An Application Of Proper Orthogonal Decomposition To Of The Stability Analysis Of Thermal Convection System

Thermal convection exists universally in nature. In general, thermal convection is needed to control. Thermal convection is mostly generated by flow field losing its stability under the driving forces, such as buoyancy, surface tension, magnetic force, centrifugal force. To study the stability in thermal convection, some stability analysis methods have already been developed and widely used, e.g., Lyapurov V-function, linear and non-linear stability analysis. These methods are mainly to determine critical value at which flow instability occur, the bifurcation and the region of control parameters. However, when more than one instabilities exists, these methods can not reveal the dominant instabilities which lead to the flow and contribution of the instabilities to the flow. Therefore, the present research aims to make the preliminary attempt and discussion in this aspect.The method of Proper Orthogonal Decomposition(POD) is used to extract spatial information from a set of time series data available on the spatio-temporal domains. These data can be obtained from experiments or numerical simulations. It can also provide quantificational contribution of each dominant to the field. So, POD was used to analysis thermal convection instability in the study.The Czochralski (CZ) crystal growth is one of the most important methods of producing single crystals from the melt. In 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. In order to control the thermal convection in the furnace better, we need to discuss the mechanism which forms the thermal convection. So as the melt in the furnace of the study object, we build a physically mathematic mold in suppose of symmetry. Melt flow are only caused by buoyancy,surface tension and circumrotation of single crystals. Simulation study to the thermal convection in the furnace is carried out using the finite volume method and HSMAC (Highly Simplified Marker and Cell) arithmetic by writing a mathematical procedure in Fortran.First direct numerical simulation is used to obtain the flow fields driven by both buoyancy and surface tension and also the flow fields driven by one of these forces alone. And it is gained that different contribution of them to the thermal convection in the furnace by direct numerical simulation. Proper orthogonal decomposition is then employed to extract the basic modes from the flow fields. By comparing the basic modes between these situations, the dominant instability involved in such complicated flows has been revealed. It is found that the basic modes corresponding to buoyancy-induced instability are global and turning and those to Marangoni-induced instability are local and traveling. It is also gained that different contribution of them to the thermal convection in different combination of them. At last we discuss the connection of dominant modes to flow field instability, and explain why dominant modes can analyze the thermal convection instability.Finally we have an attempt in two aspects. First, Circumrotation of single crystal was considered (30r/min). How circumrotation of single crystal affect to buoyancy and surface tension instability is investigated. It is found that circumrotation of single crystal inhibits to buoyancy when the buoyancy is small, otherwise accelerated. Second, Based On qualitative discussion result, a quantitative analysis method is constructed to get what contribution proportion of buoyancy and the surface tension to thermal convective instability in melts by use of the field undulation kinetic energy.By the analysis, it offers some reference data to control instability of thermal convection in the furnace. It indicates that the proper orthogonal decomposition be a powerful method in instability analysis. At the same time, it widen the study fields of proper orthogonal decomposition.