中文摘要：

为了探讨叶道涡对混流式转轮叶片的作用机理,以某高比转速混流式水轮机为研究对象,选取出现严重叶道涡的小流量工况点开展转轮的瞬态动应力数值模拟。首先基于Navier-Stokes方程和RNG k-ε湍流模型进行了全流道定常和非定常流动计算,得出了转轮内部叶道涡的形态及分布,与实际观测现象非常吻合;然后采用有限元方法对转轮进行了模态分析,获得了转轮在水中的固有频率及振型;最后采用流固耦合方法对转轮进行瞬态动力学分析。研究结果表明：叶片危险部位的动应力的频率为转轮频率的倍频,分布于转轮叶片出口靠近上冠处的局部叶道涡对转轮的作用强度最大,导致叶片出口与上冠连接处的最大动应力值高于一般水轮机转轮的许用应力值,引起转轮该位置发生破坏甚至产生裂纹。

英文摘要：

In low-discharge operating conditions, serious vortices often appear in the runner blade channels of high-specific-speed Francis turbine runners. Transient dynamic stress of the runner has been numerically simulated and examined in this study to probe the mechanism of channel vortices acting on the blades and the cause of cracks on the runner. First, we calculated the steady and unsteady turbulent flows in the full passage based on the Navier-Stokes equations and a RNG k-ε turbulence model, and obtained the patterns and distributions of channel vortices that are very similar to experimental observations. Then, a finite element method was applied to modal analysis of the runner, showing the inherent frequencies and modal shapes. Finally, we adopted a fluid-structure coupling method to analyze the transient dynamics of the runner. Results show that the frequency of channel vortices acting on the blades is a multiple of the rotational frequency of runner and the most dangerous are the local channel vortices distributed near the joints of blade tailing edges with the crown. Thus, the maximum dynamic stress in the joints is higher than the allowable stress value of common turbine runners, leading to damage even cracks around that location.