Schnerr-Sauer Cavitation Model Research Articles

Large eddy simulations of sheet-to-cloud cavitation transitions with special emphasis on the simultaneous existence of the re-entrant jet and shock waves

Sheet-to-cloud cavitation transitions are very complex owing to the simultaneous appearance of the re-entrant jet and shock waves. The objective of this paper is to investigate the physics of compressible cavitating flows with emphasis on the simultaneous existence of the re-entrant jet and shock waves. A compressible cavitating solver, which considers the compressibility effects of both the liquid and the vapour, was used to account for the different shedding characteristics induced by the re-entrant jet mechanism (RJM), the shock wave mechanism (SWM), and both the re-entrant jet and the shock waves (RJM-SMW). The solver used Large Eddy Simulations (LES) and the Schnerr-Sauer cavitation model. The numerical results are first compared with available experimental data [1] which showed satisfactory agreement for various aspects of the flow, including the pressure distribution, cavity shapes, condensation front speed, and shedding frequency. The results first show three different cavity shedding processes induced by the re-entrant jet and the shock waves. Frequency analyses show that the shock waves produce a wider frequency distribution which indicates that shock waves induce more shedding than the re-entrant jet. The quasi-periodic characteristics of the transitions between the various cavity shedding characteristics are mainly induced by the variations of the pressure, residual cavity volume and medium compressibility. Further analyses show that the different pressure, residual cavity volume and medium compressibility amplitudes determine the cavity shedding characteristics in the subsequent shedding cycle. When the conditions favour both the re-entrant jets and the shock wave effects, both the re-entrant jet and the shock waves impact the cavity shedding.

Numerical investigation on cavitation and induced noise reduction mechanisms of a three-dimensional hydrofoil with leading-edge protuberances

In this work, a National Advisory Committee for Aeronautics 66 hydrofoil with leading-edge protuberances is designed. The large eddy simulation combined with the Schnerr–Sauer cavitation model is used to obtain a satisfactory result as compared with the experimental measurement, integrating the permeable Ffowcs Williams–Hawkings equation for cavitation-induced noise analysis. It is found that the special leading-edge geometric structure deflects the incoming flow, creating two counter-rotating streamwise vortices at the peak shoulders. These lead to upwash and downwash effects and alter the pressure distribution on the suction side. The low pressure localized in the trough facilitates the advancement of the leading-edge cavitation while severely limiting the spanwise development of the cloud cavity, shortening the cavitation evolution by about 20% and reducing the maximum cavitation volume by about 35%. Analysis using the vorticity transport equation indicates that different vorticity transport equation splitting terms play dominant roles at different stages of cavitation evolution. Although the cavitation induces disturbances in the primary vortex, the effect is limited. Acoustic simulation shows that the bionic structure can reduce the total sound pressure level by 7.8–8.3 dB. The spherical noise reduction is not as effective as expected due to the similar cavitation volume acceleration processes of the two hydrofoils. However, the pressure fluctuation caused by the collapse of the cloud cavity is reduced by cavitation suppression, which reduces the linear noise. In addition, the protuberances suppress the generation of large-scale vortex systems and transform them into smaller ones, resulting in reduced spanwise correlation and coherence of the shedding vortices. This is a critical factor in noise reduction. Finally, we hypothesize that the unstable noise reduction is related to the streamwise vortices in the trough regions. These vortices increase the momentum exchange within the boundary layer, affecting its stability and weakening the acoustic feedback loop.

Effect of cavitation on vortex-induced vibration of hydrofoil

Vortex induced vibration (VIV) is frequently observed in marine structures in offshore platforms, ships and other structures. Under specific circumstances, the vortex shedding frequency is locked into the natural frequency of the structure, resulting in significant and destructive vibration. Moreover, the cavitation in the wake vortex also cause strong trailing edge vibration. In this study, the interaction between VIV and cavitation of two-dimensional hydrofoil was adopted the Shear Stress Transport K-omega model and the Schnerr–Sauer cavitation model. The research findings indicate that the frequency of the wake vortex increases with the decrease of the cavitation number, but the vibration amplitude decreases.

Numerical investigation on the cavitating wake flow around a cylinder based on proper orthogonal decomposition

The non-cavitating and cavitating wake flow of a circular cylinder, which contains multiscale vortices, is numerically investigated by Large Eddy Simulation combined with the Schnerr–Sauer cavitation model in this paper. In order to investigate the spatiotemporal evolution of cavitation vortex structures, the Proper Orthogonal Decomposition (POD) method is employed to perform spatiotemporal decomposition on the cylinder wake flow field obtained by numerical simulation. The results reveal that the low-order Proper Orthogonal Decomposition modes correspond to large-scale flow structures with relatively high energy and predominantly single frequencies in both non-cavitating and cavitating conditions. The presence of cavitation bubbles in the flow field leads to a more pronounced deformation of the vortex structures in the low-order modes compared to the non-cavitating case. The dissipation of pressure energy in the cylinder non-cavitating wake occurs faster than the kinetic energy. While in the cavitating wake, the kinetic energy dissipates more rapidly than the pressure energy.

Numerical investigation of energy loss distribution in the cavitating wake flow around a cylinder using entropy production method

The wake flow of a circular cylinder is numerically investigated by Large Eddy Simulation (LES) combined with the Schnerr–Sauer cavitation model. By comparing entropy production in the presence or absence of cavitation, the energy loss distribution in the wake flow field of a cylinder is explored, shedding light on the interactions between multiscale vortex systems and cavitation. The comparative results reveal that, under non-cavitating conditions, the energy loss region in the near-wake area is more concentrated and relatively larger. Energy dissipation in the wake flow field occurs in regions characterized by very high velocity gradients, primarily near the upper and lower surfaces of the cylinder near the leading edge. The influence of cavitation bubbles on entropy production is predominantly observed in the trailing-edge region (W1) and the near-wake region (W2). The distribution trends of wall entropy production on the cylinder’s surface are generally consistent in both conditions, with wall entropy production primarily concentrated in regions exhibiting high velocity gradients.

Revealing insights into hydrodynamic noise induced by different cavitating flows around a hydrofoil

Cavitation-induced noise hazards in marine environments have raised significant concerns. This paper presents a study on the flow noise generated by cavitating flow around a model-scale NACA66 hydrofoil, utilizing the permeable acoustic analogy method. Through Large Eddy Simulation and the Schnerr-Sauer cavitation model, the study captures the cavitation flow pattern, aligning with experimental observations. The research conducts a detailed analysis of the monopole and dipole noise components, providing insights into their characteristics under different cavitation conditions (cavitation number σ = 0.60, 0.83, 1.29, and 1.44). The results revealed a noteworthy trend where the proportion of the dipole component increases as the cavitation number σ decreases. Furthermore, the study uncovered the mechanism behind monopole noise induction in unsteady cavitating flows, offering insights into different types of sound impulse sources associated with cavitation collapse. Particularly, the collapse of clouds during secondary shedding is identified as a significant source of highly intense impulses, surpassing the levels observed in other cavitation flow stages. Additionally, deeper exploration demonstrated the co-action of vortex stretching and dilatation, contributing to the enhanced deformation, breakdown, and condensation of vapor structures, consequently significantly accelerating the collapse process.

Adaptive Mesh Refinement for Trailing Vortices Generated by Propellers in Interaction with Slipstream Obstacles

The investigation of cavitating trailing vortices emerging from marine propellers is of great interest in the industry. With the help of computational fluid dynamics (CFD), studying the cavitating trailing vortices may be facilitated. However, limitations in computational power raise the necessity to execute numerical simulations as efficiently as possible. The time-efficient simulation of cavitating trailing vortices interacting with rigid bodies is especially challenging due to the continuous change of cavity locations. This study investigates the usability, capability, and practicability of automatic adaptive refinement at every calculation time step for transient Reynolds-averaged Navier–Stokes (RANS) and large eddy CFD simulations of the cavitating tip and hub vortices, utilizing the Schnerr–Sauer cavitation model, in the presence of a rudder located in the propeller slipstream and for an isolated propeller, with additional focus on the computational effort necessary for using high frequency updating adaptive mesh refinement (AMR). It is found that AMR is suitable for resolving cavities with relative motion to the propeller and in interaction with slipstream obstacles. However, the computation time is significantly increased, which renders this method useful only if a classic AMR is not possible due to geometrical limitations. Even in the cases that benefit from the automated AMR, numerical instabilities may lead to unphysical pressure fluctuations, which reduce the suitability of the method for the evaluation of underwater radiated noise.

Numerical Study of High-Speed Vertical Water Entry of Hollow Projectiles with Different Aperture Sizes and Velocities

The hollow projectile is a new type of projectile that has complex water entry hydrodynamics characteristics and has attracted significant attention in recent years. As such, it is important to investigate the effects of different entry velocities and aperture diameters on the cavity morphology, cavitation, dynamics, and motion characteristics of hollow projectiles when entering water at high speeds. In this study, four stages of an open cavity, cavity stretching, cavity closure, and cavity contraction in the water entry processes of a hollow projectile at 50–200 m/s and four aperture diameter projectiles at 100 m/s were studied using the volume of fluid (VOF), realizable k-ε turbulence, and Schnerr-Sauer cavitation model. With an increase in the speed, the depth of the cavity closure increases, thereby advancing the closure time. The timing of the surface closure at 50 m/s is clearly different from that at 100–200 m/s. Cavitation is not obvious and is near the cavity wall at 50 m/s, although the entire cavity is almost filled with vapor at 100–200 m/s. The friction resistance has two step points when impacting the water surface and entering the water completely. As the velocity increases or the aperture ratio reduces, the splash is higher, the cavity volume is larger, the cavitation phenomenon is more obvious, the cavity closure time is delayed, and the frictional resistance of the projectile is greater. The results of this study can guide the production and application of hollow projectiles in the future.

Numerical Approach Based on Solving 3D Navier–Stokes Equations for Simulation of the Marine Propeller Flow Problems

The report presents the approach implemented in the Russian LOGOS software package for the numerical simulation of the marine propeller flow problems using unstructured computational meshes automatically generated by the mesh generator. This approach includes a computational model based on the Navier–Stokes equation system and written with respect to the physical process: the turbulent nature of flow with transient points is accounted using the Reynolds Averaged Navier–Stokes method and the k–ω SST model of turbulence by Menter along with the γ–Reθ (Gamma Re Theta) laminar-turbulent transition model; the Volume of Fluid method supplemented with the Schnerr–Sauer cavitation model is used to simulate the cavitation processes; a rotating propeller is simulated by a moving computational mesh and the GGI method to provide conformity of the solutions on adjacent boundaries of arbitrarily-shaped unstructured meshes of the two domains. The specific features of the numerical algorithms in use are described. The method validation results are given; they were obtained because of the problems of finding the performance curves of model-scale propellers in open water, namely the problems of finding the performance of propellers KP505 and IB without consideration of cavitation and the performance of propellers VP1304 and C5 under cavitation conditions. The paper demonstrates that the numerical simulation method presented allows for obtaining sufficiently accurate results to predict the main hydrodynamic characteristics for most modes of operation of the propellers.

Unsteady Cloud Cavitation on a 2D Hydrofoil: Quasi-Periodic Loads and Phase-Averaged Flow Characteristics

We perform large-eddy simulations to study a cavitating flow over a two-dimensional hydrofoil section—a scaled-down profile (1:13.26) of guide vanes of a Francis turbine—using the Schnerr–Sauer cavitation model with an adaptive mesh refinement in intensive phase transition flow areas. In the test case, the guide vane is tilted at an angle of attack of 9° to the direction of the flow, in which the Reynolds number, based on the hydrofoil chord length, equals 1.32×106, thus providing a strong adverse pressure gradient along the surface. The calculated time-averaged turbulence characteristics are compared with those measured by particle image velocimetry to verify that the flow is correctly reproduced in numerical simulations using the procedure of conditional averaging proposed and tested in our previous investigation. A re-entrant jet is identified as the primary source of vapor cloud shedding, and a spectral analysis of the cavitating flow over the profile midsection is conducted. Two characteristic frequencies corresponding to the cases, when an attached cavity detaches completely (as a whole) and two partially from the hydrofoil, are found in the flow. The study reveals that the natural frequency of partial cavity shedding is three times higher than that of full detachments. The examined regime exhibits an oscillatory system with two oscillation zones related to cavitation surge instability and unsteady cloud cavitation resulting from the re-entrant jet. Conditional averaging correlates cavitation structures with pressure distributions, forces, and torque on the guide vane. This modeling approach captures the fine details of quasi-periodic cavitation dynamics, providing insights into unsteady sheet/cloud cavitation and offering a method for developing control strategies.

Numerical Study on the Flow Field Characteristics and Efficiency of Different Underwater Gun Muzzle Brakes

The submerged gun’s mathematical and physical models were established, and an investigation was conducted on the development of the flow field and the recoiling efficiency of three representative muzzle brakes. The study employed the Schnerr-Sauer cavitation model and the k − ω transport turbulence model, both based on the Reynolds-averaged Navier-Stokes method. Numerical simulation of the underwater firing of a 12.7 mm gun’s muzzle flow field was accomplished using a combination of user-defined function (UDF) and overlapping mesh techniques. Detailed analysis was performed on the flow field characteristics encompassing density, velocity, and phase state fields, along with an in-depth examination of the efficiency of the three muzzle brakes. The simulation results demonstrated an enhanced cavitation effect when a brake was incorporated, with the impact muzzle brake exhibiting the highest efficiency, followed by the impact-reaction type, while the reaction type exhibited the lowest performance.

Study on high-speed water entry process of non-rotating vehicles

The non-rotating trans-media vehicle can better adapt to the hypersonic flight conditions, but new problems in the hydrodynamic characteristics and motion stability arise during the water entry process. With the VOF multiphase model, Realizable k-ε turbulence model, and Schnerr-Sauer cavitation model, this paper establishes a simulation method of coupling the movement of non-roating body into water with multiphase flow fields based on overset grid technology, and the accuracy of the established model is verified. The simulation calculation of the oblique water entry process of the vehicle with different ratio of short axis to long axis in cross section is carried out. And the results show that although the ratio of short axis to long axis in cross section does not change the cavitation morphology, it affects the hydrodynamic and kinematic characteristics of the vehicle by influencing the relative position of the cavitation. As the ratio of short axis to long axis decreases, the motion stability of the vehicle increases gradually. However, if the ratio of short axis to long axis is too small, the drag reduction effect will be weakened, and the structure will suffer a bigger load.

Numerical investigation of multistage cavity shedding around a cavitating hydrofoil based on different turbulence models

Multistage shedding in cavity flow processes is a challenging and crucial topic in cavitating flows. This paper employs three different turbulence models to obtain a more comprehensive understanding of the physical details of multistage shedding in compressible cavitating flows and compare the differences between the turbulence models. The study employs the Schnerr-Sauer cavitation model in combination with the volume of fluid (VOF) method to capture the details of the unsteady cavitating flow around NACA66. The results are compared to experimental data and validate the numerical method. The study reveals that the primary shedding process is dominated by the re-entrant jet mechanism, whereas the pressure wave mechanism dominates the second shedding process. The second shedding process generates multiple pressure waves that disrupt the stable vortex structure of the sheet cavity. Furthermore, wavelet analysis indicates that the higher-order coherent structure mainly originates from the second shedding stage, and the second shedding process is shorter than the primary shedding process. The study proposes the segmented dynamic mode decomposition (SDMD), which obtains the mode characteristics at different time scales within one cycle. Under the RANS model, the small-scale cavity collapse and vortex structure cannot be observed during the second shedding process. However, the LES model can predict more realistic multi-scale flow field information.

Numerical study of two types of rough groove in suppressing the tip clearance cavitation

Tip clearance cavitation (TCC) which is consisted of tip leakage vortex (TLV) cavitation and gap cavitation (occurs inside the gap region) is a common phenomenon in the gap flow filed in axial turbomachinery, and can trigger a series of negative effects. Based on the suppression mechanism of a type of prototypical horizontal casing groove, two types of rough groove structures are proposed in this paper aiming at enhancing the suppression effect on the TCC by utilizing the Coanda effect of the gap leakage jet. The gap flow field is generated via a NACA0009 hydrofoil and a solid wall. The gap size is fixed as 2 mm. The numerical simulation method is adopted. The results show that combining the detached-eddy simulation (DES) approach, SchnerrSauer cavitation model and a type of varRhoTurbVOF method on the OpenFOAM platform, accurate numerical results of cavitating gap flow fields under the small gap conditions can be obtained. The gap flow field analysis reveals that the control ability of the grooves on the leakage flow is enhanced via divergent–convergent flow passage in the roughness groove cases. The leakage rate is reduced while the local turbulence intensity is increased, which weakens the TLV and the tip separation vortex (TSV) dramatically. The rough casing grooves show a superior suppression effect on the TCC. The present work can inspire new casing treatment method for improving the anti-cavitation performance in the axial-flow hydraulic machinery.

Numerical investigation about the unsteady behavior of a free submerged cavitation jet using the SBES approach

Submerged cavitation jet has emerged as an efficient method for the removal of ship fouling. Due to the complicated revolution of cavitation cloud, it has attracted great research interest. Ascertaining the internal flow dynamics of cavitating jets is always a challenge. Thus, this paper investigates the unsteady behavior of a free submerged cavitating jet numerically in three dimensions. The turbulent cavitation flow is simulated utilizing the Stress-Blended Eddy Simulation (SBES) turbulent model combined with the Schnerr-Sauer cavitation model. The results are compared with the data from a famous experiment, and they exhibit good agreement in both time-averaged and unsteady characteristics. The cavitation life stages, i.e., the cavitation growth, shedding, contraction, and collapse are explored. In results, cavitation cloud forms around the jet core. Cavitation cloud shedding involves complex factors, including shear layer instability, complex pressure gradients, and re-entrant motion, and it may also be related to the potential core and jet core instability. Additionally, cavitation cloud development is closely related to the jet core and exhibits synchronous behavior. After the cavitation cloud collapse, a local high pressure is observed and then cavity rebound is generated, where the collapse can be either mild or intensive.

Loading noise induced by cavitating flow and its simplified model prediction

This study employs a computational fluid dynamics approach in combination with acoustic analogy to investigate the loading noise characteristics induced by cavitating flow around a NACA66 (MOD) hydrofoil. The Large Eddy Simulation coupled with the Schnerr-Sauer cavitation model is used to capture the transient motion behaviour of the cavitating flow, which agrees well with experimental observations. The study covers three typical states of cavitation: sheet cavitation (σ = 1.44), sheet/cloud transition cavitation (σ = 1.29), and cloud cavitation (σ = 0.83). The study demonstrates that the energy of the loading noise source is concentrated in the middle-frequency band for sheet cavitation, while it is concentrated in the low-frequency band for cloud cavitation. The cavitation instability promotes loading noise to generate drastic fluctuation and even several extreme impulses, which are directly related to the processes of cloud formation and cavitation multistage shedding. Finally, a simplified model for calculating the loading noise is proposed, and its errors and equivalence are evaluated. The model can effectively predict the loading noise induced by cavitating flow and enable decoupling of data from the flow field to the sound field, which may facilitate the separation of the dipole component from the total noise in experimental measurements.

Influence of cavitation state and launch angle on water-exit process of vehicle based on moving domain method

This paper, aiming at the water-exit process of the vehicle with cavitation, based on the moving domain method coupled with the SDOF (six degrees of freedom) solver, using VOF (volume of fluid) multiphase model and the Schnerr-Sauer cavitation model, carrying out numerical simulation research on multi-conditions. Comparing vertical launch vehicles with different water-exit Ca (cavitation number) cases, the sudden decrease in cavitation number is closely related to the cavitation state, and there is a maximum influent cavitation state of the cavitation collapse on the process of the water-exit. Comparing different initial launch angle cases, it is found that there is a most unstable launch angle, which makes the angular deflection of the vehicle the most severe during the water-exit process.

Numerical investigation on the formation of the re-entrant flow and the transformation of varying shedding modes in cloud cavitation

The objective of this paper is to investigate two types of cloud shedding processes around the NACA66 (mod) hydrofoil with emphasis on the formation of the re-entrant flows and the transformation of varying shedding modes. The LES method combines the Schnerr-Sauer cavitation model in OpenFOAM to capture the detailed flow structures. Combining the experimental observation, the cloud shedding process can be divided into main re-entrant flow mode, transition mode, and side re-entrant flow mode. The re-entrant flow is primed from the middle of the attached cavity closure for the main re-entrant flow pattern. The velocity is more stable as it develops in a fan shape towards the leading edge of the hydrofoil. For the side re-entrant flow mode, the rotation and local collapse of cloud cavity in the previous cycle resulted in the incipient of the side re-entrant flow. Compared with the main re-entrant flow, the velocity of the side re-entrant flow fluctuates more significantly. The transition between the side re-entrant flow mode and the main re-entrant flow mode can be characterized by the normalized cavity length (lmax/c) and the cavity shedding frequency (St number).

Study on Cavitation of Port Plate of Seawater Desalination Pump with Energy Recovery Function

To address the problem of low integration and efficiency of reverse osmosis desalination system, an energy-recovery type incurve multiple acting pump is developed with integrated functions of a high-pressure pump, energy recovery device and booster pump. In order to determine its flow range and suppress cavitation generation, a mathematical model of the port plate is established, combining the realizable k-ɛ turbulence model and the Schnerr-Sauer cavitation model to obtain the internal flow field characteristics of the port plate. The effects of different rotational speeds and inlet pressures on cavitation were analyzed to obtain the gas volume fraction distribution rules. The design is based on the pressure and mass flow monitoring test device to verify the numerical calculation results. The results show that the experimental and simulation data match accurately, and with the increase in speed and the decrease in inlet pressure, the cavitation phenomenon becomes serious and the flow coefficient is reduced. The optimal working speed of the pump in this paper is 520 r/min and the output flow is 200 L/min. Compared with conventional products, the volume is reduced by more than 40%.

Effect of Tip Clearance Size on the Cavitation Flow and Noise Characteristics of the NACA0009 Hydrofoil

The noise characteristics of NACA0009 hydrofoil with tip clearance are discussed. Select SST k- ω Turbulence model and Schnerr Sauer cavitation model simulate tip leakage cavitation flow. The results show that the simulation results are in good agreement with the original records, and the tip clearance reduces the energy characteristics of the hydrofoil. With the expansion of tip clearance model, TLV and cavitation compressive strength gradually decrease. In addition, the study of far-field noise shows that the nonspecific curve of the total noise coefficient of far-field noise shows a disc shaped symmetric structure. Compared with the original hydrofoil, when the tip clearance is 20 mm, the far-field dipole noise value at 170 ° angle is reduced by 17.68%. Tip clearance reduces offline and far-field noise. Far field noise decreases with the increase of tip clearance model.