Abstract: In order to explore the spatiotemporal evolution of inter-blade vortices in a francis turbine at unsteady load conditions, the DMD method was introduced in combination with numerical simulation and experimental verification to decouple the coherent structure of inter-blade vortices. The numerical results show that inter-blade vortices have low frequency characteristics and with the main frequency which is 0.5 times the rotation frequency of the turbine. The cavity of inter-blade vortices originates from the upper crown of the impeller in the shape of vortex tube, which is connected with the sheet vortices on the back of the blades. DMD method was applied to obtain dynamic modal of inter-blade vortices velocity field, and was compared with the POD method. The results show that the inter-blade vortices flow structure is decomposed by the DMD method at a specific frequency to obtain the single-fold frequency characteristics, which is more convenient for the flow mechanism analysis of the coherent structures. Both of two methods may reconstruct the inter-blade vortices velocity field based on the average flow mode and the main modes, but there are errors in the reconstruction of local complex inter-blade vortices regions.

Key words: inter-blade vortices, dynamic mode decomposition(DMD), proper orthogonal decomposition(POD), coherent structure, reconstruct

摘要： 为进一步探索混流式水轮机偏负荷工况下叶道涡的演变机制，引入动态模态分解方法并结合数值模拟与实验对水轮机叶道涡的非定常流场进行相干结构的解耦。数值结果表明，叶道涡呈低频特性，演化的主频为0.5倍水轮机转频；涡管状叶道涡空腔起源于叶轮上冠，并与叶片背面的片状涡连为一体。应用动态模态分解方法获得了叶道涡速度场的动态模态，并将该方法与本征正交分解方法进行了对比。结果表明，动态模态分解方法在特定频率下对叶道涡流动结构进行分解可得单倍频率特征，更便于进行相干结构的流动机理分析。两种方法都可在平均流态和主要模态的基础上对水轮机速度场流动结构进行降阶重构，但对局部复杂叶道涡区域的重构存在局限性。

关键词: 叶道涡, 动态模态分解, 本征正交分解, 相干结构, 重构