Analysis Of Thermodynamics Stability On Convection In Cz Growth System

The Czochralski (CZ) crystal growth is one of the most important methods of producing single crystals from the melt. In the single crystal growth, the quality of crystals is closely related to the transport phenomena of melt in the furnace. The observed complicated melt flows are caused by different types of instability, such as buoyancy -induced instability, Marangoni instability and vortical instability etc. In order to control the thermal convection of the melts much better, it's necessary for us to discuss each of the instability factor existed in the mechanism which forms the thermal convection. By far, the research methods used in studying the stability of thermal convection are mainly linear and non-linear stability theories, the method of Proper Orthogonal Decomposition (POD) etc. These methods are primarily from the point of dynamics to study the driving forces which lead to the instabilities of the flow, and to analyze their contribution for the instability and the dynamic actions of the flow fields. However, to the best of my knowledge, there are few researches about the thermodynamic research on stability of the flow fields. So, in this paper we will study the stability of the flow fields in the furnace during the production of single crystals by analyzing detailedly the spatial distribution of entropy production for the melt flow field and its time variation characteristics.The Lyapounov stability theory is a strong tool for discussing the stability of the solutions for the system of non-linear equations. The essential of the Lyapounov direct method is to construct the Lyapounov function, i.e. V function and then give a direct estimation about the stability of the solutions of non-linear equations according to the properties of the V function and its differential coefficient dV/dt. And in this process to solve the equations is not needed. Because in the non-equilibrium thermodynamics entropy production is directly related with the irreversible processes of the non-equilibrium systems, which is to say the entropy production in an arbitrary singular nonreversible process is positive, i.e.φ> 0, it is valuable and applicable for developing entropy production as V function and estimating the stability of flow fields by studying the property of dφ/dt with the numerical computation method.In this work, we choose the high temperature melt in the crucible of the CZ crystal growth system as the subject investigated. Under the condition of axial symmetry, its simplified physico-mathematical model has been established while only considering the effects of buoyancy and surface tension. And then, the calculation formula of entropy source intensity suited to this model has been derived at length. During the calculation, we adopt the N-S flow governing equation, and discretize the computational domain by using the finite volumetric method. Then we use central difference format, and realize the rate coupling with pressure by the HSMAC algorithm. By programming in Fortran language, a mass of numerical simulation calculations have been accomplished for the thermal convection of melt in the growth surface.In this paper, the numerical calculation results considering the following three conditions, i.e. the individual effect of buoyancy, the individual effect of surface tension and the common effect of buoyancy and surface tension, are described in detail. The curve varying with time of entropy production of the whole field is obtained, and according to the development trend of this curve the stability of the flow field has been estimated. At the same time, on the basis of the spatial distribution characteristics of the instantaneous temperature field and the entropy source intensity field, the varying trend and characteristics of the thermodynamics parameter of flow field are analyzed along with the increase of each acting force. In addition, the reason for forming the entropy source intensity distribution characteristics of the flow field is studied. The research results show that the Lyapounov stability theory can be successfully used in the analysis of the stability of the thermal convection flow field, as the entropy production can be chosen as the V function of the Lyapounov direct method. From this study, not only the research methods of the liquid instability of the thermal convection are enriched, but also the application domains of the Lyapounov stability theory are broadened.