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本文采用以压力为求解变量的原始变量法，对雷诺平均后的不可压缩Ｎ－Ｓ方程，用有限差分法离散，并用压力一速度校正法求解。混流式水轮机转轮内部的流动是流体力学中最复杂的流动之一。对Ｎ—Ｓ方程中的雷诺应力项，本文采用了目前工程中适用的标准ｋ－ε模型，在固壁附近粘性支层中的流动，采用壁面函数法。本文计算了Ｔａｙｌｏｒ弯管内的粘性流动，并与测试结果进行了比较分析，进而计算了一低比转速混流式水轮机转轮的三个工况点，与该转轮外特性的试验结果进行了比较。并对天生桥皿级电站５、６号机组进行了粘性分析设计。
In this paper, we use the original variable method with pressure as the solution variable to discretize the Reynolds-averaged incompressible N-S equation using the finite difference method and solve it with the pressure-velocity correction method. The flow inside a Francis turbine runner is one of the most complex flows in fluid mechanics. For the Reynolds stress term in the N-S equation, the standard k-ε model applied in the present project is adopted, and the flow in the viscous sub-layer near the solid wall is simulated by the wall function method. In this paper, the viscous flow in Taylor elbow is calculated and compared with the test results. Then three operating points of a low specific speed Francis turbine runner are calculated, and the experimental results of the outer characteristics of the runner Compare Tianshengqiao hydropower station 5,6 and Unit viscosity analysis design.