Francis turbine draft tube parameterization and analysis of performance characteristics using CFD techniques

The present paper focuses on the parameterization of the draft tube elbow based on the initial geometry of the GAMM Francis turbine model. The goal was to obtain a draft tube geometry that improves the hydrodynamic performance. For this purpose, CFD analyzes were carried out, considering the GAMM Francis turbine pre-distributor, distributor and rotor geometry, and different parameterized draft tube geometries. Related to the draft tube parameterization methodology, it has modified the generatrix geometry of the elbow that defines its contour. Three types of curves were used to define the elbow contour geometry: logarithmic spiral format curve, circle arc format curve and denominated hyperbolic spiral curve. These curves and their combinations were used to define the elbow contour in the longitudinal plane, resulted in four draft tubes geometries. The numerical results were compared with experimental results, showing good conformity. The efficiency of the Francis turbine was higher for the four draft tubes of this work than the original draft tube GAMM Francis turbine. Therefore, it was found that the draft tube in hyperbolic-logarithmic spiral format has the highest efficiency and the draft tube in logarithmic spiral format has the lowest loss coefficient. Consequently the hydrodynamic performance have been discussed in this work.