在混流式水轮机转轮叶片二元理论设计中,叶片微分方程的积分采用传统的近似方法时,其迭代过程出现离散,致使叶片方程无法积分。本文提出了一种数值积分法,较好地解决了叶片微分方程积分过程中的离散问题,能在各种参数情况下其叶片微分方程的积分总是收敛的。数值积分法有足够的精度,完全满足工程要求. In the dual-theory design of Francis turbine runner blades, when the integral of the blade differential equation adopts the traditional approximation method, the iteration process is discrete and the integral of the blade equation can not be integrated. In this paper, a numerical integration method is proposed to solve the discrete problem in the process of integrating the differential equations of leaves. The integrals of the differential equations can always converge under various parameters. Numerical integration method has sufficient accuracy, fully meet the engineering requirements.