On the relevance of the runner crown for flow instabilities in a Francis turbine

Abstract

The precessing vortex core (PVC), also known as vortex rope, in a draft tube of a Francis-99 hydro turbine is investigated. The goal is to increase our comprehension of the root of the PVC in order to attenuate or suppress the PVC, thus extending the stable operational range below the best efficiency point at part load conditions. Unsteady Reynolds-averaged Navier– Stokes simulations are conducted and used as a basis for all the analyses performed in this work. The discrete Fourier transform (DFT) and the spectral proper orthogonal decomposition (SPOD) as data-driven methods and the linear stability analysis (LSA) as a physics-based, operator-driven method are used to examine the PVC in detail. With the DFT and SPOD, two dominant modes are found inside the draft tube. Likewise, the LSA reveals two distinct linear instabilities of single-helical and double-helical shape, which agree with the findings of the SPOD in terms of spatial shape and temporal frequency. A particular focus is laid upon the region upstream of the draft tube. An adjoint-based sensitivity analysis reveals that both instability modes are highly sensitive to mean flow modifications inside the transitional segment between runner and draft tube, such as induced by passive control devices. The knowledge of these sensitivities will guide to an optimized runner and draft tube design for controlling the PVC and the double-helical mode.