混合流体Rayleigh-Bénard对流的线性稳定性分析

Linear stability analysis of Rayleigh-Bénard convection in binary-fluid

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。

With the perturbation method,the linear stability analysis of Rayleigh-B6nard convection in binary fluid mixture was conducted. Based on the normal mode analysis, the characteristic equations were deduced from the perturbation equations of fluid mechanics. Under the free and rigid surface boundary conditions, the characteristic equations were solved. At the same time, the critical Rayleigh number, the critical wave number and the critical frequency of the convection were obtained. The results show that the critical Rayleigh number and the critical frequency have a strong dependence on the separation ratio and Prandtl number.