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With the continuous increase in the size and power generation of turbines, the operational characteristics of turbines under off-design conditions are gradually receiving attention. In this paper, the Reynolds time-averaged method (RANS) is applied to the unsteady calculation of three different flow rate of a large Kaplan turbine under three heads: high head, rated head and low head. The focus is on the internal flow pattern of the turbine and the hydraulic excitation characteristics under low flow conditions. The unsteady characteristics of pressure pulsation, axial force of runner, radial force of runner and hydraulic torques along blade shank (τb) for six blades are analyzed. The results show that the pressure pulsation in the vaneless space is larger under low flow conditions, and frequencies of 0.33–1 fn ( fn is the rotating frequency of the runner) can be observed at monitoring points at different heights in the vaneless space. The analysis of the flow field under low flow conditions reveals the presence of larger scale vortices in the vaneless space. The position and intensity of vortices fluctuate periodically and cause larger amplitude pressure fluctuations. The frequency of 0.33–1 fn can also be observed for axial force, radial force, andτbfor six blades due to the influence of vortices in the vaneless space. The low-frequency pulsations of pressure, force andτbare much greater under the low head and high head condition than that under rated head condition. The amplitude of pulsation of various parameters is the smallest under the low flow and rated head compared to that under the low flow conditions of other heads. The flow passage under low head is more influenced by the flow rate. Low-frequency pulsations occur under both the low flow and medium flow conditions. The asymmetry of the flow in the vaneless space causes unbalanced force and hydraulic instability of the runner, which seriously threatens the safe and stable operation of the turbine.

Hydrodynamic damping is a key factor that influencing the amplitude of structural vibration under resonance conditions. In this study, the one-way FSI energy balance method by loading structure mode onto flow field is applied to simulate the hydrodynamic damping. Based on the good solution of vortex shedding frequency, structure natural frequency and mode shape, it provides a good accuracy on both flow field and structural field by predicting the hydrodynamic damping well with deviations less than 10.4%. On the basis, the hydrodynamic damping characteristics of different vibration displacements and the lock-in region are studied and analyzed in detail. Results found that the hydrodynamic damping ratio increases with the increasing of vibration displacement. A displacement interval within 6 × 10−5 m–1.2 × 10−4 m can be detected when the hydrodynamic damping ratio is slightly affected by vibration displacement. It is proved that the value of hydrodynamic damping depends on the combined area of hydrodynamic force and structural velocities. The hydrodynamic damping in the lock-in region changes nonlinearly. Under the resonance condition, the disturbance of the fluid domain increases, and a negative damping value will appear, which will increase the structure vibration amplitude.

Karman vortices forming behind blades or guide vanes may induce severe vibration and noise in hydraulic machinery. To solve these problems, the trailing edge of vanes or blades is usually trimmed as a remedy. However, this type of modification is not always effective. Based on an engineering project, two sides of the tail of an asymmetric guide vane were modified respectively. The influence of the modification on the wake flow under different inflow conditions was studied using numerical simulation. The results show that, for the studied case, a 45°-bevel cut on the side of a vane with larger velocity gradient near the trailing edge can effectively suppress the Karman vortex. However, the effect of trimming on the side with smaller velocity gradient is poor. These two ways of trimming can reduce the amplitude of the vortex-excitation force by 73.6% and 35.4%, respectively. When guide vanes opening or head increases, the trimming effect is weakened. In addition, the inflow angle and velocity magnitude have a significant impact on the wake flow behind a hydrofoil. When the attacking angle decreases from 0° to –5°, the amplitude of the vortex-excitation force doubles. When the attacking angle increases to 5°, the Karman vortex street almost disappears. The strength of the Karman vortex is related to the difference between the velocity gradient on the two sides of a vane. The greater the difference, the more stable the wake flow.

The present study aims to acquire deeper understanding of the runner blade channel vortices phenomenon by numerical simulations of the whole turbine passage. Several operating points along different specific discharge were calculated by a hybrid turbulence model, Very Large Eddy Simulation, which was proved that it was able to capture the blade channel vortices similarly. The results showed that the blade channel vortices structure and intensity were various for different runners at incipient point. The flow pattern revealed that the direct relationship of a backflow region and the blade attacking angle near the hub had a distinct variation in vortex structure and intensity. Furthermore, this paper referred a new method to evaluate the strength of blade channel vortex quantitatively, basing on the evolution of specific energy gradient over the stream-wise location. Therefore, this new method enabled the researchers to understand deeply the flow characteristics associated with the blade channel vortices formation and carry out efficiently the hydraulic optimization design.

A precessing vortex core in the draft tube of Francis turbine is considered as unstable flow conditions and the cause of many undesirable system instabilities for hydraulic power stations. The feature of vortex rope, pressure fluctuations and runner outlet velocity at part-load conditions are investigated experimentally and numerically in this paper. An obvious vortex rope could be observed at 0.88Q11BEP point and produces the most intensive periodic pressure fluctuation at the vortex rotation frequency fv along the whole passage of Francis turbine. At other conditions away from this point, the vortex rope becomes unobvious or even invisible, and the associated pressure fluctuation amplitude also reduces. This trend could be well represented by the new parameters G and Vs, which could be used to determine the strength of helical vortex field based on the gradient of time-averaged velocity on horizontal section of the draft tube cone. Transient simulations using VLES turbulence model could obtain satisfying results by comparing with experimental data, especially in terms of the time-averaged axial velocity profile resolution. Therefore, this new method enables the designers to evaluate vortex strength in engineering applications.

Guide vanes (GVs) are installed between the runner and the stay vanes for flow guidance and discharge regulation in reversible pump-turbines. The unstable torsional self-excited vibration of the guide vane (GV) may occur when running at small guide vane opening angles during the transient operations involving pump flow. In addition, the double-stage radial vanes may induce complex flow in the vanes and influence the stability of torsional self-excited vibration of the guide vane. In this study, numerical simulations were conducted at small guide vane opening angles in pump mode for two different guide vanes based on the three-dimensional computational fluid dynamics (CFD) method. The flow regime with a deflection was formed on the trailing edge with a circle in the vaneless region that rotated reversely against the runner rotation when operating at smaller guide vane opening angles for both of the two guide vanes. Based on this, the coupling simulations based on the CFD method with a single-degree-of-freedom (1DOF) oscillator were carried out under these operating conditions. Two flow types were formed at small opening angles when adopting different inlet boundary conditions. The results showed the flow regime with a deflection on the trailing edge may aggravate the instability of torsional vibration when applied as an initial flow field. Moreover, the vibration instability of the torsional self-excitation for two guide vanes was analyzed, showing that modifying the profile of guide vane airfoil is an efficient and reliable approach for weakening the torsional vibration instability.

Knowledge of the modal parameters of the guide vane is essential for evaluating the operating stability of pump-turbines. In the present investigation, experiments and simulations are designed to analyze the influence of submergence level and sidewall clearance on the vibration characteristics of a guide vane-like structure. The results show that the type of mode shape remains unchanged at different submergence levels, while the position of the node line (NL) demonstrates a slight shift. According to the angle of the NL and the free surface, the mode types are divided into parallel NL, vertical NL, and slanted NL modes. The added mass tends to increase with increasing submergence levels, while the slope of added mass in conjunction with the submergence level, is dependent on the mode type. In particular, in relation to the parallel NL mode, the slope is almost zero, if the free surface is close to the NL region; with regard to the slanted NL mode, the slope in the NL region is significantly smaller than that outside this region; in the case of the vertical NL mode, the slope remains approximately constant. The damping ratio increases with increasing submergence level for the vertical NL mode. While the damping ratios for the parallel and slanted NL modes are decreased if the free surface is close to the NL regions. In addition, as the side wall clearance increases, both the added mass and damping ratio tend to decrease.

Cavitation in central jet pumps has gained much attention for its effect on transportation efficiency and the safe and stable operation of systems. In order to investigate the mechanism of the cavitation instability in central jet pumps with large area ratios at normal cavitating conditions, numerical simulation has been carried out with Stress Blended Eddy Simulation turbulence model and Zwart-Gerber-Belamri cavitation model. The unsteady simulation predicts the periodic fluctuation of total cavity volume and the time evolution of cavities. Numerical results show that the most important factor for the cavitation instability in central jet pumps is the cavity accumulation induced by the pairing process of cavities. The cavitation instability at conditions with different cavitation intensities is a little different. Moreover, the cavitation period differs a lot at different flow ratios because of different cavitation dynamic behaviors.

The cavitation developed in the Francis turbine draft tube is known to be a source of the hydraulic instability, especially under the conditions with columnar cavitation vortex rope occurring in the draft tube. The hydraulic system will suffer from the risk of the self-excitation and the high pressure pulsations because of the dynamic features of the complex cavitation vortex rope. The links between the cavitation dynamic characteristics and the hydraulic system stability are important for an accurate system instability prediction. For this purpose, the cavitating flows in a Francis turbine operating under the overload conditions are simulated by using the Zwart-Gerber-Belamri (ZGB) cavitation model. The cavitation dynamic parameters in different cavitation development stages and the evolutions under various overload conditions are analyzed and compared in this paper. It is shown that the cavitation dynamic parameters, including the cavitation compliance, the mass flow gain factor and the wave speed, can well represent the cavitation characteristics with the vortex rope evolution. The predicted cavitation dynamic parameters are in a reasonable agreement with other available results, with an obvious dependency on the loads. The results obtained in this study are relevant to the system stability analysis.

Purpose The gaps between runner and nearby structures play an important role in the dynamic response of runner, especially for pump-turbines. This paper aims to evaluate the gap influence on the added mass and dynamic stress of pump-turbine runner and provide an improved method to predict the resonance of runner. Design/methodology/approach Acoustic-structural coupling method was used to evaluate the added mass factors of a reduced scale pump-turbine with different axial and radial gap size between runner and nearby rigid walls. Improved one-way fluid-structural interaction (FSI) simulation was used to calculate the dynamic stress of the runner, which takes into account fluid added mass effect. The time-dependent hydraulic forces on the runner surfaces that were obtained from unsteady CFD simulation were transferred to the runner structure as a boundary condition, by using mesh-matching algorithm at the FSI surfaces. Findings The results show that the added mass factors increase as the gap size decreases. The axial gaps have greater influence on the added mass factors for the in-phase (IP) modes than the counter-phase (CP) and crown-dominant (CD) modes, while the CP and CD modes are very sensitive to the radial gaps. The largest added mass factor is observed in (2 + 4)ND-CP mode (resonance mode). The results reveal that the transient structural dynamic stress analysis, with the consideration of gaps and fluid added mass, can accurately predict the resonance phenomenon. Resonance curve of the pump-turbine has been obtained which agrees well with the test result. The gap fluid has great influence on the resonance condition, while for non-resonance operating points, the effect of gaps on the dynamic stress amplitude is quite small. Originality/value This paper provides an accurate method to analyze the dynamic response during runner design stage for safety assessment. The resonance curve prediction has more significance than previous methods which predict the resonance of runner by modal or harmonic analysis.

In hydraulic machinery, the phenomenon of rotor-stator interaction will produce periodic pressure waves in the stationary cascade. These pressure waves have the same phase, and will spread and superimpose in the volute. When the pressure waves propagate and superpose, the pressure pulsation with large amplitude will be formed. This phenomenon is called phase resonance, which will threaten the safe and stable operation of the machinery. Therefore, it is necessary to study the rotor-stator interference phenomenon and analyze the risk of phase resonance. In this paper, a high head Francis turbine with phase resonance in engineering is analyzed, which is also verified by the existing theoretical analysis. The phase resonance in the turbine is analyzed by using one-dimensional hydro acoustic model and three-dimensional compressible flow CFD simulation method, and the results are consistent with the actual engineering phenomenon. In order to study the measures to improve the phase resonance phenomenon, this paper carries out the simulation calculation from changing the rotation speed, wave speed and guide vane-runner blade number combination. The results show that adjusting the above parameters can reduce the amplitude of large pressure pulsation caused by the phase resonance in different degrees, and changing the number combination of guide vanes and runner blades is the most effective and feasible measure.

The runner blade channel vortex could induce cavitation erosion, noise and vibration, when Francis turbines operate at part load condition. It's usually difficult to simulate the channel vortex exactly in runner passage, this paper attempts to predict the runner channel vortex in some operating conditions with different discharge and speed factors.The results show that the structure and intensity of runner channel vortex are various between the vortex incipient and development line. The velocity distribution indicates that there is a relationship between the channel vortex and backflow region near the hub with different specific discharge factors, while the flow incident angle has a distinct variation with different specific speed factors. Furthermore, this work enables the researchers to understand the flow field and carry out optimization design in runner hydraulic research.

Previous researches has shown that inlet backflow may occur in a centrifugal pump when running at low-flow-rate conditions and have nonnegligible effects on cavitation behaviors (e.g. mass flow gain factor) and cavitation stability (e.g. cavitation surge). To analyze the influences of backflow in impeller inlet, comparative studies of cavitating flows are carried out for two typical centrifugal pumps. A series of computational fluid dynamics (CFD) simulations were carried out for the cavitating flows in two pumps, based on the RANS (Reynolds-Averaged Naiver-Stokes) solver with the turbulence model of k- ω shear stress transport and homogeneous multiphase model. The cavity volume in Pump A (with less reversed flow in impeller inlet) decreases with the decreasing of flow rate, while the cavity volume in Pump B (with obvious inlet backflow) reach the minimum values at δ = 0.1285 and then increase as the flow rate decreases. For Pump A, the mass flow gain factors are negative and the absolute values increase with the decrease of cavitation number for all calculation conditions. For Pump B, the mass flow gain factors are negative for most conditions but positive for some conditions with low flow rate coefficients and low cavitation numbers, reaching the minimum value at condition of σ = 0.151 for most cases. The development of backflow in impeller inlet is found to be the essential reason for the great differences. For Pump B, the strong shearing between backflow and main flow lead to the cavitation in inlet tube. The cavity volume in the impeller decreases while that in the inlet tube increases with the decreasing of flow rate, which make the total cavity volume reaches the minimum value at δ = 0.1285 and then the mass flow gain factor become positive. Through the transient calculations for cavitating flows in two pumps, low-frequency fluctuations of pressure and flow rate are found in Pump B at some off-designed conditions (e.g. δ = 0.107, σ = 0.195). The relations among inlet pressure, inlet flow rate, cavity volume, and backflow are analyzed in detail to understand the periodic evolution of low-frequency fluctuations. Backflow is found to be the main reason which cause the positive value of mass flow gain factor at low-flow-rate conditions. Through the transient simulations of cavitating flow, backflow is considered as an important aspect closely related to the hydraulic stability of cavitating pumping system.

Supplemental material, sj-pdf-1-pia-10.1177_09576509211017434 for Effects of trailing-edge modification of guide vanes on the wake vortices under different inflow conditions by Xiang Xia, Lingjiu Zhou, Zhengwei Wang and Dianhai Liu in Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy

Purpose Cavitation inside pumps affects not only the steady state fluid flow, but also the unsteady or transient characteristic of the flow. However, cavitation inside pumps under transient processes is difficult to predict when the influence of the pipelines system is considered. In this paper we present a simulation method applied to a centrifugal pump and its related pipeline to analyze the induced unsteady cavitation phenomenon during the startup process. Design/methodology/approach In order to effectively predict transient processes of a pump and its pipeline system, the simulation method uses a coupled 1D and 3D scheme, which reduces the simulation cost. The simulation of the startup process of a centrifugal pump in a closed-loop pipeline system with and without cavitation has been performed to verify the proposed method. Findings The evolution of the pressure and flow rate obtained with the simulation method agrees well with the experimental results. It is found that the mass flow rate at the pump inlet and outlet is highly related to the cavitation vapor volume and that the pressure at the outlet of the impeller is greatly influenced by the discharge. Originality/value The 1D-3D coupling simulation method used in this paper is proven to be highly accurate, efficient and can be used to solve transient processes combined with cavitation or other complex phenomena.

The tip leakage vortex (TLV) cavitation is investigated by a commercial Reynolds averaged Navier-Stokes (RANS) solver. A referenced test on a NACA0009 hydrofoil is used to validate the numerical simulation. Considering the local rotation characteristics of the vortical flow, a rotation-curvature corrected Shear-Stress-Transport model (SST-CC model) is applied to simulate the time-averaged turbulent flow. Compared to the original SST model, the SST-CC model improves the prediction of the velocity in TLV on the measured sections in downstream, and the vorticity and pressure features along the TLV trajectory are analysed numerically. In order to increase the prediction accuracy for the TLV cavitation, the empirical condensation coefficient (Fc) in Zwart's cavitation model is calibrated based on the referenced experiment. By introducing a vortex identification parameter (f∗) related to the strain rate tensor and the vorticity tensor, a relationship between the Fc and f∗ is built, and the effects of the rotational motion of the vortex on the cavity are embodied in a modified Zwart's cavitation model. Compared to the conventional Zwart's cavitation model, the modified cavitation model significantly improves the prediction of the TLV cavitation and gets a better agreement with the referenced test on different conditions with various gap widths.

Fairing is one of the most effective devices to suppress vortex-induced vibration (VIV) of marine risers. However, when the rotational friction coefficient of the fairing device is too high to rotate, severe galloping oscillations occurs. In this paper, a two-dimensional mass-spring-damping system was constructed based on the commercial software ANSYS. The galloping mechanism and the two degree-of-freedom (DOF) galloping characteristics of the fairing were studied by numerical methods. In particular, the influence of the natural frequency ratio of the in-line (IL) direction and the cross-flow (CF) direction on the galloping oscillation was discussed. The mass ratio of the riser-fairing system for which the simulations were performed was 1.7, and the damping ratio was 0.003. The Reynolds number based on the cylinder diameter and the inflow velocity was 1000. The range of reduced velocities based on the natural frequency in the CF direction was 1.76–18.52. The results showed that the activation of the inherent modes of the structure and the reattachment of the shear layer in the wake had an important contribution to the generation of the galloping. The movement in the IL direction could promote the reattachment of the shear layer to a certain extent, thereby expanding the scope of the galloping conditions. When the natural frequency ratio was equal to 1 or 2, a “double peak” phenomenon was found in the vibration amplitude curve in the CF direction. In the 2-DOF vibration, the fairing moved in the shape of an “8″ or a drop-shaped trajectory in most cases. On the whole, the interaction between the movement of the fairing in the IL direction and the movement in the CF direction could not be neglected, and the natural frequency ratio also significantly affected the vibration characteristics.

It is currently in the period of high-speed construction of pumped storage projects. However, the problems caused by vibration of pump turbine units, especially the runners, are very serious. It is of great significance to study the dynamic characteristics of pump turbine runner for the safety and stability of power station. In this paper, the natural modes of a pump turbine runner in the air and in the flow channels are calculated by numerical method. The influence and mechanism of the outer edge modification on the natural frequencies of the runner are studied. The results show that, for the object studied in this paper, the frequency of most modes will be decreased by thickening the outer edge. The frequency change can be attributed to two aspects, one is the change of the mass and the stiffness of the runner, and the other is the change of added mass of the water. Furthermore, the main mechanism of outer edge modification affecting the added mass coefficient is that the height of the radial clearance is changed.

Purpose This study analyzes the blade channel vortices inside Francis runner with a particular focus on the identification of different types of vortices and their causes. Design/methodology/approach A single-flow passage of the Francis runner with refined mesh and periodic boundary conditions was used for the numerical simulation to reduce the computational resource. The steady-state Reynolds-averaged Navier–Stokes equations closed with the k-ω shear–stress transport (SST) turbulence model were solved by ANSYS CFX to determine the flow field. The vortices were identified by the second largest eigenvalue of velocity. Findings Four types of vortices were identified inside the runner. Three types were related to the inlet flow. The last one (Type 4) was caused by the reversed flow near the runner crown and had the lowest pressure inside the core near the runner outlet. Thus, in the blade channel vortex inception line, Type 4 vortex would appear earlier than the other three ones. Besides, the Type 4 vortex emerged from the crown and shed toward the blade-trailing edge. And its location moved from near the crown down to near the band when the unit speed increased or unit discharge decreased. Research limitations/implications Although the refined mesh was used and the main vortices in the Francis runner were well predicted, the current mesh is not enough to accurately predict the lowest pressure in the channel vortex core. Practical/implications This knowledge is instructive in the runner blade design and troubleshooting related to the channel vortex. Originality/value This study gives an overview of the main observed blade channel vortices and their causes, and points out the important role the reversed flow plays in the formation of blade channel vortices. This knowledge is instructive in the runner blade design and troubleshooting related to blade channel vortices.

The blade tip leakage flow with efficiency losses and cavitation phenomena is a concern for the low-head tidal power units. A simplified case of NACA0009 hydrofoil in a water tunnel is used to investigate the effects of tip clearance geometries including the foil tip shape and gap width on the flow features and foil performance. Steady non-cavitating simulations are implemented for a round tip foil and a sharp tip foil with two incidence angles (α = 10° and 5°) and different normalized gap width (τ). The minimum pressure is used to reflect the normalized vortex intensity (Γ*) and cavitation characteristics. The Γ*-τ curves at different streamwise positions show that the sharp tip foil generates relatively weaker tip leakage vortex with more flat curves, but its higher Γ* of tip separation vortex in wider gaps increases the risk of clearance cavitation. The flow features on a cross section inside the gap suggest that the sharp tip reduces the leakage flow losses and increases the velocity gradient due to the boundary layer separation. The lift coefficient is a little higher for the sharp tip foil than the round tip foil, with small differences for α = 5° but noticeable deviations for α = 10° especially within 0.3

High-speed water tunnels are typically used to investigate the single-phase and two-phase flows around hydrofoils for hydraulic machinery applications but their dynamic behavior is not usually evaluated. The modal analysis of an NACA0009 hydrofoil inside the test section was calculated with a coupled acoustic fluid–structure model, which shows a good agreement with the experimental results. This numerical model has been used to study the influence on the hydrofoil modes of vibration of the acoustic properties of the surrounding fluid and of the tunnel test section dimensions. It has been found that the natural frequencies of the acoustic domain are inversely proportional to the test section dimensions. Moreover, these acoustic frequencies decrease linearly with the reduction of the speed of sound in the fluid medium. However, the hydrofoil frequencies are not affected by the change of the speed of sound except when they match an acoustic frequency. If both mode shapes are similar, a strong coupling occurs and the hydrofoil vibration follows the linear reduction of natural frequency induced by the acoustic mode. If both mode shapes are dissimilar, a new mode appears whose frequency decreases linearly with speed of sound while keeping the acoustic mode of vibration. This new fluid–structure mode of vibration appears in between two hydrofoil structure modes and its evolution with sound speed reduction has been called “mode transition.” Overall, these findings reinforce the idea that fluid–structure interaction effects must be taken into account when studying the induced vibrations on hydrofoils inside water tunnels.

It has been found recently that the dynamic behavior of a cavitating hydrofoil is different from that in pure water in that, not only are the natural frequencies different, but the mode shapes may also change. In order to elucidate the mechanism behind this phenomenon, finite element simulations were carried out based on acoustic&ndash, structure coupling equations. It was found that the structure and acoustic modes exhibit mode transitions with the variation of the sound speed in the cavity. Further, the mode transition was caused by coupling of the structure with the acoustic modes, which was induced by the vapor mode. The amplitude of the vibration near the mode transition point was high and the mode shape was easily excited. Moreover, with the change of the sound speed in the cavity, the different distributions of the acoustic pressure mode resulted in different structure mode shapes, even on the same transition line. Considering this, a sheet cavitation was simulated by a small change of the void fraction to 0.999 and the sound speed from 343 to 275 m/s to obtain good agreement with the experimental data. Both results showed that the second bending mode under cavitation conditions became a bending&ndash, torsion coupled mode.

In the numerical simulation of flow-induced vibration using two-way fluid-structure interaction (TW-FSI) method, it is usually limited by mesh deformation, and consumes a lot of computing resources. These problems can be avoided by adopting acoustic-structure based one-way FSI (ASOW-FSI) approach. The purpose of this work is to explore the applicability of ASOW-FSI, and to analyze the similarities and differences between the two dynamic response analysis methods. A series of numerical calculations are carried out for the elastically mounted rigid cylinder at low Reynolds number. By systematically comparing the results calculated by these two methods, we found that ASOW-FSI can accurately predict the response in the range of partial reduced velocity, even closer to the experimental results than TW-FSI method. The main reason for the difference between the two methods in the whole reduced velocity range is that the ASOW-FSI method can not predict the “lock-in”. Finally, the mechanism of “lock-in” in vortex-induced vibration (VIV) is analyzed by forced oscillation. The results show that the structural vibration has the ability to dominate the vortex shedding under certain conditions. If the natural mode of the structure is excited at this time, “lock-in” will occur.

Purpose – The vortex ropes in draft tube of Francis turbine always cause fluctuation and vibration, which consequently threaten the safety and stability of hydro turbines. The purpose of this paper is to use a cavitation flow computational method to simulate spiral vortex ropes under part load conditions and columnar vortex ropes under high-load conditions in draft tube. The unsteady cavitating flow characteristics in draft tube and its interaction with runner cavitation were analyzed. Design/methodology/approach – The calculation method was verified by cavitation simulation around a 3D hydrofoil. The results show that the Large Eddy Simulation (LES) turbulence model with the Zwart-Gerber-Blemari cavitation model have comparative advantage in cavitation simulations whether from capture of cavity shape or prediction of pressure changes. So it was chosen to simulate the two-phase cavitation flow in Francis turbine. The boundary conditions for inlet and outlet were set to inlet total pressure and outlet static pressure. The finite volume method with the central difference was adopted to discretize the equations. Findings – The calculated Thoma number agreed well with the experimental data. The vortex rope diameter and length increased with the cavitation development for both of the two types of vortex ropes conditions. The maximum peak-to-peak values of pressure pulsations located in the draft tube elbow part under all of the Thoma numbers conditions. Under spiral vortex rope conditions, the pressure pulsation in the same section of draft tube cone show obviously phase shift. The vortex rope affects the development of runner cavitation, which induces the symmetric and axisymmetric cavitation region in the suction side of blades for spiral and columnar vortex rope condition, respectively. Research limitations/implications – The mesh independence had been checked only in non-cavitation flow; in addition, the mesh density did not well satisfy the requirements of LES due to the limitations of computing power. The higher mesh density on a simplified model with one blade flow path and the entire draft tube may be helpful for obtaining more precise results. Originality/value – The spiral and columnar vortex ropes in a Francis turbine were compared and analyzed. The annular hydraulic jump appeared in the columnar vortex rope conditions has little effects on the pressure pulsations. The uneven flow field caused by spiral vortex led to the asymmetric cavitation development.

When discussing potential resonances in hydraulic turbine runners, cavitation effects are usually neglected. Nevertheless, recent studies have experimentally proved, that large cavitation volumes in the proximity of flexible simple structures, such as hydrofoils, greatly modify their natural frequencies. In this paper, we analyze a resonance case in a Francis runner that leads to multiple fractures on the trailing edge of the blades, after just one day of operation at deep part load. If simple acoustic Fluid-Structure-Interaction (FSI) simulations are used, where the runner’s surrounding fluid is considered as a homogenous acoustic medium (water), the risk of structural resonances seems to be limited as the predicted natural frequencies are far enough from the excited frequencies by the flow. It is shown that the only hydraulic phenomenon which could have produced such fractures in the present case is the Rotor Stator Interaction (RSI). In order to analyze possible cavitation effects on the natural frequencies of the turbine runner, CFD simulations of the deep part load conditions have been performed, which predict large inter-blade vortex cavities. These cavities have been then introduced in the acoustical FSI model showing that under such conditions, natural frequencies of the runner increase approaching to some of the RSI excited frequencies. In particular, a possible resonance of the four-nodal diameter (4ND) mode has been found which would explain the fast behavior of the crack propagation. Furthermore, the shape and the position of the real fracture found agree with the local maximum stress spots at the junction between the trailing edges and the crown.

Recent studies have coupled blade element momentum (BEM) theory with the Reynolds Averaged Navier–Stokes equations in computational fluid dynamics (CFD) software, as the BEM-CFD method to analyse the flows in marine current turbines is with much less computational resources. The accuracy of the BEM-CFD calculation was evaluated by analysing the performance and flow field characteristics of an isolated horizontal axis marine current turbine with comparisons to a full rotor geometry simulation and experimental data. The comparisons show that the full rotor geometry simulation gives good predictions near the optimal conditions (TSR = 5–7), but is less accurate for off-design conditions. The BEM-CFD results, which are based on two-dimensional hydrofoil theory, are evaluated using the experimental and numerical lift and drag coefficients. It shows that the two-dimensional lift and drag coefficients had significant effects on the BEM-CFD predictions. Overall, the BEM-CFD based on the numerical hydrofoil data can accurately predict the thrust, but generally overestimates the power. The influence of the lift and drag terms on the BEM-CFD predictions suggest that more reasonable 2D predictions for hydrofoils and the 3D effects should be considered to improve the BEM-CFD accuracy. BEM-CFD can reasonably reflect the circumferential averaged velocity characteristics near the rotor for the optimal condition (TSR = 6) and gets symmetrical features in the wake, but it cannot predict the detailed flow features caused by the finite number of blades due to the limitations of the BEM-CFD method.

Purpose – Studies of the three-dimensional flow characteristics during hydrofoil cavitation have shown that the side walls strongly affect the flow field around the hydrofoil. The purpose of this paper is to analyze the side wall effect for three-dimensional non-cavitating flows around a hydrofoil. Design/methodology/approach – A three-dimensional non-cavitating flow field around a hydrofoil is analyzed for different attack angles using the RNG turbulence model and large eddy simulations (LES). The effect of the hydrofoil span was analyzed using LES simulations for various spans. Findings – The lift coefficient, drag coefficient and pressure coefficient on the suction side are compared with experimental values. The results from the LES model (Smagorinsky-Lilly subgrid-scale model) agree better with the experimental data than those from the RNG turbulence model. Originality/value – This paper shows that the flow around the hydrofoil has significant three-dimensional characteristics due to the side wall. For wide hydrofoils, the wall vortex region becomes essentially stable, and the width of the span has little effect on the middle region.