We report on the examination of several approaches to simulate computationally the unstable regime of a model Kaplan turbine operating at off-design load. Numerical simulations complemented by laboratory experiments have been performed for a 60:1 scaled-down laboratory turbine model using two Reynolds-averaged Navier–Stokes (RANS) models (linear eddy viscosity model (LEVM), and a Reynolds stress model (RSM), including realizable , k-ω SST, and LRR), detached eddy simulation model (DES), and large eddy simulation model (LES). Unlike the LEVM, the RSM, DES, and LES reproduced the mean velocity components and the intensities of their fluctuations and pressure pulsations well. The underperformance of the LEVM is attributed to the high eddy viscosity as a consequence of an excessive production of the turbulent kinetic energy due to the models’ inability to account for the turbulent stress anisotropy and the stress-stain phase lag, both naturally accounted for by the RSM. This led to a much larger modelled and a smaller resolved turbulent kinetic energy compared to those in the RSM.

This review addresses the current state of research into active control and suppression of vortex rope in hydroturbines under off-design operating conditions. Only active control methods that can be “switched on” when required under off-design operating conditions are considered in this work. The review focuses on air addition into the flow, as well as various auxiliary fluid jets. It includes all the best practices for vortex rope suppression in numerical and experimental studies. It can be inferred from the review that a modern flow control system should be comprehensive, designed for a specific hydroturbine geometry, and obtain feedback from the flow. Injecting ~2% of air from the impeller fairing cone appears optimal for suppressing pressure pulsations without significant efficiency loss. The cost of air injection is rarely estimated, but the use of an automatic venting system can minimize overheads and potentially improve efficiencies at low gas contents. Fluid jets ranging from 3% to 12% of the main flow rate can efficiently suppress pressure pulsations, but their high energy requirements limit their use. Azimuthal perturbation of the flow appears promising as it does not require significant energy loss, but practical implementation remains challenging as one needs to accurately know the system dynamics and be capable of real-time manipulation of the flow.

One of the mechanisms of generation of powerful pressure pulsations in the circuit of the turbine is a precessing vortex core, formed behind the runner at the operation points with partial or forced loads, when the flow has significant residual swirl. To study periodic pressure pulsations behind the runner the authors of this paper use approaches of experimental modeling and methods of computational fluid dynamics. The influence of velocity distributions at the output of the hydro turbine runner on pressure pulsations was studied based on analysis of the existing and possible velocity distributions in hydraulic turbines and selection of the distribution in the extended range. Preliminary numerical calculations have showed that the velocity distribution can be modeled without reproduction of the entire geometry of the circuit, using a combination of two blade cascades of the rotor and stator. Experimental verification of numerical results was carried out in an air bench, using the method of 3D-printing for fabrication of the blade cascades and the geometry of the draft tube of hydraulic turbine. Measurements of the velocity field at the input to a draft tube cone and registration of pressure pulsations due to precessing vortex core have allowed building correlations between the velocity distribution character and the amplitude-frequency characteristics of the pulsations.