底部加热的低Prandtl数流体自然对流换热的分岔

BIFURCATION OF NATURAL CONVECTION FOR LOW PRANDTL NUMBER FLUID HEATED FROM BELOW

本文用具有QUICK方案的SIMPLE算法对底部加热的低Prandtl数流体自然对流换热进行了数值计算,研究了这种流动与换热问题数值解的分岔问题。计算发现,在2200<Ra<5000区间数值解不唯一。当Ra≤2200时,流动和换热是稳态的和唯一的,最终的流场是稳定的4涡型流场。当Ra≥5000时,流动和换热是非稳态的,流场分别有5涡型的和4涡型的两种, 5涡型流场能够长期稳定地存在,但4涡型流场不会长期存在,当有足够的时间积累,会突然转变为5涡型流场。

The numerical simulations were performed for the natural convection of low Prandlt number fluid heated from below using SIMPLE algorithm with a kind of QUICK scheme, to study the bifurcation of numerical solution. The numerical results show that for the cases 2200<Ra <5000, the numerical solutions are not single. While Ra ≤2200, the fluid flow and heat transfer is steady and stable, and the result flow fields are single 4-vortex type. While Ra ≥5000, the fluid flow and heat transfer are unsteady, and have 5-vortex and 4-vortex type flow fields. For the cases Ra ≥5000, 5-vortex flow fields are stable and can exist long, but 4-vortex type flow fields are unstable and may suddenly change into 5-vortex type in some time.