Turbulence and cavitation models for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state, and the flow is frequently unsteady and turbulent. To assess the state-of-the-art of computational capabilities for unsteady cavitating flows, different cavitation and turbulence model combinations are conducted. The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics. The k-e turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively. We have also blended these alternative cavitation and lustrate that the eddy viscosity turbulence treatments, to ilnear the closure region can significantly influence the capture of detached cavity. From the experimental validations regarding the force analysis, frequency, and the cavity visualization, no single model combination performs best in all aspects. Furthermore, the implications of parameters contained in different cavitation models are investigated. The phase change process is more pronounced around the detached cavity, which is better illustrated by the interfacial dynamics model. Our study provides insight to aid further modeling development.

A cavitation model for computations of unsteady cavitating flows

A local vortical cavitation（LVC） model for the computation of unsteady cavitation is proposed.The model is derived from the Rayleigh–Plesset equations,and takes into account the relations between the cavitation bubble radius and local vortical effects.Calculations of unsteady cloud cavitating fows around a Clark-Y hydrofoil are performed to assess the predictive capability of the LVC model using well-documented experimental data.Compared with the conventional Zwart＇s model,better agreement is observed between the predictions of the LVC model and experimental data,including measurements of time-averaged fl w structures,instantaneous cavity shapes and the frequency of the cloud cavity shedding process.Based on the predictions of the LVC model,it is demonstrated that the evaporation process largely concentrates in the core region of the leading edge vorticity in accordance with the growth in the attached cavity,and the condensation process concentrates in the core region of the trailing edge vorticity,which corresponds to the spread of the rear component of the attached cavity.When the attached cavity breaks up and moves downstream,the condensation area fully transports to the wake region,which is in accordance with the dissipation of the detached cavity.Furthermore,using vorticity transport equations,we also fin that the periodic formation,breakup,and shedding of the sheet/cloud cavities,along with the associated baroclinic torque,are important mechanisms for vorticity production and modification When the attached cavity grows,the liquid–vapour interface that moves towards the trailing edge enhances the vorticity in the attached cav-ity closure region.As the re-entrant jet moves upstream,the wavy/bubbly cavity interface enhances the vorticity near the trailing edge.At the end of the cycle,the break-up of the stable attached cavity is the main reason for the vorticity enhancement near the suction surface.

A cavitation aggressiveness index within the Reynolds averaged Navier Stokes methodology for cavitating flows

The paper proposes a methodology within the Reynolds averaged Navier Stokes（RANS） solvers for cavitating flows capable of predicting the flow regions of bubble collapse and the potential aggressiveness to material damage. An aggressiveness index is introduced, called cavitation aggressiveness index（CAI） based on the total derivative of pressure which identifies surface areas exposed to bubble collapses, the index is tested in two known cases documented in the open literature and seems to identify regions of potential cavitation damage.

Detached-eddy Simulation for Time-dependent Turbulent Cavitating Flows

The Reynolds-averaged Navier-Stokes（RANS）,such as the original k-ω two-equation closures,have been very popular in providing good prediction for a wide variety of flows with presently available computational resource.But for cavitating flows,the above equations noticeably over-predict turbulent production and hence effective viscosity.In this paper,the detached eddy simulation（DES） method for time-dependent turbulent cavitating flows is investigated.To assess the state-of-the-art of computational capabilities,different turbulence models including the widely used RANS model and DES model are conducted.Firstly,in order to investigate the grid dependency in computations,different grid sizes are adopted in the computation.Furthermore,the credibility of DES model is supported by the unsteady cavitating flows over a 2D hydrofoil.The results show that the DES model can effectively reduce the eddy viscosities.From the experimental validations regarding the force analysis,frequency and the unsteady cavity visualizations,more favorable agreement with experimental visualizations and measurements are obtained by DES model.DES model is better able to capture unsteady phenomena including cavity length and the resulting hydrodynamic characteristics,reproduces the time-averaged velocity quantitatively around the hydrofoil,and yields more acceptable and unsteady dynamics features.The DES model has shown to be effective in improving the overall predictive capability of unsteady cavitating flows.

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.

Numerical simulation of multiphase cavitating flows around an underwater projectile

The present simulation investigates the multiphase cavitating flow around an underwater projectile.Based on the Homogeneous Equilibrium Flow assumption,a mixture model is applied to simulate the multiphase cavitating flow including ventilated cavitation caused by air injection as well as natural cavitation that forms in a region where the pressure of liquid falls below its vapor pressure. The transport equation cavitating model is applied.The calculations are executed based on a suite of CFD code.The hydrodynamics characteristics of flow field under the interaction of natural cavitation and ventilated cavitation is analyzed.The results indicate that the ventilated cavitation number is under a combined effect of the natural cavitation number and gas flow rate in the multiphase cavitating flows.

Influence of Cavitation on Unsteady Vortical Flows in a Side Channel Pump

Previous investigation on side channel pump mainly concentrates on parameter optimization and internal unsteady vortical flows.However,cavitation is prone to occur in a side channel pump,which is a challenging issue in promoting performance.In the present study,the cavitating flow is investigated numerically by the turbulence model of SAS combined with the Zwart cavitation model.The vapors inside the side channel pump firstly occur in the impeller passage near the inlet and then spread gradually to the downstream passages with the decrease of NPSHa.Moreover,a strong adverse pressure gradient is presented at the end of the cavity closure region,which leads to cavity shedding from the wall.The small scaled vortices in each passage reduce significantly and gather into larger vortices due to the cavitation.Comparing the three terms of vorticity transport equation with the vapor volume fraction and vorticity distributions,it is found that the stretching term is dominant and responsible for the vorticity production and evolution in cavitating flows.In addition,the magnitudes of the stretching term decrease once the cavitation occurs,while the values of dilatation are high in the cavity region and increase with the decreasing NPSHa.Even though the magnitude of the baroclinic torque term is smaller than vortex stretching and dilatation terms,it is important for the vorticity production along the cavity surface and near the cavity closure region.The pressure fluctuations in the impeller and side channel tend to be stronger due to the cavitation.The primary frequency of monitor points in the impeller is 24.94 Hz and in the side channel is 598.05 Hz.They are quite corresponding to the shaft frequency of 25 Hz(fshaft=1/n=25 Hz)and the blade frequency of 600 Hz(fblade=Z/n=600 Hz)respectively.This study complements the investigation on cavitation in the side channel pump,which could provide the theoretical foundation for further optimization of performance.

Motion stability and control of supercavitating vehicle with variable cavitation number

Cavitation number and speed are capable of variation during the motion of supercavitating vehicle underwater, for example, under the condition of accelerated motion stage and external disturbance. The dynamic model and control challenge associated with the longitudinal motion of supereavitating vehicle with variable cavitation number and speed have been explored. Based on the principle of cavity expansion independence the properties of cavity and the influence on planning force of body were researched. Calculation formula of efficiency of the fin was presented. Nonlinear dynamics model of variable cavitation number and speed supercavitating vehicle was established. Stabilities of the open-loop systems of different situations were analyzed. The simulations results of open-loop systems show that it is necessary to design a control method to control a supereavitating vehicle. A gain schedule controller with guaranteed H∞ performance was designed to stabilize the dive-plane dynamics of supercavitating vehicle under changing conditions.

THE WALL EFFECT ON VENTILATED CAVITATING FLOWS IN CLOSED CAVITATION TUNNELS

For ventilated cavitating flows in a closed water tunnel, the wall effect may exert an important influence on cavity shape and hydrodynamics, An isotropic mixture multiphase model was established to study the wall effect based on the RANS equations, coupled with a natural cavitation model and the RNG k-ε turbulent model. The governing equations were discretized using the finite volume method and solved by the Gauss-Seidel linear equation solver on the basis of a segregation algorithm. The algebraic multigrid approach was carried through to accelerate the convergence of solution. The steady ventilated cavitating flows in water tunnels of different diameter were simulated for a conceptual underwater vehicle model which had a disk cavitator. It is found that the choked cavitation number derived is close to the approximate solution of natural cavitating flow for a 3-D disk. The critical ventilation rate falls with decreasing diameter of the water tunnel. However, the cavity size and drag coeflicient are rising with the decrease in tunnel diameter for the same ventilation rate, and the cavity size will be much different in water tunnels of different diameter even for the same ventilated cavitation number.

Numerical Simulations of Cavitation Flows around Clark-Y Hydrofoil

Cavitation is a complex flow phenomenon including unsteady characteristics, turbulence, gas-liquid two-phase flow. This paper provides a numerical investigation on comparing the simulation performance of three different models in OpenFOAM-Merkle model, Kunz model and Schnerr-Sauer model, which is helpful for understanding the cavitation flow. Considering the influence of vapor-liquid mixing density on turbulent viscous coefficient, the modified SST k-ω model is adopted in this paper to increase the computing reliability. The InterPhaseChangeFoam solver is utilized to simulate the two-dimensional cavitation flow of the Clark-Y hydrofoil with three cavitation models. The hydrodynamic performance including lift coefficient, drag coefficient and cavitation flow shape of the hydrofoil is analyzed. Through the comparison of the numerical results and experimental data, it is found that the Schnerr-Sauer model can get the most accurate results among the three models. And from the simulation point of water and water vapor mixing, the Merkle model has the best water and water vapor mixing simulation.

Numerical Study on the Unsteady Characteristics of the Propeller Cavitation in Uniform and Nonuniform Wake Flows

Propeller cavitation is a problematic issue because of its negative effects, such as performances losses, noise,vibration and erosion. Numerical methodology is an effective and efficient technical tool for the study of propeller cavitation, however, it is hard to capture tip-vortex cavitation in the previous work by using common turbulence models based on turbulent-viscosity hypothesis. In this work, the Reynolds-Averaged Naiver-Stokes(RANS)approach, adopting the Reynolds stress turbulence model(RSM), is taken to study the unsteady characteristics of the cavitation on the four-bladed INSEAN E779 A model propeller. The numerical simulation was carried out using the commercial CFD software ANSYS Fluent 14.0. One kind of uniform wake flow and two kinds of nonuniform wake flows are considered here. The results in the uniform flow show a good agreement with previous experimental results on both the sheet cavitation and the tip vortex cavitation and prove the ability of the RSM on capturing the tip vortex cavitation. Two kinds of nonuniform wake flows are designed based on the previous experimental researches and the unsteady characteristics of the propeller cavitation are analyzed by comparing the results in the uniform and two nonuniform wake flows together.

NUMERICAL VALIDATION OF COMPUTATIONAL MODEL FOR SHEET CAVITATING FLOWS

A computational modeling for the sheet cavitating flows is presented. The cavitation model is implemented in a viscous Navier-Stokes solver. The cavity interface and shape are determined using an iterative procedure matching the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient on the wall, is taken into account in updating the cavity shape iteratively. Numerical computations are performed for the sheet cavitating flows at a range of cavitation numbers across the hemispheric headform/cylinder body with different grid numbers. The influence of the relaxation factor in the cavity shape updating scheme for the algorithm accuracy and reliability is conducted through comparison with other two cavity shape updating numerical schemes. The results obtained are reasonable and the iterative procedure of cavity shape updating is quite stable, which demonstrate the superiority of the proposed cavitation model and algorithms.

Cavitation Inception in Turbulent Flows Around a Hydrofoil

The phenomenon of cavitation inception around a hydrofoil is studied experimentally. The flow velocities around the foil are measured by a laser doppler velocimetry （LDV）. The inception cavitation aspects are observed by using a high-speed video camera. In the experiment, the Reynolds number is fixed at a value of 7.0 × 10^5. The boundary layer around the foil undergoes turbulent flow under the experiment condition. The LDV measurement results show that the flow in the boundary layer around the foil doesn＇t separate from the surface. It is found that the cavitation inception in non-separated turbulent flow is related to the coherent structures in the boundary layer. It is clear that the turbulent bursting and the hairpin-shaped vortex structure accompany the incipient cavitation.

Experimental Observations of Cavitating Flows Around a Hydrofoil

The cavitation around a hydrofoil is studied experimentally to shed light on the muhiphase fluid dynamics. Different cavitation regimes are studied by using high speed visualization and particle image veloeimetry（PIV）. As decreasing the cavitation number, four cavitating flow regimes are observed： incipient cavitation, sheet cavitation, cloud cavitation, and supercavitation. From the incipient cavitation to the cloud cavitation, bubbles become more and more. Phenomena with large-scale vortex structure and rear re-entrant jet associated with the cloud cavitation, and subsequent development in the supercavitation are described. The velocity in the cavitation regions in the different cavitation conditions is low compared to that of the free stream. The large velocity gradient is also observed in the cavitating flow region near the surface of the hydrofoil.

Computational Analyses of Cavitating Flows in Cryogenic Liquid Hydrogen

The objective of this study is to analyze the fundamental characteristics and the thermodynamic effects of cavitating flows in liquid hydrogen.For this purpose,numerical simulation of cavitating flows are conducted over a three dimensional hydrofoil in liquid hydrogen.Firstly,the efficiency of this computational methodology is validated through comparing the simulation results with the experimental measurements of pressure and temperature.Secondly,after analysing the cavitating flows in liquid hydrogen and water,the characteristics under cryogenic conditions are highlighted.The results show that the thermodynamic effects play a significant role in the cavity structure and the mass transfer,the dimensionless mass transfer rate of liquid hydrogen is much larger,and the peak value is about ninety times as high as water at room temperature.Furthermore,a parametric study of cavitating flows on hydrofoil is conducted by considering different cavitation number and dimensionless thermodynamic coefficient.The obtained results provide an insight into the thermodynamic effect on the cavitating flows.

Recent Developments in Hydrodynamic Cavitation Reactors:Cavitation Mechanism,Reactor Design,and Applications

Hydrodynamic cavitation is considered to be a promising technology for process intensification,due to its high energy efficiency,cost-effective operation,ability to induce chemical reactions,and scale-up possibilities.In the past decade,advancements have been made in the fundamental understanding of hydrodynamic cavitation and its main variables,which provide a basis for applications of hydrodynamic cavitation in radical-induced chemical reaction processes.Here,we provide an extensive review of these research efforts,including the fundamentals of hydrodynamic cavitation,the design of cavitation reactors,cavitation-induced reaction enhancement,and relevant industrial applications.Two types of hydrodynamic cavitation reactors—namely,stationary and rotational—are compared.The design parameters of a hydrodynamic cavitation reactor and reactor performance at the laboratory and pilot scales are discussed,and recommendations are made regarding optimal operation and geometric conditions.The commercial cavitation reactors that are currently on the market are reviewed here for the first time.The unique features of hydrodynamic cavitation have been widely applied to various chemical reactions,such as oxidization reactions and wastewater treatment,and to physical processes,such as emulsion generation and component extraction.The roles of radicals and gas bubble implosion are also thoroughly discussed.

Investigation of hydroxyl-terminated polybutadiene propellant breaking characteristics and mechanism impacted by submerged cavitation water jet

A submerged cavitation water jet(SCWJ)is an effective method to recycle solid propellant from obsolete solid engines by the breaking method.Solid propellant's breaking modes and mechanical process under SCWJ impact are unclear.This study aims to understand those impact breaking mechanisms.The hydroxyl-terminated polybutadiene(HTPB)propellant was chosen as the research material,and a self-designed test system was used to conduct impact tests at four different working pressures.The high-speed camera characterized crack propagation,and the DIC method calculated strain change during the impact process.Besides,micro and macro fracture morphologies were characterized by scanning electron microscope(SEM)and computed tomography(CT)scanning.The results reveal that the compressive strain concentration region locates right below the nozzle,and the shear strain region distributes symmetrically with the jet axis,which increases to 4% at first 16th ms,the compressive strain rises to 2% and 6% in the axial and transverse direction,respectively.The two tensile cracks formed first at the compression strain concentrate region,and there generate many shear cracks around the tensile cracks,and those shear cracks that develop and aggregate cause the cracks to become wider and cut through the tensile cracks,forming the tensile-shear cracks and the impact parts eventually fail.The HTPB propellant forms a breaking hole shaped conical after impact 10 s.The mass loss increases by 17 times at maximum,with the working pressure increasing by three times.Meanwhile,the damage value of the breaking hole remaining on the surface increases by 7.8 times while 2.9 times in the depth of the breaking hole.The breaking efficiency is closely affected by working pressures.The failure modes of HTPB impacted by SCWJ are classified as tensile crack-dominated and tensile-shear crack-dominated damage mechanisms.

Cavitation vortex dynamics of unsteady sheet/cloud cavitating flows with shock wave using different vortex identification methods

Cavitation is a complex multiphase flow phenomenon with an abrupt transient phase change between the liquid and the vapor, including multiscale vortical motions. The transient cavitation dynamics is closely associated with the evolution of the cavitation vortex structures. The present paper investigates the cavitation vortex dynamics using different vortex identification methods, including the vorticity method, the Q criterion method, the Omega method (Ω), the method and the Rortex method. The Q criterion is an eigenvalue-based criterion, and in the Ω method, the parameter is normalized, is independent of the threshold value and in most conditions Ω= 0.52 . The Rortex method is based on an eigenvector-based criterion. Numerical simulations are conducted using the implemented compressible cavitation solver in the open source software OpenFOAM for the sheet/cloud cavitating flows around a NACA66 (mod) hydrofoil fixed at a = 6°,= 1.25 and Re = 7.96 × 10^5 . The flow is characterized by the alternate interactions of the re-entrant flow and the collapse induced shock wave. Results include the vapor structures and the vortex dynamics in the unsteady sheet/cloud cavitating flows, with emphasis on the vortex structures in thecavitation region, the cavity interface, the cavity closure, the cavity wakes, and the foil wakes with the shedding cavity. The comparisons of the various methods, including that the vorticity method, the Q criterion method, the Ω method, the λ2 method and the Rortex method, show the performances of different methods in identifying the cavitation vortex structures. Generally, during the attached cavity growth stage, the Q criteria can well predict the vortex structures in the cavitation region and at the foil trailing edge in the pure liquid region, while with the Ω method and the Rortex method, the vortex structures outside the attached cavity and on the foil pressure side can also be predicted. The λ2 method can well predict the vortex structures in the cavity closure region. During the re-entrant jet development stage, the vortex structures in the re-entrant jet region is weak. During the cavity cloud shedding stage, the vortex dynamics at the foil leading edge covered by newly grown cavity sheet is different from that during the attached cavity sheet growth stage. During the shock wave formation and propagation stage, strong vortex structures with both the size and the strength are observed owing to the cavity cloud shedding and collapse behavior. The influence of the small parameter ε in the Ω method on the cavitation vortex identification is discussed.

Computational modeling of cavitating flows in liquid nitrogen by an extended transport-based cavitation model

Developing a robust computational strategy to address the rich physical characteristic involved in the thermcdynamic effects on the cryogenic cavitation remains a challenge in research. The objective of the present study is to focus on developing mod- elling strategy to simulate cavitating flows in liquid nitrogen. For this purpose, numerical simulation over a 2D quarter caliber hydrofoil is investigated by calibrating cavitation model parameters and implementing the thermodynamic effects to the Zwart cavitation model. Experimental measurements of pressure and temperature are utilized to validate the extensional Zwart cavi- tation model. The results show that the cavitation dynamics characteristic under the cryogenic environment ale different from that under the isothermal conditions： the cryogenic case yields a substantially shorter cavity around the hydrofoil, and the pre- dicted pressure and temperature inside the cavity are steeper under the cryogenic conditions. Compared with the experimental data, the computational predictions with the modified evaporation and condensation parameters display better results than the default parameters from the room temperature liquids. Based on a wide range of computations and comparisons, the extension- al Zwart cavitation model may predict more accurately the quasi-steady cavitation over a hydrofoil in liquid nitrogen by pri- marily altering the evaporation rate near the leading edge and the condensation rate in the cavity closure region.

LES investigation of cavitating flows around a sphere with special emphasis on the cavitation–vortex interactions

Large eddy simulation(LES)was coupled with a homogeneous cavitation model to study turbulent cavitating flows around a sphere.The simulations are in good agreement with available experimental data and the simulated accuracy has been evaluated using the LES verification and validation method.Various cavitation numbers are simulated to study important flow characteristics in the sphere wake,e.g.periodic cavity growth/contraction,interactions between the cloud and sheet cavitations and the vortex structure evolution.The spectral characteristics of the wake for typical cloud cavitation conditions were classified as the periodic cavitation mode,high Strouhal number mode and low Strouhal number mode.Main frequency distributions in the wake were analyzed and different dominant flow structures were identified for each of the three modes.Further,the cavitation and vortex relationship was also studied,which is an important issue associated with complex cavitating sphere wakes.Three types of cavitating vortex structures alternate,which indicates that three different cavity shedding regimes may exist in the wake.Analysis of vorticity transport equation shows a significant vorticity increase at the cavitation closure region and in the vortex cavitation region.This study provides a physical perspective to further understand the flow mechanisms in cavitating sphere wakes.