Unsteady Cavitation Research Articles

Numerical study on cavitation–vortex–noise correlation mechanism and dynamic mode decomposition of a hydrofoil

The large eddy simulation model coupled with the modified Schnerr–Sauer cavitation model has been used to numerically simulate the unsteady cavitation and noncavitation flow of the three-dimensional NACA66 (National Advisory Committee for Aeronautics) hydrofoil under different operating conditions. The results show that the magnitude of the cavitation number plays a decisive role in the hydrofoil cavitation quasiperiodic phenomenon. The cavitation number of 1.25 is used as a typical working condition for analysis. Using the Ffowcs Williams–Hawkings acoustic analogy approach accompanied by the vorticity transport equation splitting, the growth and shedding of cavitation also lead to the growth and shedding of the vortex structure. The cavitation–vortex interaction is mainly influenced by the vortex stretching term and vortex dilatation term and amplitude of them are larger than 500. The baroclinic torque term may be responsible for generating vorticity during the cloud cavitation collapse and has a lower amplitude about 200. The cavity volume acceleration is the main influencing factor of the low-frequency pressure fluctuation around the cavitating hydrofoil. Moreover, the NACA66 hydrofoil surface-pressure data are collected for dynamic mode decomposition to locate the hydrofoil surface noise sources. The alternate high and low amplitude regions in the mode results overlap highly with the cavitation transformation regions. The cavity transformation and pressure fluctuations are the main reason for the generation of periodic low-frequency noise source regions on the hydrofoil surface. Moreover, the corresponding frequencies of each order mode are linearly correlated with the cavitation shedding frequency of 5.70 Hz. Combined with the results of the multiple mode comparisons, it can be inferred that the hydrofoil suction surface under the cavitation effect will generate quasiperiodic waves starting from upstream and moving downstream.

On the transient cavitation characteristics of viscous fluids around a hydrofoil

Cavitation is a transient phase transition process between liquid and vapour, and it often occurs in machines using viscous fluids as working media owing to complex operating environments and the trend toward high temperature, high velocity, and high power density. To investigate the cavitation properties of viscous fluids, a visualization experimental system was proposed and developed in this study. In addition, a three-dimensional computational fluid dynamics (CFD) model considering cavitation was developed based on the finite volume method (FVM) to study the cavitation characteristics and unsteady cavitation behaviors of the cavitating flow in viscous oil around a NACA0012 (National Advisory Committee for Aeronautics) hydrofoil under various conditions. The results showed that cavitation started on the suction surface of the hydrofoil near the head, and the critical cavitation number and the critical velocity were 5.2 and 10 m/s at an operating pressure of zero. Smaller cavitation numbers and higher fluid velocity induced and intensified the cavitation. Additionally, the cavitation process of the viscous oil around the hydrofoil was highly unstable and periodic, and its development included birth, growth, separation, and disintegration, with an evolution frequency of 47 Hz. This study provides a theoretical basis, experimental means, and data support for cavitation of viscous fluids, especially oil. It has significant engineering applications for the development of fluid machinery.

LES investigation into the cavity shedding dynamics and cavitation–vortex interaction around a surface-piercing hydrofoil

Recent experiments have found that there is unstable vaporous cavitation around a surface-piercing hydrofoil at high Froude numbers and small yaw angles, and it would promote ventilation formation [R. Huang et al., “Investigations into the ventilated cavities around a surface-piercing hydrofoil at high Froude numbers,” Phys. Fluids 34, 043304 (2022)], but the cavity shedding dynamics and the mechanism of cavitation–vortex interaction are still open problems. In this paper, the unstable vaporous cavities around a surface-piercing hydrofoil are numerically investigated using the large-eddy simulation coupled with the Schnerr–Sauer cavitation model. Numerical simulations can predict the cavity features, including an aerated base cavity aft of the hydrofoil trailing edge, vaporous cavitation at the hydrofoil suction surface, and tip–vortex cavitation. A U-shaped vapor cloud shedding together with a horseshoe vortex is observed during the unsteady cavitation evolution, that is, the cavity development, cutoff, and collapse. This irregular shedding is related to the three-dimensional reentrant jet induced by the velocity reflection at the vaporous cavity closure line. Furthermore, the effects of the vaporous cavitation on the vorticity generation are attributed to vortex stretching, baroclinic torque, and vortex dilatation by using the vorticity transport equation. This study could contribute to the novel hydrofoil designs and their flow control.

Assessment of unsteady cavitating flow around modified NACA4412 hydrofoil

Cavitation is a complex two-phase flow phenomenon that includes unsteady characteristics. This work performs an unsteady 2D numerical analysis of cavitating flow on (i) cambered NACA4412 hydrofoil and (ii) the same hydrofoil geometry modified with dimple. The analysis is done with the objective of estimating the effect of the dimple on the hydrodynamic performance of the cavitating hydrofoil. The numerical simulations are performed using a flow solver by employing Realizable κ-ε turbulence model and Zwart-Gerber-Belamri (ZGB) cavitation model. The hydrodynamic performance is quantified in terms of coefficient of lift, coefficient of drag, lift to drag ratio, static pressure distribution, and cavity length at various cavitation numbers and angles of attack. From the assessment, it is observed that for 8⁰ angle of attack, the coefficient of drag on NACA4412 hydrofoil with the dimple is less as compared to NACA4412 without dimple. For higher angles of attack (α = 12⁰&16⁰) NACA4412 hydrofoil with the dimple has higher coefficient of lift compared to NACA4412 without dimple.

CFD predictions of unsteady cavitation for a marine propeller in oblique inflow

In this paper the Potsdam Propeller Test Case is numerically investigated in oblique inflow conditions. We consider three different topics: open water performance curves, cavitation observations, and pressure pulses induced by the propeller to the ceiling of the cavitation tunnel. In the oblique flow case, the inflow is not uniform from the perspective of the propeller, which results in the dependency of the propeller blade loading and cavitation on the blade rate frequency. The numerical simulations were compared to experimental results for each investigated case. Additionally, we analyzed the unsteady features of the cavitation on the blades as well as the pressure peaks in the propeller wake due to collapsing cavities. We found that the global performance and cavitation patterns close to the blades agree well with the tests in the numerical simulations. The agreement with the tests for the pressure pulses on the tunnel ceiling was better in the non-cavitating case. The unsteady cavitation shed behind the propeller and the subsequent collapse events induced a vast increase in recorded maximum pressure values. Root cavitation collapse produced pressure pulses an order of magnitude greater than the collapse of tip vortex cavitation. Also the collapse of cavities on the blades contributed to a significant increase in the pressure fluctuations on the blades.

A Lagrangian analysis of partial cavitation growth and cavitation control mechanism

Partial cavitation has a strong unsteadiness, which will cause serious damage to the hydraulic machinery. The spanwise obstacle is nearly the most efficient method for controlling unsteady cavitation. In this study, numerical simulations of partial cavitating flows around NACA (National Advisory Committee for Aeronautics) 66 hydrofoils in two dimensions (2D) were carried out both with and without obstruction. The obstruction is placed at 0.37c, and its height is 0.1c. Utilizing the finite-time Lyapunov exponent, the Lagrangian coherent structures (LCSs) were developed to investigate the dynamic characteristics of the unsteady flow. By showing the dynamic evolution of the Lagrangian behaviors, the time-dependent LCSs over the two different flows demonstrate the effectiveness of LCSs in explaining the evolution of the vortex during the partial cavitation process. With the use of LCSs, the vortex boundary and reentrant jet can be easily located, and the link between the vortexes can be readily seen. In the meantime, the vortex's origin and destination are shown by the stable and unstable manifolds, respectively. LCSs were then utilized to examine how the obstruction had an impact, and the following conclusions were reached. First, the obstruction can stop a portion of reentrant jets from passing through it. Second, the obstruction can curve the pathway of the reentrant jet, which has passed through it. Third, the obstruction prevents the cavity from flowing downstream. Finally, the obstruction continuously obliterates the expanding cavity across it. Simply said, the Lagrangian analysis based on LCSs provides a better understanding of the vortex dynamics than traditional visualization techniques, which is essential to understanding the great performance of the cavitation-induced unsteady flow.

Thermodynamic Suppression Effect of Cavitation Arising in a Hydrofoil in 140 °C Hot Water

Abstract The thermodynamic suppression effect of cavitation arising in a NACA0015 single hydrofoil is experimentally investigated in water at mainstream temperatures of T∞ = 20 °C to 140 °C in the present study. The cavity length at T∞ = 140 °C is shorter than that at T∞ = 20 °C at a constant cavitation number for all cavity patterns from inception to supercavitation. On the other hand, the cavity length at T∞ = 80 °C is slightly shorter than that at 20 °C in a certain region in which unsteady sheet-cloud cavitation occurs. This indicates that the thermodynamic suppression effect appears easily in unsteady cavitation. In addition, the temperature reduction inside cavities in water is accurately measured using thermistors, which are inserted from the sidewall directly into the cavity. The temperature measurement is performed at a mainstream temperature of less than 80 °C due to limitation of calibration for the sensor. The temperature reduction at 140 °C is then predicted from the measured cavity length. It is shown that the temperature reduction inside the cavity is approximately ΔT = 0.3 °C at T∞ = 80 °C and ΔT = 0.05 °C at T∞ = 20 °C under supercavitation conditions. The predicted temperature reduction inside the cavity is ΔT = 1.1 K at T∞ = 140 °C under supercavitation conditions. Finally, Fruman's prediction equation for ΔT is examined by fitting to the measured and predicted ΔT values with assuming a volume coefficient of evaporation CQ as a fitting parameter.

Investigation on multiscale features of cavitating flow in convergent-divergent test section using Eulerian–Lagrangian method

Cavitating flows in fluid machineries always present complicated phase morphologies including a wide range of interface length scales. In the present work, an Eulerian–Lagrangian cavitation model is proposed for simulating the unsteady cavitating flow and investigating the multiscale cavitating flow features in a convergent-divergent test section. Most importantly, a two-way transition algorithm is newly developed mainly based on the shape of resolved cavities and the relative size of microscale bubbles compared to the cells, for taking the transition between microscale discrete bubbles and macroscale vapor cavities into consideration. The transient flow field of the two-phase system is described by the filtered Navier–Stokes equation and the sub-grid scale model. The volume of fluid (VOF) method and a discrete bubble model (DBM) are combined for simulating resolvable water-vapor interfaces and unresolvable discrete bubbles, respectively. Applying the proposed multiscale modeling framework, the dissipated bubbles caused by the collapse of shedding cavities that are unable to be represented by the VOF method are well predicted. The results show that the VOF-DBM model is less sensitive to the mesh resolution compared to the VOF method and it is found the dissipated bubbles are transporting around the vortex core region. Detailed bubble dynamics including DBM to VOF and VOF to DBM transitions and the interaction between macroscale cavities and microscale bubbles are well presented, indicating that the proposed VOF-DBM model is a promising approach to reveal the multiscale cavitation characteristics within limited computing resources.

Unsteady cavitation dynamics and frequency lock-in of a freely vibrating hydrofoil at high Reynolds number

In this paper, we numerically investigate the influence of unsteady partial cavitation on the fluid–structure interaction of a freely vibrating hydrofoil section at high Reynolds numbers. We consider an elastically-mounted NACA66 hydrofoil section that is free to vibrate in the transverse flow direction. The fluid–structure interaction of this system is of interest in characterizing the cavitation-induced vibration and noise of marine propellers. The coupled cavitation dynamics and the fluid–structure system are solved using a body-fitted variational framework based on homogeneous mixture-based cavitation with a hybrid URANS-LES turbulence modeling. Specifically, we explore the occurrence of large-amplitude vibrations during unsteady partial cavitating conditions that are absent in the non-cavitating flow configuration. We examine a frequency lock-in phenomenon as the main source of sustained large-amplitude vibration whereby the unsteady lift force locks into a sub-harmonic of the hydrofoil’s natural frequency. We determine the origin of this flow unsteadiness in the vicinity of the trailing edge of the hydrofoil through the interplay between the growing cavity and the adverse pressure gradient. We systematically analyze the impact of flow-induced structural vibration on the combined vortex and cavity synchronization.

Numerical investigation on the inhibition mechanisms of unsteady cavitating flow around stepped hydrofoils

In this work, the influence of obstacles on the control of unsteady cavitating flows is investigated numerically within the framework of homogeneous flow. The predicted Strouhal number of the cavity shedding around the smooth hydrofoil is close to the experimental value, indicating the accuracy of the numerical simulation. Four installation sites are examined, including 10%, 20%, 30%, and 40% of the chord length from the leading edge. The instantaneous and time-averaged hydrodynamics in conjunction with the unsteady cavity behaviors are discussed in detail. The results indicate that all cases display similar flow patterns within one shedding cycle, including the development of the attached sheet cavity, sheet/cloud transformation, and cloud cavity collapse. The hydraulic lift is governed by the partial cavity oscillation but could be significantly modified by the trailing wake vortices, especially after installing the obstacle. The recommended optimal position of the obstacle is X/L=0.4, and the corresponding pressure fluctuations and lift-to-drag ratio achieve the best performance. However, the mean vapor volume is significantly reduced when the obstacle is located at X/L=0.3, indicating the minimum risk of cavitation erosion. Installing the obstacle at different locations along the suction surface will provide different effects on oscillation based on the analyses of the Lagrangian coherent structures. The corresponding primary frequency varies in a narrow range between 106.67 Hz ∼ 121.33 Hz. Proper orthogonal decomposition (POD) analyses of the vapor fraction reveal the contribution of flow morphology to the partial cavity oscillation. Installing the obstacle could significantly limit the size of each pattern, especially for X/L=0.4.

Unsteady cavitating hydrofoil surface pressure prediction based on long short-term memory network

<p indent="0mm">As a typical nonlinear dynamic problem, the evolution law and hydrodynamic characteristics of an unsteady cavitating flow are affected by noise and computer accuracy, thus, rendering it difficult to be predicted for a long time. In this paper, a long short-term memory network is used to develop a multivariable pressure prediction model, wherein the input is the velocity value and the vapor volume fraction, and the output is the time series of the pressure coefficient. The large eddy simulation (LES) data of the hydrofoil is predicted via extrapolation. The results show that the prediction results agree with LES simulation results well, demonstrating good generalization and the ability to predict more future results.

The characteristics of unsteady cavitation around a NACA0015 hydrofoil with emphasis on the thermodynamic effect

This paper aims to numerically investigate the characteristics of unsteady cavitation around a NACA0015 hydrofoil, emphasizing the thermodynamic effect. A homogeneous mixture model coupled with a filter-based density correction turbulence model and a modified Zwart cavitation model is employed to conduct the simulation. The simulation results give the unsteady process of cavitation at different shedding stages (i.e., no shedding stage, partially shedding stage, and fully shedding stage) with emphasis on the thermodynamic effect. The vorticity transport equation is employed to reveal the thermodynamic impact in detail. The importance of stretching, dilation, and baroclinic term are identified to understand the evolution mechanism of cavitating flow in fluoroketone around a NACA0015 hydrofoil with thermal effects. Besides, the “anti-thermodynamic effect” phenomenon was captured in the fully shedding stage. This research could be potentially used to understand the complex dynamic mechanism of the cavitating flow in fluoroketone with thermal effects.

Unsteady cavitation around submerged and water-exit projectiles under the effect of the free surface: A numerical study

The growth, shedding, and collapse regime of cavitation under the effect of a free surface is complicated by projectiles moving near and across the free surface and three phases (air, liquid, and vapor due to evaporation) of a fluid. In this work, the flow behaviors of cavitation around projectiles moving beneath a free surface and exiting the free surface were numerically investigated in detail using a dual-time preconditioned Navier–Stokes (NS) model for three-phase flows. First, the cavitation flow structure around a submerged projectile moving parallel to the free surface at a constant velocity was computed to validate the numerical method. Comparisons between numerical and experimental data on cavity growth are presented. Second, the vertical and oblique water exits of the cavitating projectiles under different flow conditions were investigated. Special features of the flows, such as cavitation growth, shedding, and collapse under the effect of the free surface and the detailed pressure peaks on the surface of the projectiles from the collapse of the cavitation, were obtained, through which the physical mechanism of this flow was clearly observed. The findings are significant for the design and control of submerged vehicles and projectiles operating in such flow fields.

Numerical Analysis and Experimental Investigation of Cavitating Flows Considering Thermal and Compressibility Effects

This article deals with the numerical simulation of unsteady cavitating flow around hydrofoils, supported by experimental research realized in a cavitation tunnel situated in the Centre of Hydraulic Research. Two straight NACA hydrofoils (NACA0020 and NACA2412) were employed. The comprehensive unsteady CFD analysis was based on scale-resolving simulations (hereinafter SRS) with the aim of capturing correctly the interactions between the cavitation structures and re-entrant flow as well as the compressibility and thermal effects of cavitation. The static pressure fluctuations during the cavity oscillation cycles and the evaporation and condensation processes are discussed in detail. To predict correctly the high-pressure peaks during the bubble cloud collapses and the pressure pulse propagation speed, the real properties of water and the mixture total energy conservation equation were considered. In addition, the estimated content of undissolved air was taken into account. The numerical simulations were validated by means of already published experiments or compared with experiments conducted by the authors, and with good agreement.

Mesh dependence analysis for simulating unsteady cavitation around a plane convex hydrofoil

The mesh significantly influences the quality of the numerical results in computational fluid dynamics (CFD) problems due to its correlation with turbulence models. In the present paper a structured mesh was generated using Gmsh and two semi-structured meshes were generated using snappyHexMesh to determine the suitable mesh distribution for simulating unsteady cavitation around a plane convex hydrofoil. The numerical simulation was conducted by using the software OpenFOAM with the k-ω SST SAS turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. Besides, the experimental results obtained by the Laboratory for Hydraulic Machines of École Polytechnique Fédérale de Lausanne were used to validate the numerical results. The results showed that both structured and semi-structured meshes predicted the cavitation pattern and the maximum cavity length. The semi-structured mesh with suitable refinement reproduced in detail the dynamic behavior of unsteady cavitation, while the structured mesh efficiently reproduced the phenomenon.

Optimization of turbine start-up sequence of a full size frequency converter variable speed pump-turbine

The stability of the electricity grid will be disrupted by the massive integration of new renewable energies. Hydropower plants have a major role to play in this transformation of the electricity market by increasing their operational flexibility and their ability to provide ancillary services. However, this flexibility may lead to an accelerated degradation of mechanical components. By changing the turbine operating point far from the best efficiency point or by increasing the number of transient manoeuvres such as start and stop sequences, unsteady flow phenomena, cavitation development and additional wear and tear stress the unit’s components and impact its lifetime. The present work aims to provide preliminary insight on the optimization of the start-up sequence of a 5 MW reversible Francis pump-turbine equipped with a Full Size Frequency Converter (FSFC). The goal of the optimization approaches are to determine a start-up sequence which minimizes the runner damage, the penstock fatigue and the water losses. The objective functions are evaluated by 1D hydraulic transient simulations with the SIMSEN software and which it allow to compare the relative mitigation between the conventional fixed-speed start-up and the linear variable-speed start-up equipped with a Full Size Frequency Converter.

Vortex and cavity dynamics for the tip-leakage cavitation over a hydrofoil

Large eddy simulations were used to investigate unsteady tip-leakage cavitating flow over a National Advisory Committee for Aeronautics 0009 hydrofoil. The proper orthogonal decomposition (POD) was combined with fast Fourier transforms to help better understand the deformation dynamics of the vortex and cavity. The results show three typical vortices, i.e., the tip-leakage vortex (TLV), tip-separation vortex (TSV), and shedding–trailing vortex (STV) with their own helical core lines in the averaged cavitating flows. Upstream of x/C = 1.8, the mean TLV core carries the breathing mode waves through the vortex dilatation effect, while the TSV core generates the dilatation, shrinkage, and bending distortions near the cavity interface by vortex stretching and deflection effects. Further downstream, the TLV starts to intertwine with the TSV, and the STV gradually diffuses. The TLV wandering encourages large cavity deformations dominated by the breathing and bending modes. However, in the lower-order POD modes, the contribution of bending modes to the cavity fluctuation energy is greatly weakened due to the variation of the relative cavity radius, r*, which indicates that the breathing mode and the double helix mode play major roles in the cavity interfacial waves. The results also show that the cavity interfacial oscillations are highly correlated with the surrounding velocity fluctuations. Moreover, a modified theoretical dispersion equation can well reproduce the quantitative relation between the vibration frequencies and the axial wavenumbers of the TLV cavity, especially for the wave dynamics of the breathing modes and the double helix modes.

Numerical simulation of cavitating flows: comparison between two-fluid and homogeneous approaches

The paper presents a new two-phase flow approach to simulate unsteady cavitating flows. The study applied the in-house code neptune_cfd, which allows two-fluid modelling of liquid-vapor flows [1]. The code solves the ensemble-averaged equations of mass, momentum and energy conservation for each phase (liquid and vapour) for a total of six conservation equations. The equations system requires closure laws for the interfacial terms that represent the mass, momentum and energy transfers occurring between the liquid and vapor phases. An original approach is implemented by using an energy-source term based on the difference between the local enthalpy and its saturation value. 2D and 3D simulations are carried out for a NACA 65−012 hydrofoil with an angle of attack of 6°, a cavity length of 40% of the hydrofoil chord and different flow velocities. The methodology to obtain the cavity length and the main frequency of its periodic behavior is presented. Then the numerical results are compared with those previously obtained by a homogeneous approach [2] and with the available experimental data [3]. The quantitative predictions of the hydrodynamic characteristics (i.e. cavitation sigma number, cavity length, shedding frequency and cavity shape) obtained from two-phase flow modeling appear in better accordance with experimental data.

Intermittent cavitating flow field in tandem cascades of Kaplan turbines

Within the framework of the classical turbine design setup, we present a numerical investigation of unsteady cavitating flow in tandem cascades of guide vanes and rotor blades. The practical relevance of the present investigation is ensured by choosing real blade profiles and domain geometry for the large Kaplan turbines (9.5 m rotor diameter) from the Iron Gates I hydropower plant on the Danube River. The 2D tandem cascade setup is obtained with a conformal mapping of the circular guide vane cascade into a straight cascade, while the rotor blade cascade is by default a straight one for axial turbines. Both single-phase and two-phase cavitating flows results are presented and analysed. The single-phase liquid flow displays rather modest pressure and tangential force fluctuations, with the characteristic blade passing frequency, due to the interaction of the rotor blades with the wakes of guide vanes. The two-phase cavitating flow displays a completely different dynamics in comparison to the liquid flow, with periodic cavitation growth and collapse at a specific frequency lower than the blade-passing one. Moreover, the tangential force on the rotor blade displays severe intermittency and the force fluctuations are almost one order of magnitude larger than in the single-phase flow.

Estimation of cavitation erosion area in unsteady cavitating flows using a modified approach

Estimation of cavitation erosion area remains a challenging issue. Only an accurate estimation of the erosion-sensitive area can effectively reveal the various mechanisms of cavitation erosion. In this study, large eddy simulation is applied to simulate the unsteady cavitating flows, and an energy approach is developed to estimate cavitation erosion area. This approach is modified by taking into account hydrodynamic efficiency, which is deduced from the perspective of shock wave decays. The numerical estimation is then validated based on an axisymmetric nozzle cavitating flow. The numerical simulation results indicate that the modified approach can reasonably estimate the cavitation erosion area. In addition, various hydrodynamic cavitation erosion mechanisms are numerically analyzed based on the cavitating flow around a NACA0015 hydrofoil. The numerical simulation is able to reproduce the experimentally observed U-shaped cavitation structure. The interaction between cavitation and vortex has an important influence on the distribution of cavitation erosion. The areas in which the U-shaped cavitation pass may be in high erosion risk.