封闭腔内自然对流数值方法研究

Study of the Numerical Method for Solving the Natural Convection in an Enclosure

在文献 [1]的基础上 ,将非定常流函数涡量方程的数值求解方法推广至非等距网格剖分 ,其中流函数一阶导数即速度项采用二阶精度公式 ,包含温度在内的离散方程组采用ADI迭代方法求得定常解 ,以封闭腔内自然对流为例 ,进行了不同瑞利数 (Ra)条件下数值试验 ,对Ra =10 6的计算进行了必要的处理 .计算结果表明 ,该数值方法推导简单 ,计算稳定 ,为采用K -ε模式计算封闭腔内层流到湍流的转捩打下基础 .

Based on the paper , the method for solving the unsteady equations of stream and vorticity functions has been used to the case of non equidistance grid analysis. The second order acuracy finite difference is usd for the first partial derivatives of stream function(i.e.velocities). The ADI successive method is used for solving the equations which contain temperature equation to obtain the steady solutions. The laminar natural convection flow and heat transfer in an enclosure are simulated for various Rayleigh numbers, for Rayleigh number 10 6 some special methods are used, which are different from that of Rayleigh numbers 10 3 to 10 5. The calculation results are consistent with the results of the other numerical methods. The calculations are stable and lay a foundation for the simulations of the transition flow from laminar to turbulence in an enclosure with the K ε model.