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波样耗散结构的空间构成及形成过程

Spatial composition and formation process of wave dissipative structure

  • 摘要: 以直拉法单晶生长系统中熔体热对流波样耗散结构为研究对象, 通过大规模数值模拟,首先获得了不同波数稳定波样流动的耗散结构, 并应用正交分解法抽出了波样耗散结构的基本流动模式, 分析了由基本流动模式形成耗散结构的动力学过程. 结果表明: (1) 构成宏观波样耗散结构的基本流动模式具有明显的规律性: (a)基本流动模式成组出现, (b) 波数为n的波样耗散结构, 每组包含n个基本流动模式,(c)流动基本模式在周向的波数随组序以n增加, 在径向由1层增至多层; (2) 波样耗散结构宏观上的旋转运动, 是由于不同基本模式的轮番``出演''所致. 研究结果丰富了人们对耗散结构的认识.

     

    Abstract: Since the theory of dissipative structures has beenproposed, many researches on them were performed. However, these studiesmostly focused on the thermodynamic theory, laws and stability ofdissipative structures, few studies were carried out on the basicstructure-cells and their interaction in the dissipative structures. Since1970's, different dissipative structures (patterns) have been found incrystal growth system, such as spoke patterns, rotating spoke patterns andwave patterns. In this paper a famous wave dissipative structure wasinvestigated, observed in the melt thermal convections in Czockralski (Cz)crystal growth system. The wave patterns with different wave numbers n areobtained numerically in a Cz oxide melt thermal convection system withcrucible radius r_c=100mm and crystal disc radius r_s=50\,mm. The oxidemelt is filled in a rest crucible, whose aspect ratio is r_c:h (radius:height). The motion of the oxide melt is induced by sidewall heating of thecrucible and a rotating disc. The disc has a common axis with the crucibleand just contacts with the free surface of the oxide melt. The rotating rateof the disc is \Omega_s. The governing equations of LiNbO_3 meltflows were solved by a block- structured boundary-fitted-coordinate method. Toensure the correct coupling of pressure and velocity fields, the well-knownmomentum interpolation technique of Rhie and Chow was applied. For theconvective term, QUICK scheme was applied. A pressure - correction equationis derived according to SIMPLE algorithm. By changing r:h and\Omega_s, numericalsimulations are conducted to obtain stable n-folded wave patterns. Properorthogonal decomposition (POD) is applied to extract the basic modes of then-folded wave patterns (n=2,3,4 in the present paper). According to POD, thebasic modes are optimal structures to form the parental n-folded wavepatterns and consist of many small-scale vortexes in general. In the presentpaper some interesting findings are achieved: (1) n-folded wave dissipativestructure is made up of many small-scale basic modes; (2) basic modes appearin groups; (3) each group has n similar basic modes but of different phaseangle; (4) with the increase of group order, the number of the vortex in thebasic modes increases by twice. The contribution of the basic modes to formthe parental dissipative structure is different and time-dependent. Themacroscale wave dissipative structure is found to be formed by thealternative appearance and disappearance of the basic modes. These resultsenrich the knowledge of dissipative structure.

     

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