An experimental investigation of the rotating stall in reduced scale model of a low specific speed radial pump-turbine at runaway and turbine brake conditions in generating mode is achieved. Measurements of wall pressure in the stator are performed along with high-speed flow visualizations in the vaneless gap with the help of air bubbles injection. When starting from the best efficiency point (BEP) and increasing the impeller speed, a significant increase of the pressure fluctuations is observed mainly in the wicket gates channels. The spectral analysis shows a rise of a low frequency component (about 70% of the impeller rotational frequency) at runaway, which further increases as the zero discharge condition is approached. Analysis of the instantaneous pressure peripheral distribution in the vaneless gap reveals one stall cell rotating with the impeller at sub-synchronous speed. High-speed movies reveal a quite uniform flow pattern in the guide vanes channels at the normal operating range, whereas at runaway the flow is highly disturbed by the rotating stall passage. The situation is even more critical at very low positive discharge, where backflow and vortices in the guide vanes channels develop during the stall cell passage. A specific image processing technique is applied to reconstruct the rotating stall evolution in the entire guide vanes circumference for a low positive discharge operating point. The findings of this study suggest that one stall cell rotates with the impeller at sub-synchronous velocity in the vaneless gap between the impeller and the guide vanes. It is the result of rotating flow separations developed in several consecutive impeller channels which lead to their blockage.

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a b s t r a c tWe introduce and validate a novel mathematical model for computing the radial profiles of both axial and circumferential velocity components, respectively, of the swirling flow exiting the runner of hydraulic turbines within the full operating range. We assume an incompressible, inviscid, axisymmetrical, and steady swirling flow, with vanishing radial velocity at runner outlet. First we find the correlation between the flux of moment of momentum downstream the turbine runner and the operating regime given by turbine's discharge and head. Second, we express the relationship between the axial and circumferential velocity components, corresponding to the fixed pitch runner blades, using the swirl-free velocity instead of the traditional relative flow angle at runner outlet. It is shown that the swirl-free velocity profile practically does not change with the operating regime. Third, we introduce a constrained variational problem corresponding to the minimization of the flow force while maintaining the prescribed discharge and flux of moment of momentum. This formulation also accounts for a possible central stagnant region to develop when operating the turbine far from the best efficiency point. Fourth, we show that by representing the unknown axial velocity profile with a suitable Fourier-Bessel series, the discharge constraint can be automatically satisfied. The resulting numerical algorithm is robust and produces results in good agreement with available data for both axial and circumferential velocity profiles measured on a model Francis turbine at several operating regimes. Our mathematical model is suitable for the early optimization stages of the runner design, as it provides the swirling flow configuration at runner outlet without actually computing the runner. By optimizing the parameterized swirl-free velocity profile one can achieve through the inverse design approaches the most suitable runner blades configuration at the trailing edge.

The flow hydrodynamics in a low specific speed radial pump-turbine reduced scale model is experimentally investigated under off-design operating conditions in generating mode. Wall pressure measurements, in the stator, synchronized with high-speed flow visualizations in the vaneless space between the impeller and the guide vanes using air bubbles injection are performed. When starting from the best efficiency point and increasing the runner speed, a significant increase of the pressure fluctuations is observed mainly in channels between wicket gates. The spectral analysis shows a rise of one stall cell, rotating with about 70% of the impeller frequency, at runaway, which further increases as the zero discharge condition is approached. Then a specific image processing technique is detailed and applied to create a synthetic instantaneous view of the flow pattern on the entire guide vanes circumference for an operating point in turbine-brake mode, where backflow and vortices accompany the stall passage.