In radial pumps and turbines, the leakage flow (centripetal through-flow) is quite common from the outer radius of the impeller to the impeller eye, which has major impact on frictional torque. There is still an uncertainty on the impact of surface roughness on the moment coefficient. Part of the 2D Daily&Nece diagram where the flow is categorized into four regimes is extended into 3D with the third axis of through-flow coefficient by distinguishing the profiles of tangential velocity. After classifying the flow regimes with respect to the centripetal through-flow, two correlations are developed to predict the impact of the axial gap, the global Reynolds number, the through-flow coefficient and the surface roughness on the moment coefficient according to the experimental results for both regime III and regime IV. Using the proposed equations for the moment coefficient, the influence of the centripetal through-flow and surface roughness can be better considered when designing radial pumps and turbines.

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