The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF6 b...The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF6 bubble is studied by the numerical method VAS2D. As a validation, the experiments of a SF6 bubble accelerated by a planar shock were performed. The results indicate that, due to the mismatch of acoustic impedance, the way of jet formation in heavy gas bubble with different species is diversified under the same initial condition. With respect to the same bubble, the manner of jet formation is also distinctly different under different shock strengths. The disparities of the acoustic impedance result in different effects of shock focusing in the bubble, and different behaviors of shock wave inside and outside the bubble. The analyses of the wave pattern and the pressure variation indicate that the jet formation is closely associated with the pressure perturbation. Moreover, the analy- sis of the vorticity deposition, and comparisons of circulation and baroclinic torque show that the baroclinic vorticity also contributes to the jet formation. It is concluded that the pres- sure perturbation and baroclinic vorticity deposition are the two dominant factors for the jet formation in shock-heavy gas bubble interaction.展开更多
Effects of Reynolds(Re)number and Schmidt(Sc)number on the flow structures and variable density mixing are numerically investigated through the canonical shock cylindrical bubble interaction.By determining the viscosi...Effects of Reynolds(Re)number and Schmidt(Sc)number on the flow structures and variable density mixing are numerically investigated through the canonical shock cylindrical bubble interaction.By determining the viscosity and diffusivity within a wide range,the controlling parameters,total vortex circulation,and compression rate,are conservative under a broad range of Re and Sc numbers(Re≈10^(3)-10^(5)and Sc≈0.1-5)in the same shock Mach(Ma)number condition(Ma=2.4).As for the Re number effect,the circulation of secondary baroclinic vorticity(SBV),induced by the main vortex centripetal acceleration,is observed to be higher in high Re number and vice versa.Based on the vorticity transport equation decomposition,a growth-inhibition vorticity dynamics balance mechanism is revealed:the vorticity viscous term grows synchronously with baroclinic production to inhibit SBV production in low Re number.By contrast,the viscous term terminates the baroclinic term with a time lag in high Re number,leading to the SBV production.Since the SBV reflects the local stretching enhancement based on the advection-diffusion equation,mixing is influenced by the Sc number in a different behavior if different Re numbers are considered.The time-averaged variable density mixing rate emerges a scaling law with Sc number asχ^(∗)=β·Sc^(−α),where the coefficientβ∼Re−0.2 and the scaling exponentα∼Re−0.385.The understanding of Re number and Sc number effect on variable density mixing provides an opportunity for mixing enhancement from the perspective of designing the viscosity and diffusivity of the fluid mixture.展开更多
The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method （PPM）, in which the viscous and turbulence effects are both conside...The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method （PPM）, in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers （Ma）. The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 （2007） 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.展开更多
Flotation is an efficient pre-treatment technology for oily water.In this work,the interaction process between the moving oil droplet and the gas bubble was studied by high-speed camera and Bassset-Boussinesq-Oseen(BB...Flotation is an efficient pre-treatment technology for oily water.In this work,the interaction process between the moving oil droplet and the gas bubble was studied by high-speed camera and Bassset-Boussinesq-Oseen(BBO)theoretical model,and the experimental and simulation results of the oil droplet trajectory were compared.Moreover,the micro-particle image velocimetry system was utilized to observe the flow inside and outside of the moving oil droplet.The results show that the BBO model with the mobile bubble’s surface can reflect the velocity change trend of the oil droplet during the interaction process between the moving oil droplet and the gas bubble,but there are some significant differences between the experimental and simulation results.While the oil droplet is moving on the bubble’s surface,the velocity of the area near the contact point of oil droplet–gas bubble is less than that of the other areas inside the oil droplet.Meanwhile,the flow of water above the oil drop is more biased towards the gas bubble.展开更多
We present computational results on the evolution of the shock-accelerated heavy bubbles surrounded by nitrogen with the Atwood number At = 0.497–0.677 and the emphasis is on the jet phenomenon caused by the shock fo...We present computational results on the evolution of the shock-accelerated heavy bubbles surrounded by nitrogen with the Atwood number At = 0.497–0.677 and the emphasis is on the jet phenomenon caused by the shock focusing. The multi-fluid Eulerian equation is solved by a finite volume method based on MUSCL-Hancock approach. Based on the numerical schlieren and the distributions of density and pressure, it is found that there are three typical jet structures(outward jet, no jet, inward jet) for different combinations of gas mixture inside the bubble which determine the position of shock focusing relative to the downstream pole of the heavy bubble(upstream of the pole, at the pole, downstream the pole). Compared with the inward jet, the velocity of outward jet is obviously larger. As At increases, the moment of jet formation is postponed, and the maximal values and magnifications of pressure and density increase distinctly. Therefore, the energy convergence effects are heavily enhanced with the increase of bubble gas density.展开更多
The mutual interaction between cavitation bubbles plays an important role in the physical processes of cavitation. In this paper, a complete model is developed for modelling the mutual interaction between cavitation b...The mutual interaction between cavitation bubbles plays an important role in the physical processes of cavitation. In this paper, a complete model is developed for modelling the mutual interaction between cavitation bubbles with the effects of liquid compressibility fully included. It is found that the liquid compressibility is an important parameter in the determination of the direction of the force （the attraction or repulsion force）, as well as the magnitude of the force. The influences of the liquid compre- ssibility on the mutual interaction force can be categorized into three terms： the first is a new term added on the mutual interaction force in incompressible liquids and this term will vanish if the sizes of two bubbles are equal, the second is the radiation damping term, the third one can be considered as a correction of the mutual interaction force in incompressible liquids with a coefficient and this correction will be prominent for small bubbles and a high ambient pressure.展开更多
Detachment size determination with an acoustic method has been carried out for two interacting bubble plumes formed at neighboring needles in quiescent water. Two sets of needle pairs, one with 1.5mm and 0.8mm inner d...Detachment size determination with an acoustic method has been carried out for two interacting bubble plumes formed at neighboring needles in quiescent water. Two sets of needle pairs, one with 1.5mm and 0.8mm inner diameters and the other with the equal 1.5mm inner diameters, were separately used as the bubble pair injectors in the experiments. Consequently, four typical patterns of bubble plumes interaction could be observed in the two cases of needle pair matches. Through measuring the pressure pulses radiated by the bubble pairs immediately after their 'pinching-off ' and by making use of a sophisticated relation between oscillation frequency of volume mode and radius of gas bubble, the detachment size of the bubble plumes have been determined from the amplitude/frequency spectrum of the sound pressure pulses. The experimental results demonstrate that the acoustical method is valid in both of the interacting and non-interacting circumstances in bubble field and the bubble size measurements by this acoustical method agree well with the measurements from photographic analysis. Finally, a comparison has been made on the strong and weak points of the acoustical method with the other size determination methods.展开更多
Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow ch...Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow characteristics including interfacial forces,void fraction distribution,and interfacial area transport.Throughout the flow progression,the BSD changes along the channel due to variations in pressure and interactions among bubbles.Accurately predicting the evolution of BSD can enhance the modeling of two-phase flow.This study presents a novel BSD evolution(BSDE) model,where the governing equation for the probability density function is formulated by considering the conservation of bubbles within a onedimensional control volume in the channel.The downstream BSD is predicted based on the upstream BSD and the effects of pressure variations and bubble interactions along the channel.To account for the multiscale nature of the two-phase flow,the bubbles are categorized into small groups(G_(1)) and large groups(G_(2)).Six distinct source term distributions for intra/inter bubble interactions have been developed.Each source term accounts for the distributions of consumed and generated bubbles,ensuring the conservation of bubble volume through constraints on model coefficients.The model has been tested on a tight-lattice rod bundle using experimental data,with deviations of less than 5% and 15% for G_(1)and G_(2) flow,respectively.Since the model development is independent of specific geometry,the framework of the BSDE model can also be effectively applied to channels of varying shapes.展开更多
Bubble flow interaction can be important in many practical engineering applications. For instance, cavitation is a problem of interaction between nuclei and local pressure field variations including turbulent oscillat...Bubble flow interaction can be important in many practical engineering applications. For instance, cavitation is a problem of interaction between nuclei and local pressure field variations including turbulent oscillations and large scale pressure variations. Various types of behaviours fundamentally depend on the relative sizes of the nuclei and the length scales of the pressure variations as well as the relative importance of bubble natural periods of oscillation and the characteristic time of the field pressure variations. Similarly, bubbles can significantly affect the performance of lifting devices or propulsors. We present here some fundamental numerical studies of bubble dynamics and deformation, then a practical method using a multi-bubble Surface Averaged Pressure （DF-Multi-SAP ） to simulate cavitation inception and scaling, and connect this with more precise 3-D simulations. This same method is then extended to the study of two-way coupling between a viscous compressible flow and a bubble population in the flow field.展开更多
The bending moment acting on the overhung shaft of a gas-sparged vessel stirred by a Rushton turbine,as one of the results of fluid and structure interactions in stirred vessels,was measured using a moment sensor equi...The bending moment acting on the overhung shaft of a gas-sparged vessel stirred by a Rushton turbine,as one of the results of fluid and structure interactions in stirred vessels,was measured using a moment sensor equipped with digital telemetry.An analysis of the shaft bending moment amplitude shows that the amplitude distribution of the bending moment,which indicates the elasticity nature of shaft material against bending deformation,follows the Weibull distribution.The trends of amplitude mean,standard deviation and peak deviation characteristics manifest an "S" shape versus gas flow.The "S" trend of the relative mean bending moment over gas flow rate,depending on the flow regime in gas-liquid stirred vessels,resulted from the competition among the nonuniformity of bubbly flow around the impeller,the formation of gas cavities behind the blades,and the gas direct impact on the impeller when gas is introduced.A further analysis of the bending moment power spectral density shows that the rather low frequency and speed frequency are evident.The low-frequency contribution to bending moment fluctuation peaks in the complete dispersion regime.展开更多
The present paper describes the nonlinear behavior of bubble formation from a single submerged orifice and induced liquid motion (micro convection) surrounding the bubble. The experimental data reveals that depart...The present paper describes the nonlinear behavior of bubble formation from a single submerged orifice and induced liquid motion (micro convection) surrounding the bubble. The experimental data reveals that departing periods of successive bubbles evolve multiple periods from single to triple periods when the gas flow rate is increased and that the micro convection evolves bifurcation phenomena similar to the so called 'period doubling' in chaos dynamics. The photographic observation using high speed video movies and data analysis indicate that the nonlinear features come from the deformation of the bubble and also the interaction between consecutive bubbles. A new comprehensive theoretical model is developed for describing the instantaneous bubble behaviors during formation and ascendance processes and for predicting the departing periods and sizes of successive bubbles for constant flow rate conditions. Owing to the estimation of instantaneous interactions between successive bubbles and the incorporation of the wake effect of previous bubbles, the present model describes the evolution process and mechanisms of bubble departing periods corresponding to different gas flow rate regimes. The theoretical results are in good agreement with experimental results.展开更多
基金supported by the National Natural Science Foundation of China (10972214 and 11172278)the Fundamental Research Funds for the Central Universities (WK2090050014)
文摘The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF6 bubble is studied by the numerical method VAS2D. As a validation, the experiments of a SF6 bubble accelerated by a planar shock were performed. The results indicate that, due to the mismatch of acoustic impedance, the way of jet formation in heavy gas bubble with different species is diversified under the same initial condition. With respect to the same bubble, the manner of jet formation is also distinctly different under different shock strengths. The disparities of the acoustic impedance result in different effects of shock focusing in the bubble, and different behaviors of shock wave inside and outside the bubble. The analyses of the wave pattern and the pressure variation indicate that the jet formation is closely associated with the pressure perturbation. Moreover, the analy- sis of the vorticity deposition, and comparisons of circulation and baroclinic torque show that the baroclinic vorticity also contributes to the jet formation. It is concluded that the pres- sure perturbation and baroclinic vorticity deposition are the two dominant factors for the jet formation in shock-heavy gas bubble interaction.
基金This work was supported by the National Natural Science Foundation of China(NSFC)(Grant No.91941301)the Key Research and Development Project of Sichuan Province(Grant No.2019ZYZF0002)。
文摘Effects of Reynolds(Re)number and Schmidt(Sc)number on the flow structures and variable density mixing are numerically investigated through the canonical shock cylindrical bubble interaction.By determining the viscosity and diffusivity within a wide range,the controlling parameters,total vortex circulation,and compression rate,are conservative under a broad range of Re and Sc numbers(Re≈10^(3)-10^(5)and Sc≈0.1-5)in the same shock Mach(Ma)number condition(Ma=2.4).As for the Re number effect,the circulation of secondary baroclinic vorticity(SBV),induced by the main vortex centripetal acceleration,is observed to be higher in high Re number and vice versa.Based on the vorticity transport equation decomposition,a growth-inhibition vorticity dynamics balance mechanism is revealed:the vorticity viscous term grows synchronously with baroclinic production to inhibit SBV production in low Re number.By contrast,the viscous term terminates the baroclinic term with a time lag in high Re number,leading to the SBV production.Since the SBV reflects the local stretching enhancement based on the advection-diffusion equation,mixing is influenced by the Sc number in a different behavior if different Re numbers are considered.The time-averaged variable density mixing rate emerges a scaling law with Sc number asχ^(∗)=β·Sc^(−α),where the coefficientβ∼Re−0.2 and the scaling exponentα∼Re−0.385.The understanding of Re number and Sc number effect on variable density mixing provides an opportunity for mixing enhancement from the perspective of designing the viscosity and diffusivity of the fluid mixture.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11232011 and 11402262the 111 Project under Grant No B07033the China Postdoctoral Science Foundation Funded Project under Grant No 2014M561833
文摘The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method （PPM）, in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers （Ma）. The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 （2007） 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.
基金supported by the National Natural Science Foundation of China(51578239)the Education and Scientific Research Projects of Shanghai(17DZ1202802)。
文摘Flotation is an efficient pre-treatment technology for oily water.In this work,the interaction process between the moving oil droplet and the gas bubble was studied by high-speed camera and Bassset-Boussinesq-Oseen(BBO)theoretical model,and the experimental and simulation results of the oil droplet trajectory were compared.Moreover,the micro-particle image velocimetry system was utilized to observe the flow inside and outside of the moving oil droplet.The results show that the BBO model with the mobile bubble’s surface can reflect the velocity change trend of the oil droplet during the interaction process between the moving oil droplet and the gas bubble,but there are some significant differences between the experimental and simulation results.While the oil droplet is moving on the bubble’s surface,the velocity of the area near the contact point of oil droplet–gas bubble is less than that of the other areas inside the oil droplet.Meanwhile,the flow of water above the oil drop is more biased towards the gas bubble.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172278,11302201,11472253 and 11202195)Science Foundation of China Academy of Engineering Physics(Grant No.2014B0201017)
文摘We present computational results on the evolution of the shock-accelerated heavy bubbles surrounded by nitrogen with the Atwood number At = 0.497–0.677 and the emphasis is on the jet phenomenon caused by the shock focusing. The multi-fluid Eulerian equation is solved by a finite volume method based on MUSCL-Hancock approach. Based on the numerical schlieren and the distributions of density and pressure, it is found that there are three typical jet structures(outward jet, no jet, inward jet) for different combinations of gas mixture inside the bubble which determine the position of shock focusing relative to the downstream pole of the heavy bubble(upstream of the pole, at the pole, downstream the pole). Compared with the inward jet, the velocity of outward jet is obviously larger. As At increases, the moment of jet formation is postponed, and the maximal values and magnifications of pressure and density increase distinctly. Therefore, the energy convergence effects are heavily enhanced with the increase of bubble gas density.
基金Project supported by the National Natural Science Foun-dation of China(Grant Nos.51506051,51606221)
文摘The mutual interaction between cavitation bubbles plays an important role in the physical processes of cavitation. In this paper, a complete model is developed for modelling the mutual interaction between cavitation bubbles with the effects of liquid compressibility fully included. It is found that the liquid compressibility is an important parameter in the determination of the direction of the force （the attraction or repulsion force）, as well as the magnitude of the force. The influences of the liquid compre- ssibility on the mutual interaction force can be categorized into three terms： the first is a new term added on the mutual interaction force in incompressible liquids and this term will vanish if the sizes of two bubbles are equal, the second is the radiation damping term, the third one can be considered as a correction of the mutual interaction force in incompressible liquids with a coefficient and this correction will be prominent for small bubbles and a high ambient pressure.
基金Supported by the Post-Doctorate Science Foundation.
文摘Detachment size determination with an acoustic method has been carried out for two interacting bubble plumes formed at neighboring needles in quiescent water. Two sets of needle pairs, one with 1.5mm and 0.8mm inner diameters and the other with the equal 1.5mm inner diameters, were separately used as the bubble pair injectors in the experiments. Consequently, four typical patterns of bubble plumes interaction could be observed in the two cases of needle pair matches. Through measuring the pressure pulses radiated by the bubble pairs immediately after their 'pinching-off ' and by making use of a sophisticated relation between oscillation frequency of volume mode and radius of gas bubble, the detachment size of the bubble plumes have been determined from the amplitude/frequency spectrum of the sound pressure pulses. The experimental results demonstrate that the acoustical method is valid in both of the interacting and non-interacting circumstances in bubble field and the bubble size measurements by this acoustical method agree well with the measurements from photographic analysis. Finally, a comparison has been made on the strong and weak points of the acoustical method with the other size determination methods.
基金supported by the National Natural Science Foundation of China (12322510 and 12275174)the Shanghai Rising-Star Program (22QA1404500)+1 种基金the Science and Technology Commission of Shanghai Municipality (24DZ3100300)the Lingchuang Project of China National Nuclear Corporation
文摘Two-phase flow with complex phase interfaces is commonly observed in both nature and industrial processes.The bubble size distribution(BSD) is a crucial parameter in gas-liquid two-phase flow,impacting various flow characteristics including interfacial forces,void fraction distribution,and interfacial area transport.Throughout the flow progression,the BSD changes along the channel due to variations in pressure and interactions among bubbles.Accurately predicting the evolution of BSD can enhance the modeling of two-phase flow.This study presents a novel BSD evolution(BSDE) model,where the governing equation for the probability density function is formulated by considering the conservation of bubbles within a onedimensional control volume in the channel.The downstream BSD is predicted based on the upstream BSD and the effects of pressure variations and bubble interactions along the channel.To account for the multiscale nature of the two-phase flow,the bubbles are categorized into small groups(G_(1)) and large groups(G_(2)).Six distinct source term distributions for intra/inter bubble interactions have been developed.Each source term accounts for the distributions of consumed and generated bubbles,ensuring the conservation of bubble volume through constraints on model coefficients.The model has been tested on a tight-lattice rod bundle using experimental data,with deviations of less than 5% and 15% for G_(1)and G_(2) flow,respectively.Since the model development is independent of specific geometry,the framework of the BSDE model can also be effectively applied to channels of varying shapes.
文摘Bubble flow interaction can be important in many practical engineering applications. For instance, cavitation is a problem of interaction between nuclei and local pressure field variations including turbulent oscillations and large scale pressure variations. Various types of behaviours fundamentally depend on the relative sizes of the nuclei and the length scales of the pressure variations as well as the relative importance of bubble natural periods of oscillation and the characteristic time of the field pressure variations. Similarly, bubbles can significantly affect the performance of lifting devices or propulsors. We present here some fundamental numerical studies of bubble dynamics and deformation, then a practical method using a multi-bubble Surface Averaged Pressure （DF-Multi-SAP ） to simulate cavitation inception and scaling, and connect this with more precise 3-D simulations. This same method is then extended to the study of two-way coupling between a viscous compressible flow and a bubble population in the flow field.
文摘The bending moment acting on the overhung shaft of a gas-sparged vessel stirred by a Rushton turbine,as one of the results of fluid and structure interactions in stirred vessels,was measured using a moment sensor equipped with digital telemetry.An analysis of the shaft bending moment amplitude shows that the amplitude distribution of the bending moment,which indicates the elasticity nature of shaft material against bending deformation,follows the Weibull distribution.The trends of amplitude mean,standard deviation and peak deviation characteristics manifest an "S" shape versus gas flow.The "S" trend of the relative mean bending moment over gas flow rate,depending on the flow regime in gas-liquid stirred vessels,resulted from the competition among the nonuniformity of bubbly flow around the impeller,the formation of gas cavities behind the blades,and the gas direct impact on the impeller when gas is introduced.A further analysis of the bending moment power spectral density shows that the rather low frequency and speed frequency are evident.The low-frequency contribution to bending moment fluctuation peaks in the complete dispersion regime.
文摘The present paper describes the nonlinear behavior of bubble formation from a single submerged orifice and induced liquid motion (micro convection) surrounding the bubble. The experimental data reveals that departing periods of successive bubbles evolve multiple periods from single to triple periods when the gas flow rate is increased and that the micro convection evolves bifurcation phenomena similar to the so called 'period doubling' in chaos dynamics. The photographic observation using high speed video movies and data analysis indicate that the nonlinear features come from the deformation of the bubble and also the interaction between consecutive bubbles. A new comprehensive theoretical model is developed for describing the instantaneous bubble behaviors during formation and ascendance processes and for predicting the departing periods and sizes of successive bubbles for constant flow rate conditions. Owing to the estimation of instantaneous interactions between successive bubbles and the incorporation of the wake effect of previous bubbles, the present model describes the evolution process and mechanisms of bubble departing periods corresponding to different gas flow rate regimes. The theoretical results are in good agreement with experimental results.
