水电站过渡过程计算中的反击式水轮机边界条件及迭代收敛条件

Boundary condition and convergence condition of iteration in numerical calculation of transient process for reactive hydro turbine system

探讨了水电站过渡过程数值计算中水轮机边界条件基本方程及其迭代算法稳定性问题,从理论上推导出两种迭代算法的收敛判别条件。得到反映水流动能(或惯性)与势能比值的收敛判别变量T,当水流势能占优势时,即T≤1,第一迭代算法收敛;当水流惯性占优势时,即T>1,第二迭代算法收敛。这两个条件互补,从而证明反击式水轮机边界条件是全范围内可求解的。该判别条件已经在实际工程计算中得到验证和运用。

The basic equations for boundary conditions of reactive hydro turbine in numerical calculation of transient process and the stability of iteration are studied theoretically. Two iterative methods and corresponding discriminative condition of convergence are proposed. A convergence discrimination variable T, which is the ratio of kinetic energy to potential energy of water flow is suggested. When the potential energy is prominent, T≤1, the first iterative method is convergent, and when kinetic energy is prominent, T>1, the second iterative method is convergent. These two conditions are inter-complementary, it illuminates that the boundary condition of reactive turbine can be well solved during the numerical calculation of the whole transient process. The proposed discrimination condition is applied to practical engineering calculation and its validity is verified.