Considering the compressibility of the cavity in the cavitating flow, this paper presents a modified k-ω model for predicting the cavitating flow in a centrifugal pump, in which the modified k-ω model and Schnerr-Sa...Considering the compressibility of the cavity in the cavitating flow, this paper presents a modified k-ω model for predicting the cavitating flow in a centrifugal pump, in which the modified k-ω model and Schnerr-Sauer cavitation model were combined with ANSYS CFX. To evaluate the modified and standard k-co models, numerical simulations were performed with these two models, respectively, and the calculation results were compared with the experimental data. Numerical simulations were executed with three different values of the flow coefficient, and the simulation results of the modified k-ω model showed agreement with most of the experimental data. The cavitating flow in the centrifugal pump obtained by the modified k-ω model at the design flow coefficient of 0.102, was analyzed. When the cavitation number decreases, the cavity initially generates on the suction side of the blade near the leading edge and then expands to the outlet of the impeller, and the decrease of the total pressure coefficient mainly occurs upstream of the impeller passage, while the downstream remains almost unaffected by the development of cavitation.展开更多
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 bub...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.展开更多
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 c...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.展开更多
The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collap...The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.展开更多
The influence of phase-change coefficients variations in the Singhal cavitation model on the calculation results has been numerically studied. By comparing the numerical results and experimental data, the relationship...The influence of phase-change coefficients variations in the Singhal cavitation model on the calculation results has been numerically studied. By comparing the numerical results and experimental data, the relationship between the coefficients and cavitation numbers is obtained. The calculation results of 2d axisymmetrical cylinder with 45-degree cone cavitator show that under different cavitation numbers, there are three typical kind of cavities, which are respectively main cavity, secondary cavity and rear cavity. The coefficients variations have a great influence respectively on the three type cavities in shape, collapse position, collapse strength, etc, and different cavitation numbers are corresponding to different phase-change coefficients. The cavitation flow field can be divided into three typical zones according to the cavitation number: weak-cavitation zone, secondary-cavitation zone and supercavitation zone. For 45-degree cone cavitator cylinder, the evaporation coefficients will firstly decrease and then increase with the decrease of cavitation numbers in secondary-cavitation zone, while the condensation coefficients keep relatively lower and almost unchanged. In weak-cavitation zone, there only exists the smaller main cavity attached to the model head or there is no obvious cavity. In supercavitation zone, the secondary cavity attached to the model will fall off and merge into the new rear cavity.展开更多
Ventilated cavitation plays an important role on the drag reduction of underwater vehicles and surface ships. For the modelling of ventilated cavitation, the minimum speed of the pressure wave is a crucial parameter f...Ventilated cavitation plays an important role on the drag reduction of underwater vehicles and surface ships. For the modelling of ventilated cavitation, the minimum speed of the pressure wave is a crucial parameter for the closure of the pressure-density coupling relationship. In this study, the minimum wave speed is determined based on a theoretical model coupling the wave equation and the bubble interface motion equation. The influences of several paramount parameters （e.g., frequency, bubble radius and void fraction） on the minimum wave speed are quantitatively demonstrated and discussed. Compared with the minimum wave speed in the traditional cavitation, values for the ventilated cavitation are much higher. The physical mechanisms for the above difference are briefly discussed with the suggestions on the usage of the present findings.展开更多
Considering the lack of theoretical models and ingredients necessary to explain the scaling of the results of propeller cavitation inception and cavitating hydroacoustics from model tests to full scale currently, and ...Considering the lack of theoretical models and ingredients necessary to explain the scaling of the results of propeller cavitation inception and cavitating hydroacoustics from model tests to full scale currently, and the insufficient reflection of the nuclei effects on cavitation in the numerical methods, the cavitating hydrodynamics and cavitation low frequency noise spectrum of three geometrically similar 7-bladed highly skewed propellers with non-uniform inflow are addressed. In this process, a numerical bridge from the multiphase viscous simulation of propeller cavitation hydrodynamics to its hydro-acoustics is built, and the scale effects on performances and the applicability of exist scaling law are analyzed. The effects of non-condensable gas（NCG） on cavitation inception are involved explicitly in the improved Sauer＇s cavitation model, and the cavity volume acceleration related to its characteristic length is used to produce the noise spectrum. Results show that, with the same cavitation number, the cavity extension on propeller blades increases with diameter associated with an earlier shift of the beginning point of thrust decline induced by cavitation, while the three decline slopes of thrust breakdown curves are found to be nearly the same. The power of the scaling law based on local Reynolds number around 0.9R section is determined as 0.11. As for the smallest propeller, the predominant tonal noise is located at blade passing frequency（BPF）, whereas 2BPF for the middle and both 2BPF and 3BPF for the largest, which shows the cavitating line spectrum is fully related to the interaction between non-uniform inflow and fluctuated cavity volume. The predicted spectrum level exceedance from the middle to the large propeller is 6.65 dB at BPF and 5.94 dB at 2BPF. Since it just differs less than 2 dB to the increment obtained by empirical scaling law, it is inferred that the scale effects on them are acceptable with a sufficient model scale, and so do the scaling law. The numerical implementation of cavitating hydrodynamics and hydro-acoustics prediction of propeller in big scale in wake has been completed.展开更多
In order to predict the effects of cavitation on a hydrofoil, the state equations of the cavitation model were combined with a linear viscous turbulent method for mixed fluids in the computational fluid dynamics (CFD)...In order to predict the effects of cavitation on a hydrofoil, the state equations of the cavitation model were combined with a linear viscous turbulent method for mixed fluids in the computational fluid dynamics (CFD) software FLUENT to simulate steady cavitating flow. At a fixed attack angle, pressure distributions and volume fractions of vapor at different cavitation numbers were simulated, and the results on foil sections agreed well with experimental data. In addition, at the various cavitation numbers, the vapor fractions at different attack angles were also predicted. The vapor region moved towards the front of the airfoil and the length of the cavity grew with increased attack angle. The results show that this method of applying FLUENT to simulate cavitation is reliable.展开更多
Self-propelled nozzle is a critical component of the radial jet drilling technology.Its backward orifice structure has a crucial influence on the propulsive force and the drilling performance.To improve the working pe...Self-propelled nozzle is a critical component of the radial jet drilling technology.Its backward orifice structure has a crucial influence on the propulsive force and the drilling performance.To improve the working performance of the nozzle,the numerical simulation model is built and verified by the experimental results of propulsive force.Then the theoretical model of the energy efficiency and energy coefficient of the nozzle is built to reveal the influence of the structural parameters on the jet performance of the nozzle.The results show that the energy efficiency and energy coefficient of the backward orifice increase first and then decrease with the angle increases.The energy coefficient of forward orifice is almost constant with the angle increases.With the increase in the number and diameter,energy efficiency and energy coefficient of the forward orifice gradually decrease,but the backward orifice energy coefficient first increases and then decreases.Finally,it is obtained that the nozzle has better jet performance when the angle of backward orifice is 30°,the number of backward orifice is 6,and the value range of diameter is 2-2.2 mm.This study provides a reference for the design of efficiently self-propelled nozzle for radial jet drilling technology.展开更多
In the present research, a bubble dynamics based model for cavitating flow simulations is extended to higher void fraction region for wider range of applications. The present bubble model is based on the so-called Ray...In the present research, a bubble dynamics based model for cavitating flow simulations is extended to higher void fraction region for wider range of applications. The present bubble model is based on the so-called Rayleigh-Plesset equation that calculates a temporal bubble radius with the surrounding liquid pressure and is considered to be valid in an area below a certain void fraction. The solution algorithm is modified so that the Rayleigh-Plesset equation is no more solved once the bubble radius （or void fraction） reaches at a certain value till the liquid pressure recovers above the vapor pressure in order to overcome this problem. This procedure is expected to stabilize the numerical calculation. The results of simple two-dimensional flow field are presented compared with the existing bubble model.展开更多
Unsteady cavitating flow is extremely complicated and brings more serious damages and unignorable problems compared with steady cavitating flow.CFD has become a practical way to model cavitation;however,the popularly ...Unsteady cavitating flow is extremely complicated and brings more serious damages and unignorable problems compared with steady cavitating flow.CFD has become a practical way to model cavitation;however,the popularly used full cavitation model cannot reflect the pressure-change that the bubble experiences during its life path in the highly unsteady flow like cloud cavitating.Thus a dynamic cavitation model(DCM)is proposed and it has been considered to have not only the first-order pressure effects but also zero-order effect and can provide greater insight into the physical process of bubble producing,developing and collapsing compared to the traditional cavitation model.DCM has already been validated for steady cavitating flow,and the results were reported.Furthermore,DCM is designed and supposed to be more accurate and efficient in modeling unsteady cavitating flow,which is also the purpose of this paper.The basic characteristic of the unsteady cavitating flow,such as the vapor volume fraction distribution and the evolution of pressure amplitude and frequency at different locations of the hydrofoil,are carefully studied to validate DCM.It is found that not only these characteristics mentioned above accord well with the experimental results,but also some detailed transient flow information is depicted,including the re-entrant jet flow that caused the shedding of the cavity,and the phenomenon of two-peak pressure fluctuation in the vicinity of the cavity closure in a cycle.The numerical results validate the capability of DCM for the application of modeling the complicated unsteady cavitating flow.展开更多
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 st...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.展开更多
The present paper investigates the turbulent cavitating flow around the Clark-Y hydrofoil with special emphasis on the influence of cavitation models by verification and validation(V&V)method.RANS solver coupled w...The present paper investigates the turbulent cavitating flow around the Clark-Y hydrofoil with special emphasis on the influence of cavitation models by verification and validation(V&V)method.RANS solver coupled with the three major cavitation models(i.e.,Zwart-Gerber-Belamri,Schnerr and Sauer and full cavitation model,which are abbreviated to ZGB model,SS model and FC model respectively)is employed in this paper.The results indicate that the three cavitation models can properly reproduce the cavitation evolutions.ZGB model and SS model give better prediction in the overall cavitation patterns.FC model exhibits an obvious under-estimation for the sheet cavity,and the predicted volume fraction is closely related to the turbulent flow.The verification and validation procedure is involved to quantitatively assess the accuracy of these three cavitation models.It is indicated that the V&V procedure is suitable for the unsteady cavitating flow.The errors estimate is robust and conservative within the cavitation region,while gets closer to zero in the no-cavitation region.In addition,ZGB model exhibits the highest overall accuracy among the three models,which further verifies its wide applicability.展开更多
This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is ...This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid（VOF） method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.展开更多
The present article focuses on modeling issues to simulate cryogenic fluid cavitating flows.A revised cavitation model,in which the thermal effect is considered,is derivated and established based on Kubota model.Cavit...The present article focuses on modeling issues to simulate cryogenic fluid cavitating flows.A revised cavitation model,in which the thermal effect is considered,is derivated and established based on Kubota model.Cavitating flow computations are conducted around an axisymmetric ogive and a 2D quarter caliber hydrofoil in liquid nitrogen implementing the revised model and Kubota model coupled with energy equation and dynamically updating the fluid physical properties,respecitively.The results show that the revised cavitation model can better describe the mass transport process in the cavitation process in cryogenic fluids.Compared with Kubota model,the revised model can reflect the observed"frosty"appearance within the cavity.The cavity length becomes shorter and it can capture the temperature and pressure depressions more consistently in the cavitating region,particularly at the rear of the cavity.The evaporation rate decreases,and while the magnitude of the condensation rate becomes larger because of the thermal effect terms in the revised model compared with the results obtained by the Kubota model.展开更多
Cavitation within the tip vortex(TV)flow remains a challenging issue in the design of high-speed and low-noise hydraulic machinery.In this paper,the TV cavitating flow around an elliptical hydrofoil is calculated by u...Cavitation within the tip vortex(TV)flow remains a challenging issue in the design of high-speed and low-noise hydraulic machinery.In this paper,the TV cavitating flow around an elliptical hydrofoil is calculated by using large eddy simulation(LES)combined with a modified Schnerr-Sauer(S-S)cavitation model.The original S-S cavitation model is modified by taking into account the typical effect of vortex flow.The partial pressure term which can describe the vortex quantitatively and qualitatively is confirmed asρ_(m)ω^(2) x r _(c)^(2) ,and is considered into the R-P equation of the modified S-S cavitation model.Comparison between the numerical and experimental results shows good agreement in the form and evolution of cavities,including attached cavities(AC)and tip vortex cavities(TVC).The vorticity transport equation is utilized to investigate the dynamic mechanisms of the vortex development around the TVC.Further analyses indicate that cavitation in the TV flow influences the pressure in the core of the cavity and the local flow patterns.Typical vortex structures in the TV cavitating flow include TV,secondary vortex(SV)and wake vortex(WV).The direction and magnitude of the rotation effect can be described by axial vorticity which is drawn on the iso-surface of Q=1×105 s−2.The development of the TV cavitating flow can be divided into two stages:Stage I,the development and fusion of TV,SV,stage II,the dissipation of SV.The stretching term dominates the evolution of TV,and the dilatation term is the main reason in the mergence process of SV.展开更多
Quadratic and cubic Non-Linear Eddy-Viscosity Models （NLEVMs） at low Reynolds number （Re） correction were introduced into the present Computational Fluid Dynamics （CFD） framework, to provide better numerical tre...Quadratic and cubic Non-Linear Eddy-Viscosity Models （NLEVMs） at low Reynolds number （Re） correction were introduced into the present Computational Fluid Dynamics （CFD） framework, to provide better numerical treatment about the anisotropic turbulence stress in cavitating flows, which have large density ratio and large-scaled swirling flow structures. The applications of these NLEVMs were carried out through a self-developed cavitation code, coupled with a cavitation model based on the transport equation of liquid phase. These NLEVMs were firstly validated by the benchmark of disk supercavity, and found able to obtain more accurate capture of the hydrodynamic properties than the linear models. One of such models was further applied on the cavitation problem of submerged vehicles. Ultimately, the supercavitating flows around an especially designed underwater vehicle were predicted using the cubic k - e turbulence model, and its cavitation behaviors were studied.展开更多
Aiming at modeling the cavitation bubble cluster,we propose a novel nonlinear dynamic cavitation model(NDCM)considering the second derivative term in Rayleigh-Plesset equation through strict mathematical derivation.Th...Aiming at modeling the cavitation bubble cluster,we propose a novel nonlinear dynamic cavitation model(NDCM)considering the second derivative term in Rayleigh-Plesset equation through strict mathematical derivation.There are two improvements of the new model:i)the empirical coefficients are eliminated by introduction of the nonuniform potential functions of ψ_(v) and ψ_(c) for growth and collapse processes respectively,and ii)only two model parameters are required,which both base on physical quantities–the Blake critical radius Rb and the average maximum growth radius R_(m).The corresponding cavitation solver was developed by using OpenFOAM in which we implemented the modified momentum interpolation(MMI)method to ensure that the calculated results are independent of time step size.Three validation cases,namely numerical bubble cluster collapse,ultrasonic horn experiment,and hydrodynamic cavitation around slender body are employed.The results indicate that ψ_(v) and ψ_(c) can reveal the nonlinear characteristics for cavity accurately,and R_(b) and R_(m) can reflect the relevance between cavitation model and actual physical quantities.Moreover,it is discussed the potentiality of NDCM that is generally applied on the cavitating flow possessing with dispersed bubbly cloud.展开更多
A pressure-based algorithm for the prediction of cavitating flows is presented.The algorithm employs a set of equations including the Navier-Stokes equations and a cavitation model explaining the phase change between ...A pressure-based algorithm for the prediction of cavitating flows is presented.The algorithm employs a set of equations including the Navier-Stokes equations and a cavitation model explaining the phase change between liquid and vapor.A pressure-based method is used to construct the algorithm and the coupling between pressure and velocity is considered.The pressure correction equation is derived from a new continuity equation which employs a source term related to phase change rate instead of the material derivative of density Dρ/Dt.This pressure-based algorithm allows for the computation of steady or unsteady,2-D or 3-D cavitating flows.Two 2-D cases,flows around a flat-nose cylinder and around a NACA0015 hydrofoil,are simulated respectively,and the periodic cavitation behaviors associated with the re-entrant jets are captured.This algorithm shows good capability of computating time-dependent cavitating flows.展开更多
The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large...The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation （ILES） is app- lied to analyze the three-dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic conditions, which were experimentally tested at the high speed cavitation tunnel of the l^cole Polytechnique F6d＆ale de Lausanne （EPFL）, clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasona- bly well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.展开更多
基金supported by the National Natural Science Foundation of China (Grants No. 51179075 and 51239005) A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Considering the compressibility of the cavity in the cavitating flow, this paper presents a modified k-ω model for predicting the cavitating flow in a centrifugal pump, in which the modified k-ω model and Schnerr-Sauer cavitation model were combined with ANSYS CFX. To evaluate the modified and standard k-co models, numerical simulations were performed with these two models, respectively, and the calculation results were compared with the experimental data. Numerical simulations were executed with three different values of the flow coefficient, and the simulation results of the modified k-ω model showed agreement with most of the experimental data. The cavitating flow in the centrifugal pump obtained by the modified k-ω model at the design flow coefficient of 0.102, was analyzed. When the cavitation number decreases, the cavity initially generates on the suction side of the blade near the leading edge and then expands to the outlet of the impeller, and the decrease of the total pressure coefficient mainly occurs upstream of the impeller passage, while the downstream remains almost unaffected by the development of cavitation.
基金supported by the National Natural Science Foundation of China (Grants 11172040,51239005)
文摘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.
基金supported by the National Natural Science Foundation of China (10802026)
文摘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.
基金support from the National Natural Science Foundation of China (11402276)
文摘The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51149003)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.2013033)
文摘The influence of phase-change coefficients variations in the Singhal cavitation model on the calculation results has been numerically studied. By comparing the numerical results and experimental data, the relationship between the coefficients and cavitation numbers is obtained. The calculation results of 2d axisymmetrical cylinder with 45-degree cone cavitator show that under different cavitation numbers, there are three typical kind of cavities, which are respectively main cavity, secondary cavity and rear cavity. The coefficients variations have a great influence respectively on the three type cavities in shape, collapse position, collapse strength, etc, and different cavitation numbers are corresponding to different phase-change coefficients. The cavitation flow field can be divided into three typical zones according to the cavitation number: weak-cavitation zone, secondary-cavitation zone and supercavitation zone. For 45-degree cone cavitator cylinder, the evaporation coefficients will firstly decrease and then increase with the decrease of cavitation numbers in secondary-cavitation zone, while the condensation coefficients keep relatively lower and almost unchanged. In weak-cavitation zone, there only exists the smaller main cavity attached to the model head or there is no obvious cavity. In supercavitation zone, the secondary cavity attached to the model will fall off and merge into the new rear cavity.
基金Supported by the National Natural Science Foundation of China under Grant No 51506051
文摘Ventilated cavitation plays an important role on the drag reduction of underwater vehicles and surface ships. For the modelling of ventilated cavitation, the minimum speed of the pressure wave is a crucial parameter for the closure of the pressure-density coupling relationship. In this study, the minimum wave speed is determined based on a theoretical model coupling the wave equation and the bubble interface motion equation. The influences of several paramount parameters （e.g., frequency, bubble radius and void fraction） on the minimum wave speed are quantitatively demonstrated and discussed. Compared with the minimum wave speed in the traditional cavitation, values for the ventilated cavitation are much higher. The physical mechanisms for the above difference are briefly discussed with the suggestions on the usage of the present findings.
基金supported by National Natural Science Foundation of China(Grant No.51009144)
文摘Considering the lack of theoretical models and ingredients necessary to explain the scaling of the results of propeller cavitation inception and cavitating hydroacoustics from model tests to full scale currently, and the insufficient reflection of the nuclei effects on cavitation in the numerical methods, the cavitating hydrodynamics and cavitation low frequency noise spectrum of three geometrically similar 7-bladed highly skewed propellers with non-uniform inflow are addressed. In this process, a numerical bridge from the multiphase viscous simulation of propeller cavitation hydrodynamics to its hydro-acoustics is built, and the scale effects on performances and the applicability of exist scaling law are analyzed. The effects of non-condensable gas（NCG） on cavitation inception are involved explicitly in the improved Sauer＇s cavitation model, and the cavity volume acceleration related to its characteristic length is used to produce the noise spectrum. Results show that, with the same cavitation number, the cavity extension on propeller blades increases with diameter associated with an earlier shift of the beginning point of thrust decline induced by cavitation, while the three decline slopes of thrust breakdown curves are found to be nearly the same. The power of the scaling law based on local Reynolds number around 0.9R section is determined as 0.11. As for the smallest propeller, the predominant tonal noise is located at blade passing frequency（BPF）, whereas 2BPF for the middle and both 2BPF and 3BPF for the largest, which shows the cavitating line spectrum is fully related to the interaction between non-uniform inflow and fluctuated cavity volume. The predicted spectrum level exceedance from the middle to the large propeller is 6.65 dB at BPF and 5.94 dB at 2BPF. Since it just differs less than 2 dB to the increment obtained by empirical scaling law, it is inferred that the scale effects on them are acceptable with a sufficient model scale, and so do the scaling law. The numerical implementation of cavitating hydrodynamics and hydro-acoustics prediction of propeller in big scale in wake has been completed.
文摘In order to predict the effects of cavitation on a hydrofoil, the state equations of the cavitation model were combined with a linear viscous turbulent method for mixed fluids in the computational fluid dynamics (CFD) software FLUENT to simulate steady cavitating flow. At a fixed attack angle, pressure distributions and volume fractions of vapor at different cavitation numbers were simulated, and the results on foil sections agreed well with experimental data. In addition, at the various cavitation numbers, the vapor fractions at different attack angles were also predicted. The vapor region moved towards the front of the airfoil and the length of the cavity grew with increased attack angle. The results show that this method of applying FLUENT to simulate cavitation is reliable.
基金the paper was supported by the Natural Science Foundation of China(No.51974036 and No.51604039)the Yangtze Fund for Youth Teams of Science and Technology Innovation(No.2016cqt01)。
文摘Self-propelled nozzle is a critical component of the radial jet drilling technology.Its backward orifice structure has a crucial influence on the propulsive force and the drilling performance.To improve the working performance of the nozzle,the numerical simulation model is built and verified by the experimental results of propulsive force.Then the theoretical model of the energy efficiency and energy coefficient of the nozzle is built to reveal the influence of the structural parameters on the jet performance of the nozzle.The results show that the energy efficiency and energy coefficient of the backward orifice increase first and then decrease with the angle increases.The energy coefficient of forward orifice is almost constant with the angle increases.With the increase in the number and diameter,energy efficiency and energy coefficient of the forward orifice gradually decrease,but the backward orifice energy coefficient first increases and then decreases.Finally,it is obtained that the nozzle has better jet performance when the angle of backward orifice is 30°,the number of backward orifice is 6,and the value range of diameter is 2-2.2 mm.This study provides a reference for the design of efficiently self-propelled nozzle for radial jet drilling technology.
文摘In the present research, a bubble dynamics based model for cavitating flow simulations is extended to higher void fraction region for wider range of applications. The present bubble model is based on the so-called Rayleigh-Plesset equation that calculates a temporal bubble radius with the surrounding liquid pressure and is considered to be valid in an area below a certain void fraction. The solution algorithm is modified so that the Rayleigh-Plesset equation is no more solved once the bubble radius （or void fraction） reaches at a certain value till the liquid pressure recovers above the vapor pressure in order to overcome this problem. This procedure is expected to stabilize the numerical calculation. The results of simple two-dimensional flow field are presented compared with the existing bubble model.
基金supported by the National Natural Science Foundation of China(Grant No.51276157)Zhejiang Provincial Natural Science Foundation(Grant No.LY12E060026)
文摘Unsteady cavitating flow is extremely complicated and brings more serious damages and unignorable problems compared with steady cavitating flow.CFD has become a practical way to model cavitation;however,the popularly used full cavitation model cannot reflect the pressure-change that the bubble experiences during its life path in the highly unsteady flow like cloud cavitating.Thus a dynamic cavitation model(DCM)is proposed and it has been considered to have not only the first-order pressure effects but also zero-order effect and can provide greater insight into the physical process of bubble producing,developing and collapsing compared to the traditional cavitation model.DCM has already been validated for steady cavitating flow,and the results were reported.Furthermore,DCM is designed and supposed to be more accurate and efficient in modeling unsteady cavitating flow,which is also the purpose of this paper.The basic characteristic of the unsteady cavitating flow,such as the vapor volume fraction distribution and the evolution of pressure amplitude and frequency at different locations of the hydrofoil,are carefully studied to validate DCM.It is found that not only these characteristics mentioned above accord well with the experimental results,but also some detailed transient flow information is depicted,including the re-entrant jet flow that caused the shedding of the cavity,and the phenomenon of two-peak pressure fluctuation in the vicinity of the cavity closure in a cycle.The numerical results validate the capability of DCM for the application of modeling the complicated unsteady cavitating flow.
基金supported by the Natural Science Foundation of Heilongjiang Province of China(Grant No.A201409)the Special Fund Project for Technology Innovation Talent of Harbin(Grant No.2013RFLXJ007)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.201159)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No. 52176041).
文摘The present paper investigates the turbulent cavitating flow around the Clark-Y hydrofoil with special emphasis on the influence of cavitation models by verification and validation(V&V)method.RANS solver coupled with the three major cavitation models(i.e.,Zwart-Gerber-Belamri,Schnerr and Sauer and full cavitation model,which are abbreviated to ZGB model,SS model and FC model respectively)is employed in this paper.The results indicate that the three cavitation models can properly reproduce the cavitation evolutions.ZGB model and SS model give better prediction in the overall cavitation patterns.FC model exhibits an obvious under-estimation for the sheet cavity,and the predicted volume fraction is closely related to the turbulent flow.The verification and validation procedure is involved to quantitatively assess the accuracy of these three cavitation models.It is indicated that the V&V procedure is suitable for the unsteady cavitating flow.The errors estimate is robust and conservative within the cavitation region,while gets closer to zero in the no-cavitation region.In addition,ZGB model exhibits the highest overall accuracy among the three models,which further verifies its wide applicability.
基金supported by the NSWC Carderock ILIR programby the US Office of Naval Research(Grant No.N000141-01-00-1-7)
文摘This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid（VOF） method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.
基金supported by the National Natural Science Foundation of China(Grant No.50979004)the Doctor Reserch Fund of Univercity(Grant No.20080070027)
文摘The present article focuses on modeling issues to simulate cryogenic fluid cavitating flows.A revised cavitation model,in which the thermal effect is considered,is derivated and established based on Kubota model.Cavitating flow computations are conducted around an axisymmetric ogive and a 2D quarter caliber hydrofoil in liquid nitrogen implementing the revised model and Kubota model coupled with energy equation and dynamically updating the fluid physical properties,respecitively.The results show that the revised cavitation model can better describe the mass transport process in the cavitation process in cryogenic fluids.Compared with Kubota model,the revised model can reflect the observed"frosty"appearance within the cavity.The cavity length becomes shorter and it can capture the temperature and pressure depressions more consistently in the cavitating region,particularly at the rear of the cavity.The evaporation rate decreases,and while the magnitude of the condensation rate becomes larger because of the thermal effect terms in the revised model compared with the results obtained by the Kubota model.
基金supported by the National Natural Science Foundation of China(Grant No.52009001)supported by the Postdoctoral Research Foundation of China(Granr No.2020M680380)+1 种基金the Natural Science Foundation Projectof Chongqing,Chongqing Science and Technology Commission(Grant No.cstc2021jcyj-msxmX1046)the Beijing Institute of Technology Research Fund Program for Young Scholars(Grant No.XSQD-202003008).
文摘Cavitation within the tip vortex(TV)flow remains a challenging issue in the design of high-speed and low-noise hydraulic machinery.In this paper,the TV cavitating flow around an elliptical hydrofoil is calculated by using large eddy simulation(LES)combined with a modified Schnerr-Sauer(S-S)cavitation model.The original S-S cavitation model is modified by taking into account the typical effect of vortex flow.The partial pressure term which can describe the vortex quantitatively and qualitatively is confirmed asρ_(m)ω^(2) x r _(c)^(2) ,and is considered into the R-P equation of the modified S-S cavitation model.Comparison between the numerical and experimental results shows good agreement in the form and evolution of cavities,including attached cavities(AC)and tip vortex cavities(TVC).The vorticity transport equation is utilized to investigate the dynamic mechanisms of the vortex development around the TVC.Further analyses indicate that cavitation in the TV flow influences the pressure in the core of the cavity and the local flow patterns.Typical vortex structures in the TV cavitating flow include TV,secondary vortex(SV)and wake vortex(WV).The direction and magnitude of the rotation effect can be described by axial vorticity which is drawn on the iso-surface of Q=1×105 s−2.The development of the TV cavitating flow can be divided into two stages:Stage I,the development and fusion of TV,SV,stage II,the dissipation of SV.The stretching term dominates the evolution of TV,and the dilatation term is the main reason in the mergence process of SV.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11102110,10832007)
文摘Quadratic and cubic Non-Linear Eddy-Viscosity Models （NLEVMs） at low Reynolds number （Re） correction were introduced into the present Computational Fluid Dynamics （CFD） framework, to provide better numerical treatment about the anisotropic turbulence stress in cavitating flows, which have large density ratio and large-scaled swirling flow structures. The applications of these NLEVMs were carried out through a self-developed cavitation code, coupled with a cavitation model based on the transport equation of liquid phase. These NLEVMs were firstly validated by the benchmark of disk supercavity, and found able to obtain more accurate capture of the hydrodynamic properties than the linear models. One of such models was further applied on the cavitation problem of submerged vehicles. Ultimately, the supercavitating flows around an especially designed underwater vehicle were predicted using the cubic k - e turbulence model, and its cavitation behaviors were studied.
基金supported by National Key Project GJXM92579 and National Sci.&Tech.Major Project(2017-II-0004-0016).
文摘Aiming at modeling the cavitation bubble cluster,we propose a novel nonlinear dynamic cavitation model(NDCM)considering the second derivative term in Rayleigh-Plesset equation through strict mathematical derivation.There are two improvements of the new model:i)the empirical coefficients are eliminated by introduction of the nonuniform potential functions of ψ_(v) and ψ_(c) for growth and collapse processes respectively,and ii)only two model parameters are required,which both base on physical quantities–the Blake critical radius Rb and the average maximum growth radius R_(m).The corresponding cavitation solver was developed by using OpenFOAM in which we implemented the modified momentum interpolation(MMI)method to ensure that the calculated results are independent of time step size.Three validation cases,namely numerical bubble cluster collapse,ultrasonic horn experiment,and hydrodynamic cavitation around slender body are employed.The results indicate that ψ_(v) and ψ_(c) can reveal the nonlinear characteristics for cavity accurately,and R_(b) and R_(m) can reflect the relevance between cavitation model and actual physical quantities.Moreover,it is discussed the potentiality of NDCM that is generally applied on the cavitating flow possessing with dispersed bubbly cloud.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10602030)the National Key Basic Research Program of China (973 Program, Grant No. 2009CB724303)the Fundamental Research Funds for the Central Universities (Grant No. 2010QNA4015)
文摘A pressure-based algorithm for the prediction of cavitating flows is presented.The algorithm employs a set of equations including the Navier-Stokes equations and a cavitation model explaining the phase change between liquid and vapor.A pressure-based method is used to construct the algorithm and the coupling between pressure and velocity is considered.The pressure correction equation is derived from a new continuity equation which employs a source term related to phase change rate instead of the material derivative of density Dρ/Dt.This pressure-based algorithm allows for the computation of steady or unsteady,2-D or 3-D cavitating flows.Two 2-D cases,flows around a flat-nose cylinder and around a NACA0015 hydrofoil,are simulated respectively,and the periodic cavitation behaviors associated with the re-entrant jets are captured.This algorithm shows good capability of computating time-dependent cavitating flows.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51306018,51536008 and 51179091)
文摘The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation （ILES） is app- lied to analyze the three-dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic conditions, which were experimentally tested at the high speed cavitation tunnel of the l^cole Polytechnique F6d＆ale de Lausanne （EPFL）, clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasona- bly well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.
