This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunzia...This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.展开更多
The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of pre...The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of predicted gas velocity and temperature distributions with experimental results for the cases without liquid spray shows pretty good agreement. Gas-droplet two-phase flow predictions give plausible droplet trajectories, fuel-vapor concentration distribution, gas-phase velocity and temperature field in presence of liquid droplets. One run of computation with this method is made for a particular afterburner. The results indicate that the location of the atomizers is not favorable to flame stabilization and combustion efficiency. The proposed numerical modeling can also be adopted for optimization design and performance evaluation of afterburner combustors of turbo-fan jet engines.展开更多
An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating c...An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.展开更多
In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows...In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.展开更多
The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision ter...The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.展开更多
Modelling and simulations are conducted on velocity slip and interfacial momentum transfer for supersonic two-pha.se (gas-droplet) flow in the transient section inside and outside a Laval jet(LJ). The initial velocity...Modelling and simulations are conducted on velocity slip and interfacial momentum transfer for supersonic two-pha.se (gas-droplet) flow in the transient section inside and outside a Laval jet(LJ). The initial velocity slip between gas and droplets causes an interfacial momentum transfer flux as high as (2.0-5.0) x 104 Pa. The relaxation time corresponding to this transient process is in the range of 0.015-0.090ms for the two-phase flow formed inside the LJ and less than 0.5ms outside the LJ. It demonstrates the unique performance of this system for application to fast chemical reactions using electrically active media with a lifetime in the order of 1 ms. Through the simulations of the transient processes with initial Mach number Mg from 2.783 to 4.194 at different axial positions inside the LJ, it is found that Mg has the strongest effect on the process. The momentum flux increases as the Mach number decreases. Due to compression by the shock wave at the end of the LJ, the flow pattern becomes two dimensional and viscous outside the LJ. Laser Doppler velocirneter (LDV) measurements of droplet velocities outside the LJ are in reasonably good agreement with the results of the simulation.展开更多
The flow patterns and the void fraction related to a gas-liquid two-phase flow in a small channel are experimentally studied.The test channel is a transparent quartz glass circular channel with an inner diameter of 6....The flow patterns and the void fraction related to a gas-liquid two-phase flow in a small channel are experimentally studied.The test channel is a transparent quartz glass circular channel with an inner diameter of 6.68 mm.The working fluids are air and water and their superficial velocities range from 0.014 to 8.127 m/s and from 0.0238 to 0.556 m/s,respectively.The void fraction is determined using the flow pattern images captured by a high-speed camera,while quick closing valves are used for verification.Four flow patterns are analyzed in experiments:slug flow,bubbly flow,annular flow and stratified flow.For intermittent flows(bubbly flow and slug flow),the cross-sectional void fraction is in a borderline condition while its probability distribution function(PDF)image displays a bimodal structure.For continuous flows(annular flow and stratified flow)the cross-sectional void fraction behaves as a fluctuating continuous curve while the(PDF)image displays a single peak structure.The volumetric void fraction data are also compared with available predictive formulas,and the results show that the agreement is very good.An effort is also provided to improve the so-called Gregory and Scott model using the available data.展开更多
The gas-solid two-phase flous of the precalciner were simulated by different multiphase models,such as mixture model,the Enderium model,including mixture and dispersed,and discrete phase model（DPM）,The results of th...The gas-solid two-phase flous of the precalciner were simulated by different multiphase models,such as mixture model,the Enderium model,including mixture and dispersed,and discrete phase model（DPM）,The results of the different multiphase models were analyzed and compared.showing the rationality of the diffusion and mixture of the cenment raic meals and coal poroder some extent Moreover,the results also shose the rationality of the given inlets parameters of actual process of the precalciner.展开更多
A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase ...A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.展开更多
We propose a hybrid scheme for computations of incompressible two-phase flows. The incompressible constraint has been replaced by a pressure Poisson-like equation and then the pressure is updated by the modified marke...We propose a hybrid scheme for computations of incompressible two-phase flows. The incompressible constraint has been replaced by a pressure Poisson-like equation and then the pressure is updated by the modified marker and cell method. Meanwhile, the moment equations in the incompressible Navier-Stokes equations are solved by our semidiscrete Hermite central-upwind scheme, and the interface between the two fluids is considered to be continuous and is described implicitly as the 0.5 level set of a smooth function being a smeared out Heaviside function. It is here named the hybrid scheme. Some numerical experiments are successfully carried out, which verify the desired efficiency and accuracy of our hybrid scheme.展开更多
A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carr...A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.展开更多
Particle-gas two-phase flows show significantly different behaviors compared to single gas flow through a convergent-divergent nozzle. Non-equilibrium effects, thermal and velocity lag results to the inefficiency of n...Particle-gas two-phase flows show significantly different behaviors compared to single gas flow through a convergent-divergent nozzle. Non-equilibrium effects, thermal and velocity lag results to the inefficiency of nozzle performance. In the present studies, theoretical analysis and numerical simulations were carried out to investigate particle-gas flows in a C-D nozzle. Homogeneous equilibrium model that no lag in velocity and temperature occurs between particles and gas phase was used to derive mass flow rate and sound speed of multiphase flows. Two-phase flows are regarded as isentropic flows that isentropic relations can be used for homogeneous equilibrium model. Discrete phase model （DPM） where interaction with continuous phase and discrete random walk model were considered was used to calculate particle- gas flows. Particle mass loadings were varied to investigate their effects on choking phenomena of particle-gas flows. Mass flow rate and sound speed of mixture flows were theoretically calculated by homogeneous equilibrium model and compared with numerical results. Shock wave structure and particle number density were also obtained to be different at different particle mass loading and operating pressure conditions.展开更多
In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dim...In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the flow parameters for the gas and particle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.展开更多
In this paper,we propose a novel probe to identify phases in any two-phase flows where one phase is conductive and the other nonconductive.We can further obtain many parameters such as void fraction,bubble velocity,an...In this paper,we propose a novel probe to identify phases in any two-phase flows where one phase is conductive and the other nonconductive.We can further obtain many parameters such as void fraction,bubble velocity,and interfacial area concentration.Compared with the traditional probe,the novel probe has unique advantages that it is less dependent on water conductance or distance between the electrodes,and that the amplitude is bigger between high and low levels.Theoretical analyses showed that the measurement error became higher when water conductance decreases or distance increases,which is consistent with the theoretical analyses.Experimental results showed that the output signal kept constant with salt content of 0-5% and electrode distance of 0-30 mm in tap water.The level difference was up to 6.4 V,resulting in identifying two phases easily.Time traces of phase identification were completely consistent with the flow structures.展开更多
Cleat serves as the primary flow pathway for coalbed methane(CBM)and water.However,few studies consider the impact of local contact on two-phase flow within cleats.A visual generalized model of endogenous cleats was c...Cleat serves as the primary flow pathway for coalbed methane(CBM)and water.However,few studies consider the impact of local contact on two-phase flow within cleats.A visual generalized model of endogenous cleats was constructed based on microfluidics.A microscopic and mesoscopic observation technique was proposed to simultaneously capture gas-liquid interface morphology of pores and throat and the two-phase flow characteristics in entire cleat system.The local contact characteristics of cleats reduced absolute permeability,which resulted in a sharp increase in the starting pressure.The reduced gas flow capacity narrowed the co-infiltration area and decreased water saturation at the isotonic point in a hydrophilic environment.The increased local contact area of cleats weakened gas phase flow capacity and narrowed the co-infiltration area.Jumping events occurred in methane-water flow due to altered porosity caused by local contact in cleats.The distribution of residual phases changed the jumping direction on the micro-scale as well as the dominant channel on the mesoscale.Besides,jumping events caused additional energy dissipation,which was ignored in traditional two-phase flow models.This might contribute to the overestimation of relative permeability.The work provides new methods and insights for investigating unsaturated flow in complex porous media.展开更多
Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishe...Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.展开更多
With the increasing miniaturization of systems and surging demand for power density,accurate prediction and control of two-phase flow pressure drop have become a core challenge restricting the performance of microchan...With the increasing miniaturization of systems and surging demand for power density,accurate prediction and control of two-phase flow pressure drop have become a core challenge restricting the performance of microchannel heat exchangers.Pressure drop,a critical hydraulic characteristic,serves as both a natural constraint for cooling systems and determines the power required to pump the working fluid through microchannels.This paper reviews the characteristics,prediction models,and optimization measures of two-phase flow pressure drop for low-boiling-point working fluids in microchannels.It systematically analyzes key influencing factors such as fluid physical properties,operating conditions,channel geometry,and flow patterns,and discusses the complex mechanisms of pressure drop under the coupling effect of multi-physical fields.Mainstream prediction models are reviewed:the homogeneous flow model simplifies calculations but shows large deviations at low quality;the separated flow model considers interphase interactions and can be applied to micro-scales after modification;the flow-pattern-based model performs zoned modeling but relies on subjective classification;machine learning improves prediction accuracy but faces the“black-box”problem.In terms of optimization,channel designs are improved through porous structures and micro-rib arrays,and flow rate distribution is optimized using splitters to balance pressure drop and heat transfer performance.This study provides theoretical support for microchannel thermal management in high-power-density devices.展开更多
Shale gas production involves complex gas-water two-phase flow,with flow patterns in proppant-filled fractures playing a critical role in determining production efficiency.In this study,3D geometric models of 40/70 me...Shale gas production involves complex gas-water two-phase flow,with flow patterns in proppant-filled fractures playing a critical role in determining production efficiency.In this study,3D geometric models of 40/70 mesh ceramic particles and quartz sand proppant clusters were elaborated using computed tomography(CT)scanning.These models were used to develop a numerical simulation framework based on the lattice Boltzmann method(LBM),enabling the investigation of gas-water flow behavior within proppant-filled fractures under varying driving forces and surface tensions.Simulation results at a closure pressure of 15 MPa have revealed that ceramic particles exhibit a simpler and more porous internal structure than quartz sand of the same size.Under identical flow conditions,ceramic proppants demonstrate higher fluid replacement efficiency.Replacement efficiency increases with higher porosity,greater driving force,and lower surface tension.Furthermore,fluid displacement is strongly influenced by pore geometry:flow is faster in straighter and wider channels,with preferential movement through larger pores forming dominant flow paths.The replacement velocity exhibits a characteristic time evolution,initially rapid,then gradually decreasing,correlating positively with the development of these dominant channels.展开更多
Clayey-silt natural gas hydrate reservoirs in the South China Sea exhibit loose and unconsolidated structures, heterogeneous pore structures, high clay mineral contents, and strong hydrophilicity. These characteristic...Clayey-silt natural gas hydrate reservoirs in the South China Sea exhibit loose and unconsolidated structures, heterogeneous pore structures, high clay mineral contents, and strong hydrophilicity. These characteristics complicate the gas-water two-phase flow process in porous media following hydrate decomposition, posing challenges for efficient development. This study examines the transport response of clayey-silt reservoir samples from the Shenhu area using gas-water two-phase flow experiments and CT scanning to explore changes in pore structure, gas-water distribution, and relative permeability under varying flow conditions. The results indicate that pore heterogeneity significantly influences flow characteristics. Gas preferentially displaces water in larger pores, forming fracture-like pores, which serve as preferential flow channels for gas migration. The preferential flow channels enhance gas-phase permeability up to 19 times that of the water phase when fluid pressures exceed total stresses. However,small pores retain liquid, leading to a high residual water saturation of 0.561. CT imaging reveals that these hydro-fractures improve gas permeability but also confine gas flow to specific channels. Pore network analysis shows that gas injection expands the pore-throat network, enhancing connectivity and forming fracture-like pores. Residual water remains trapped in smaller pores and throats, while structural changes, including new fractures, improve gas flow pathways and overall connectivity. Relative permeability curves demonstrate a narrow gas-water cocurrent-flow zone, a right-shifted iso-permeability point and high reservoir capillary pressure, indicating a strong "water-blocking" effect. The findings suggest that optimizing reservoir stimulation techniques to enhance fracture formation, reduce residual water saturation, and improve gas flow capacity is critical for efficient hydrate reservoir development.展开更多
In photothermal power(solar energy)generation systems,purging residual molten salt from pipelines using highpressure gas poses a significant challenge,particularly in clearing the bottom of regulating valves.Ineffecti...In photothermal power(solar energy)generation systems,purging residual molten salt from pipelines using highpressure gas poses a significant challenge,particularly in clearing the bottom of regulating valves.Ineffective purging can lead to crystallization of the molten salt,resulting in blockages.To address this issue,understanding the gas-liquid two-phase flow dynamics during high-pressure gas purging is crucial.This study utilizes the Volume of Fluid(VOF)model and adaptive dynamic grids to simulate the gas-liquid two-phase flow during the purging process in a DN50 PN50 conventional molten salt regulating valve.Initially,the reliability of the CFD simulations is validated through comparisons with experimental data and findings from the literature.Subsequently,simulation experiments are conducted to analyze the effects of various factors,including purge flow rates,initial liquid accumulation masses,purge durations,and the profiles of the valve bottom flow channels.The results indicate that the purging process comprises four distinct stages:Initial violent surge stage,liquid discharge stage,liquid partial fallback stage,liquid dissipation stage.For an initial liquid height of 17 mm at the bottom of the valve,the critical purge flow rate lies between 3 and 5 m/s.Notably,the critical purge flow rate is independent of the initial liquid accumulation mass.As the purge gas flow rate increases,the volume of liquid discharged also increases.Beyond the critical purge flow rate,higher purge gas velocities lead to shorter purge durations.Interestingly,the residual liquid mass after purging remains unaffected by the initial liquid accumulation.Additionally,the flow channel profile at the bottom of the valve significantly influences both the critical purge speed and the efficiency of the purging process.展开更多
基金funded by the Italian Ministry of Education,University and Research(MIUR)in the frame of the Departments of Excellence Initiative 2018-2027 attributed to DICAM of the University of Trento(grant L.232/2016)in the frame of the PRIN 2017 project Innovative numerical methods for evolutionary partial differential equations and applications,the PRIN 2022 project High order structure-preserving semi-implicit schemes for hyperbolic equations.D.is member of INdAM GNCS and was also co-funded by the European Union NextGenerationEU(PNRR,Spoke 7 CN HPC).Views and opinions expressed are however those of the author(s)only and do not necessarily reflect those of the European Union or the European Research Council.Neither the European Union nor the granting authority can be held responsible for them.
文摘This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.
文摘The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of predicted gas velocity and temperature distributions with experimental results for the cases without liquid spray shows pretty good agreement. Gas-droplet two-phase flow predictions give plausible droplet trajectories, fuel-vapor concentration distribution, gas-phase velocity and temperature field in presence of liquid droplets. One run of computation with this method is made for a particular afterburner. The results indicate that the location of the atomizers is not favorable to flame stabilization and combustion efficiency. The proposed numerical modeling can also be adopted for optimization design and performance evaluation of afterburner combustors of turbo-fan jet engines.
基金the National Natural Science Foundation of China(50779069 and 90510007)the Start-up Scientific Research Foundation of China Agricultural University(2006021)the Beijing Natural Science Foundation(3071002).
文摘An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.
文摘In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.
基金The project supported by the National Natural Science Foundation of China (50176022)
文摘The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.
基金Supported by the National Natural Science Foundation of China (No. 29876022) and Grant of State Key Laboratory of High Speed Hydrodynamics (No. 2007).
文摘Modelling and simulations are conducted on velocity slip and interfacial momentum transfer for supersonic two-pha.se (gas-droplet) flow in the transient section inside and outside a Laval jet(LJ). The initial velocity slip between gas and droplets causes an interfacial momentum transfer flux as high as (2.0-5.0) x 104 Pa. The relaxation time corresponding to this transient process is in the range of 0.015-0.090ms for the two-phase flow formed inside the LJ and less than 0.5ms outside the LJ. It demonstrates the unique performance of this system for application to fast chemical reactions using electrically active media with a lifetime in the order of 1 ms. Through the simulations of the transient processes with initial Mach number Mg from 2.783 to 4.194 at different axial positions inside the LJ, it is found that Mg has the strongest effect on the process. The momentum flux increases as the Mach number decreases. Due to compression by the shock wave at the end of the LJ, the flow pattern becomes two dimensional and viscous outside the LJ. Laser Doppler velocirneter (LDV) measurements of droplet velocities outside the LJ are in reasonably good agreement with the results of the simulation.
基金This work was supported by the Guangdong Basic and Applied Basic Research Foundation(2019A1515111116)Key R&D Program of Shandong Province(Nos.2019GSF109051,2019GGX101030)+1 种基金Shandong Provincial Postdoctoral Innovation Project(No.201902002)Foundation of Shandong University for Young Scholar’s Future Plans.
文摘The flow patterns and the void fraction related to a gas-liquid two-phase flow in a small channel are experimentally studied.The test channel is a transparent quartz glass circular channel with an inner diameter of 6.68 mm.The working fluids are air and water and their superficial velocities range from 0.014 to 8.127 m/s and from 0.0238 to 0.556 m/s,respectively.The void fraction is determined using the flow pattern images captured by a high-speed camera,while quick closing valves are used for verification.Four flow patterns are analyzed in experiments:slug flow,bubbly flow,annular flow and stratified flow.For intermittent flows(bubbly flow and slug flow),the cross-sectional void fraction is in a borderline condition while its probability distribution function(PDF)image displays a bimodal structure.For continuous flows(annular flow and stratified flow)the cross-sectional void fraction behaves as a fluctuating continuous curve while the(PDF)image displays a single peak structure.The volumetric void fraction data are also compared with available predictive formulas,and the results show that the agreement is very good.An effort is also provided to improve the so-called Gregory and Scott model using the available data.
文摘The gas-solid two-phase flous of the precalciner were simulated by different multiphase models,such as mixture model,the Enderium model,including mixture and dispersed,and discrete phase model（DPM）,The results of the different multiphase models were analyzed and compared.showing the rationality of the diffusion and mixture of the cenment raic meals and coal poroder some extent Moreover,the results also shose the rationality of the given inlets parameters of actual process of the precalciner.
基金Supported by the Spanish CICYTR &D National Programs,under contract PB91-0699.
文摘A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.
文摘We propose a hybrid scheme for computations of incompressible two-phase flows. The incompressible constraint has been replaced by a pressure Poisson-like equation and then the pressure is updated by the modified marker and cell method. Meanwhile, the moment equations in the incompressible Navier-Stokes equations are solved by our semidiscrete Hermite central-upwind scheme, and the interface between the two fluids is considered to be continuous and is described implicitly as the 0.5 level set of a smooth function being a smeared out Heaviside function. It is here named the hybrid scheme. Some numerical experiments are successfully carried out, which verify the desired efficiency and accuracy of our hybrid scheme.
文摘A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.
文摘Particle-gas two-phase flows show significantly different behaviors compared to single gas flow through a convergent-divergent nozzle. Non-equilibrium effects, thermal and velocity lag results to the inefficiency of nozzle performance. In the present studies, theoretical analysis and numerical simulations were carried out to investigate particle-gas flows in a C-D nozzle. Homogeneous equilibrium model that no lag in velocity and temperature occurs between particles and gas phase was used to derive mass flow rate and sound speed of multiphase flows. Two-phase flows are regarded as isentropic flows that isentropic relations can be used for homogeneous equilibrium model. Discrete phase model （DPM） where interaction with continuous phase and discrete random walk model were considered was used to calculate particle- gas flows. Particle mass loadings were varied to investigate their effects on choking phenomena of particle-gas flows. Mass flow rate and sound speed of mixture flows were theoretically calculated by homogeneous equilibrium model and compared with numerical results. Shock wave structure and particle number density were also obtained to be different at different particle mass loading and operating pressure conditions.
文摘In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the flow parameters for the gas and particle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.
基金Support by the National Natural Science Foundation of China (No. 51006068)
文摘In this paper,we propose a novel probe to identify phases in any two-phase flows where one phase is conductive and the other nonconductive.We can further obtain many parameters such as void fraction,bubble velocity,and interfacial area concentration.Compared with the traditional probe,the novel probe has unique advantages that it is less dependent on water conductance or distance between the electrodes,and that the amplitude is bigger between high and low levels.Theoretical analyses showed that the measurement error became higher when water conductance decreases or distance increases,which is consistent with the theoretical analyses.Experimental results showed that the output signal kept constant with salt content of 0-5% and electrode distance of 0-30 mm in tap water.The level difference was up to 6.4 V,resulting in identifying two phases easily.Time traces of phase identification were completely consistent with the flow structures.
基金the financial support from the National Natural Science Foundation of China (No.42102127)the Postdoctoral Research Foundation of China (No.2024 M751860)。
文摘Cleat serves as the primary flow pathway for coalbed methane(CBM)and water.However,few studies consider the impact of local contact on two-phase flow within cleats.A visual generalized model of endogenous cleats was constructed based on microfluidics.A microscopic and mesoscopic observation technique was proposed to simultaneously capture gas-liquid interface morphology of pores and throat and the two-phase flow characteristics in entire cleat system.The local contact characteristics of cleats reduced absolute permeability,which resulted in a sharp increase in the starting pressure.The reduced gas flow capacity narrowed the co-infiltration area and decreased water saturation at the isotonic point in a hydrophilic environment.The increased local contact area of cleats weakened gas phase flow capacity and narrowed the co-infiltration area.Jumping events occurred in methane-water flow due to altered porosity caused by local contact in cleats.The distribution of residual phases changed the jumping direction on the micro-scale as well as the dominant channel on the mesoscale.Besides,jumping events caused additional energy dissipation,which was ignored in traditional two-phase flow models.This might contribute to the overestimation of relative permeability.The work provides new methods and insights for investigating unsaturated flow in complex porous media.
基金funded by the National Key R&D Program of China,China(Grant No.2023YFB4005500)National Natural Science Foundation of China,China(Grant Nos.52379113 and 52379114).
文摘Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.
基金supported by the Beijing Municipal Science&Technology Commission(Z231100006123010).
文摘With the increasing miniaturization of systems and surging demand for power density,accurate prediction and control of two-phase flow pressure drop have become a core challenge restricting the performance of microchannel heat exchangers.Pressure drop,a critical hydraulic characteristic,serves as both a natural constraint for cooling systems and determines the power required to pump the working fluid through microchannels.This paper reviews the characteristics,prediction models,and optimization measures of two-phase flow pressure drop for low-boiling-point working fluids in microchannels.It systematically analyzes key influencing factors such as fluid physical properties,operating conditions,channel geometry,and flow patterns,and discusses the complex mechanisms of pressure drop under the coupling effect of multi-physical fields.Mainstream prediction models are reviewed:the homogeneous flow model simplifies calculations but shows large deviations at low quality;the separated flow model considers interphase interactions and can be applied to micro-scales after modification;the flow-pattern-based model performs zoned modeling but relies on subjective classification;machine learning improves prediction accuracy but faces the“black-box”problem.In terms of optimization,channel designs are improved through porous structures and micro-rib arrays,and flow rate distribution is optimized using splitters to balance pressure drop and heat transfer performance.This study provides theoretical support for microchannel thermal management in high-power-density devices.
文摘Shale gas production involves complex gas-water two-phase flow,with flow patterns in proppant-filled fractures playing a critical role in determining production efficiency.In this study,3D geometric models of 40/70 mesh ceramic particles and quartz sand proppant clusters were elaborated using computed tomography(CT)scanning.These models were used to develop a numerical simulation framework based on the lattice Boltzmann method(LBM),enabling the investigation of gas-water flow behavior within proppant-filled fractures under varying driving forces and surface tensions.Simulation results at a closure pressure of 15 MPa have revealed that ceramic particles exhibit a simpler and more porous internal structure than quartz sand of the same size.Under identical flow conditions,ceramic proppants demonstrate higher fluid replacement efficiency.Replacement efficiency increases with higher porosity,greater driving force,and lower surface tension.Furthermore,fluid displacement is strongly influenced by pore geometry:flow is faster in straighter and wider channels,with preferential movement through larger pores forming dominant flow paths.The replacement velocity exhibits a characteristic time evolution,initially rapid,then gradually decreasing,correlating positively with the development of these dominant channels.
基金the National Natural Science Foundation of China (Nos. 42302143, 42172159)China Geological Survey Project (No. DD20211350)support from the G. Albert Shoemaker endowment
文摘Clayey-silt natural gas hydrate reservoirs in the South China Sea exhibit loose and unconsolidated structures, heterogeneous pore structures, high clay mineral contents, and strong hydrophilicity. These characteristics complicate the gas-water two-phase flow process in porous media following hydrate decomposition, posing challenges for efficient development. This study examines the transport response of clayey-silt reservoir samples from the Shenhu area using gas-water two-phase flow experiments and CT scanning to explore changes in pore structure, gas-water distribution, and relative permeability under varying flow conditions. The results indicate that pore heterogeneity significantly influences flow characteristics. Gas preferentially displaces water in larger pores, forming fracture-like pores, which serve as preferential flow channels for gas migration. The preferential flow channels enhance gas-phase permeability up to 19 times that of the water phase when fluid pressures exceed total stresses. However,small pores retain liquid, leading to a high residual water saturation of 0.561. CT imaging reveals that these hydro-fractures improve gas permeability but also confine gas flow to specific channels. Pore network analysis shows that gas injection expands the pore-throat network, enhancing connectivity and forming fracture-like pores. Residual water remains trapped in smaller pores and throats, while structural changes, including new fractures, improve gas flow pathways and overall connectivity. Relative permeability curves demonstrate a narrow gas-water cocurrent-flow zone, a right-shifted iso-permeability point and high reservoir capillary pressure, indicating a strong "water-blocking" effect. The findings suggest that optimizing reservoir stimulation techniques to enhance fracture formation, reduce residual water saturation, and improve gas flow capacity is critical for efficient hydrate reservoir development.
文摘In photothermal power(solar energy)generation systems,purging residual molten salt from pipelines using highpressure gas poses a significant challenge,particularly in clearing the bottom of regulating valves.Ineffective purging can lead to crystallization of the molten salt,resulting in blockages.To address this issue,understanding the gas-liquid two-phase flow dynamics during high-pressure gas purging is crucial.This study utilizes the Volume of Fluid(VOF)model and adaptive dynamic grids to simulate the gas-liquid two-phase flow during the purging process in a DN50 PN50 conventional molten salt regulating valve.Initially,the reliability of the CFD simulations is validated through comparisons with experimental data and findings from the literature.Subsequently,simulation experiments are conducted to analyze the effects of various factors,including purge flow rates,initial liquid accumulation masses,purge durations,and the profiles of the valve bottom flow channels.The results indicate that the purging process comprises four distinct stages:Initial violent surge stage,liquid discharge stage,liquid partial fallback stage,liquid dissipation stage.For an initial liquid height of 17 mm at the bottom of the valve,the critical purge flow rate lies between 3 and 5 m/s.Notably,the critical purge flow rate is independent of the initial liquid accumulation mass.As the purge gas flow rate increases,the volume of liquid discharged also increases.Beyond the critical purge flow rate,higher purge gas velocities lead to shorter purge durations.Interestingly,the residual liquid mass after purging remains unaffected by the initial liquid accumulation.Additionally,the flow channel profile at the bottom of the valve significantly influences both the critical purge speed and the efficiency of the purging process.
