A New Method Of Investigating The Stability Of Thermal Convection

A simplified physical and mathematical model based on the Czochlarski crystal growth system was designed in this study. The model dealt with the thermal convection in a cavity of length to height being 2 to 1. The thermal convection was driven by two forces: buoyancy, described by Grashof number Gr, and surface tension, described by Marangoni number Ma. A lot of numerical simulations shew that various flow regimes occurred under various sets of Gr and Ma. When both Gr and Ma are small, stationary solutions are common. With the increase of Gr and Ma, oscillatory solution occurred. The main interest of the studies was focused on the contribution of Gr and/or Ma to the formation of flow field. Proper orthogonal decomposition (POD) was applied to investigate the role played by Gr and Ma. POD is a powerful method of analyzing the flow structure, with which basic flow modes of any complex flow could be extracted. By the comparison of the basic flow modes and other characteristics such as average values and vortices of flow fields caused by Gr and/or Ma, it was suggested that POD could found its important application in analyzing the mechanism of thermal convection. The details are as follows.The many characteristics of flow were investigated. In order to find the transition region between the stationary state and oscillatory state, researcher adjusted the surface tension and buoyancy by changing the value of Gr and Ma. By comparing the values and the distributions of variables at stationary states and the change with time and the average value of variables at oscillatory state, researcher reached conclusion about the contribution of the surface tension and buoyancy to the flow under different conditions. The mechanism of thermal convection was made clearer, with which a new way to suppress thermal convection was suggested.It is the first time that using POD to decompose oscillatory flow and get useful information about the fluctuation, such as the basic flow modes and the percent of every basic flow mode to thermal convection. This Study put forward a new method of investigation the instability of thermal convection by comparingthe major information of the flow field. The contribution of the surface tension and the buoyancy to the instability of thermal convection was revealed. A new way to control the instability of thermal convection was suggested. A proper surface tension could suppress the instability of thermal convection caused by buoyancy.This study proposed and tested a new way to analyze oscillatory flow. It will enrich the method of thermal convection instability analysis. Researcher put forward a suggestion of how to control the instability of thermal convection for crystal growth, where stable flows are strictly required. The crystal of high quality and large diameter may be grown.In order to increase dimensions and the number of driven forces in continuing studies, the purpose of this study is to try out the feasibility of this new method. Researcher hopes reaching not only qualitatively but also quantitatively the conclusion of the percent of different driven force under different conditions at last.