The present study focuses on the study of topological properties of flow in a turbine cascade. Critical-point theory is used to explain the flow phenomenon. Examination and analysis of skin-friction line patterns on three-dimensional bodies such as turbine cascade, compressor cascade, cylinder, etc. enables enhanced understanding of the three-dimensional flow. Topology of flow means types of critical points formed, their interconnection, and relation between numbers of different types of critical points. Present work focuses on rules with regard to the topological consistency of a flow field. It consists of two parts, one is the connectivity of different critical points, and another is deriving the relation between the number of nodal and saddle points of a tangent vector field. Relation between the number of nodal and saddle points is derived for flows such as a turbine cascade with and without tip clearance, turbine cascade with the end wall fence, flow over a three-dimensional obstacle, etc. Relevant mathematical background necessary for derivation is discussed. The results derived for the turbine cascade is independent of the end wall contouring, leading edge modification, trailing edge modification, and blade shape. The derived relations also hold for a compressor cascade. Flow visualization based on CFD calculations is presented for the turbine cascade with and without an end wall fence.

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