No abstract

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.

No abstract

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.

a b s t r a c tWe introduce and validate a novel mathematical model for computing the radial profiles of both axial and circumferential velocity components, respectively, of the swirling flow exiting the runner of hydraulic turbines within the full operating range. We assume an incompressible, inviscid, axisymmetrical, and steady swirling flow, with vanishing radial velocity at runner outlet. First we find the correlation between the flux of moment of momentum downstream the turbine runner and the operating regime given by turbine's discharge and head. Second, we express the relationship between the axial and circumferential velocity components, corresponding to the fixed pitch runner blades, using the swirl-free velocity instead of the traditional relative flow angle at runner outlet. It is shown that the swirl-free velocity profile practically does not change with the operating regime. Third, we introduce a constrained variational problem corresponding to the minimization of the flow force while maintaining the prescribed discharge and flux of moment of momentum. This formulation also accounts for a possible central stagnant region to develop when operating the turbine far from the best efficiency point. Fourth, we show that by representing the unknown axial velocity profile with a suitable Fourier-Bessel series, the discharge constraint can be automatically satisfied. The resulting numerical algorithm is robust and produces results in good agreement with available data for both axial and circumferential velocity profiles measured on a model Francis turbine at several operating regimes. Our mathematical model is suitable for the early optimization stages of the runner design, as it provides the swirling flow configuration at runner outlet without actually computing the runner. By optimizing the parameterized swirl-free velocity profile one can achieve through the inverse design approaches the most suitable runner blades configuration at the trailing edge.

No abstract

We introduce and validate a novel mathematical model for computing the radial profiles of both axial and circumferential velocity components, respectively, of the swirling flow exiting the runner of hydraulic turbines within the full operating range. We assume an incom-pressible, inviscid, axisymmetrical, and steady swirling flow, with vanishing radial velocity at runner outlet. First we find the correlation between the flux of moment of momentum downstream the turbine runner and the operating regime given by turbine's discharge and head. Second, we express the relationship between the axial and circumferential velocity components, corresponding to the fixed pitch runner blades, using the swirl-free velocity instead of the traditional relative flow angle at runner outlet. It is shown that the swirl-free velocity profile practically does not change with the operating regime. Third, we introduce a constrained variational problem corresponding to the minimization of the flow force while maintaining the prescribed discharge and flux of moment of momentum. This formulation also accounts for a possible central stagnant region to develop when operating the turbine far from the best efficiency point. Fourth, we show that by representing the unknown axial velocity profile with a suitable Fourier-Bessel series, the discharge constraint can be automatically satisfied. The resulting numerical algorithm is robust and produces results in good agreement with available data for both axial and circumferential velocity profiles measured on a model Francis turbine at several operating regimes. Our mathematical model is suitable for the early optimization stages of the runner design, as it provides the swirling flow configuration at runner outlet without actually computing the runner. By optimizing the parameterized swirl-free velocity profile one can achieve through the inverse design approaches the most suitable runner blades configuration at the trailing edge.