Analysis of the Leakage Behavior of Francis Turbines and Its Impact on the Hydraulic Efficiency—A Validation of an Analytical Model Based on Computational Fluid Dynamics Results

Abstract

The present contribution addresses the analysis of the leakage behavior of a small hydro Francis turbine using an analytical approach, which was validated based on the results of computational fluid dynamics (CFD). For a custom-designed Francis turbine with a specific speed of nq = 41.9 rpm, the flow chambers resulting from the labyrinth geometry were added to a traditional full CFD model of the turbine and numerical simulations were performed for several operation points ranging from part load (Qmin = 0.5 × Qopt) to over load (Qmax = 1.3 × Qopt). Consequently, the single losses occurring in the runner seals on crown and band side as well as the pressure distribution within the runner side spaces could be evaluated and compared to the results gained with an analytical approach, which was originally developed to calculate the leakage flow of centrifugal pumps. The comparison of the pressure distribution achieved with the numerical simulation and the analytical calculation shows that both approaches match well if the angular velocity of the fluid ωFluid trapped in the runner side spaces is calculated in an appropriate way. Furthermore, the achieved results demonstrate that the use of the analytical model enables the calculation of the disk friction and leakage losses with sufficient accuracy. This paper contributes to the improvement of the performance prediction of Francis turbines based on combined numerical and analytical calculations.