| Summary: | 碩士 === 國立臺灣大學 === 應用力學研究所 === 107 === This paper simulates and analyzes three dimensional double diffusive flow structure on a stratified fluid of lateral heating by the commercial software package－COMSOL Multiphysics using a finite element method. Since our studies are three dimensional simulations, we divide the flow field into the transverse plane and the longitudinal plane. In the past, most of numerical simulations generally studied the layered convection in the transverse plane. However, the double diffusive convection in the longitudinal plane is still not negligible. In each of the convection cells, after impulsively applying temperature difference, warm and solute-rich fluid flows from the hot to cold wall along the top of the cell while the return of the cool and solute-poor fluid is along the bottom of the cell. This situation is conducive to the so-called salt-finger convection and it can be observed in the longitudinal plane. Therefore, this paper focuses on the layered convection with the development of time in three dimensional space. And we discuss the flow structure of convection cell under different boundary conditions.
The result shows that once a fully developed convection layer is generated with changing the geometric shape or boundary conditions of the tank, and layered convection can be stably present in the solution, the flow field corresponds to the stability boundary of B region (salt-finger regime). However, if the thickness of layered convection is larger than the height of the tank, convection is a single circulation over all the tank, which is similar to the thermal convection model. The flow field corresponds to the stability boundary of A region (thermal-diffusive regime). In B region, we discuss the layered convection with the development of time at three different temperature differences. The results show that when the temperature difference is small, the thickness of layered convection is relatively small, and the time for fully developed flow becomes longer. In the longitudinal plane, a horizontal row of small vortices are generated in layered convection, whose axes aligned in the direction of the temperature gradient. Nevertheless, when the temperature difference is gradually increased, the thickness of layered convection is relatively large. And small vortices have more space to grow in layered convection. The vortices form a long vortex and are present in the upper and lower horizontal boundaries. In A region, because the flow is similar to the thermal convection model, it is presented as a single circulation in the flow field. In the longitudinal plane, vortices are turbulent and their speeds are relatively smaller than the transverse plane.
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