Unsubmerged cavitating abrasive waterjet(UCAWJ)has been shown to artificially create a submerged environment that produces shear cavitation,which effectively enhances rock-breaking performance.The shear cavitation gen...Unsubmerged cavitating abrasive waterjet(UCAWJ)has been shown to artificially create a submerged environment that produces shear cavitation,which effectively enhances rock-breaking performance.The shear cavitation generation and collapse intensity depend on the pressure difference between the intermediate high-speed abrasive waterjet and the coaxial low-speed waterjet.However,the effect of the pressure of the coaxial low-speed waterjet is pending.For this purpose,the effect of low-speed waterjet pressure on rock-breaking performance at different standoff distances was experimentally investigated,and the effects of erosion time and ruby nozzle diameter on erosion performance were discussed.Finally,the micromorphology of the sandstone was observed at different locations.The results show that increased erosion time and ruby nozzle diameter can significantly improve the rock-breaking performance.At different standoff distances,the mass loss increases first and then decreases with the increase of low-speed waterjet pressure,the maximum mass loss is 10.4 g at a low-speed waterjet pressure of0.09 MPa.The surface morphology of cavitation erosion was measured using a 3D profiler,the increase in both erosion depth and surface roughness indicated a significant increase in the intensity of the shear cavitation collapse.At a low-speed waterjet pressure of 0.18 MPa,the cavitation erosion surface depth can reach 600μm with a roughness of 127μm.展开更多
To improve the rock breaking ability, cavitating waterjet and abrasive waterjet are combined by using a coaxial low-speed waterjet generated around the periphery of a high-speed abrasive waterjet, and a new type of wa...To improve the rock breaking ability, cavitating waterjet and abrasive waterjet are combined by using a coaxial low-speed waterjet generated around the periphery of a high-speed abrasive waterjet, and a new type of waterjet called unsubmerged cavitating abrasive waterjet(UCAWJ) is thus produced. The rock breaking performance of UCAWJ was compared with submerged cavitating abrasive waterjet(SCAWJ)and unsubmerged abrasive waterjet(UAWJ) by impinging sandstone specimens. Moreover, the effects of jet pressure, standoff distance, abrasive flow rate and concentration were studied by evaluating the specific energy consumption, and the area, depth, and mass loss of the eroded specimen. The results show that the artificially generated submerged environment in UCAWJ is able to enhance the rock breaking performance under the same operating parameters. Furthermore, the rock breaking performance of UCAWJ is much better at higher jet pressures and smaller standoff distances when compared with UAWJ. The greatest rock breaking ability of UCAWJ appears at jet pressure of 50 MPa and standoff distance of 32 mm, with the mass loss of sandstone increased by 370.6% and the energy dissipation decreased by 75.8%. In addition, under the experimental conditions the optimal abrasive flow rate and concentration are 76.5 m L/min and 3%, respectively.展开更多
Morphology of hydraulic fracture surface has significant effects on oil and gas flow,proppant migration and fracture closure,which plays an important role in oil and gas fracturing stimulation.In this paper,we analyze...Morphology of hydraulic fracture surface has significant effects on oil and gas flow,proppant migration and fracture closure,which plays an important role in oil and gas fracturing stimulation.In this paper,we analyzed the fracture surface characteristics induced by supercritical carbon dioxide(SC-CO_(2))and water in open-hole and perforation completion conditions under triaxial stresses.A simple calculation method was proposed to quantitatively analyze the fracture surface area and roughness in macro-level based on three-dimensional(3D)scanning data.In micro-level,scanning electron micrograph(SEM)was used to analyze the features of fracture surface.The results showed that the surface area of the induced fracture increases with perforation angle for both SC-CO_(2)and water fracturing,and the surface area of SC-CO_(2)-induced fracture is 6.49%e58.57%larger than that of water-induced fracture.The fractal dimension and surface roughness of water-induced fractures increase with the increase in perforation angle,while those of SC-CO_(2)-induced fractures decrease with the increasing perforation angle.A considerable number of microcracks and particle peeling pits can be observed on SC-CO_(2)-induced fracture surface while there are more flat particle surfaces in water-induced fracture surface through SEM images,indicating that fractures tend to propagate along the boundary of the particle for SC-CO_(2)fracturing while water-induced fractures prefer to cut through particles.These findings are of great significance for analyzing fracture mechanism and evaluating fracturing stimulation performance.展开更多
Cavity flow oscillations in the axisymmetric cavity are critical to the operating efficiency of self-excited pulsed waterjets,which are widely employed in many practical applications.In this study,the behaviors of a t...Cavity flow oscillations in the axisymmetric cavity are critical to the operating efficiency of self-excited pulsed waterjets,which are widely employed in many practical applications.In this study,the behaviors of a turbulent flow in axisymmetric cavities causing cavity flow oscillations are investigated based on wall pressure characteristics.Experiments are performed using four Helmholtz nozzles with varying length-to-radius ratios at flow velocities of 20–80 m/s.Three orders of hydrodynamic modes in axisymmetric cavity are obtained through the spectral analysis of wall pressure.Based on the experimental results,the empirical coefficient of Rossiter’s formula is modified,and the values of the parameter phase lag and the ratio of convection velocity to free stream velocity are obtained as 0.061 and 0.511,respectively.In addition,the spectral peak with a relatively constant frequency shows that the flow-acoustic resonance is excited significantly.A modified model is introduced based on the fluidic networks to predict the lockon frequency.The results obtained can provide a basis for the structural optimization of the nozzle to improve the performance of self-excited pulsed waterjets.展开更多
The current research on self-resonating cavitating waterjet（SRCW） mainly focuses on the generation mechanism and structure optimization.Researches relating to the influences of disturbances at nozzle inlet on the ch...The current research on self-resonating cavitating waterjet（SRCW） mainly focuses on the generation mechanism and structure optimization.Researches relating to the influences of disturbances at nozzle inlet on the characteristics of the jet are rarely available.In order to further improve the performance of SRCW,effects of area discontinuity（enlargement and contraction） are experimentally investigated using three organ-pipe nozzles.Axial pressure oscillation peak and amplitude as well as aggressive erosion intensity of the jet are used to evaluate the effects.The results reveal that area enlargement and contraction affect the peak differently,depending on the inlet pressure,nozzle geometry,and standoff distance;while area contraction always improves the amplitude regardless of these factors.At inlet pressures of 10 MPa and 20 MPa,area discontinuity improves the peak at almost all the testing standoff distances,while this only happens at smaller standoff distances with the inlet pressure increased to 30 MPa.The capability of area discontinuity for improving the amplitude is enhancing with increasing inlet pressure.Moreover,the cavitation erosion ability of the jet can be largely enhanced around the optimum standoff distance,depending on the type of area discontinuity and nozzle geometry.A preliminary analysis of the influence of area discontinuity on the disturbance waves in the flow is also performed.The proposed research provides a new method for effectively enhancing the performance of SRCW.展开更多
The exploitation of shale gas is promising due to depletion of the conventional energy and intensification of the greenhouse effect.In this paper,we proposed a heat-fluid-solid coupling damage model of supercritical C...The exploitation of shale gas is promising due to depletion of the conventional energy and intensification of the greenhouse effect.In this paper,we proposed a heat-fluid-solid coupling damage model of supercritical CO_(2)(SC-CO_(2))compound fracturing which is expected to be an efficient and environmentally friendly way to develop shale gas.The coupling model is solved by the finite element method,and the results are in good agreement with the analytical solutions and fracturing experiments.Based on this model,the fracture propagation characteristics at the two stages of compound fracturing are studied and the influence of pressurization rate,in situ stress,bedding angle,and other factors are considered.The results show that at the SC-CO_(2)fracturing stage,a lower pressurization rate is conducive to formation of the branches around main fractures,while a higher pressurization rate inhibits formation of the branches around main fractures and promotes formation of the main fractures.Both bedding and in situ stress play a dominant role in the fracture propagation.When the in situ stress ratio(δ_(x)/δ_(y))is 1,the presence of bedding can reduce the initiation pressure and failure pressure.Nevertheless,it will cause the fracture to propagate along the bedding direction,reducing the fracture complexity.In rocks without bedding,hydraulic fracturing has the lengthening and widening effects for SC-CO_(2)induced fracture.In shale,fractures induced at the hydraulic fracturing stage are more likely to be dominated by in situ stresses and have a shorter reorientation radius.Therefore,fracture branches propagating along the maximum principal stress direction may be generated around the main fractures induced by SC-CO_(2)at the hydraulic fracturing stage.When the branches converge with the main fractures,fracture zones are easily formed,and thus the fracture complexity and damage area can be significantly increased.The results are instructive for the design and application of SC-CO_(2)compound fracturing.展开更多
The use of mechanical drilling in accessing energy resources stored in deep and hard rock formations is becoming increasingly challenging.Thus,laser irradiation has emerged as a novel drilling method with considerable...The use of mechanical drilling in accessing energy resources stored in deep and hard rock formations is becoming increasingly challenging.Thus,laser irradiation has emerged as a novel drilling method with considerable in this context.This study examines the variation of rock fracture length,fracture tortuosity,hole size,and rock breaking efficiency for a different number of holes and laser power,based on the constant total energy of laser irradiation.As indicated by the results,increasing the laser power increases the laser intensity,which helps increase the hole diameter and depth.Moreover,for the same laser power,increasing the number of irradiated holes reduces the laser energy absorbed by each hole,which is not conducive to increasing the hole depth.As the number of holes increases,the mass loss of the rock also increases,while both specific energy(SE)and modified specific energy(MSE)decrease.When the number of holes remains the same,the mass of the shale removed by low power is less than that removed by high power,while SE and MSE have an inverse relation with power.Therefore,high laser power and multiple-hole irradiation are more conducive to rock breaking.Besides,the fracture length and fracture tortuosity of the rock irradiated by the low laser power will increase first and then decrease with the increase in the number of holes,and reach the peak value when the irradiation takes place through three holes.When a high-power laser irradiates the rock,the fracture length and tortuosity will increase with the increase in the number of irradiation holes.This is because a rock irradiated by low power dissipates more energy,with the result that the energy absorbed by the sample with four irradiation holes is not enough to break the rock quickly.This study is expected to provide some guidance to break rock for drilling deep reservoirs and hard rock formations using laser irradiation.展开更多
A slug flow model considering the dispersed bubbles entrained from the tail of Taylor bubble(TB) and recoalesced with the successive TB was proposed. Experiment was conducted to test the validity of this model by usin...A slug flow model considering the dispersed bubbles entrained from the tail of Taylor bubble(TB) and recoalesced with the successive TB was proposed. Experiment was conducted to test the validity of this model by using a high-speed camcorder and particle image velocimetry(PIV). It was found that the model was valid for predicting the characteristics of slug flow in airlift pump within average error of 14%. Moreover, large pipe diameter was found to accelerate the rise velocity of TB and decreases void fraction in liquid slug by a small margin.展开更多
To investigate fracture generation and strain variation during SC-CO_(2)(supercritical carbon dioxide)jet fracturing,the model of induced strain is established and the experiments are comprehensively studied.The influ...To investigate fracture generation and strain variation during SC-CO_(2)(supercritical carbon dioxide)jet fracturing,the model of induced strain is established and the experiments are comprehensively studied.The influence factors are comprehensively explored,such as jet pressure,ambient pressure,etc.With the increasing jet pressure,the fracture morphology changes from parallel cracks to oblique cracks.Both the mass loss of specimen and CO_(2) absorption increase significantly,and the growth rate and minimum value of strain also rise exponentially.Under a high ambient pressure of 8.0 MPa,the main fractures mostly propagated from the surface to the bottom surface of the specimen.The maximum strain and the stable duration under higher ambient pressure are 1.5 times and 10 times,respectively,of the case under the ambient pressure of 5.0 MPa.The comparison shows that the optimal jet distance is 5-7 times the nozzle diameter,resulting in massive mass loss,large CO_(2)absorption,and peak strain.Moreover,the nonlinear variation of strain curve during jet pressurization is related to the type of rock and ambient pressure.These studies clearly show the relationship between the fracture morphology and induced strain,which are crucial for SC-CO_(2)fracturing in shale gas reservoirs.展开更多
Experiments were conducted to investigate the flow characteristics in the riser pipe and the suction pipe of airlift pump at a series of air flow rates and submergence ratios by using a high speed camcorder and a Lase...Experiments were conducted to investigate the flow characteristics in the riser pipe and the suction pipe of airlift pump at a series of air flow rates and submergence ratios by using a high speed camcorder and a Laser Doppler Velocimetvy system （LDV）. A modified model was developed to predict the performance of airlift pump operating in gas-liquid two-phase flow, The results show that an unstable flow structure composed by a water falling film, a bubbly mixture, a water ascending film appearing alternately in riser pipe dominates the performance of airlift pump at large air flow rates. The bubbly mixture with a strongest capacity for pumping water first increases to its maximum and then slightly decreases. In suction pipe, the average velocity shows a flat profile and increases with increasing submergence ratio. Moreover, the predicted results of modified model are in good agreement with the experimental data in a margin of ± 12%.展开更多
Thermally-induced changes in the fracture properties of geological reservoir rocks can influence their stability,transport characteristics,and performance related to various deep subsurface energy projects.The modifie...Thermally-induced changes in the fracture properties of geological reservoir rocks can influence their stability,transport characteristics,and performance related to various deep subsurface energy projects.The modified maximum tangential stress(MMTS)criterion is a classical theory for predicting the fracture instability of rocks.However,there is a lack of research on the accuracy of MMTS theory when rocks are subjected to different temperatures.In this study,mechanical theoretical analysis and failure and fracture mechanics experiments of granite under the influence of temperatures ranging from 20℃to 600℃are carried out.The results showed that the theoretical estimated value of MMTS differs significantly from the experimental data at 20℃-600℃.The Keff/KIC ratio is less than the experimental test value due to the critical crack growth radius(rc)estimated by the conventional method being larger than the critical crack growth radius(rce)derived from the experimental data.Varied temperatures affect the fracture process zone size of fine-grained,compact granite,and the MMTS theoretical estimation results.Therefore,it is essential to modify the critical crack growth radius for MMTS theory to accurately predict the fracture characteristics of thermally damaged rocks.In addition,the variation of the rock’s me-chanical properties with temperature and its causes are obtained.Between 20℃and 600℃,the mode-Ⅰ,mode-Ⅱ,and mixed-mode(a-30℃and 45℃)fracture toughness and Brazilian splitting strength of the granite decrease by 80%and 73%,respectively.When the rock is heated above 400℃,its deterioration is mainly caused by a widening of its original cracks.展开更多
The tip-leakage vortex(TLV)cavitation is a challenging issue for a variety of axial hydraulic turbines and pumps from both technical and scientific viewpoints.The flow characteristics of the TLV cavitation were widely...The tip-leakage vortex(TLV)cavitation is a challenging issue for a variety of axial hydraulic turbines and pumps from both technical and scientific viewpoints.The flow characteristics of the TLV cavitation were widely studied in the past decades,but the knowledge about the tip-leakage cavitating flow is still limited.The present paper reviews the progresses in the researches of the TLV cavitation,including the numerical methods for the TLV cavitation,the flow characteristics of the TLV,the influences of the TLV cavitation on the local flow field and the control strategies of the TLV cavitation.It is indicated that the non-condensable gas may play an important role in the development of the TLV cavitation,and this fact should be considered during a careful simulation of the TLV cavitation.It is also suggested that the development of the TLV cavitation will significantly influence the distributions of the vorticity and the turbulence kinetic energy.Due to the complexity of the TLV cavitation,it is still an open question how to suppress the TLV cavitation in a simple but effective way.Finally,based on these understandings,some advanced topics for the future work are suggested to further promote the study of the TLV cavitation,for a deeper knowledge about the TLV cavitation.展开更多
In this paper, the turbulent attached cavitating flow around a Clark-Y hydrofoil is investigated by the large eddy simula- tion （LES） method coupled with a homogeneous cavitation model. The predicted lift coefficien...In this paper, the turbulent attached cavitating flow around a Clark-Y hydrofoil is investigated by the large eddy simula- tion （LES） method coupled with a homogeneous cavitation model. The predicted lift coefficient and the cavity volume show a distinctly quasi-periodic process with cavitation shedding and the results agree fairly well with the available experimental data. The present simulation accurately captures the main features of the unsteady cavitation transient behavior including the attached cavity growth, the sheet/cloud cavitation transition and the cloud cavitation collapse. The vortex shedding structure from a hydrofoil cavitating wake is identified by the Q- criterion, which implies that the large scale structures might slide and roll down along the suction side of the hydrofoil while being further developed at the downstream. Further analysis demonstrates that the turbulence level of the flow is clearly related to the cavitation and the turbulence velocity fluctuation is much influenced by the cavity shedding.展开更多
In the present paper, the Vortex Identified Zwart-Gerber-Belamri（VIZGB） cavitation model coupled with the SST-CC turbulence model is used to investigate the unsteady tip-leakage cavitating flow induced by a NACA0009...In the present paper, the Vortex Identified Zwart-Gerber-Belamri（VIZGB） cavitation model coupled with the SST-CC turbulence model is used to investigate the unsteady tip-leakage cavitating flow induced by a NACA0009 hydrofoil. A qualitative comparison between the numerical and experimental results is made. In order to quantitatively evaluate the reliability of the numerical data, the verification and validation（V＆V） procedures are used in the present paper. Errors of numerical results are estimated with seven error estimators based on the Richardson extrapolation method. It is shown that though a strict validation cannot be achieved, a reasonable prediction of the gross characteristics of the tip-leakage cavitating flow can be obtained. Based on the numerical results, the influence of the cavitation on the tip-leakage vortex（TLV） is discussed, which indicates that the cavitation accelerates the fusion of the TLV and the tip-separation vortex（TSV）. Moreover, the trajectory of the TLV, when the cavitation occurs, is close to the side wall.展开更多
In this paper, we investigate the verification and validation（V＆V） procedures for the URANS simulations of the turbulent cavitating flow around a Clark-Y hydrofoil. The main focus is on the feasibility of various R...In this paper, we investigate the verification and validation（V＆V） procedures for the URANS simulations of the turbulent cavitating flow around a Clark-Y hydrofoil. The main focus is on the feasibility of various Richardson extrapolation-based uncertainty estimators in the cavitating flow simulation. The unsteady cavitating flow is simulated by a density corrected model（DCM） coupled with the Zwart cavitation model. The estimated uncertainty is used to evaluate the applicability of various uncertainty estimation methods for the cavitating flow simulation. It is shown that the preferred uncertainty estimators include the modified Factor of Safety（FS1）, the Factor of Safety（FS） and the Grid Convergence Index（GCI）. The distribution of the area without achieving the validation at the U v level shows a strong relationship with the cavitation. Further analysis indicates that the predicted velocity distributions, the transient cavitation patterns and the effects of the vortex stretching are highly influenced by the mesh resolution.展开更多
A series of large-scale molecular dynamics(MD) simulations has been performed to study the effects of grain size and ligament diameter on the mechanical properties of nanocrystalline nanoporous gold. Such simulations ...A series of large-scale molecular dynamics(MD) simulations has been performed to study the effects of grain size and ligament diameter on the mechanical properties of nanocrystalline nanoporous gold. Such simulations indicate that the principal deformation mechanism is a combination of grain boundary sliding, grain rotation and dislocation movement. The results of uniaxial tensile tests reveal the presence of a reverse Hall-Petch relation between strength and nominal grain size, rather than the conventional Hall-Petch relationship in the present range of nominal grain size(7.9–52.7 nm). An increase of flow stress may possibly attribute to the lower total proportion of grain boundary sliding and grain rotation in the deformation of samples with larger grain size. The Young's modulus shows a linear relation with the reciprocal of nominal grain size, which depends largely on the volume fraction of grain boundaries and thus decreasing grain size leads to relatively lower Young's modulus. MD simulations on samples with ligament diameter ranging from 4.07 to 8.10 nm are also carried out and results show that the increasing ligament diameter resulted in decreased flow stress and increased Young's modulus.展开更多
Auxetic metastructures have attracted tremendous attention because of their robust multifunctional properties and promising potential industrial applications.This paper studies the in-plane mechanical behaviors of a c...Auxetic metastructures have attracted tremendous attention because of their robust multifunctional properties and promising potential industrial applications.This paper studies the in-plane mechanical behaviors of a chiral S-shaped metastructure subjected to tensile loading in both X-direction and Y-direction and wave propagation properties using the finite element(FE)method.The relationships between structural parameters and elastic behaviors are also discussed.The results indicate that the orientation of chiral S-shaped metastructure under tensile loading in the X-direction exhibits higher auxeticity and stiffness.Then,the band structures and the edge modes of each band gap of the chiral S-shaped metastructure are explored,and the relations between band gap properties and structural parameters are also systematically analyzed.Moreover,we explore the wave mitigation of the chiral S-shaped metastructures by regulating the structural parameters.Finally,the transmission properties of the finite chiral S-shaped periodic metastructures are studied to confirm the results of band gap simulation.This study promotes the engineering application of vibration isolation of chiral structures based on the band gap theory.展开更多
Annular jet pumps that are used in hydraulic machinery have a very simple structure but very complex internal flow fields. Large eddy simulations were used to study the coherent structures in the turbulent flows in an...Annular jet pumps that are used in hydraulic machinery have a very simple structure but very complex internal flow fields. Large eddy simulations were used to study the coherent structures in the turbulent flows in annular jet pumps with various area ratios,m. The distribution, movement and evolution of the coherent structure in the annular jet pumps are described based on vorticity,pressure and Q criteria. All the criteria demonstrate that the vortexes are mainly distributed in the recirculation region and in the mixing and the boundary layers, which have large velocity gradients. The various characteristics of the coherent structures are shown by the different criteria with the vorticity criterion describing the distribution, movement and evolution of the vortexes,the pressure criterion describing the movement and the Q criterion describing the vortex movement and evolution. The vorticity variation in the spanwise direction is larger than the variation in the streamwise direction; however, the streamwise vortex is the main mechanism driving the entrainment of the secondary flow and the mixing. The annular jet pump with m=3.33 had a higher vortex shedding frequency(about 1000 Hz) than that with m=1.72(313–417 Hz). The azimuthal instability is the main reason for the generation of the streamwise vortex from the spanwise vortex. The vortex structures in the recirculation region are very strong,but small and disordered with no periodic vortex rings.展开更多
This paper studies the unsteady three-dimensional cavitating turbulent flow in a jet pump.Specifically,thefocus is on the unstable limited operation stage,and both the computational and experimental methods are used.I...This paper studies the unsteady three-dimensional cavitating turbulent flow in a jet pump.Specifically,thefocus is on the unstable limited operation stage,and both the computational and experimental methods are used.In the experiments,the distribution of the wall pressure,as well as the evolution of cavitation over time,are obtained for a jet pump.Computation is carried out using the large eddy simulation,combined with a mass transfer cavitation model.The numerical results are compared with the experimental results,including the fundamental performances(the pressure ratio h and the efficiencyη),as well as the wall pressure distribution.Both the experimental and computational results indicate that the evolution of the cavitation over time in a jet pump is a quasi-periodic process during the unstable limited operation stage.The annular vortex cavitation inception,development and collapse predicted by the large eddy simulation agree fairly well with the experimental observations.Furthermore,the relationship between the cavitation and the vortex structure is discussed based on the numerical results,and it is shown that the development of the vortex structures in the jet pump is closely related to the evolution of the cavitation.The cavitation-vortex interaction is thoroughly analyzed based on the vorticity transport equation.This analysis reveals that the cavitation in a jet pump dramatically influences the distribution and the production of the vorticity.The process of the annular cavitation inception,development,and collapse involves a significant increase of the vorticity.展开更多
In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model（FBDCM）, a turbulence model and the Zwart-Gerber-Belamri（...In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model（FBDCM）, a turbulence model and the Zwart-Gerber-Belamri（ZGB） cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures（LCSs）. Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet,the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage Ⅲ, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.展开更多
基金financially supported by the National Natural Science Foundation of China (Nos.52175245 and 52274093)the Natural Science Foundation of Hubei Province (No.2021CFB462)the Knowledge Innovation Special Project of Wuhan (whkxjsj007)。
文摘Unsubmerged cavitating abrasive waterjet(UCAWJ)has been shown to artificially create a submerged environment that produces shear cavitation,which effectively enhances rock-breaking performance.The shear cavitation generation and collapse intensity depend on the pressure difference between the intermediate high-speed abrasive waterjet and the coaxial low-speed waterjet.However,the effect of the pressure of the coaxial low-speed waterjet is pending.For this purpose,the effect of low-speed waterjet pressure on rock-breaking performance at different standoff distances was experimentally investigated,and the effects of erosion time and ruby nozzle diameter on erosion performance were discussed.Finally,the micromorphology of the sandstone was observed at different locations.The results show that increased erosion time and ruby nozzle diameter can significantly improve the rock-breaking performance.At different standoff distances,the mass loss increases first and then decreases with the increase of low-speed waterjet pressure,the maximum mass loss is 10.4 g at a low-speed waterjet pressure of0.09 MPa.The surface morphology of cavitation erosion was measured using a 3D profiler,the increase in both erosion depth and surface roughness indicated a significant increase in the intensity of the shear cavitation collapse.At a low-speed waterjet pressure of 0.18 MPa,the cavitation erosion surface depth can reach 600μm with a roughness of 127μm.
基金financially supported by the National Natural Science Foundation of China (Nos. 52175245 and 52274093)the Natural Science Foundation of Hubei Province (No. 2021CFB462)。
文摘To improve the rock breaking ability, cavitating waterjet and abrasive waterjet are combined by using a coaxial low-speed waterjet generated around the periphery of a high-speed abrasive waterjet, and a new type of waterjet called unsubmerged cavitating abrasive waterjet(UCAWJ) is thus produced. The rock breaking performance of UCAWJ was compared with submerged cavitating abrasive waterjet(SCAWJ)and unsubmerged abrasive waterjet(UAWJ) by impinging sandstone specimens. Moreover, the effects of jet pressure, standoff distance, abrasive flow rate and concentration were studied by evaluating the specific energy consumption, and the area, depth, and mass loss of the eroded specimen. The results show that the artificially generated submerged environment in UCAWJ is able to enhance the rock breaking performance under the same operating parameters. Furthermore, the rock breaking performance of UCAWJ is much better at higher jet pressures and smaller standoff distances when compared with UAWJ. The greatest rock breaking ability of UCAWJ appears at jet pressure of 50 MPa and standoff distance of 32 mm, with the mass loss of sandstone increased by 370.6% and the energy dissipation decreased by 75.8%. In addition, under the experimental conditions the optimal abrasive flow rate and concentration are 76.5 m L/min and 3%, respectively.
基金National Natural Science Foundation of China(Grant No.51804318)the China Postdoctoral Science Foundation Founded Project(Grant No.2019M650963)National Key Basic Research and Development Program of China(Grant No.2014CB239203).
文摘Morphology of hydraulic fracture surface has significant effects on oil and gas flow,proppant migration and fracture closure,which plays an important role in oil and gas fracturing stimulation.In this paper,we analyzed the fracture surface characteristics induced by supercritical carbon dioxide(SC-CO_(2))and water in open-hole and perforation completion conditions under triaxial stresses.A simple calculation method was proposed to quantitatively analyze the fracture surface area and roughness in macro-level based on three-dimensional(3D)scanning data.In micro-level,scanning electron micrograph(SEM)was used to analyze the features of fracture surface.The results showed that the surface area of the induced fracture increases with perforation angle for both SC-CO_(2)and water fracturing,and the surface area of SC-CO_(2)-induced fracture is 6.49%e58.57%larger than that of water-induced fracture.The fractal dimension and surface roughness of water-induced fractures increase with the increase in perforation angle,while those of SC-CO_(2)-induced fractures decrease with the increasing perforation angle.A considerable number of microcracks and particle peeling pits can be observed on SC-CO_(2)-induced fracture surface while there are more flat particle surfaces in water-induced fracture surface through SEM images,indicating that fractures tend to propagate along the boundary of the particle for SC-CO_(2)fracturing while water-induced fractures prefer to cut through particles.These findings are of great significance for analyzing fracture mechanism and evaluating fracturing stimulation performance.
基金National Natural Science Foundation of China(Grant Nos.52175245,51805188)Fundamental Research Funds for the Central Universities of China(Grant No.2042020kf0001)National Key Research and Development Program of China(Grant No.2018YFC0808401).
文摘Cavity flow oscillations in the axisymmetric cavity are critical to the operating efficiency of self-excited pulsed waterjets,which are widely employed in many practical applications.In this study,the behaviors of a turbulent flow in axisymmetric cavities causing cavity flow oscillations are investigated based on wall pressure characteristics.Experiments are performed using four Helmholtz nozzles with varying length-to-radius ratios at flow velocities of 20–80 m/s.Three orders of hydrodynamic modes in axisymmetric cavity are obtained through the spectral analysis of wall pressure.Based on the experimental results,the empirical coefficient of Rossiter’s formula is modified,and the values of the parameter phase lag and the ratio of convection velocity to free stream velocity are obtained as 0.061 and 0.511,respectively.In addition,the spectral peak with a relatively constant frequency shows that the flow-acoustic resonance is excited significantly.A modified model is introduced based on the fluidic networks to predict the lockon frequency.The results obtained can provide a basis for the structural optimization of the nozzle to improve the performance of self-excited pulsed waterjets.
基金Supported by National Key Basic Research Program of China(973 Program,Grant No.2014CB239203)National Natural Science Foundation of China(Grant No.51474158)China Scholarship Council(Grant No.201406270047)
文摘The current research on self-resonating cavitating waterjet（SRCW） mainly focuses on the generation mechanism and structure optimization.Researches relating to the influences of disturbances at nozzle inlet on the characteristics of the jet are rarely available.In order to further improve the performance of SRCW,effects of area discontinuity（enlargement and contraction） are experimentally investigated using three organ-pipe nozzles.Axial pressure oscillation peak and amplitude as well as aggressive erosion intensity of the jet are used to evaluate the effects.The results reveal that area enlargement and contraction affect the peak differently,depending on the inlet pressure,nozzle geometry,and standoff distance;while area contraction always improves the amplitude regardless of these factors.At inlet pressures of 10 MPa and 20 MPa,area discontinuity improves the peak at almost all the testing standoff distances,while this only happens at smaller standoff distances with the inlet pressure increased to 30 MPa.The capability of area discontinuity for improving the amplitude is enhancing with increasing inlet pressure.Moreover,the cavitation erosion ability of the jet can be largely enhanced around the optimum standoff distance,depending on the type of area discontinuity and nozzle geometry.A preliminary analysis of the influence of area discontinuity on the disturbance waves in the flow is also performed.The proposed research provides a new method for effectively enhancing the performance of SRCW.
基金the funding support from the National Natural Science Foundation of China(Nos.52274093 and 52004236).
文摘The exploitation of shale gas is promising due to depletion of the conventional energy and intensification of the greenhouse effect.In this paper,we proposed a heat-fluid-solid coupling damage model of supercritical CO_(2)(SC-CO_(2))compound fracturing which is expected to be an efficient and environmentally friendly way to develop shale gas.The coupling model is solved by the finite element method,and the results are in good agreement with the analytical solutions and fracturing experiments.Based on this model,the fracture propagation characteristics at the two stages of compound fracturing are studied and the influence of pressurization rate,in situ stress,bedding angle,and other factors are considered.The results show that at the SC-CO_(2)fracturing stage,a lower pressurization rate is conducive to formation of the branches around main fractures,while a higher pressurization rate inhibits formation of the branches around main fractures and promotes formation of the main fractures.Both bedding and in situ stress play a dominant role in the fracture propagation.When the in situ stress ratio(δ_(x)/δ_(y))is 1,the presence of bedding can reduce the initiation pressure and failure pressure.Nevertheless,it will cause the fracture to propagate along the bedding direction,reducing the fracture complexity.In rocks without bedding,hydraulic fracturing has the lengthening and widening effects for SC-CO_(2)induced fracture.In shale,fractures induced at the hydraulic fracturing stage are more likely to be dominated by in situ stresses and have a shorter reorientation radius.Therefore,fracture branches propagating along the maximum principal stress direction may be generated around the main fractures induced by SC-CO_(2)at the hydraulic fracturing stage.When the branches converge with the main fractures,fracture zones are easily formed,and thus the fracture complexity and damage area can be significantly increased.The results are instructive for the design and application of SC-CO_(2)compound fracturing.
基金supported by the National Natural Science Foundation of China(No.52174004 and No.51804318)the National Key Research and Development Program of China(No.2018YFC0808401)
文摘The use of mechanical drilling in accessing energy resources stored in deep and hard rock formations is becoming increasingly challenging.Thus,laser irradiation has emerged as a novel drilling method with considerable in this context.This study examines the variation of rock fracture length,fracture tortuosity,hole size,and rock breaking efficiency for a different number of holes and laser power,based on the constant total energy of laser irradiation.As indicated by the results,increasing the laser power increases the laser intensity,which helps increase the hole diameter and depth.Moreover,for the same laser power,increasing the number of irradiated holes reduces the laser energy absorbed by each hole,which is not conducive to increasing the hole depth.As the number of holes increases,the mass loss of the rock also increases,while both specific energy(SE)and modified specific energy(MSE)decrease.When the number of holes remains the same,the mass of the shale removed by low power is less than that removed by high power,while SE and MSE have an inverse relation with power.Therefore,high laser power and multiple-hole irradiation are more conducive to rock breaking.Besides,the fracture length and fracture tortuosity of the rock irradiated by the low laser power will increase first and then decrease with the increase in the number of holes,and reach the peak value when the irradiation takes place through three holes.When a high-power laser irradiates the rock,the fracture length and tortuosity will increase with the increase in the number of irradiation holes.This is because a rock irradiated by low power dissipates more energy,with the result that the energy absorbed by the sample with four irradiation holes is not enough to break the rock quickly.This study is expected to provide some guidance to break rock for drilling deep reservoirs and hard rock formations using laser irradiation.
基金Supported by the National Key Basic Research Development Program of China(2014CB239200)the National Natural Science Foundation of China(51574173,51705372)+1 种基金the Hubei Provincial Natural Science Foundation(2015CFA154)Jiangsu Provincial Natural Science Foundation of China(No.BK20170411)
文摘A slug flow model considering the dispersed bubbles entrained from the tail of Taylor bubble(TB) and recoalesced with the successive TB was proposed. Experiment was conducted to test the validity of this model by using a high-speed camcorder and particle image velocimetry(PIV). It was found that the model was valid for predicting the characteristics of slug flow in airlift pump within average error of 14%. Moreover, large pipe diameter was found to accelerate the rise velocity of TB and decreases void fraction in liquid slug by a small margin.
基金the National Natural Science Foundation of China(Grant No.52004236)Sichuan Science and Technology Program(Grant No.2021JDRC0114)+3 种基金the Starting Project of SWPU(Grant No.2019QHZ009)the China Postdoctoral Science Foundation(Grant No.2020M673285)the Open Project Program of Key Laboratory of Groundwater Resources and Environment(Jilin University),Ministry of Education(Grant No.202005009KF)the National Key Basic Research Program of China(Grant No.2014CB239203)for the financial support of this work。
文摘To investigate fracture generation and strain variation during SC-CO_(2)(supercritical carbon dioxide)jet fracturing,the model of induced strain is established and the experiments are comprehensively studied.The influence factors are comprehensively explored,such as jet pressure,ambient pressure,etc.With the increasing jet pressure,the fracture morphology changes from parallel cracks to oblique cracks.Both the mass loss of specimen and CO_(2) absorption increase significantly,and the growth rate and minimum value of strain also rise exponentially.Under a high ambient pressure of 8.0 MPa,the main fractures mostly propagated from the surface to the bottom surface of the specimen.The maximum strain and the stable duration under higher ambient pressure are 1.5 times and 10 times,respectively,of the case under the ambient pressure of 5.0 MPa.The comparison shows that the optimal jet distance is 5-7 times the nozzle diameter,resulting in massive mass loss,large CO_(2)absorption,and peak strain.Moreover,the nonlinear variation of strain curve during jet pressurization is related to the type of rock and ambient pressure.These studies clearly show the relationship between the fracture morphology and induced strain,which are crucial for SC-CO_(2)fracturing in shale gas reservoirs.
基金Supported by the National Key Basic Research Development Program of China(2014CB239200)the National Natural Science Foundation of China(51474158)
文摘Experiments were conducted to investigate the flow characteristics in the riser pipe and the suction pipe of airlift pump at a series of air flow rates and submergence ratios by using a high speed camcorder and a Laser Doppler Velocimetvy system （LDV）. A modified model was developed to predict the performance of airlift pump operating in gas-liquid two-phase flow, The results show that an unstable flow structure composed by a water falling film, a bubbly mixture, a water ascending film appearing alternately in riser pipe dominates the performance of airlift pump at large air flow rates. The bubbly mixture with a strongest capacity for pumping water first increases to its maximum and then slightly decreases. In suction pipe, the average velocity shows a flat profile and increases with increasing submergence ratio. Moreover, the predicted results of modified model are in good agreement with the experimental data in a margin of ± 12%.
基金supported by the open fund of the Key Laboratory of Deep Earth Science and Engineering(Sichuan University),the Ministry of Education(Grant No.DESEYU202206)the Young Elite Scientists Sponsorship Program by CAST of China(Grant No.2021QNRC001)the Natural Science Foundation of Sichuan Province,China(Grant No.52104143),which are greatly appreciated。
文摘Thermally-induced changes in the fracture properties of geological reservoir rocks can influence their stability,transport characteristics,and performance related to various deep subsurface energy projects.The modified maximum tangential stress(MMTS)criterion is a classical theory for predicting the fracture instability of rocks.However,there is a lack of research on the accuracy of MMTS theory when rocks are subjected to different temperatures.In this study,mechanical theoretical analysis and failure and fracture mechanics experiments of granite under the influence of temperatures ranging from 20℃to 600℃are carried out.The results showed that the theoretical estimated value of MMTS differs significantly from the experimental data at 20℃-600℃.The Keff/KIC ratio is less than the experimental test value due to the critical crack growth radius(rc)estimated by the conventional method being larger than the critical crack growth radius(rce)derived from the experimental data.Varied temperatures affect the fracture process zone size of fine-grained,compact granite,and the MMTS theoretical estimation results.Therefore,it is essential to modify the critical crack growth radius for MMTS theory to accurately predict the fracture characteristics of thermally damaged rocks.In addition,the variation of the rock’s me-chanical properties with temperature and its causes are obtained.Between 20℃and 600℃,the mode-Ⅰ,mode-Ⅱ,and mixed-mode(a-30℃and 45℃)fracture toughness and Brazilian splitting strength of the granite decrease by 80%and 73%,respectively.When the rock is heated above 400℃,its deterioration is mainly caused by a widening of its original cracks.
基金the National Natural Science Foundation of China(Grant Nos.51822903,1772239)the China Postdoctoral Science Foundation(Grant No.2020M682471).
文摘The tip-leakage vortex(TLV)cavitation is a challenging issue for a variety of axial hydraulic turbines and pumps from both technical and scientific viewpoints.The flow characteristics of the TLV cavitation were widely studied in the past decades,but the knowledge about the tip-leakage cavitating flow is still limited.The present paper reviews the progresses in the researches of the TLV cavitation,including the numerical methods for the TLV cavitation,the flow characteristics of the TLV,the influences of the TLV cavitation on the local flow field and the control strategies of the TLV cavitation.It is indicated that the non-condensable gas may play an important role in the development of the TLV cavitation,and this fact should be considered during a careful simulation of the TLV cavitation.It is also suggested that the development of the TLV cavitation will significantly influence the distributions of the vorticity and the turbulence kinetic energy.Due to the complexity of the TLV cavitation,it is still an open question how to suppress the TLV cavitation in a simple but effective way.Finally,based on these understandings,some advanced topics for the future work are suggested to further promote the study of the TLV cavitation,for a deeper knowledge about the TLV cavitation.
基金Project supported by the National Natural Science Foun-dation of China(Grant Nos.51576143,11472197)
文摘In this paper, the turbulent attached cavitating flow around a Clark-Y hydrofoil is investigated by the large eddy simula- tion （LES） method coupled with a homogeneous cavitation model. The predicted lift coefficient and the cavity volume show a distinctly quasi-periodic process with cavitation shedding and the results agree fairly well with the available experimental data. The present simulation accurately captures the main features of the unsteady cavitation transient behavior including the attached cavity growth, the sheet/cloud cavitation transition and the cloud cavitation collapse. The vortex shedding structure from a hydrofoil cavitating wake is identified by the Q- criterion, which implies that the large scale structures might slide and roll down along the suction side of the hydrofoil while being further developed at the downstream. Further analysis demonstrates that the turbulence level of the flow is clearly related to the cavitation and the turbulence velocity fluctuation is much influenced by the cavity shedding.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51576143,11772239 and 91752105)the Science and Technology on Water Jet Propulsion Laboratory(Grant No.61422230101162223002)
文摘In the present paper, the Vortex Identified Zwart-Gerber-Belamri（VIZGB） cavitation model coupled with the SST-CC turbulence model is used to investigate the unsteady tip-leakage cavitating flow induced by a NACA0009 hydrofoil. A qualitative comparison between the numerical and experimental results is made. In order to quantitatively evaluate the reliability of the numerical data, the verification and validation（V＆V） procedures are used in the present paper. Errors of numerical results are estimated with seven error estimators based on the Richardson extrapolation method. It is shown that though a strict validation cannot be achieved, a reasonable prediction of the gross characteristics of the tip-leakage cavitating flow can be obtained. Based on the numerical results, the influence of the cavitation on the tip-leakage vortex（TLV） is discussed, which indicates that the cavitation accelerates the fusion of the TLV and the tip-separation vortex（TSV）. Moreover, the trajectory of the TLV, when the cavitation occurs, is close to the side wall.
基金Project supported by the National Natural Science Foundation of China(Project Nos.51576143,11472197)
文摘In this paper, we investigate the verification and validation（V＆V） procedures for the URANS simulations of the turbulent cavitating flow around a Clark-Y hydrofoil. The main focus is on the feasibility of various Richardson extrapolation-based uncertainty estimators in the cavitating flow simulation. The unsteady cavitating flow is simulated by a density corrected model（DCM） coupled with the Zwart cavitation model. The estimated uncertainty is used to evaluate the applicability of various uncertainty estimation methods for the cavitating flow simulation. It is shown that the preferred uncertainty estimators include the modified Factor of Safety（FS1）, the Factor of Safety（FS） and the Grid Convergence Index（GCI）. The distribution of the area without achieving the validation at the U v level shows a strong relationship with the cavitation. Further analysis indicates that the predicted velocity distributions, the transient cavitation patterns and the effects of the vortex stretching are highly influenced by the mesh resolution.
基金supported by the National Natural Science Foundation of China(Grant Nos.11102140&51575404)
文摘A series of large-scale molecular dynamics(MD) simulations has been performed to study the effects of grain size and ligament diameter on the mechanical properties of nanocrystalline nanoporous gold. Such simulations indicate that the principal deformation mechanism is a combination of grain boundary sliding, grain rotation and dislocation movement. The results of uniaxial tensile tests reveal the presence of a reverse Hall-Petch relation between strength and nominal grain size, rather than the conventional Hall-Petch relationship in the present range of nominal grain size(7.9–52.7 nm). An increase of flow stress may possibly attribute to the lower total proportion of grain boundary sliding and grain rotation in the deformation of samples with larger grain size. The Young's modulus shows a linear relation with the reciprocal of nominal grain size, which depends largely on the volume fraction of grain boundaries and thus decreasing grain size leads to relatively lower Young's modulus. MD simulations on samples with ligament diameter ranging from 4.07 to 8.10 nm are also carried out and results show that the increasing ligament diameter resulted in decreased flow stress and increased Young's modulus.
基金supported by the National Natural Science Foundation of China under the Grant Number of 12072241 and the Fundamental Research Funds for the Central Universities under the Grant Number of 2042022kf0009.
文摘Auxetic metastructures have attracted tremendous attention because of their robust multifunctional properties and promising potential industrial applications.This paper studies the in-plane mechanical behaviors of a chiral S-shaped metastructure subjected to tensile loading in both X-direction and Y-direction and wave propagation properties using the finite element(FE)method.The relationships between structural parameters and elastic behaviors are also discussed.The results indicate that the orientation of chiral S-shaped metastructure under tensile loading in the X-direction exhibits higher auxeticity and stiffness.Then,the band structures and the edge modes of each band gap of the chiral S-shaped metastructure are explored,and the relations between band gap properties and structural parameters are also systematically analyzed.Moreover,we explore the wave mitigation of the chiral S-shaped metastructures by regulating the structural parameters.Finally,the transmission properties of the finite chiral S-shaped periodic metastructures are studied to confirm the results of band gap simulation.This study promotes the engineering application of vibration isolation of chiral structures based on the band gap theory.
基金supported by the National Natural Science Foundation of China(Grant Nos.51179134&11472197)
文摘Annular jet pumps that are used in hydraulic machinery have a very simple structure but very complex internal flow fields. Large eddy simulations were used to study the coherent structures in the turbulent flows in annular jet pumps with various area ratios,m. The distribution, movement and evolution of the coherent structure in the annular jet pumps are described based on vorticity,pressure and Q criteria. All the criteria demonstrate that the vortexes are mainly distributed in the recirculation region and in the mixing and the boundary layers, which have large velocity gradients. The various characteristics of the coherent structures are shown by the different criteria with the vorticity criterion describing the distribution, movement and evolution of the vortexes,the pressure criterion describing the movement and the Q criterion describing the vortex movement and evolution. The vorticity variation in the spanwise direction is larger than the variation in the streamwise direction; however, the streamwise vortex is the main mechanism driving the entrainment of the secondary flow and the mixing. The annular jet pump with m=3.33 had a higher vortex shedding frequency(about 1000 Hz) than that with m=1.72(313–417 Hz). The azimuthal instability is the main reason for the generation of the streamwise vortex from the spanwise vortex. The vortex structures in the recirculation region are very strong,but small and disordered with no periodic vortex rings.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51679169,11472197).
文摘This paper studies the unsteady three-dimensional cavitating turbulent flow in a jet pump.Specifically,thefocus is on the unstable limited operation stage,and both the computational and experimental methods are used.In the experiments,the distribution of the wall pressure,as well as the evolution of cavitation over time,are obtained for a jet pump.Computation is carried out using the large eddy simulation,combined with a mass transfer cavitation model.The numerical results are compared with the experimental results,including the fundamental performances(the pressure ratio h and the efficiencyη),as well as the wall pressure distribution.Both the experimental and computational results indicate that the evolution of the cavitation over time in a jet pump is a quasi-periodic process during the unstable limited operation stage.The annular vortex cavitation inception,development and collapse predicted by the large eddy simulation agree fairly well with the experimental observations.Furthermore,the relationship between the cavitation and the vortex structure is discussed based on the numerical results,and it is shown that the development of the vortex structures in the jet pump is closely related to the evolution of the cavitation.The cavitation-vortex interaction is thoroughly analyzed based on the vorticity transport equation.This analysis reveals that the cavitation in a jet pump dramatically influences the distribution and the production of the vorticity.The process of the annular cavitation inception,development,and collapse involves a significant increase of the vorticity.
基金Project supported by the National Natural Science Foundation of China(Project Nos.11772239,51576143 and91752105)the Outstanding Youth Foundation of Natural Science Foundation of Hubei Province(Grant No.2017CFA048)
文摘In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model（FBDCM）, a turbulence model and the Zwart-Gerber-Belamri（ZGB） cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures（LCSs）. Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet,the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage Ⅲ, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.
