摘要
利川分岔理论研究了多孔介质底部加热所引起的非达西自然对流，用有限差分方法计算 了对流的分岔；确定了Ｂｅｔａ数与临界瑞利数的关系，结果表明：随着Ｂｅ从０增大到１， 出现分岔的单胞对流的临界瑞利数Ｒａｃ从３９．３５ 单调地增大到４１．１５．双胞对流亦有类似的趋 势．这说明惯性－湍流效应有使对流稳定性增强的趋势．
The non-Darcy free convection is a two-dimensional saturated porous medium cavity heated from below is studied. 1. Physical and mathematical models We consider a rectangular cross section of cavity with width W and height H, and aspect ratio γ-W/H. The temperature of isothermal top and bottom are T - △T/2 and T + △T/2(△T > 0) respectively, the lateral walls are adiabatic, and all boundaries are assumed impermeable. The Beta number Be = αBK/vW, where B denotes the Beta factor of non-Darcy flow, α=k/(ρcp)f is the effective thermal diffusive coefficients; k is effective thermal conductivity; K is permeability; v is kinematics viscosity of fluid. It is assumed that Boussinesq approximation hold, and β denotes thermal expansion coefficient of fluid and cr the ratio of heat capacities. Thus the set of differential equations is given by Eqs.(1)-(3), where V is the seepage velocity. The velocity square term ρB\V\V in Eq.(2) is called the non-Darcy modified term or the inertia-turbulent term. Introducing the stream function ψ and these quantities are non-dimensionalized using Eq.(4), the governing equations for stream and temperature function ijj,& are given by (5) and (6), and the boundary conditions by (7). 2. Basic solution and linear stability analysis Eqs.(5)-(7) have basic solutions b= 0, Using a linear stability analysis, the critical Rayleigh number are obtained as shown in Eq.(12). 3. Numerical calculation These equations are solved by finite difference method. In order for increase computed precision, the staggered network is adopted in x direction. The temperature function 0 is continued for half net at the lateral walls, while the stream function ip is not so. Because the boundary conditions on the lateral walls are and x = 0, i.e. they are of first and second kinds respectively. 4. Analysis of stability of solution branches A concise sufficient condition on criterion for stability of solution branches is suggested. Let A denote Gu. If real parts of all eigenvalues of A are negative, moduli
出处
《力学学报》
EI
CSCD
北大核心
2002年第2期177-185,共9页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金项目(19772053)资助.
