The paper presents result from model measurements of the efficiency and pressure pulsation intensities for two low-specific-speed hydraulic turbines operated at variable speed, namely, one splitter-bladed Francis turbine marked with "F99" and one reversible pump-turbine marked with "RPT" and operated in a turbine mode. Both turbines have similar specific speeds, i.e. 𝑛 𝑄𝐻 (𝐹99) = 21.88 and 𝑛 𝑄𝐻 (𝑅𝑃𝑇) = 27.26, and for their best efficiency points, both have similar guide-vane opening angles but different operating parameters (i.e., speed factor and discharge factor). Pressure pulsation measurements were conducted for a wide operating range and at specific locations in the (1) vaneless space and (2) draft tube. Histogram method was used to obtain the peak-to-peak amplitudes of the fluctuating pressure for all operating points used to construct the performance hill-charts of the turbines. To the best of the authors' knowledge, very little or no effort has been made so far to explore the amplitudes of pressure pulsations in the turbine when operated at rotational speeds specifically optimized for maximization of the hydraulic efficiency. Results show that operation of Francis turbines at optimized rotational speeds can increase the hydraulic efficiency of the turbine, while decreasing or maintaining the same pressure pulsation amplitudes in the entire operational range. Also, it was found that the level of efficiency gain and reduction of the pressure pulsations is greatly dependent on the hydraulic design of the turbine and should be investigated individually for each case.

Previous studies suggested variable speed operation (VSO) of Francis turbines as a measure to improve the efficiency at off-design operating conditions. This is, however, strongly dependent on the hydraulic design and, for an existing turbine, improvements can be expected only with a proper redesign of the hydraulic surfaces. Therefore, an optimization algorithm is proposed and applied to the runner of a low specific speed Francis turbine, with an optimization strategy specifically constructed to improve the variable speed performance. In the constrained design space of the reference turbine, the geometry of the replacement runner is parametrically defined using 15 parameters. Box–Behnken method was used to populate the design space with 421 unique samples, needed to train fully quadratic response surface models of three characteristic efficiencies defined by the proposed objective function. Computational fluid dynamics (CFD) was used to calculate the responses for each sample. The parametric study showed that the anticipated variation of the shape of the hill chart, needed to improve the variable speed performance of the turbine, is limited within a narrow range. The presented method is general and can be applied to any specific speed in the Francis turbine range, for both synchronous speed and variable speed optimization tasks.

Hydropower plays an essential role in maintaining energy flexibility. Modern designs focus on sustainability and robustness using different numerical tools. Automatic optimization of the turbines is widely used, including low, mini and micro head turbines. The numerical techniques are not always foolproof in the absence of experimental data, and hence accurate verification is a key component of automatic optimization processes. This work aims to investigate the newly designed Francis runner for flexible operation. Unsteady simulations at 80 operating points of the turbine were conducted. The numerical model consisted of 16 million nodes of hexahedral mesh. A SAS-SST (scale adaptive simulation-shear stress transport) model was enabled for resolving/modeling the turbulent flow. The selected time-step size was equivalent to one-degree angular rotation of the runner. Global parameters, such as efficiency, torque, head and flow rate were considered for proper verification and validation. (1) A complete hill diagram of the turbine was prepared and verified with the reference case. (2) The relative error in hydraulic efficiency was computed and the over trend was studied. This allowed us to investigate the consistency of the numerical model under extreme operating conditions, far away from the best efficiency point. (3) Unsteady fluctuations of runner output torque were studied to identify unstable regions and magnitude of torque oscillations.

This paper is focused on the guide vane cascade as one of the most crucial stationary sub-systems of the hydraulic turbine, which needs to provide efficient inflow hydraulic conditions to the runner. The guide vanes direct the flow from the spiral casing and the stay vanes towards the runner, regulating the desired discharge. A parametric design tool with normalized geometrical constraints was created in MATLAB, suitable for generating guide vane cascade geometries for Francis turbines. The goal is to determine the limits of these constraints, which will lead to future faster prediction of initial guide vane configurations in the turbine optimal operating region. Several geometries are developed using preliminary design data of the turbine and are investigated using CFD simulations close to the best efficiency point (BEP) of the turbine. This research is part of the Horizon-2020—HydroFlex project led by the Norwegian University of Science and Technology (NTNU), focusing on the development of a flexible hydropower generation.

The paper presents a simplified one-dimensional calculation of the efficiency hill-chart for Francis turbines, based on the velocity triangles at the inlet and outlet of the runner's blade. Calculation is done for one streamline, namely the shroud streamline in the meridional section, where an efficiency model is established and iteratively approximated in order to satisfy the Euler equation for turbomachines at a wide operating range around the best efficiency point (BEP). Using the presented method, hill charts are calculated for one splitter-bladed Francis turbine runner and one Reversible Pump-Turbine (RPT) runner operated in the turbine mode. Both turbines have similar and relatively low specific speeds of n_sQ = 23.3 and n_sQ = 27, equal inlet and outlet diameters and are designed to fit in the same turbine rig for laboratory measurements (i.e. spiral casing and draft tube are the same). Calculated hill charts are compared against performance data obtained experimentally from model tests according to IEC standards for both turbines. Good agreement between theoretical and experimental results is observed when comparing the shapes of the efficiency contours in the hill-charts. The simplified analysis identifies the design parameters that defines the general shape and inclination of the turbine's hill charts and, with some additional improvements in the loss models used, it can be used for quick assessment of the performance at off-design conditions during the design process of hydraulic turbines.

The presence of a gap between guide vanes and top-bottom covers and rotating-stationary geometries induces the secondary flows in Francis turbines. The secondary flow developed in the clearance gap of guide vanes induces the leakage vortex that travels towards turbine downstream affecting the runner. Likewise, secondary flows from the gap between rotor-stator component enter the upper and lower labyrinth region. Francis turbines when operated with the sediment-laden water, sediment contained flows affect these gaps thus increasing the size of the gap and increasing the leakage flow. This work examines the secondary flows developing at these locations of Francis turbine and consequent sediment erosion effects. A reference Francis turbine of Bhilangana III Hydropower Plant (HPP), India with a specific speed (Ns=85.4) severely affected by sediment erosion problem was selected for this study. All the components of the turbine were modelled and a reference numerical model was developed. This numerical model was validated with the numerical uncertainty measurement and with the experimental results. Erosion at guide vanes were due to the development of leakage flow inside the guide vane clearance gaps. At the runner inlet, erosion was mainly due to leakage vortex from clearance gap and leakage flow from rotor-stator gaps.