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The flow in the draft tube cone of Francis turbines operated at partial discharge is a complex hydrodynamic phenomenon where an incoming steady axisymmetric swirling flow evolves into a three-dimensional unsteady flow field with precessing helical vortex (also called vortex rope) and associated pressure fluctuations. The paper addresses the following fundamental question: is it possible to compute the circumferentially averaged flow field induced by the precessing vortex rope by using an axisymmetric turbulent swirling flow model? In other words, instead of averaging the measured or computed 3D velocity and pressure fields we would like to solve directly the circumferentially averaged governing equations. As a result, one could use a 2D axi-symmetric model instead of the full 3D flow simulation, with huge savings in both computing time and resources. In order to answer this question we first compute the axisymmetric turbulent swirling flow using available solvers by introducing a stagnant region model (SRM), essentially enforcing a unidirectional circumferentially averaged meridian flow as suggested by the experimental data. Numerical results obtained with both models are compared against measured axial and circumferential velocity profiles, as well as for the vortex rope location. Although the circumferentially averaged flow field cannot capture the unsteadiness of the 3D flow, it can be reliably used for further stability analysis, as well as for assessing and optimizing various techniques to stabilize the swirling flow. In particular, the methodology presented and validated in this paper is particularly useful in optimizing the blade design in order to reduce the stagnant region extent, thus mitigating the vortex rope and expending the operating range for Francis turbines.

The variable demand of the energy market requires that hydraulic turbines operate at variable conditions, which includes regimes far from the best efficiency point. The vortex rope developed at partial discharges in the conical diffuser is responsible for large pressure pulsations, runner blades breakdowns and may lead to power swing phenomena. A novel method introduced by Resiga et al. (2006, “Jet Control of the Draft Tube in Francis Turbines at Partial Discharge,” Proceedings of the 23rd IAHR Symposium on Hydraulic Machinery and Systems, Yokohama, Japan, Paper No. F192) injects an axial water jet from the runner crown downstream in the draft tube cone to mitigate the vortex rope and its consequences. A special test rig was developed at “Politehnica” University of Timisoara in order to investigate different flow control techniques. Consequently, a vortex rope similar to the one developed in a Francis turbine cone at 70% partial discharge is generated in the rig’s test section. In order to investigate the new jet control method an auxiliary hydraulic circuit was designed in order to supply the jet. The experimental investigations presented in this paper are concerned with pressure measurements at the wall of the conical diffuser. The pressure fluctuations’ Fourier spectra are analyzed in order to assess how the amplitude and dominating frequency are modified by the water injection. It is shown that the water jet injection significantly reduces both the amplitude and the frequency of pressure fluctuations, while improving the pressure recovery in the conical diffuser.

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