The paper presents a new method for in site discharge estimation in pressured pipes. The method consists in using the water hammer equations solved with the method of characteristics with an unsteady friction factor model. The differential pressure head variation measured during a complete valve closure is used to derive the initial flow rate, similarly to the pressure-time (Gibson) method. The method is validated with a numerical experiment, and tested with experimental laboratory measurements. The results show that the proposed method can reduce the discharge estimation error by 0.6% compared to the standard pressure-time (Gibson) method for the flow rate investigation.

Hydropower plants are currently being intensively employed for electrical grid regulation. As a consequence, the frequency of start/stops and load variations is considerably increasing, leading to the operation of hydraulic turbines under improper conditions. During the last years, studies have focused on Francis turbines. The present paper aims to investigate a Kaplan turbine model. The flow through the turbine is modelled during transient operation, from the best efficiency point to a part load operating point, using a moving mesh for the guide vane displacement. The simulations are validated against experimental velocity profiles. A time step sensitivity analysis is performed in order to determine the optimum discretization time. The possibility of using large time steps is explored. The numerically simulated unsteady pressure pulsations on the runner blades are analysed. The influence of the inlet boundary conditions on the accuracy of numerical simulations is studied. The results show that a linear flow rate variation defined during the guide vane closure leads to an overestimation of the turbine head compared to the experimental value due to an overestimation of losses. The second type of boundary conditions, a constant total pressure, results in an underestimation of the flow rate compared to the experimental value due again to an overestimation of the losses.

This paper investigates the accuracy of Reynolds-averaged Navier-Stokes (RANS) turbulence modelling applied to complex industrial applications. In the context of the increasing instability of the energy market, hydropower plants are frequently working at off-design parameters. Such operation conditions have a strong impact on the efficiency and life span of hydraulic turbines. Therefore, research is currently focused on improving the design and increasing the operating range of the turbines. Numerical simulations represent an accessible and cost efficient alternative to model testing. The presented test case is the Porjus U9 Kaplan turbine model operated at best efficiency point (BEP). Both steady and unsteady numerical simulations are carried out using different turbulence models: k-epsilon, RNG k-epsilon and k-omega Shear Stress Transport (SST). The curvature correction method applied to the SST turbulence model is also evaluated showing nearly no sensitivity to the different values of the production correction coefficient Cscale. The simulations are validated against measurements performed in the turbine runner and draft tube. The numerical results are in good agreement with the experimental time-dependent velocity profiles. The advantages and limitations of RANS modelling are discussed. The most accurate results were provided by the simulations using the k-epsilon and the SST-CC turbulence models but very small differences were obtained between the different tested models. The precision of the numerical simulations decreased towards the outlet of the computational domain. In a companion paper, the pressure profiles obtained numerically are investigated and compared to experimental data.

This paper presents a comparison between steady turbulent flow simulation results in the U9 Kaplan turbine draft tube and experimental velocity and pressure measurements. Two turbulence models were tested, k-epsilon and Shear StressTransport (SST). The results show that the k-epsilon model performs better than the SST model.The objective is to find a correlation between the pressure measured below the runner in the draft tube cone, and the optimal guide vane angle for a given bladeangle. Such correlation may allow the continuous online optimization of the cam characteristic. For this purpose, the influence of the tangential velocity on the pressure in the draft tube was specifically investigated.

The aim of the paper is to investigate the limitations of unsteady Reynolds-averaged Navier-Stokes (RANS) simulations of the flow in an axial turbine. The study is focused on modelling the pressure pulsations monitored on the runner blades. The scanned blade geometry renders the meshing process more difficult. As the pressure monitor points are defined on the blade surface the simulation relies on the wall functions to capture the flow and the pressure oscillations. In addition to the classical turbulence models, a curvature correction model is evaluated aiming to better capture the rotating flow near curved, concave wall boundaries. Given the limitations of Reynolds-averaged Navier-Stokes models to predict pressure fluctuations, the Scale Adaptive Simulation-Shear Stress Transport (SAS-SST) turbulence model is employed as well. The considered test case is the Porjus U9, a Kaplan turbine model, for which pressure measurements are available in the rotating and stationary frames of reference. The simulations are validated against time-dependent experimental data. Despite the frequencies of the pressure fluctuations recorded on the runner blades being accurately captured, the amplitudes are considerably underestimated. All turbulence models estimate the correct mean wall pressure recovery coefficient in the upper part of the draft tube.