Evaluation of a Francis turbine draft tube flow at part load using hybrid RANS-LES turbulence modelling

Abstract

It is well known that part-load operation of Francis turbines is dominated by time-dependent phenomena. A high swirl level at the turbine runner outlet constitutes a complex inlet boundary condition for the draft tube flow at this condition. The draft tube flow simulation using a quasi-steady approach of typical two-equation turbulence modelling (k-ω SST) can provide good agreement between measurements and computational calculation for the optimum point. Global main structures of the flow as well as secondary flows can be well predicted. For part load condition this hypothesis is quite questionable due to different time scales which are associated to the different effects that can be observed at this condition. Steady state simulations do not predict the physics of the flow accurately. This work presents an evaluation of the part-load simulation results when applying a hybrid RANS-LES turbulence modelling approach using the finite volume method. Firstly, steady state results employing the k-ω SST turbulence model are presented. Then transient calculations employing both k-ω SST and SAS SST, a 2nd generation hybrid turbulence model, are also presented. In this model, a spatial filtering based on the grid size is not the main criteria applied to determinate the smallest calculated scales of the flow, but the instabilities of the flow field itself are the trigger for the reduction of eddy viscosity production. The effects of the mesh resolution on the solved turbulent structures are also evaluated. The numerical results are compared to time-averaged velocity profile data obtained by LDA (Laser-Doppler-Anemometry) measurements at the inlet of the draft tube diffuser of an nq=55 1/min Francis turbine. Velocity components in flow direction and transversal to it are evaluated. The investigation shows that the steady state results present considerable deviations when compared to those measurements. The transient calculations using the unsteady k-ω SST approach shows some improvement, but the tendencies are similar to steady state calculations. Calculations employing the SAS SST model shows overall better concordance between simulations and measurements. The results calculated with a finer grid model do not present significant improvement on the velocity profiles prediction when compared with the coarser grid one, although allowing the calculation of smaller eddies.