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采用扰动方法对混合流体的Rayleigh-Bénard对流进行了线性稳定性研究。基于模态分析,从流体力学扰动方程组出发,推导出了特征方程。在自由和固壁两类边界条件下,求解了特征方程,得到了对流发生的临界瑞利数,临界波数及临界频率;分析了临界瑞利数及临界频率对分离比及普朗特数的依赖关系。结果表明临界瑞利数及临界频率对分离比及普朗特数有较强的依赖关系。
The perturbation method was used to study the linear stability of Rayleigh-Bénard convection of mixed fluids. Based on the modal analysis, the eigenvalue equation is deduced from the hydrodynamic perturbation equations. Under free and solid wall boundary conditions, the eigenvalue equation was solved and the critical Rayleigh number, critical wave number and critical frequency of convection were obtained. The effects of critical Rayleigh number and critical frequency on the separation ratio and Prandtl number Dependencies. The results show that the critical Rayleigh number and critical frequency have strong dependence on the separation ratio and Prandtl number.