behaves as temperature and velocity fluctuation waves traveling in the azimuthal direction. The wave propagation velocity and direction, fluctuation amplitude, and wave number depend on the interaction of the thermocapillary, buoyancy, centrifugal and Coriolis forces. The critical conditions for the flow transition are determined. It is found that the critical thermocapillary Reynolds number initially increases before decreasing with the increase of the disk rotation rate, but the rotation of cylinder always retards the flow instability. In addition, the mechanisms of the flow instabilities are discussed and briefly summarized.

Three-dimensional flow driven by iso- and counter-rotation of a shallow pool and a disk on the free surface

In order to understand the fundamental characteristics of the forced flow driven by iso- and counter-rotation of a shallow pool and a disk on the free surface, we conducted a series of unsteady three-dimensional numerical simulations in a shallow pool. The ratio of the disk to pool radius is Rs=0.3 and the aspect ratio of pool is H=0.06. The results indicated that the forced flow driven by disk and pool rotation is axisymmetric and steady at the small rotation Reynolds number. However, when Reynolds number exceeds a critical value, the flow will undergo a transition to three-dimensional oscillatory flow, which is characterized by the velocity fluctuation waves traveling in the azimuthal direction. The propagating direction and the velocity of the waves depend on the rotation rates and directions of the disk and pool. Besides, the critical conditions for the onset of the oscillatory flow were determined. The details of the flow fields were discussed and the mechanism of the flow pattern transition was also...

Rayleigh-Bénard convection of cold water near its density maximum in a cubical cavity

In order to understand the characteristics of Rayleigh-Benard convection of cold water near its density maximum in a cubical cavity with different thermal boundaries on the sidewalls, a series of direct numerical simulations were carried out by using the control volume approach. Flow pattern structures and their bifurcation series were detailedly analyzed through the bifurcation diagram, and the heat transfer ability of each branch was discussed. Results showed that both the flow pattern and heat transfer characteristic of Rayleigh-Benard convection of cold water have many notable differences as compared with those of common fluids satisfying the Boussinesq approximation; the flow behavior depends both qualitatively and quantitatively on the thermal boundary conditions on the sidewalls. Furthermore, there are multiple flow pattern coexistence and hysteresis phenomenon during the flow pattern transition.

Aspect ratio and radius ratio dependence of flow pattern driven by differential rotation of a cylindrical pool and a disk on the free surface

The aspect ratio and radius ratio dependence of the flow pattern driven by the differential rotation of a cylindrical pool and a disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations. The aspect ratio, which is defined as the height to the radius ratio of the pool, varies from 0.06 to 2.0 and the radius ratio of the disk to the cylindrical pool varies from 0.15 to 0.9. The rotation Reynolds numbers of the pool and disk range from 0 to 4730 and 0 to −5677, respectively, where the minus sign means the rotation direction of the disk is contrary to that of the cylindrical pool. The results show that the basic flow state is axisymmetric and steady but has rich structures at the meridian plane depending on the aspect and radius ratios. With the increase of the rotation Reynolds number, the flow transits to three-dimensional oscillatory flow, characterized by the velocity fluctuation waves traveling in the counter-clockwise or clockwise direction at differe...

Thermal-solutal capillary-buoyancy flow of a low Prandtl number binary mixture with a −1 capillary ratio in an annular pool

A series of three-dimensional numerical simulations on thermal-solutal capillary-buoyancy flow in an annular pool were carried out. The pool was filled with silicon-germanium melt with an initial silicon mass fraction of 1.99%. The Prandtl number and the Lewis number of the working fluid are 6.37 × 10−3 and 2197.8, respectively. Both the radial temperature gradient and the solute concentration gradient were applied to the annular pool. The capillary ratio was assumed to be −1, which means that the solutal and thermal capillary effects were equal and opposite. Results show that the thermal-solutal capillary-buoyancy flow always occurs at this special case with the capillary ratio of −1, and even in a shallow annular pool with an aspect ratio of 0.05. With the increase of the thermal Marangoni number, four kinds of flow patterns appear orderly, including concentric rolls, petal-like, spoke, and rosebud-like patterns. These flow patterns are strongly influenced by the local interaction between the solutal and thermal capillary effects and the vertical solute concentration gradient near the outer cylinder. A small vortex driven by the dominant solutal capillary effect emerges near the inner cylinder, which is different from the flow pattern in a pure fluid. In addition, the critical thermal Marangoni number of the initial three-dimensional flow decreases with the increase of the aspect ratio of the annular pool.

Numerical Simulation of Natural Convection of Water Near Its Density Maximum Around a Cylinder Inside a Concentric Triangular Enclosure

In this paper, a series of numerical simulations for natural convection of water near its maximum-density around a cylinder inside a concentric triangular enclosure were conducted using finite volume method. The effects of the density inversion parameter, the aspect ratio, the Rayleigh number and the inclination angle on natural convection were discussed. Furthermore, the flow and temperature fields, the local and average Nusselt numbers at different parameters were obtained and analyzed. The results show that the flow pattern and temperature distribution are unique for various density inversion parameters and inclination angles. The density inversion parameter, the aspect ratio, the Rayleigh number all have significant effects on the overall heat transfer rates, except for the inclination angle. The present results can also contribute further information on the natural convection of non-Boussinesq fluid in enclosures.© 2012 ASME