Despite widespread interest in variable-speed pump-turbines, the effects of rotational speed on runner modal characteristics remain unclear. This study models the runner as a rotating disk and experimentally investigates its natural frequencies and hydrodynamic damping behaviours over 0–720 r/min. Nodal diameter (ND) modal families and coupled nodal diameter-nodal circle (ND-NC) hybrid modes of the disk were identified, with mode splitting into co-rotating and counter-rotating components observed exclusively in ND families. For all ND modes, the natural frequency of co-rotating modes exhibited a monotonic decrease with increasing rotational speed, whereas counter-rotating modes showed an opposite trend. The resulting frequency gap exhibited a linear dependence on rotational speed, and the center frequency gradually drifted downward with increasing rotational speed. When the reduced frequency is adopted as the independent variable, the natural frequencies of co-rotating and counter-rotating modes were distributed almost symmetrically with respect to the center frequency, for which a second-order polynomial regression model was proposed to characterize this unified behavior. Rotational speed was also found to exert a strong influence on hydrodynamic damping ratios: counter-rotating modes exhibited up to 54.07% lower damping compared to their co-rotating counterparts, highlighting a pronounced asymmetry in fluid-structure interaction. The evolution of damping with rotational speed exhibited two regimes, with nearly constant damping at low speeds and a monotonic increase at higher speeds.

The reversible pump turbine (RPT) is likely to enter the S-characteristic zone, thereby inducing pressure fluctuations and oscillations to the grid connection. An innovative optimization framework of RPT runner is presented to mitigate the detrimental flow conditions associated with the S-curve under turbine mode. Comprehensive runner geometric parameters were considered with the optimal Latin hypercube (OLH) sampling technique to generate different designs. Computational fluid dynamics (CFD) was adopted to characterize the RPT hydraulic efficiency and unstable S-characteristics curve, in which the position of the second inflection point was innovatively selected as the objective function. The CFD-driven surrogate-based design methodology was achieved by artificial neural network (ANN). The multi-objective optimization evolutionary algorithm guided the search for the optimal runner configuration with high efficiency and improved S-characteristics. The vortices in the runner channels and high-speed water ring in the vanless area both blocking the flow passage are alleviated in the two selected optimized RPT runners. The total pressure head associated with the intensity of vortices is deceased in the optimized runner, resulting in the improved S-shape characteristic. Runner with higher arches and negative blade lean angle of leading edge is conducive to the smooth streamline and avoidance of the flow separation.

The integration of intermittent renewable energy sources requires hydropower units to operate more flexibly and reliably over a wider load range. However, the flexible operation of Francis turbines, in particular high-head ones, is often constrained by flow instabilities, particularly rotating vortex rope (RVR) induced pressure pulsations under partial-load operating conditions. This study proposes a cost-effective multi-objective optimization framework to identify draft tube adjustable guide vanes (DTGV) configurations that mitigate RVR induced instabilities without compromising hydraulic efficiency under partial load (PL) operation. The framework combines design of experiments, computational fluid dynamics, a back-propagation neural network surrogate model, and a multi-objective genetic algorithm. To accelerate the optimization process, a steady-state mean swirl number is introduced as a practical surrogate indicator for RVR induced pressure pulsations. The close agreement between the back-propagation neural network predicted values and CFD results demonstrates the accuracy and efficiency of the proposed framework. The selected optimized DTGV reduces the low-frequency pressure pulsations amplitude by more than 70% compared to the traditional draft tube. Flow analysis reveals that the DTGV disrupts the main helical RVR into several tip vortices, substantially reduces the tangential velocity and confines flow unsteadiness to the shear layer between the outer and central regions, preventing the RVR formation. These results demonstrate that optimized DTGVs can provide a practical retrofit strategy for enhancing high head Francis's turbine stability and operational flexibility, supporting the integration of renewable energy into power systems.

Modeling the turbulent flow within different draft tube configurations in a cost-effective way is essential for efficient turbine optimization and exploring the underlying flow mechanics. In this study, a convolution neural network (CNN) based surrogate model was proposed to predict local flow parameters within different inclined Francis turbine draft tubes. Three symbolic representations denoting the complex geometry and boundary conditions were set as the input, and pressure and velocity were the output. The adopted CNN framework consists of the U-Net architecture with a contracting path and four expansive paths. Six representative hyperparameters were considered to analyze their influence on the performance and generalization ability of the CNN model. The results show that the predicting accuracy of the CNN model with a U-Net network is 7.53% higher than the traditional CNN model, as skip connections improve image segmentation accuracy. The CNN model with a larger convolution kernel can more comprehensively capture the main features of the flow field. The model with three input variables improves prediction accuracy by 2.4% as more geometrical features correlate with the key flow patterns. For the four different image resolutions, the model with a resolution of 200 × 400 performs exceptionally well. In addition, appropriately increasing the number of convolutional layers or blocks can significantly improve the prediction accuracy of the CNN model. The proposed innovative surrogate model is useful for facilitating the optimization of hydraulic turbine components. 

Increased utilization of hydraulic turbines as a regulatory tool for electrical grid stabilization forces some turbines to operate away from their design point, thus increasing wear and tear. In here, rotating vortex rope (RVR) mitigation by means of radial insertion of cylindrical rods in the draft tube is investigated experimentally on a 10 MW Kaplan turbine operating as a propeller. Pressure measurements in the draft tube, runner chamber and spiral casing, along with strain and acceleration measurements on the turbine shaft are performed to scrutinize the effectiveness of the mitigation system. Three part-load operating points are investigated, corresponding to 83%, 72%, and 68% of the guide vane servo stroke relative to the best-efficiency point opening. It is shown that the mitigation system dampens the harmful effects of the vortex rope at all operating points, especially at lower part-load conditions. Specifically, the pressure amplitude of the RVR fundamental mode inside the runner chamber reduces by 84%, 63%, and 73% at the three investigated operating points, relative to the amplitudes without mitigation. On the turbine shaft, the fundamental mode of the axial thrust oscillations at the RVR frequency reduces by 65%, 83%, and 95%. It is shown that the mitigation does not come with a high cost on the turbine time-averaged efficiency over the course of the measurements, the penalty being 2%, 2.5%, and 3.2% at the protrusion length where optimal mitigation is achieved at each operating point. For high-head machines, the penalty is expected to be lower since the relative importance of the draft tube diminishes for higher heads.

Francis turbines develop an unfavorable flow pattern in the draft tube under off-design conditions when operating as an energy regulator in hydro-wind-solar integrated systems. An adjustable hydrofoil (ADRO) system was newly tested in a high-head Francis draft tube cone model with promising experimental results. This work reproduces numerically the work to elucidate the mechanism and potential in mitigating spiral vortex breakdown. Two part-load operations are investigated, corresponding to 58% and 70% of the designed flow rate. The numerical simulations are validated against experimental results, including global performance, pressure pulsation, and velocity profile with and without ADRO, demonstrating high fidelity. With the ADRO, the vortex rope-induced pressure pulsation amplitude is effectively reduced by >50%, consistent with experimental observations. The observed reduction in vortex rope intensity is associated with a significant decrease in the swirl number, driven by a lowered mean tangential velocity in the ADRO region. The residual vortex rope structures exhibit intermittent amplitude and frequency dependent on the operation investigated, indicating the need to radially adjust the ADRO to further decrease the swirl number and thus the pressure pulsation completely. The revealed mitigating mechanism is useful to inspire the invention of new active wall-mounted control measures for draft tube flows.

Nowadays, hydraulic turbines are more often operated under off-design conditions due to the increase in intermittent energy production (wind and solar). In these operating conditions, dynamic phenomena in hydraulic circuit are observed, such as flow instabilities, secondary flows, vortex rope developed in the draft tube etc. These phenomena can lead to pressure pulsations and structural vibrations of the hydraulic turbine structure, that affect the hydraulic turbine performance and its lifespan. In the present paper a wall model, developed by Manhart et al. (2008), is used with the k-ω SST turbulence model to study numerically the pulsating flows which can occur in a hydraulic turbine during part load operation. The Manhart wall model considers the adverse pressure gradient and has the advantage of being used on a coarser mesh (dimensionless distance, y+, can result in values up to 5), leading to smaller simulation time and computational demands when compared to the general approaches. The numerical analysis is carried on using the open-source software, Code_Saturne, and considers a geometry that is similar to the draft tube of a hydraulic turbine.

Various flow regimes and their correlation with the vortex shedding are investigated numerically using the γ − Reθt transition turbulence model over a hydrofoil. The purpose is obtaining a numerical model able to accurately simulate the vortex shedding. The study is done on a 2D NACA0009 hydrofoil with two configurations. First configuration has fully smooth surfaces, and the second one has two rough layers of sand grain added near the leading edge of the hydrofoil. The presented are in good agreement with experimental data from the literature. The added roughness is forcing an early transition around 0.08 of the total chord length compared to the smooth surface at 0.8. Furthermore, the boundary layer thickness increases which leads to a reduced frequency and amplitude of the von Karman vortices.

Under off-design and transient operations of hydraulic turbines, these machines are subjected to harmful pressure fluctuations originating from the presence of vortical flow. These oscillations increase stress-induced fatigue damage on the turbine runner, shortening turbine life and reducing its reliability. This study investigates how cylindrical rods in the draft tube affect the runner blade strains and their consequent fatigue damage during transient and off-design steady-state operations. Different part-load conditions of an axial model turbine and two transients between speed-no-load and best efficiency point were experimentally studied using time-resolved pressure and runner blade strain measurements. The proposed adjustable flow control technique effectively reduced the runner damage, particularly at lower loads where reductions as high as 70% were obtained. In addition, draft tube pressure data were used for fatigue estimation, and a correlation with blade stress damage was observed at lower loads where high-amplitude load cycles occurred. The results showed that different protrusion lengths should be used function of the prevailing operating condition to obtain optimal damage reductions with lower efficiency penalties. Therefore, the proposed technique can provide an adjustable solution that mitigates off-design pressure oscillations and their consequent damage while limiting efficiency losses.