An experimental and theoretical investigation of the flow at the outlet of a Francis turbine runner is carried out in order to elucidate the causes of a sudden drop in the draft tube pressure recovery coefficient at a discharge near the best efficiency operating point. Laser Doppler anemometry velocity measurements were performed for both axial and circumferential velocity components at the runner outlet. A suitable analytical representation of the swirling flow has been developed taking the discharge coefficient as independent variable. It is found that the investigated mean swirling flow can be accurately represented as a superposition of three distinct vortices. An eigenvalue analysis of the linearized equation for steady, axisymmetric, and inviscid swirling flow reveals that the swirl reaches a critical state precisely (within 1.3%) at the discharge where the sudden variation in draft tube pressure recovery is observed. This is very useful for turbine design and optimization, where a suitable runner geometry should avoid such critical swirl configuration within the normal operating range.

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.

We perform a numerical analysis of the decelerated swirling flow into the discharge cone of a model Francis turbine operated at variable discharge and constant head, using an axisymmetric turbulent swirling flow model and a corresponding simplified computational domain. Inlet boundary conditions correspond to velocity and turbulent kinetic energy profiles measured downstream the Francis runner. Our numerical results are validated against experimental data on a survey section further downstream in the cone, showing that the Reynolds stress turbulence model with a quadratic pressure-strain term correctly captures the flow field. It is shown that the diffuser performance quickly deteriorates as the turbine discharge decreases, due to the occurrence and development of vortex breakdown, with a central quasistagnant region. We investigate a novel flow control technique, which uses a water jet injected from the runner crown tip along the axis. It is shown that the jet discharge can be optimized for minimum overall losses, while the vortex breakdown is eliminated. This flow control method is useful for mitigating the Francis turbine flow instabilities when operating at partial discharge.

When reaction hydraulic turbines are operated far from the design operating regime, particularly at partial discharge, swirling flow instability is developed downstream of the runner, in the discharge cone, with a precessing helical vortex and its associated severe pressure fluctuations. Bosioc et al. (2012, “Unsteady Pressure Analysis of a Swirling Flow With Vortex Rope and Axial Water Injection in a Discharge Cone,” ASME J. Fluids Eng., 134(8), p. 081104) showed that this instability can be successfully mitigated by injecting a water jet along the axis. However, the jet discharge is too large to be supplied with high pressure water bypassing the runner, since this discharge is associated with the volumetric loss. In the present paper we demonstrate that the control jet injected at the inlet of the conical diffuser can actually be supplied with water collected from the discharge cone outlet, thus introducing a new concept of flow feedback. In this case, the jet is driven by the pressure difference between the cone wall, where the feedback spiral case is located, and the pressure at the jet nozzle outlet. In order to reach the required threshold value of the jet discharge, we also introduce ejector pumps to partially compensate for the hydraulic losses in the return pipes. Extensive experimental investigations show that the wall pressure fluctuations are successfully mitigated when the jet reaches 12% of the main flow discharge for a typical part load turbine operating regime. About 10% of the jet discharge is supplied by the plain flow feedback, and only 2% boost is insured by the ejector pumps. As a result, this new approach paves the way towards practical applications in real hydraulic turbines.

The flow unsteadiness generated in a swirl apparatus is investigated experimentally and numerically. The swirl apparatus has two parts: a swirl generator and a test section. The swirl generator which includes two blade rows, one stationary and one rotating, is designed such that the emanating flow at free runner rotational speed resembles that of a Francis hydroturbine operated at partial discharge. The test section consists of a conical diffuser similar to the draft tube cone of a Francis turbine. Several swirling flow regimes are produced, and the laser Doppler anemometry (LDA) measurements are performed along three survey axes in the test section for different runner rotational speeds (400–920 rpm), with a constant flow rate, 30 l/s. The measured mean velocity components and its fluctuating parts are used to validate the results of unsteady numerical simulations, conducted using the foam-extend-3.0 CFD code. Furthermore, phase-averaged pressure measured at two positions in the draft tube is compared with those of numerical simulations. A dynamic mesh is used together with the sliding general grid interfaces (GGIs) to mimic the effect of the rotating runner. The delayed detached-eddy simulation method, conjugated with the Spalart–Allmaras turbulence model (DDES–SA), is applied to achieve a deep insight about the ability of this advanced modeling technique and the physics of the flow. The RNG $k−ε$ model is also used to represent state-of-the-art of industrial turbulence modeling. Both models predict the mean velocity reasonably well while DDES–SA presents more realistic flow features at the highest and lowest rotational speeds. The highest level of turbulence occurs at the highest and lowest rotational speeds which DDES–SA is able to predict well in the conical diffuser. The special shape of the blade plays more prominent role at lower rotational speeds and creates coherent structures with opposite sign of vorticity. The vortex rope is captured by both turbulence models while DDES–SA presents more realistic one at higher rotational speeds.

The swirling flow exiting the runner of a hydraulic turbine is further decelerated in the discharge cone of the draft tube to convert the excess of dynamic pressure into static pressure. When the turbine is operated far from the best efficiency regime, particularly at part load, the decelerated swirling flow develops a self-induced instability with a precessing helical vortex and the associated severe pressure fluctuations. This phenomenon is investigated numerically in this paper, for a swirl apparatus configuration. The unsteady three-dimensional (3D) flow field is analyzed using a proper orthogonal decomposition (POD), and within this framework we examine the effectiveness of an axial jet injection for mitigating the flow instability. It is shown that a limited number of modes can be used to reconstruct the flow field. Moreover, POD enables to reveal influence of the jet injection on the individual modes of the flow and illustrates continuous suppression of the modes from higher-order modes to lower-order modes as the jet discharge increases. Application of POD offers new view for the future control effort aimed on vortex rope mitigation because spatiotemporal description of the flow is provided. Thereby, POD enables better focus of the jets or other flow control devices.