This paper aims to numerically explore the characteristics of unsteady cavitating flow around a NACA0015 hydrofoil,with a focus on vorticity attributes.The simulation utilizes a homogeneous mixture model coupled with ...This paper aims to numerically explore the characteristics of unsteady cavitating flow around a NACA0015 hydrofoil,with a focus on vorticity attributes.The simulation utilizes a homogeneous mixture model coupled with a filter-based density correction turbulence model and a modified Zwart cavitation model.The study investigates the dynamic cavitation features of the thermal fluid around the hydrofoil at various incoming flow velocities.It systematically elucidates the evolution of cavitation and vortex dynamics corresponding to each velocity condition.The results indicate that with increasing incoming flow velocity,distinct cavitation processes take place in the flow field.展开更多
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 resour...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.展开更多
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 ac...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.展开更多
The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in go...The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.展开更多
Verification and validation(V&V)is a helpful tool for evaluating simulation errors,but its application in unsteady cavitating flow remains a challenging issue due to the difficulty in meeting the requirement of an...Verification and validation(V&V)is a helpful tool for evaluating simulation errors,but its application in unsteady cavitating flow remains a challenging issue due to the difficulty in meeting the requirement of an asymptotic range.Hence,a new V&V approach for large eddy simulation(LES)is proposed.This approach offers a viable solution for the error estimation of simulation data that are unable to satisfy the asymptotic range.The simulation errors of cavitating flow around a projectile near the free surface are assessed using the new V&V method.The evident error values are primarily dispersed around the cavity region and free surface.The increasingly intense cavitating flow increases the error magnitudes.In addition,the modeling error magnitudes of the Dynamic Smagorinsky-Lilly model are substantially smaller than that of the Smagorinsky-Lilly model.The present V&V method can capture the decrease in the modeling errors due to model enhancements,further exhibiting its applicability in cavitating flow simulations.Moreover,the monitoring points where the simulation data are beyond the asymptotic range are primarily dispersed near the cavity region,and the number of such points grows as the cavitating flow intensifies.The simulation outcomes also suggest that the re-entrant jet and shedding cavity collapse are the chief sources of vorticity motions,which remarkably affect the simulation accuracy.The results of this study provide a valuable reference for V&V research.展开更多
In the present study, firstly, the unsteady cavitating flows around a hydrofoil are studied based on the flow visualization and detail velocity measurement, a high-speed video camera is used to visualize the flow stru...In the present study, firstly, the unsteady cavitating flows around a hydrofoil are studied based on the flow visualization and detail velocity measurement, a high-speed video camera is used to visualize the flow structures, and a particle image velocimetry （PIV） technique is applied to the measurement of the time-averaged and instantaneous velocity and vorticity fields. The results show that the unsteadiness of mass transfer process between the vapor and the two-phase regions is substantial, a self-oscillatory behavior of the whole sheet cavitation is obtained, with large length fluctuations and vapor cloud shedding, and also the cavitation structure depends on the interaction of the water-vapor mixture and the periodic vortex shedding. The main purpose of this experimental study is to offer information for validating computational models, and shed light on the unsteady multiphase transport process of cavitating flows. Furthermore, with an emphasis on the dynamics of the attached turbulent cavitating flows, a filter-based model （FBM） is derived from the k-6 two-equation model, a conditional averaging method aimed at improving unsteady simulation is applied to computation. In comparison to the standard k-ε model, overall, the filter-based model is shown to improve the predictive capability considerably.展开更多
The objective of this paper is to investigate transient cavitating flows around a hydrofoil via combined physical and numerical studies. The aims are to 1) investigate the periodic formation, breakup, shedding, and co...The objective of this paper is to investigate transient cavitating flows around a hydrofoil via combined physical and numerical studies. The aims are to 1) investigate the periodic formation, breakup, shedding, and collapse of the sheet/cloud cavities, 2) provide a better insight in the physical mechanism that governs the dynamics and structures of the sheet/cloud cavitation, 3) quantify the influence of cavitation on the surrounding flow structures. Results are presented for a Clark-Y hydrofoil fixed at an angle of attack of a=8° at a moderate Reynolds number, Re=7×105 , for sheet/cloud cavitating conditions. The experimental studies were conducted in a cavitation tunnel at Beijing Institute of Technology, China. The numerical simulations are performed by solving the incompressible, multiphase unsteady Reynolds-averaged Navier-Stokes (URANS) equations via the commercial code CFX using a transport equation-based cavitation model; a filter-based density corrected model (FBDCM) is used to regulate the turbulent eddy viscosity in both the cavitation regions near the foil and in the wake. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding in accordance with the quantitative features observed in the experiment. Regarding vapor shedding in the cavitating flow around the three-dimensional foil, it is primarily attributed to the effect of the re-entrant flow, which is formed due to the strong adverse pressure gradient. The results show strong correlation between the cavity and vorticity structures, demonstrating that the inception, growth, shedding, and collapse of sheet/cloud cavities are important mechanisms for vorticity production and modification.展开更多
The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are perf...The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed at ？= 6？ and ？= 1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages：（1） the growth of the attached cavity sheet,（2） development of re-entrant flow and attached cavity sheet breakup,（3） attached cavity sheet rolling up and cavity cloud shedding, and（4） cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.展开更多
A modification to the PANS(partially averaged Navier-Stokes) model is proposed to simulate unsteady cavitating flows. In the model, the parameter fk is modified to vary as a function of the ratios between the water de...A modification to the PANS(partially averaged Navier-Stokes) model is proposed to simulate unsteady cavitating flows. In the model, the parameter fk is modified to vary as a function of the ratios between the water density and the mixture density in the local flows. The objective of this study is to validate the modified model and further understand the interaction between turbulence and cavitation around a Clark-Y hydrofoil. The comparisons between the numerical and experiment results show that the modified model can be improved to predict the cavity evolution, vortex shedding frequency and the lift force fluctuating in time fairly well, as it can effectively modulate the eddy viscosity in the cavitating region and various levels of physical turbulent fluctuations are resolved. In addition, from the computational results, it is proved that cavitation phenomenon physically influences the turbulent level, especially by the vortex shedding behaviors. Also, the mean u-velocity profiles demonstrate that the attached cavity thickness can alter the local turbulent shear layer.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
Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a hig...Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a high-resolution mesh.The present work,within OpenFOAM,proposes an effective modeling framework using the large eddy simulation(LES)approach along with the volume of fluid(VOF)method to simulate the two-phase flow system and applies the Schnerr-Sauer model to calculate the mass-transfer rate between water and vapor.The adaptive mesh refinement(AMR)which is a powerful tool for allocating high-resolution grids only to the region of the greatest concern is adopted for improving the solution of interfacial structures.The effect of grid size is firstly investigated and the time-averaged quantities are verified against the experimental data,and then simulations of cavitating flows are successfully achieved to precisely characterize the features of cavitation with automatically and dynamically refining the mesh.As the refinement only takes place in the interfacial region,high-precision simulations can be achieved with limited computational resources,and the method shows promising prospects for modeling of the multi-scale,time-critical and computationally intensive cavitating flows.展开更多
This paper investigates the unsteady structures and the hydrodynamics of cavitating flows. Experimental results are presented for a Clark-Y hydrofoil fixed at ？= 0？, 5？ and 8？, for various cavitation numbers, from...This paper investigates the unsteady structures and the hydrodynamics of cavitating flows. Experimental results are presented for a Clark-Y hydrofoil fixed at ？= 0？, 5？ and 8？, for various cavitation numbers, from subcavitating flow to supercavitation. The high-speed video camera and the particle image velocimetry（PIV） are applied to observe the transient flow structures. Statistics of the cavity lengths, the velocity and vorticity distributions, as well as the turbulent intensities are presented to quantify the unsteady process. Meanwhile, the dynamic measurement system is used to record the dynamic characteristics. The experimental results show that the flow structures and the hydrodynamics of the cavitation vary considerably with various combinations of angles of attack and cavitation numbers. Under various conditions, the cavitation can be generally grouped as the inception cavitation, the sheet cavitation, the cloud cavitation and the supercavitation. The cloud cavitation exhibits noticeable unsteady characteristics. Experimental evidence indicates that the hydrodynamics are clearly affected by the cavitating flow structures, the amplitude of the load fluctuation is much higher in the cloud cavitating cases.展开更多
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 d...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.展开更多
A numerical treatment for the prediction of cavitating flows is presented and assessed. The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms. A central difference finit...A numerical treatment for the prediction of cavitating flows is presented and assessed. The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms. A central difference finite volume scheme with suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Euler equations. The Euler equations are utilized herein for the cavitation modeling, because some certain characteristics of cavitating flows can be obtained using the solution of this system of equations with relative low computational effort. In addition, the Euler equations are appropriate for the assessment of the numerical method used, because of the sensitivity of the solution to the numerical instabilities. For this reason, a sensitivity study is conducted to evaluate the effects of various parameters, such as numerical dissipation coefficients and grid size, on the accuracy and performance of the solution. The computations are performed for steady cavitating flows around the NACA 0012 and NACA 66 （MOD） hydrofoils and also an axisymmetric hemispherical fore-body under different conditions and the results are compared with the available numerical and experimental data. The solution procedure presented is shown to be accurate and efficient for predicting steady sheet- and super-cavitation for 2D/axisymmetric geometries.展开更多
Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state,and the flow is frequently unsteady and turbulent.The Reynolds-Averaged Navier-Stokes（RANS）approach...Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state,and the flow is frequently unsteady and turbulent.The Reynolds-Averaged Navier-Stokes（RANS）approach has been popular for turbulent flow computations.The most widely used ones,such as the standard k-εmodel,have well-recognized deficiencies when treating time dependent flow field.To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures,conditional averaging is adopted for the Navier-Stokes equation,and one more parameter,based on the filter size,is introduced into the k-εmodel.In the Partially Averaged Navier-Stokes（PANS）model,the filter width is mainly controlled by the ratio of unresolved-to-total kinetic energy1f.This model is assessed in unsteady cavitating flows over a Clark-Y hydrofoil.From the experimental validations regarding the forces,frequencies,cavity visualizations and velocity distributions,the PANS model is shown to improve the predictive capability considerably,in comparison to the standard k-ε model,and also,it is observed the value of1f in the PANS model has substantial influence on the predicting result.As the filter width1f is decreased,the PANS model can effectively reduce the eddy viscosity near the closure region which can significantly influence the capture of the detach cavity,and this model can reproduce the time-averaged velocity quantitatively around the hydrofoil.展开更多
A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow...A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.展开更多
A two-phase mixture model was established to study unsteady cavitating flows. A local compressible system of equations was derived by introducing a density-pressure function to account for the two-phase flow of water/...A two-phase mixture model was established to study unsteady cavitating flows. A local compressible system of equations was derived by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for solving the variable-density Navier-Stokes equations of cavitating flow problem was put forward. The numerical results for unsteady characteristics of cavitating flows on a 2D NACA hydrofoil coincide well with experimental data.展开更多
The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model, the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil. T...The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model, the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil. The effects of pitching rate on the sub- cavitating and cavitating response of the pitching hydrofoil are also investigated. In particular, we focus on the interactions between cavity inception, growth, and shedding and the vortex flow structures, and their impacts on the hydrofoil performance. The calculations are 2-D and performed by solving the incompressible, multiphase Unsteady Reynolds Averaged Navier Stokes （URANS） equations via the commercial CFD code CFX. The k-co SST （Shear Stress Transport） turbulence model is used along with the transport equation-based cavitation models. The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density. The calculation results are validated with experiments conducted by Ducoin et al. （see Computational and experimental investigation of flow over a transient pitching hydrofoil, Eur J Mech/B Fluids, 2009, 28：728-743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in vari- ous flow regimes including cavitating flow, Eur J Mech B/fluids, 2012, 36： 63-74）. Results are shown for a NACA66 hydro- foil subject to slow （quasi static, t2=6~/s, ＆＊ =0.18） and fast （dynamic, ＆=63~/s, dr＂ =1.89） pitching motions from a =0~ to a =15~. Both subcavitaing （or =8.0） and cavitating （cr=3.0） flows are considered. For subcavitating flow （or=8.0）, low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall, and delay of stall is ob- served with increasing pitching velocity. For cavitating flow （tr=3.0）, small leading edge cavities are observed with the slow pitching case, which significantly modified the vortex dynamics at high angles of attack, leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate. On the other hand, for the fast pitching case at or=3.0, large-scale sheet/cloud cavitation is observed, the cavity behavior is un- steady and has a strong impact on the hydrodynamic response, which leads to high amplitude fluctuations of the hydrodynamic coefficients, as well as significant changes in the stall and post-stall behavior. The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region, which significantly modifies the cavity lengths and shedding frequencies, particularly for the fast pitching case. In general, compared with the experimental visualiza- tions, the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.展开更多
Cavitating flows around skewed propellers are investigated numerically by means of the unsteady Reynolds Averaged Navier-Stokes （RANS） Equation method. The standard k - c turbulence and the modified Z-G-B cavitation...Cavitating flows around skewed propellers are investigated numerically by means of the unsteady Reynolds Averaged Navier-Stokes （RANS） Equation method. The standard k - c turbulence and the modified Z-G-B cavitation models are employed. A measured nominal wake is used for the inlet velocity boundary condition. Predicted cavitating evolution processes and tip cavity patterns are compared with experimental observations. In addition, the influence of the skew angles on the cavitation and unsteadiness performances of propellers operating in a non-uniform wake is also studied. Results show that the modified Z-G-B cavitation model performs better to simulate the cavitating flow cases studied in this paper. Comparisons demonstrate that the skewed propeller with a skew angle of 20~ is the best choice for a given stern wake with a assigned thrust and the minimum force fluctuations.展开更多
To apply the measurements of model experiment in water tunnel to the actual sailing condition, it is necessary to know accurately the strut effect and its rule. In the present work, the corresponding interferences of ...To apply the measurements of model experiment in water tunnel to the actual sailing condition, it is necessary to know accurately the strut effect and its rule. In the present work, the corresponding interferences of one-side strut and two-side strut on the natural cavitating flows around a submerged vehicle in water tunnel were investigated numerically, using the homogeneous equilibrium two-phase model coupled with a natural cavitation model. The numerical simulation results show that the strut types have distinct effects on the hydrodynamic properties. For the same given upstream velocity and downstream pressure, the existence of the strut leads to an increment of natural cavitation number, reduces the low-pressure region and depresses the pressure on the vehicle surface near the sides of strut. In the case of given cavitaiton number, the influences of the two-side strut on the drag and lift coefficients are both enhanced along with the increment of attack angle, however the influence of the one-side strut gradually gets stronger on the drag coefficient but weaker on the lift coefficient contrarily. In addition, based on the present numerical results, a correction method by introducing the sigmoidal logistic function is proposed to eliminate the interference from the foil-shaped strut.展开更多
文摘This paper aims to numerically explore the characteristics of unsteady cavitating flow around a NACA0015 hydrofoil,with a focus on vorticity attributes.The simulation utilizes a homogeneous mixture model coupled with a filter-based density correction turbulence model and a modified Zwart cavitation model.The study investigates the dynamic cavitation features of the thermal fluid around the hydrofoil at various incoming flow velocities.It systematically elucidates the evolution of cavitation and vortex dynamics corresponding to each velocity condition.The results indicate that with increasing incoming flow velocity,distinct cavitation processes take place in the flow field.
基金supported by National Natural Science Foundation of China (Grant No.11172040)
文摘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.
基金This work was financially supported by the National Natural Science Foundation of China(Grants 51822903 and 11772239)the Natural Science Foundation of Hubei Province(Grant 2018CFA010).The numerical calculations were done on the supercomputing system in the Supercomputing Center of Wuhan University.
文摘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.
基金the National Key R&D Program of China(Grants 2016YFC0300800 and 2016YFC0300802)the National Natural Science Foundation of China(Grants 11772340 and 11672315)the Science and Technology on Water Jet Propulsion Laboratory(Grant 6142223190101).
文摘The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.
基金Supported by the National Key R&D Program of China(2022YFB3303501)the National Natural Science Foundation of China(Project Nos.52176041 and 12102308)the Fundamental Research Funds for the Central Universities(Project Nos.2042023kf0208 and 2042023kf0159).
文摘Verification and validation(V&V)is a helpful tool for evaluating simulation errors,but its application in unsteady cavitating flow remains a challenging issue due to the difficulty in meeting the requirement of an asymptotic range.Hence,a new V&V approach for large eddy simulation(LES)is proposed.This approach offers a viable solution for the error estimation of simulation data that are unable to satisfy the asymptotic range.The simulation errors of cavitating flow around a projectile near the free surface are assessed using the new V&V method.The evident error values are primarily dispersed around the cavity region and free surface.The increasingly intense cavitating flow increases the error magnitudes.In addition,the modeling error magnitudes of the Dynamic Smagorinsky-Lilly model are substantially smaller than that of the Smagorinsky-Lilly model.The present V&V method can capture the decrease in the modeling errors due to model enhancements,further exhibiting its applicability in cavitating flow simulations.Moreover,the monitoring points where the simulation data are beyond the asymptotic range are primarily dispersed near the cavity region,and the number of such points grows as the cavitating flow intensifies.The simulation outcomes also suggest that the re-entrant jet and shedding cavity collapse are the chief sources of vorticity motions,which remarkably affect the simulation accuracy.The results of this study provide a valuable reference for V&V research.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50679001 and 50979004)
文摘In the present study, firstly, the unsteady cavitating flows around a hydrofoil are studied based on the flow visualization and detail velocity measurement, a high-speed video camera is used to visualize the flow structures, and a particle image velocimetry （PIV） technique is applied to the measurement of the time-averaged and instantaneous velocity and vorticity fields. The results show that the unsteadiness of mass transfer process between the vapor and the two-phase regions is substantial, a self-oscillatory behavior of the whole sheet cavitation is obtained, with large length fluctuations and vapor cloud shedding, and also the cavitation structure depends on the interaction of the water-vapor mixture and the periodic vortex shedding. The main purpose of this experimental study is to offer information for validating computational models, and shed light on the unsteady multiphase transport process of cavitating flows. Furthermore, with an emphasis on the dynamics of the attached turbulent cavitating flows, a filter-based model （FBM） is derived from the k-6 two-equation model, a conditional averaging method aimed at improving unsteady simulation is applied to computation. In comparison to the standard k-ε model, overall, the filter-based model is shown to improve the predictive capability considerably.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11172040, 50979004)
文摘The objective of this paper is to investigate transient cavitating flows around a hydrofoil via combined physical and numerical studies. The aims are to 1) investigate the periodic formation, breakup, shedding, and collapse of the sheet/cloud cavities, 2) provide a better insight in the physical mechanism that governs the dynamics and structures of the sheet/cloud cavitation, 3) quantify the influence of cavitation on the surrounding flow structures. Results are presented for a Clark-Y hydrofoil fixed at an angle of attack of a=8° at a moderate Reynolds number, Re=7×105 , for sheet/cloud cavitating conditions. The experimental studies were conducted in a cavitation tunnel at Beijing Institute of Technology, China. The numerical simulations are performed by solving the incompressible, multiphase unsteady Reynolds-averaged Navier-Stokes (URANS) equations via the commercial code CFX using a transport equation-based cavitation model; a filter-based density corrected model (FBDCM) is used to regulate the turbulent eddy viscosity in both the cavitation regions near the foil and in the wake. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding in accordance with the quantitative features observed in the experiment. Regarding vapor shedding in the cavitating flow around the three-dimensional foil, it is primarily attributed to the effect of the re-entrant flow, which is formed due to the strong adverse pressure gradient. The results show strong correlation between the cavity and vorticity structures, demonstrating that the inception, growth, shedding, and collapse of sheet/cloud cavities are important mechanisms for vorticity production and modification.
基金Project supported by the National Natural Science Foundation of China(Grant No.91752105)the Natural Science Foundation of Beijing(Grant No.3172029)
文摘The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed at ？= 6？ and ？= 1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages：（1） the growth of the attached cavity sheet,（2） development of re-entrant flow and attached cavity sheet breakup,（3） attached cavity sheet rolling up and cavity cloud shedding, and（4） cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172040 and 51239005)the Beijing Municipal Natural Science Foundation(Grant No.3144043)
文摘A modification to the PANS(partially averaged Navier-Stokes) model is proposed to simulate unsteady cavitating flows. In the model, the parameter fk is modified to vary as a function of the ratios between the water density and the mixture density in the local flows. The objective of this study is to validate the modified model and further understand the interaction between turbulence and cavitation around a Clark-Y hydrofoil. The comparisons between the numerical and experiment results show that the modified model can be improved to predict the cavity evolution, vortex shedding frequency and the lift force fluctuating in time fairly well, as it can effectively modulate the eddy viscosity in the cavitating region and various levels of physical turbulent fluctuations are resolved. In addition, from the computational results, it is proved that cavitation phenomenon physically influences the turbulent level, especially by the vortex shedding behaviors. Also, the mean u-velocity profiles demonstrate that the attached cavity thickness can alter the local turbulent shear layer.
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Project supported by the China Postdoctoral Science Foundation(Grant No.2018M630502)This work was supported by the Jiangsu Province Science Foundation for Youths(Grant No.BK20180505)the Fundamental Research Funds for the Central Universities(Grant No.2019B14914)。
文摘Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a high-resolution mesh.The present work,within OpenFOAM,proposes an effective modeling framework using the large eddy simulation(LES)approach along with the volume of fluid(VOF)method to simulate the two-phase flow system and applies the Schnerr-Sauer model to calculate the mass-transfer rate between water and vapor.The adaptive mesh refinement(AMR)which is a powerful tool for allocating high-resolution grids only to the region of the greatest concern is adopted for improving the solution of interfacial structures.The effect of grid size is firstly investigated and the time-averaged quantities are verified against the experimental data,and then simulations of cavitating flows are successfully achieved to precisely characterize the features of cavitation with automatically and dynamically refining the mesh.As the refinement only takes place in the interfacial region,high-precision simulations can be achieved with limited computational resources,and the method shows promising prospects for modeling of the multi-scale,time-critical and computationally intensive cavitating flows.
基金Project supported by the National Natural Science Foundation of China(Grant No.51306020)the Natural Science Foundation of Beijing(Grant No.3144034)
文摘This paper investigates the unsteady structures and the hydrodynamics of cavitating flows. Experimental results are presented for a Clark-Y hydrofoil fixed at ？= 0？, 5？ and 8？, for various cavitation numbers, from subcavitating flow to supercavitation. The high-speed video camera and the particle image velocimetry（PIV） are applied to observe the transient flow structures. Statistics of the cavity lengths, the velocity and vorticity distributions, as well as the turbulent intensities are presented to quantify the unsteady process. Meanwhile, the dynamic measurement system is used to record the dynamic characteristics. The experimental results show that the flow structures and the hydrodynamics of the cavitation vary considerably with various combinations of angles of attack and cavitation numbers. Under various conditions, the cavitation can be generally grouped as the inception cavitation, the sheet cavitation, the cloud cavitation and the supercavitation. The cloud cavitation exhibits noticeable unsteady characteristics. Experimental evidence indicates that the hydrodynamics are clearly affected by the cavitating flow structures, the amplitude of the load fluctuation is much higher in the cloud cavitating cases.
基金funding from the People Programme(Marie Curie Actions)of the European Union's Seventh Framework Programme FP7/2007-2013/under REA grant agreement No.324313
文摘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.
基金Sharif University of Technology for financial support of this research
文摘A numerical treatment for the prediction of cavitating flows is presented and assessed. The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms. A central difference finite volume scheme with suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Euler equations. The Euler equations are utilized herein for the cavitation modeling, because some certain characteristics of cavitating flows can be obtained using the solution of this system of equations with relative low computational effort. In addition, the Euler equations are appropriate for the assessment of the numerical method used, because of the sensitivity of the solution to the numerical instabilities. For this reason, a sensitivity study is conducted to evaluate the effects of various parameters, such as numerical dissipation coefficients and grid size, on the accuracy and performance of the solution. The computations are performed for steady cavitating flows around the NACA 0012 and NACA 66 （MOD） hydrofoils and also an axisymmetric hemispherical fore-body under different conditions and the results are compared with the available numerical and experimental data. The solution procedure presented is shown to be accurate and efficient for predicting steady sheet- and super-cavitation for 2D/axisymmetric geometries.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50679001, 50979004)the Fundation from State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology
文摘Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state,and the flow is frequently unsteady and turbulent.The Reynolds-Averaged Navier-Stokes（RANS）approach has been popular for turbulent flow computations.The most widely used ones,such as the standard k-εmodel,have well-recognized deficiencies when treating time dependent flow field.To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures,conditional averaging is adopted for the Navier-Stokes equation,and one more parameter,based on the filter size,is introduced into the k-εmodel.In the Partially Averaged Navier-Stokes（PANS）model,the filter width is mainly controlled by the ratio of unresolved-to-total kinetic energy1f.This model is assessed in unsteady cavitating flows over a Clark-Y hydrofoil.From the experimental validations regarding the forces,frequencies,cavity visualizations and velocity distributions,the PANS model is shown to improve the predictive capability considerably,in comparison to the standard k-ε model,and also,it is observed the value of1f in the PANS model has substantial influence on the predicting result.As the filter width1f is decreased,the PANS model can effectively reduce the eddy viscosity near the closure region which can significantly influence the capture of the detach cavity,and this model can reproduce the time-averaged velocity quantitatively around the hydrofoil.
文摘A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.
基金Project supported by the National Natural Science Foundation of China (Grant No: 10372061) and the National Defense Key Laboratory on Hydrodynamics
文摘A two-phase mixture model was established to study unsteady cavitating flows. A local compressible system of equations was derived by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for solving the variable-density Navier-Stokes equations of cavitating flow problem was put forward. The numerical results for unsteady characteristics of cavitating flows on a 2D NACA hydrofoil coincide well with experimental data.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172040 and 51306020)
文摘The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model, the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil. The effects of pitching rate on the sub- cavitating and cavitating response of the pitching hydrofoil are also investigated. In particular, we focus on the interactions between cavity inception, growth, and shedding and the vortex flow structures, and their impacts on the hydrofoil performance. The calculations are 2-D and performed by solving the incompressible, multiphase Unsteady Reynolds Averaged Navier Stokes （URANS） equations via the commercial CFD code CFX. The k-co SST （Shear Stress Transport） turbulence model is used along with the transport equation-based cavitation models. The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density. The calculation results are validated with experiments conducted by Ducoin et al. （see Computational and experimental investigation of flow over a transient pitching hydrofoil, Eur J Mech/B Fluids, 2009, 28：728-743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in vari- ous flow regimes including cavitating flow, Eur J Mech B/fluids, 2012, 36： 63-74）. Results are shown for a NACA66 hydro- foil subject to slow （quasi static, t2=6~/s, ＆＊ =0.18） and fast （dynamic, ＆=63~/s, dr＂ =1.89） pitching motions from a =0~ to a =15~. Both subcavitaing （or =8.0） and cavitating （cr=3.0） flows are considered. For subcavitating flow （or=8.0）, low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall, and delay of stall is ob- served with increasing pitching velocity. For cavitating flow （tr=3.0）, small leading edge cavities are observed with the slow pitching case, which significantly modified the vortex dynamics at high angles of attack, leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate. On the other hand, for the fast pitching case at or=3.0, large-scale sheet/cloud cavitation is observed, the cavity behavior is un- steady and has a strong impact on the hydrodynamic response, which leads to high amplitude fluctuations of the hydrodynamic coefficients, as well as significant changes in the stall and post-stall behavior. The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region, which significantly modifies the cavity lengths and shedding frequencies, particularly for the fast pitching case. In general, compared with the experimental visualiza- tions, the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.
文摘Cavitating flows around skewed propellers are investigated numerically by means of the unsteady Reynolds Averaged Navier-Stokes （RANS） Equation method. The standard k - c turbulence and the modified Z-G-B cavitation models are employed. A measured nominal wake is used for the inlet velocity boundary condition. Predicted cavitating evolution processes and tip cavity patterns are compared with experimental observations. In addition, the influence of the skew angles on the cavitation and unsteadiness performances of propellers operating in a non-uniform wake is also studied. Results show that the modified Z-G-B cavitation model performs better to simulate the cavitating flow cases studied in this paper. Comparisons demonstrate that the skewed propeller with a skew angle of 20~ is the best choice for a given stern wake with a assigned thrust and the minimum force fluctuations.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11002089,10832007)the Shanghai Leading Academic Discipline Project (Grant No.B206)
文摘To apply the measurements of model experiment in water tunnel to the actual sailing condition, it is necessary to know accurately the strut effect and its rule. In the present work, the corresponding interferences of one-side strut and two-side strut on the natural cavitating flows around a submerged vehicle in water tunnel were investigated numerically, using the homogeneous equilibrium two-phase model coupled with a natural cavitation model. The numerical simulation results show that the strut types have distinct effects on the hydrodynamic properties. For the same given upstream velocity and downstream pressure, the existence of the strut leads to an increment of natural cavitation number, reduces the low-pressure region and depresses the pressure on the vehicle surface near the sides of strut. In the case of given cavitaiton number, the influences of the two-side strut on the drag and lift coefficients are both enhanced along with the increment of attack angle, however the influence of the one-side strut gradually gets stronger on the drag coefficient but weaker on the lift coefficient contrarily. In addition, based on the present numerical results, a correction method by introducing the sigmoidal logistic function is proposed to eliminate the interference from the foil-shaped strut.
