DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE SWIRLING FLOW EXITING THE RUNNER OF A HYDRAULIC TURBINE

The paper introduces a mathematical model for computing the swirling flow exiting the Francis turbine runner without actually computing the three-dimensional flow in the inter-blade channels. Such models are useful for a-priori assessment of the draft tube hydrodynamics, as well as for runner outlet optimization to achieve a best match with a given draft tube. Moreover, the model can be used within a range of operating regimes, provided that no severe flow detachment from the runner blade occurs. Since we assume an inviscid, steady and axisymmetric swirling flow, and the model is restricted to an arbitrary hub-to-shroud line, we assess the impact of these assumptions on the model accuracy and point out the direction for further refinements.