Simplified hydrodynamic analysis on the general shape of the hill charts of Francis turbines using shroud-streamline modeling

Abstract

The paper presents a simplified one-dimensional calculation of the efficiency hill-chart for Francis turbines, based on the velocity triangles at the inlet and outlet of the runner's blade. Calculation is done for one streamline, namely the shroud streamline in the meridional section, where an efficiency model is established and iteratively approximated in order to satisfy the Euler equation for turbomachines at a wide operating range around the best efficiency point (BEP). Using the presented method, hill charts are calculated for one splitter-bladed Francis turbine runner and one Reversible Pump-Turbine (RPT) runner operated in the turbine mode. Both turbines have similar and relatively low specific speeds of nsQ = 23.3 and nsQ = 27, equal inlet and outlet diameters and are designed to fit in the same turbine rig for laboratory measurements (i.e. spiral casing and draft tube are the same). Calculated hill charts are compared against performance data obtained experimentally from model tests according to IEC standards for both turbines. Good agreement between theoretical and experimental results is observed when comparing the shapes of the efficiency contours in the hill-charts. The simplified analysis identifies the design parameters that defines the general shape and inclination of the turbine's hill charts and, with some additional improvements in the loss models used, it can be used for quick assessment of the performance at off-design conditions during the design process of hydraulic turbines.