Spatial Composition And Forming Process Of Wavy Dissipative Structure

The phenomena of wave dissipative structures appear in the Czochralski(Cz) crystal growth. As a complicated melt flow,the observed wave dissipative structures are caused by different types of instability such as buoyancy -induced instability, Marangoni instability and rotation instability.The single crystal with large diameter and high quality is always manufacturers' target. The wave dissipative structures appear on the free surface of melt in growing large-scale single crystals, so study for producing large-scale single crystal is very important.Since the wave dissipative structure being discovered, many scholars did a lot of studies on the phenomena, but a few of studies is on what the small cells which composing the macro structure are and how the small cells form the macrostructure. Further more, what is the instability which do great contribution to the system stability?In this paper melt thermal convections in Czockralski (CZ) crystal growth system were investigated and famous dissipative structures - wave patterns with differernt folds were obtained numerically. The basic modes of the wave dissipative structures were extracted out by Proper Orthogonal Decomposition(POD). The basic modes that form wave dissipative structures and the dynamic formation process, and the major instability have been analysed.It is found that: (1). The main basic modes of the the wave dissipative structures very regularily,the macroscopic wave patterns take form of a lot of small basis Vortices. The main basic modes of the two-folds wave dissipative structures appears in pair, and 4 small vortices regularly increased in the azimothial direction. As the same, the three-folds wave dissipative structures appear in three, and in the azimothial direction 6 small vortices regularly increased. In the radial, the wave patterns with two and three-folds all increased from 1 storeyb to more.(2). The original temperature filed of wave dissipative structures can be linearly reconstructed from average temperature fileds and instantaneous temperature filed.The isotherms of the average temperature filed of the wave dissipative structures with 2 or 3 folds distribute as ordinary concentric circles.By adding the basic modes on the average temperature field one by one,we found the macroscopic temperature field on the rotation are caused by the appearance and disappearance of the basic modes in turn.(3). In order to know which kind of instability make a greater contribution to the phenomena of the wave dissipative structures, we numerically investigated the case of the single buoyancy -induced instability or the single rotation instability respectively. The isotherm distribution on the free surface in the case of single buoyancy -induced instability are same as that in the case of single rotation instability, being ordinary concentric circles. By comparing the main basic modes of the two cases, we found the basic modes were not same. At last, by comparing the two case's main basic modes with the original temperature field's, we obtained a conclusion: The buoyancy -induced instability play a major role in the wave patterns studied in this paper.The results of this paper enrich the knowledge on the wave dissipative structures.We hope it can be a theoretical base for the future study of the distinguishing flow pattern. Also we wish the conclusion of this paper can supply theoretical instruction for the production of single crystal.