多孔介质中热对流的分叉机理研究

MECHANISM OF BIFURCAIION FOR THERMAL CONVECTION IN FLOW OF POROUS MEDIA AND NUMERICAL SIMULATION

摘要

摘要:本文利用解析分析方法研究了数值模拟发现的多孔介质层中出现的对流分叉机理，指出控制方程中的Ｒａｙｌｅｉｇｈ数，是决定流动的特征参数。当Ｒａｙｌｅｉｇｈ数小于临界数值时，多孔介质内流动处于静止传热状态，并且这种状态是稳定的。如果Ｒａｙｌｅｉｇｈ数大于临界数值，非线性方程出现分叉解，文中指出，存在多个使平凡解失稳而分叉的临界Ｒａｙｌｅｉｇｈ数，当Ｒａｙｌｅｉｇｈ数由小到大经历这些临界数值时，其由平凡解发展起来的分叉解的流态，依次由单回流区转变为双回流区及三回流区。理论分析给出了分叉解和分叉解的振幅方程，阐明了分叉的机理，其结论和数值结果定性一致．

Abstract:The mechanism of bifurcations for the thermal convection flow of porousmedia is studied by analytical method.It is pointed out that the Rayleigh number Ra in thenonlinear flow equations is an important parameter to determine the fiow characteristics。If Ra is less than the critical Rayleigh number Ra_c,the fluid in the porous medium is instatic state,which is stable.If Ra>Ra_c,the solution of the flow equations in the porousmedia will bifurcate.There are a lot of criticaI Rayleigh numbers,and we can write th...