里亚普诺夫理论在热对流稳定性分析中的应用

Application of Lyapounov theory to stability analysis of thermal convection system

以熵产作为里亚普诺夫V-函数,以轴对称直拉法单晶生长系统中熔体热对流为应用对象,通过发展里亚普诺夫数值V-函数方法,研究了里亚普诺夫V-函数在数值热对流稳定性分析中的应用。结果表明:对于稳定定态,系统熵产生震荡减小;对于不稳定震荡对流,系统熵产生震荡增大。里亚普诺夫稳定性法所得稳定性结果与直接法和正交稳定性分析方法所得结果一致。研究找到了熵源强度分布和产生原因。

An application of Lyapounov V-function to numerical stability analysis of thermal convection system was studied by taking entropy production as Lyapounov V-function. The thermal convection system was an axisymmetrical melt flow in Czockralski （CZ） crystal growth system. The Lyapounov V-function was developed to numerical method. The results indicated that entropy production oscillatorily decay in the case of stationary convection, while entropy production oscillatorily increase in the case of unstable oscillatory convection. The obtained results are indentical to those obtained by direct numerical simulation （DNS） and the stability proper orthogonal decomposition （SPOD）. This study also looked into the distribution and regime of entropy production.