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Experimental research was conducted on the performance curves and the cavity evolution for different flow and geometric parameters in jet pumps for zero flow-ratio (ZFR) conditions. New pressure ratio, Pr, and flow ratio, qr, were used in place of the conventional performance parameters h and q, to characterize the jet pump flow performance. A super cavitation cavity in the jet pump was observed to fill most of the flow channel, which hindered further increases of the flow rate and increased qr to one, thus, created a critical point on the new Pr-qr2 curve. Before the critical point, Pr was proportional to qr2 with a coefficient that was much more sensitive to the area ratio than the relative throat length and the diffusion angle. After the critical point, the flow rate reached its maximum, the limiting flow rate, which only depended on the total inlet pressure and the area ratio. The total inlet pressure was proportional to the square of the limiting flow rate with a flow coefficient that was only a quadratic function of the area ratio.

Cavity shedding mechanisms, such as those due to re-entrant jets (RJ) and condensation shocks (CS), are important but challenging topics in cavitating flows. This study investigates unsteady cavity shedding around a NACA66 hydrofoil using a self-defined compressible cavitation solver based on OpenFOAM with a dynamic cubic nonlinear subgrid-scale model. The predictions give satisfactory agreement with experimental data for the quantitative pressure evolution and the cavity shedding behavior induced by the re-entrant jet and the pressure wave. Moreover, the numerical data provides deeper insight into the pressure wave characteristics (e.g. propagation speed, wave intensity, shock Mach number, etc.) during cavity contraction. Multi-perspective analyses demonstrate that the pressure wave is a condensation shock which is responsible for the attached cavity abruptly disappearing. Additionally, the different influences of the re-entrant jet and the condensation shock on the local flow patterns are compared in detail in terms of the duration, average motion velocity, cavity behavior, formation mechanism and pressure intensity. The results show the condensation shock is characterized by fast propagation speed, short duration and high pressure pulse, which differs from the re-entrant jet features. This research provides an improved understanding of the cavity shedding mechanism around a cavitating hydrofoil and demonstrates the effectiveness of the current compressible cavitation solver.

Large eddy simulations of tip vortex cavitation (TVC) around an elliptical hydrofoil is performed to study its scale effect. A satisfying agreement is obtained between the numerical and experimental data. It indicates that the scale effect of TVC is remarkable. With the increase of scale ratio or incoming velocity, the intensity of TVC significantly increases. Based on our results, two mechanisms for the scale effect of TVC are proposed, i.e., the roll-up of boundary layer and the interaction between tip vortex (TV), secondary vortex and trailing vortex. As incoming velocity increases, the fusion of TV and secondary vortex enhances and the boundary layer thickness decreases, which lead to larger circulation and smaller vortex core radius, tending to intensify TV. As scale ratio increases, the fusion of TV and secondary vortex enhances and the boundary layer thickness increases slightly, which lead to much higher circulation and slight increase of vortex core radius, promoting the occurrence of TVC in general. In addition, with equal cavitation number and Reynolds number, TVC in the large scale is stronger than that in the small scale, indicating that it seems not so reasonable to equate the velocity-induced scale effect with the scale-ratio-induced one.

In this paper, the large eddy simulation (LES) method in conjunction with the Zwart cavitation model is adopted for the assessment of the erosion risk on a hydrofoil surface. The numerical results are in good agreement with the experiments. On this basis, three methods, namely the intensity function method (IFM), the time-averaged aggressiveness indicators (TAIs) and the gray level method (GLM), are applied for the assessment of the erosion risk. It is shown that the erosion intensity index of the IFM is extremely sensitive to the artificially selected thresholds, which greatly limits the application of the method. The erosion risk predicted by four indicators in the TAIs does not agree well with the experimental results. Further analysis demonstrates that the GLM using the instantaneous pressure field is relatively satisfactory, which can provide a reasonable assessment of the erosion and is not very sensitive to the artificially selected thresholds. To further improve the accuracy of the GLM for the erosion risk prediction, the time-average pressure field is adopted in the GLM for the erosion evaluation. It is suggested that the erosion assessment by using the time-averaged pressure field is in better agreement with the experimental results when compared with that by using the instantaneous pressure field.

The acoustic propagation characteristics of the cavitating flow are essential for the noise suppression, but were not well studied. In the current paper, a new technique concerning the propagation path of the monopole acoustic energy is presented and two typical thermodynamic cavitation modes (the inertial and thermal modes) are selected to investigate the effect of the cavity shedding dynamics on the acoustic propagation path. In the inertial mode, the temporal variation and the spatial distributions of the monopole acoustic energy as well as the divergence of the monopole acoustic pressure are both more powerful and concentrated than that in the thermal mode. The acoustic propagation path in the thermal mode strictly satisfies the feature of the convective amplification, while there exists another propagation direction close to the normal direction of the foil surface in the inertial mode. Furthermore, the occurrence of the normal direction propagation will make the path deviate from the convective direction.

The tip-leakage vortex (TLV) cavitation is a challenging issue for a variety of axial hydraulic turbines and pumps from both technical and scientific viewpoints. The flow characteristics of the TLV cavitation were widely studied in the past decades, but the knowledge about the tip-leakage cavitating flow is still limited. The present paper reviews the progresses in the researches of the TLV cavitation, including the numerical methods for the TLV cavitation, the flow characteristics of the TLV, the influences of the TLV cavitation on the local flow field and the control strategies of the TLV cavitation. It is indicated that the non-condensable gas may play an important role in the development of the TLV cavitation, and this fact should be considered during a careful simulation of the TLV cavitation. It is also suggested that the development of the TLV cavitation will significantly influence the distributions of the vorticity and the turbulence kinetic energy. Due to the complexity of the TLV cavitation, it is still an open question how to suppress the TLV cavitation in a simple but effective way. Finally, based on these understandings, some advanced topics for the future work are suggested to further promote the study of the TLV cavitation, for a deeper knowledge about the TLV cavitation.

The turbulent cavitating flow around the propelling pump tip clearance is numerically simulated using the large eddy simulation (LES) method coupled with the Zwart-Gerber-Belamri (ZGB) cavitation model to investigate the cavitation-vortex interaction mechanism. The calculated cavitation structures around the blades are in a remarkable agreement with the experimental results. The distributions of the tip clearance vortex under two cavitation conditions are obtained and compared. The results show that the cavitation development enhances the vorticity generation and the flow unsteadiness around the tip clearance of a propelling pump. Vortices are basically located around the cavitation areas, particularly in the tip clearance region, during the cavitation. The relative vorticity transport equation is applied for the cavitating turbulent flows and it is further indicated that the vortex stretching term makes the main contribution in the vortex production, and the baroclinic torque and dilation terms are important source terms for the vorticity generation in the cavitating flow. In addition, the viscous diffusion term and the Coriolis force term are significant in modifying the vorticity field inside the blade tip clearance.

The accuracy of large eddy simulation (LES) is highly dependent on the performance of sub-grid scale (SGS) model. In the present paper, a dynamic cubic nonlinear sub-grid scale model (DCNM) proposed by Huang et al. is implemented for the simulation of unsteady cavitating flow around a 3-D Clark-Y hydrofoil in OpenFOAM. Its performance in predicting the evolution of cloud cavitation is discussed in detail. The simulation with a linear model, the dynamic Smagorinsky model (DSM), is also conducted as a comparison. The results with DCNM show a better agreement with the available experimental observation. The comparison between DCNM and DSM further suggests that the DCNM is able to predict the backscatter more precisely, which is an important feature in LES. The characteristics of DCNM is analyzed to account for its advantages in the prediction of unsteady cloud cavitation as well. The results reveal that it is the nonlinear terms of DCNM that makes DCNM capture sub-grid scale vortices better and more suitable for studying the transient behaviors of cloud cavitation than DSM.

In the present paper, the turbulent cavitating flow generated by a Clark-Y hydrofoil is investigated by large eddy simulation (LES) combined with Zwart-Gerber-Belamri (ZGB) cavitation model. In order to shed light on the influence of cavitation on turbulent energy distribution among scales, energy spectrum obtained from the three-dimensional velocity field is firstly applied to turbulent cavitating flow. Spatial and spectral distributions of turbulent kinetic energy are studied for both non-cavitating flow and cavitating flow. Cavitation is found to have a significant effect on the original turbulent flow by inducing more large-scale turbulent structures. The energy spectrum of cloud cavitating flow also experiences a periodic evolution as cavitation develops, and a large amount of turbulent kinetic energy is found to generate as the first shedding, cutoff and second shedding of cavities happen.

Cavitation within a tip leakage flow remains a challenging issue in a variety of axial hydraulic machines. It is still not possible nowadays to predict cavitation occurrence in such a flow with acceptable accuracy. In the present study, we have carried out numerical simulations of a tip leakage cavitating flow, generated by a straight NACA0009 hydrofoil. We have used the LES method combined with the Schnerr–Sauer cavitation model. The numerical results agree well with experimental data. The evolution of the tip leakage cavitating flow, involving tip-leakage vortex (TLV), tip-separation vortex (TSV) and induced vortex (IV), is analyzed from Eulerian and Lagrangian viewpoints. The results show that the spatial evolution of the tip leakage cavitating flow can be divided into three stages: Stage Ⅰ, Independent development of the TLV and TSV; Stage Ⅱ, Fusion of the TLV and TSV; and Stage Ⅲ, Development of the IV and dissipation of the TLV. The Lagrangian coherent structures (LCSs) obtained from the numerical results indicate that the TLV cavitation significantly influence the local flow patterns. The vorticity transport equation was then used to further analyze the influence of the cavitation on the vortices. The results demonstrate that the stretching term dominates the TLV evolution and the dilatation term is responsible for the vorticity reduction inside the TLV cavity. The results also show how the cavitation influences the local turbulence and that the transport term in the turbulent kinetic energy equation influences the turbulence distribution near the TLV cavity.

This paper investigates the effect of gap size on the inception of tip leakage vortex cavitation (TLVC) with a hybrid Eulerian–Lagrangian model. Good agreement is achieved between the simulation results and experimental data for velocity distributions around the TLV, bubble motion, and its size oscillations. It is found that the minimum pressure criterion is not accurate enough for the prediction of TLVC inception due to the significant effect of pressure fluctuation and increased concentration of nuclei in the TLV core region. The pressure fluctuation in the TLV core is noted to be a non-negligible factor, while the corresponding effect on nuclei dynamics in the TLV core is still unclear. To deal with this problem, the inducement of this excited turbulence is further analyzed and discussed in detail, which shows a close relationship with the TLV instability raised by the vortical interaction between TLV and tip-separation vortex/induced vortex. Our work provides an insight into the mechanism of TLVC inception through the flow characteristics in the TLV core region, which is helpful for controlling TLVC inception in engineering designs.

The large eddy simulation (LES) method is used to simulate cavitating flow in a venturi tube. The simulated results agree fairly well with the experimental data. To quantitatively describe the relationship between cavitation evolution and excited pressure fluctuation in the venturi tube, a modified prediction model is proposed and its accuracy is verified by the LES results. Based on the original one-dimensional model for the external cavitating flow around a hydrofoil, this model is corrected according to the internal cavitating flow characteristics in the venturi tube. The results show that the original one-dimensional model ignores the choking effect of cavitating flow, which is obvious in a venturi tube with a narrow flow channel, thus leading to an inaccurate prediction of pressure fluctuation in the venturi tube. The modified model can significantly overcome its deficiencies and improve the accuracy of the pressure fluctuation prediction, providing a theoretical basis and guidance for engineering application to controlling the pressure fluctuation in a venturi tube or for other internal flows.

Jet pump is a type of cavitation reactor with great potential because of strong shear flow. In the present paper, experiments were carried out to investigate the cavitation characteristics of jet pump cavitation reactors (JPCRs) with different throat lengths, throat types and diffuser angles. Cavitation images and sound pressure signals in water corresponding to the hydraulic parameters are introduced to judge the aggressive intensity of cavitation in JPCRs. The flow ratios varying from the maximum limited value to -1 were measured for all JPCRs. It suggests that throat structure plays a more important role in the cavitation and flow characteristics of JPCR when compared with diffuser structure. Specifically, convergent throat results in large bubble density in the diffuser while divergent throat results in choke in the throat compared to the original JPCR. And cavitation bubble density in throat increases with increasing throat length. With the decrease of the flow ratio (q 0), sound pressure level (SPL) decreases from the maximum to the minimum and then increases again. As the flow ratio decreases further (q 0), SPL keeps on increasing first and then decreases, finally it takes a turn and increases to a stable level. Further study on actual SPL induced by cavitation in JPCR indicates that small diffuser angle, divergent and long throat enhance the aggressive intensity of cavitation. This result is of great significance to the design of JPCR.

This paper studies the unsteady three-dimensional cavitating turbulent flow in a jet pump. Specifically, thefocus is on the unstable limited operation stage, and both the computational and experimental methods are used. In the experiments, the distribution of the wall pressure, as well as the evolution of cavitation over time, are obtained for a jet pump. Computation is carried out using the large eddy simulation, combined with a mass transfer cavitation model. The numerical results are compared with the experimental results, including the fundamental performances (the pressure ratio h and the efficiency η), as well as the wall pressure distribution. Both the experimental and computational results indicate that the evolution of the cavitation over time in a jet pump is a quasi-periodic process during the unstable limited operation stage. The annular vortex cavitation inception, development and collapse predicted by the large eddy simulation agree fairly well with the experimental observations. Furthermore, the relationship between the cavitation and the vortex structure is discussed based on the numerical results, and it is shown that the development of the vortex structures in the jet pump is closely related to the evolution of the cavitation. The cavitation-vortex interaction is thoroughly analyzed based on the vorticity transport equation. This analysis reveals that the cavitation in a jet pump dramatically influences the distribution and the production of the vorticity. The process of the annular cavitation inception, development, and collapse involves a significant increase of the vorticity.

In the current paper, Large Eddy Simulation on the confined tip leakage cavitating flow generated by a straight NACA0009 hydrofoil with a clearance size gap = 10 mm is performed. TLV cavitation and TSV cavitation are reasonably captured. Different vortex identification methods of all three generations, including vorticity, Q-criterion, Ω method and Liutex method are compared in detail with the simulated tip leakage cavitating results. It is observed that the Ω method and the Liutex method, show advantages in visualizing vortical structures in the currently studied flow regime with a strong capability in filtering out shearing contaminations. Both Liutex vector field and Liutex iso-surface show potentials in investigating vortical cavitating flow. Differences of cavitating and non-cavitating tip vortices mainly lie in their sizes and the generation of small-scale vortices around the TSV, which indicates the effect of cavitation.

In the present study, a two-way coupling Eulerian–Lagrangian approach is developed to assess the cavitation erosion risk in an axisymmetric nozzle. Macroscopic cavitation structures are simulated using the large eddy simulation along with the volume of fluid method. The compressible Rayleigh–Plesset equation and the bubble motion equation are introduced to resolve the microscopic bubble dynamics. The calculated results agree favorably with the experimental data and can capture more flow details, which is associated with the potential erosion risk. Based on the bubble information in multi-scale cavitating flow, a new asymmetric bubble collapse model is proposed to calculate the impact pressure, which is then used to quantitatively assess the cavitation erosion risk in the nozzle. The results show that, compared with the traditional Euler method, the location and value of the potential maximum cavitation erosion risk predicted by this new method are closer to the experimental measurement. The advantages of the newly proposed method are further elaborated systematically. The study found that the high environmental pressure triggered by the collapse of shedding clouds can cause the near-wall bubbles to shrink and even collapse, releasing impulsive pressure, which directly damages the material surface. This phenomenon is considered to be closer to the actual cavitation erosion process. Finally, analyzing the relationship between multi-scale cavitation structures and erosion risk reveals that the high risk of cavitation erosion is mainly due to the oscillation and collapse of near-wall bubbles which are generated near the attached cavity closure line or surrounding the shedding clouds.

The unsteady cavity dynamics induced by the reverse flow and shock wave is a crucial issue in studies of cloud cavitation. In the current meeting paper, numerical simulation of cavitating flow around the NACA66 hydrofoil is performed based on the self-developed program. LES method is introduced to adequately account for the transient turbulence effects in compressible cavitating flow. The simulation agrees favorably with the previous experiment for the cavity shedding behaviors. The results showed that the unsteady cavity dynamics is induced by both the reverse flow and shock wave mechanism. Besides, the different cavity shedding behaviors of the reverse flow and shock wave are compared in details.

In this paper, the cavitating flow in a venturi tube is simulated by LES combined with the ZGB cavitation model. A satisfying agreement between the numerical and experimental results is obtained. The comparison among Liutex method, vorticity method, Q method, λ ci method and Ω method has shown that Liutex method could suppress interference of shearing and preserve intensity of vortex. Thus, Liutex vortex identification method was selected to analyse the interaction between cavitation and vortex based on our numerical results. It is found that the strong vortex ring in the throat induces the cavitation ring. The ring shape cavitation cloud develops into the diffuser and separates from the wall, where small vortices occur. Forced by the re-entrant flow and small vortices, the thickness of cavities reduces, resulting in the breaking and shedding of cavities. Shedding cavities rapidly collapse, strengthening the intensity of vortices around the cavities.

In the present paper, a new control method for tip-leakage vortex (TLV) cavitation is proposed. This method, which combines the effects of grooves and winglets, is made of overhanging grooves (OHGs) fitted at the tip of a hydrofoil. Experimental and numerical investigations are conducted to evaluate the performances of OHGs in terms of TLV cavitation suppression. The results are systematically compared with the baseline, conventional grooves (CGs) and anti-cavitation lip (ACL) and a significant improvement of TLV cavitation suppression is obtained with the OHGs. We also carried out a primary optimization design of the OHGs and a more effective suppression on TLV cavitation is obtained for small gaps and TLV cavitation is almost suppressed for middle and large gaps. The underlying reasons for TLV cavitation mitigation are discussed in detail with the help of numerical simulations. It indicates that for small gap sizes, OHGs can effectively weaken the strength of both TLV and tip-separation vortex (TSV) and mitigate TLV cavitation. For middle and large gap sizes, it is found that OHGs will induce an increase in the TLV core size, which further increases local minimum pressure. The influence of OHGs on the performance of hydrofoil is also examined, which indicates that the fluctuation of TLV cavitation can be effectively suppressed by OHGs and no significant alteration of time-averaged drag and lift is induced by OHGs. Our work shows that the OHGs can effectively suppress TLV cavitation with limited influence on the performances of hydrofoil in a large range of the gap sizes, which is a promising method for the control of TLV cavitation in hydraulic machinery.

In this paper, the cavitation performance and corresponding pressure pulsation, noise and vibration induced by the choked cavitating flow in a Venturi reactor are investigated experimentally under different cavitation conditions by using high-speed camera and high frequency sensors. Based on the instantaneous continuous cavitation images, the Proper Orthogonal Decomposition (POD), a tool to analyze the large-scale cavitation flow structure, is applied to investigate the choked cavitating flow dynamics. The POD results show that two mechanisms, re-entrant jet flow mechanism and shock wave mechanism, govern the shedding and collapse of cavitation cloud at different pressure ratios. These mechanisms contribute to the variation of pressure pulsation, noise and vibration at different pressure ratios. The pressure pulsation spectrum behaves differently in various cavitation regions induced by the choked cavitating flow. Due to the existence of low pressure in re-entrant region, the influence of high frequency fluctuation on pressure pulsation caused by re-entrant flow is small. Moreover, with the increase of pressure ratio, the induced noise and vibration intensity decreases gradually, then increases and reaches a maximum value. Finally, it drops to a low and stable level. Despite different inlet pressures, the intensity of cavitation noise and vibration reaches the maximum value at the same pressure ratio. Specifically, the FFT analysis of noise and vibration signals indicates that low frequency component prevails at small pressure ratio owing to the re-entrant jet mechanism, while high frequency component prevails at large pressure ratio owing to the shock wave mechanism. The relationship between the choked cavitation dynamics and the induced pressure pulsation, noise and vibration in the Venturi reactor is highlighted. The results can provide guidance for the optimal operation condition of the Venturi reactor for cavitation applications such as water treatment.

In the present paper, cavitation noise induced by sheet cavity and tip leakage vortex cavity (TLVC) together generated by a NACA0009 hydrofoil are numerically investigated with Ffowcs Williams-Hawkings (FW-H) equations. Large eddy simulation (LES) combined with Schnerr-Sauer cavitation model is utilized and a satisfactory result is obtained as compared with the referenced experimental measurements. It is found that even though the volume of TLV cavity is much smaller than that of sheet cavity, their acoustic levels are comparable to each other. A close relationship is indicated between cavity evolutions and their radiated noises, which vary periodically for both sheet and TLV cavities. Moreover, intense sound pulses of pseudo-thickness and pseudo-loading noise are observed especially during the collapse process. It is indicated that the rise in far field pressure and action of the dilatation term inside the cavities may trigger the collapse of both kinds of cavities in the flow, resulting in sound impulses. It is worth mentioning that in agreement with previous investigations, high pressure distribution and jets at the ends of sub-TLVCs are noted to have a close relationship with the collapse of sub-TLVCs. Noise generated by sheet cavity is higher than that generated by TLV cavity at the dominant Strouhal number of 0.74, with relatively high values of both pseudo-thickness and pseudo-loading noises at the dominant Strouhal number. While noise of TLV cavitating flow has acoustic energy concentrated at either low Strouhal numbers or high Strouhal numbers for the two terms, respectively.

Experiments were conducted to investigate the cavity length pulsation characteristics in jet pumps with different area ratios during limited operation stage. Images of various cavitating flows were captured and analyzed to study the cavity length pulsation characteristics by high speed camera technology. It was found that the development tendency of time-averaged cavity length can be divided into two sections with different pulsation intensity by throat length. Further analysis indicated that the time-averaged cavity length is a function of area ratio and outlet pressure ratio independent of the inlet pressure. And the time-averaged cavity length decreases slowly and then faster with the increase of comprehensive parameters. Meanwhile, the cavity length pulsation can be decomposed into low frequency component and high frequency component. The pulsation intensity of low frequency component is relatively high during unstable limited operation stage, while it is at a low level during stable limited operation stage. Besides, smaller area ratio and inlet pressure result in larger pulsation intensity of low frequency component during unstable limited operation stage. The experimental points of high frequency component pulsation intensity collapsed around a V-shaped curve and it reached the minimum value when time-averaged cavity length is approximate to the throat length.

In the present paper, flow configurations of cavitating flow around a straight NACA0009 foil with a gap between the foil tip and sidewall are investigated numerically by large eddy simulation (LES) coupled with Zwart-Gerber-Belamri (ZGB) cavitation model. A Cartesian cut-cell method is used for mesh generation, which is of good orthogonality and high quality. A good agreement is obtained between simulation and experiment. Two influencing factors on vorticity distributions, the interaction between different vortices and the occurrence of cavitation, are discussed in detail based on the numerical results. A series of Ω- shaped loops are observed during the development of the induced vortex, which is a result of the instability of vortex pair. This finding may provide a new viewpoint to control the evolution of tip-leakage vortex (TLV) cavitation. Moreover, it is found that the dilatation term plays a much more important role in the evolution of TLV cavitation compared with that in sheet cavitation.

In the present paper, the Vortex Identified Zwart-Gerber-Belamri (VIZGB) cavitation model coupled with the SST-CC turbulence model is used to investigate the unsteady tip-leakage cavitating flow induced by a NACA0009 hydrofoil. A qualitative comparison between the numerical and experimental results is made. In order to quantitatively evaluate the reliability of the numerical data, the verification and validation (V&V) procedures are used in the present paper. Errors of numerical results are estimated with seven error estimators based on the Richardson extrapolation method. It is shown that though a strict validation cannot be achieved, a reasonable prediction of the gross characteristics of the tip-leakage cavitating flow can be obtained. Based on the numerical results, the influence of the cavitation on the tip-leakage vortex (TLV) is discussed, which indicates that the cavitation accelerates the fusion of the TLV and the tip-separation vortex (TSV). Moreover, the trajectory of the TLV, when the cavitation occurs, is close to the side wall.

In this letter, the attached turbulent cavitating flow around the Clark-Y hydrofoil is investigated by the numerical simulation with special emphasis on error analysis of large eddy simulation (LES) for the unsteady cavitation simulation. The numerical results indicate that the present simulation can capture the periodic cavity shedding behavior and show a fairly good agreement with the available experimental data. Further analysis demonstrates that the cavitation has a great influence on LES numerical error and modeling error. The modeling error and numerical error are almost on the same order of magnitude, while the modeling error often shows a little bit larger magnitude than numerical error. The numerical error and modeling error sometimes can partially offset each other if they have the opposite sign. Besides, our results show that cavitation can extend the magnitudes and oscillation levels of numerical error and modeling error.

In the present paper, large eddy simulations combined with the Zwart cavitation model are conducted to simulate the transient cavitating turbulent flow around a Delft Twisted hydrofoil. Numerical results show a reasonable agreement with the available experimental data. A three dimensional Lagrangian technology is developed to provide an alternative method for the analyses in cavitating flow, which is based on Lagrangian viewpoint. With this technology, the track lines of re-entrant and side-entrant jets are straightforwardly displayed and clearly indicate that collisions of the mainstream, the re-entrant jet and the side-entrant jet play an important role in the primary and secondary shedding. The evolution of U-type structures and the interactions between cavitation and vortices are well captured and discussed in detail from the Eulerian viewpoint. The numerical results show that during the stage of attached cavity, the topology of the cavity leaves an important influence on the vortex structure. Once the cavity is cut off, the vortex structure evolution will affect significantly the local cavitating flow. Further analysis demonstrates that the lift acting on U-type structures, which is induced by velocity circulation around U-type structures, significantly affects the formation and the development of U-type structures. Lagrangian Coherent Structures (LCSs) obtained with the three dimensional Lagrangian technology are used to reveal the influence of U-type structures on local flow patterns and it shows that there is a close relationship between the local flow separation and vortex structures. Our work provides an insight into the interactions of cavitation-vortex in the cavitating flow around a twisted hydrofoil and demonstrates the potential of 3D LCSs in the analyses of cavitating flow.

In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model (FBDCM), a turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures (LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet, the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage III, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.

In the present paper, a novel machine-learning-assisted RANS method is proposed and utilized to investigate the unsteady cavitating flow around a Clark-Y hydrofoil. A data-driven machine learning model for turbulent eddy viscosity (TEV) is constructed based on high-fidelity LES results first and then makes a prediction for TEV in RANS simulation. The machine-learning-predicted TEV successfully imitates the TEV distribution characteristics of LES that there is a concentration around cavities and negative TEV in the wake. Based on the more accurate TEV field, the machine-learning-assisted RANS method makes more accurate predictions about velocity profile and basic performance parameters of the hydrofoil and gives a better representation of shedding process of sheet cavitation when compared with original RANS results. Finally, generalization performance of the machine learning model is assessed by simulating cavitating flows under different inlet velocity conditions. The results indicate that cavitation exhibits more periodicity with the decrease of inlet velocity in the range of investigated conditions, which may be associated with different TEV distribution characteristics.

Unsteady cavitating turbulent flow around a three-dimension Clark-Y hydrofoil is investigated using the integral method and numerical simulations with the filter-based density correction model turbulence model (Huang et al., 2014). The numerical results are validated with experimental data. The interaction between the cavitation and the fluid vortex is analyzed with the vorticity transport equation. The results demonstrate that the vortex stretching is mainly in the center of the cloud cavity and changes quasi-periodically as the cloud cavity evolves. The correlation between the entrainment ability of upstream flow and cavitation is built in a three dimensional case. The numerical results and the theoretical analysis show that the evolution of total vapor volume determines the overall entrainment ability and the behavior of re-entrant jet significantly impacts the variations of entrainment ability. The correlation between the flow field and the entrainment ability provides a new perspective for the study in cavitation, especially the re-entrant jet dynamics around hydrofoil. The relationship between the cavity volume pulsations and the pressure fluctuations around the hydrofoil is analyzed with a simplified one dimensional model. The model demonstrates that the second derivative of the total vapor volume is mainly responsible for the cavitation excited pressure fluctuations.

Stable operation is a challenge for hydropower stations with multi-turbine hydraulic coupled division systems with a common penstock. In this paper, the serious power fluctuations in a power station with such a division system are analyzed. The fluctuations occur in many conditions without any movement of the regulating system. The mathematical analysis illustrates that pressure fluctuation is responsible for power fluctuations. The computational fluid dynamics (CFD) method provided by ANSYS is used to study the flow pattern in penstocks. The vortex caused by the irrational structure of trifurcation is the reason for pressure fluctuations. Several methods are proposed to optimize the flow stability and three cases are simulated based on these measures. The calculation results of three cases prove the effectiveness of these measures. The measure of setting the new guide plate is finally conducted, and the output power fluctuations vanish. The flow calculation plays a role in the analysis and optimization of the hydraulic system of the hydropower unit. Some rules are summarized from the cases and are helpful in the design of trifurcation in a division system with a common penstock.

Numerical simulation of tip vortex cavitation (TVC) remains a challenging task in a variety of applications, such as axial turbines and pumps as well as marine propellers. Although it is well known that TVC is highly sensitive to gas content, be it dissolved or not, numerical models do not consider this aspect so far. As a result, numerical simulations usually underestimate the development or the intensity of TVC. In the present paper, we propose an new Euler-Lagrangian cavitation model based on Rayleigh-Plesset (R-P) equation, taking into account the non-condensable gas. In this model, the Euler method is used to solve the global flow field and the Lagrangian method is used to track the migration of non-condensable gas bubbles into the vortex core. Based on the simplified R-P equation, the connection between local gas concentration and its effect on cavitation is modeled and the mass source terms in the original Schnerr-Sauer (S-S) cavitation model are modified. We applied the new cavitation model to a simplified case study, made of an elliptical NACA-16020 hydrofoil and compared the results with experimental observation. We obtained a significant improvement of the TVC prediction. Our work illustrates the major role of the gas content in sustaining cavitation downstream of the hydrofoil through an efficient attraction of nuclei, fueled by the low pressure induced by the vortex flow.

Unsteady cavitating turbulent flow around twisted hydrofoil is simulated with Zwart cavitation model combined with the filter-based density correction model (FBDCM). Numerical results simulated the entire process of the 3-D cavitation shedding including the re-entrant jet and side-entrant jet dynamics and were compared with the available experimental data. The distribution of finite-time Lyapunov exponent (FTLE) was used to analyze the 3-D behavior of the re-entrant jet from the Lagrangian viewpoint, which shows that it can significantly influence the particle trackers in the attached cavity. Further analysis indicates that the different flow behavior on the suction side with different attack angle can be identified with Lagrangian coherent structures (LCS). For the area with a large attack angle, the primary shedding modifies the flow pattern on the suction side. With the decrease in attack angle, the attached cavity tends to be steady, and LCS A is close to the upper wall. A further decrease in attack angle eliminates LCS A in the boundary layer. The FTLE distribution also indicates that the decreasing attack angle induces a thinner boundary layer along the foil surface on the suction side.

The sheet/cloud cavitating flow always contains complex multiscale vortex structures generated by the cavity cloud shedding and collapsing. In this study, the transient sheet/cloud cavitating flow around a Clark-Y hydrofoil is numerically investigated using the Large Eddy Simulation (LES) method coupled with the Zwart–Gerber–Belamri (ZGB) cavitation model. The simulation accurately reproduces the unsteady cavitation evolution process, and the predicted time-averaged lift and drag coefficients, total vapor volume variation and velocity distribution agree fairly well with the experimental measurements. The cavitation vortex dynamics are studied in detail with different vortex identification methods including the vorticity method, the [Formula: see text]-criterion method, the [Formula: see text] method, the [Formula: see text] method and the Liutex method. The vortex identification ability of the different methods in the transient sheet/cloud cavitating flow is also discussed. Generally, the Liutex method combines the advantages of the other methods and can accurately identify both the vortex position and strength. Further analysis of cavitation-vortex interactions demonstrates that the cavity cloud shedding and collapsing have a pronounced influence on the vortex structure.

In the present paper, a new cavitation model proposed by Cheng et al. (2020a) combined with LES is utilized to simulate the tip-leakage cavitating flow around a NACA0009 hydrofoil, which considers the effect of non-condensable gas on cavitation. The predicted tip-leakage vortex (TLV) cavitation agrees well with available experimental observations. Based on the numerical results, the influence of different tip clearance sizes on tip-leakage cavitating flow is discussed in detail. It is shown that with the increase of tip clearance size, the intensity of tip-separation vortex (TSV) cavitation decreases, while the intensity of TLV cavitation increases first and then decreases. Their fusion position moves downstream with the increase of tip clearance size. Moreover, the numerical result implies that the size of tip clearance also has an impact on characteristics of sheet cavitation, such as its length and shape. Finally, the vorticity transport equation is utilized to investigate mechanisms of vortex development around TLV cavitation. As tip clearance size increases, the effect of stretching term decreases, while that of dilatation and baroclinic torque terms increases first and then decreases. However, it is found that the stretching term is dominant in all investigated cases regardless of tip clearance size.