Endwall loss, also known as secondary flow loss, is one of the main energy losses of the turbine cascade. It contributes significant amount 33% to overall losses of the impeller mechanical turbine cascade.¹ Scholars have done extensive research on the loss mechanism of secondary flow, and proposed the Langston model,² the Sharma–Butler model,³ the Goldstein–Spores model,⁴ and the Wang Hai-Pin model.⁵ In addition, Liu and Lei⁶ also studied the loss mechanism of the secondary flow (tip-leakage vortex (TLV)) between the clearance of blade and endwall in a pump turbine and they indicated that tip clearance has great influence on TLV and pump as turbine (PAT) cavitation performance. Same conclusions were summarized by Hao and Tan.⁷ Although a unified and standard theory summarized to accurately describe the origin and development of the secondary flow is not available because the three-dimensional (3D) flow inside the impeller machinery is extremely complicated, there is still a general consensus that the secondary flow formed is caused by a horseshoe vortex situated at the upstream of the leading edge of the blade. As shown in Figure 1, the inlet endwall boundary layer is formed and entrained in the horseshoe vortex, which splits at the leading edge of the blade near the endwall, with one leg of the vortex (pressure side (PS)) in one airfoil passage and the other leg (suction side (SS)) in adjacent passage. The PS branch of the horseshoe vortex merges with the adjacent cascade SS under the cross-channel reverse pressure gradient of the cascade and rolls up far away from the endwall along the spanwise direction, forming a passage vortex and causing flow losses.⁸

中文翻译：

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非轴对称端壁轮廓改善水轮机叶栅性能的研究

端壁损耗（也称为二次流损耗）是涡轮机叶栅的主要能量损耗之一。它为叶轮机械涡轮叶栅的总体损失贡献了33％的可观量。¹学者对次流的损失机理进行了广泛的研究，提出了Langston模型，² Sharma-Butler模型，³ Goldstein-Spores模型，⁴和Wang Hai-Pin模型。⁵另外，刘和雷⁶我们还研究了水泵水轮机叶片与端壁间隙之间的二次流（叶尖泄漏涡（TLV））的损失机理，并指出叶尖间隙对TLV和水泵涡轮（PAT）空化性能有很大影响。郝和谭总结了相同的结论。⁷尽管由于叶轮机械内部的三维（3D）流动极其复杂，所以无法提供用于精确描述次级流的起源和发展的统一标准理论，但仍存在共识，即形成的次级流这是由位于叶片前缘上游的马蹄涡引起的。如图1所示，入口端壁边界层形成并夹带在马蹄涡流中，该涡流在叶片的前缘靠近端壁处裂开，涡流的一个分支（压力侧（PS））在一个翼型通道中，而另一分支（吸气侧（SS））。马蹄涡流的PS分支在叶栅的跨通道反向压力梯度下与相邻的叶栅SS合并，并沿翼展方向卷起远离端壁，形成通道涡流并造成流量损失。⁸