Motivated by inconveniences of present hybrid methods,a gradient-augmented hybrid interface capturing method（GAHM） is presented for incompressible two-phase flow.A front tracking method（FTM） is used as the skeleto...Motivated by inconveniences of present hybrid methods,a gradient-augmented hybrid interface capturing method（GAHM） is presented for incompressible two-phase flow.A front tracking method（FTM） is used as the skeleton of the GAHM for low mass loss and resources.Smooth eulerian level set values are calculated from the FTM interface,and are used for a local interface reconstruction.The reconstruction avoids marker particle redistribution and enables an automatic treatment of interfacial topology change.The cubic Hermit interpolation is employed in all steps of the GAHM to capture subgrid structures within a single spacial cell.The performance of the GAHM is carefully evaluated in a benchmark test.Results show significant improvements of mass loss,clear subgrid structures,highly accurate derivatives（normals and curvatures） and low cost.The GAHM is further coupled with an incompressible multiphase flow solver,Super CE/SE,for more complex and practical applications.The updated solver is evaluated through comparison with an early droplet research.展开更多
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
Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on e...Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.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
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
This study investigates the droplet formation for the liquid–liquid two-phase flow within a square T-junction microchannel through numerical simulation using volume of fluid method and experimental visualization usin...This study investigates the droplet formation for the liquid–liquid two-phase flow within a square T-junction microchannel through numerical simulation using volume of fluid method and experimental visualization using high-speed camera imaging.The T-junction microchannel has a cross-sectional width of 0.6 mm and a total length of 27.3 mm.The solution of cyclohexane with 2%and 3%mass concentrations of sorbitan trioleate surfactant were used as the continuous phase,and water was used as the dispersed phase.Slug flow,characteristic of squeezing regime,were predominantly observed.The effects of liquid–liquid two-phase flow rate ratio,and dimensionless number on droplet size,and pressure drop were investigated.The squeezing regime was mapped for 0.0005≤Ca_(c)≤0.0052(capillary number)and 0.1≤q≤10(flow rate ratio).The pressure drops of slugs were in the range from 40 Pa to 200 Pa.The slug lengths were measured between 1 mm and 9 mm.A universal flow map dependent on Ca_(c)Re_(d)^(0.5) are projected to investigate the droplet formation behavior in T-junction microchannel.Correlation expressions are proposed to predict pressure drops and the slug lengths for liquid–liquid two-phase flow in a square T-junction microchannel,using dimensionless numbers such as flow rate ratio and capillary number.The result shows that large continuous phase flow rates facilitate smaller slugs,whereas higher dispersed phase flow rates result in longer shorts.展开更多
A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of th...A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of the one-fluid Euler solvers,differing from them by the presence of a void ratio transport-equation.The model and the system of equations to be simulated are presented.Results are displayed for shock and expansion tube problems,shock-bubble interaction and underwater explosion.Close agreement with reference solutions,obtained from explicit finite volume approaches,is demonstrated.Different numerical methods are additionally displayed to provide comparable and improved computational efficiency to the model and the system of equations.The overall procedure is therefore very well suited for use in general two-phase fluid flow simulations.展开更多
The comparative study on seven equation models with two different six equations modelfor compressible two-phase flow analysis is proposed. The seven equations model isderived for compressible two-phase flow that is in...The comparative study on seven equation models with two different six equations modelfor compressible two-phase flow analysis is proposed. The seven equations model isderived for compressible two-phase flow that is in the nonconservation form. In thepresent work, two different six equations model are derived for two pressures, two velocities and single temperature with the derivation of the equation of state. The closingequation for one of the six equations model is energy conservation equation while anotherone is closed by entropy balance equation. The partial differential form of governingequations is hyperbolic and written in the conservative form. At this point, the set ofgoverning equations are derived based on the principle of extended thermodynamics.The method of solving single temperature from both six equation models are simple anddirect solution can be obtained. Numerical simulation has been tried using one of the sixequation models for air–water shock tube problems. Explicit fourth order Runge–Kuttascheme is used with Finite Volume Shock Capturing method for solving the governingequations numerically. The pressure, velocity and volume fraction variations are captured along the shock tube length through flow solver. Experimental work is carried outto magnify the initial stage of liquid injection into a gas. The outcome of six equationsmodel for compressible two-phase flow has revealed the multi-phase flow characteristicsthat are similar to the actual conditions.展开更多
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.展开更多
Underwater gas-liquid two-phase propulsion technology is an emerging propulsion method that offers high efficiency and unrestricted navigation speed.The integration of this technology into water ramjet engines can sig...Underwater gas-liquid two-phase propulsion technology is an emerging propulsion method that offers high efficiency and unrestricted navigation speed.The integration of this technology into water ramjet engines can significantly enhance propulsion efficiency and holds substantial potential for broad applications.However,forming a gas-liquid two-phase flow within the nozzle requires introducing a large amount of rammed seawater.At this time,there is a complex phase transition problem of combustion products in the combustion chamber,which makes the thermodynamic calculation for gas-liquid two-phase water ramjet engines particularly challenging.This paper proposes a thermodynamic calculation method for gas-liquid two-phase water ramjet engines,based on the energy equation for gas-liquid two-phase flow and traditional thermodynamic principles,enabling thermodynamic calculations under conditions of ultra-high water-fuel ratios.Additionally,ground ignition tests of the gas-liquid two-phase engine were conducted,yielding critical engine test parameters.The results demonstrate that the gas-liquid two-phase water ramjet engine achieves a high specific impulse,with a theoretical maximum specific impulse of up to 7000(N s)/kg.The multiphase flow effects significantly impact engine performance,with specific impulse losses reaching up to 25.86%.The error between the thrust and specific impulse in the ground test and the theoretical values is within 10%,validating the proposed thermodynamic calculation method as a reliable reference for further research on gas-liquid two-phase water ramjet engines.展开更多
Deep-sea mineral resource transportation predominantly utilizes hydraulic pipeline methodology.Environmental factors induce vibrations in flexible pipelines,thereby affecting the internal flow characteristics.Therefor...Deep-sea mineral resource transportation predominantly utilizes hydraulic pipeline methodology.Environmental factors induce vibrations in flexible pipelines,thereby affecting the internal flow characteristics.Therefore,real-time monitoring of solid–liquid two-phase flow in pipelines is crucial for system maintenance.This study develops an autoencoder-based deep learning framework to reconstruct three-dimensional solid–liquid two-phase flow within flexible vibrating pipelines utilizing sparse wall information from sensors.Within this framework,separate X-model and F-model with distinct hidden-layer structures are established to reconstruct the coordinates and flow field information on the computational domain grid of the pipeline under traveling wave vibration.Following hyperparameter optimization,the models achieved high reconstruction accuracy,demonstrating R^(2)values of 0.990 and 0.945,respectively.The models’robustness is evaluated across three aspects:vibration parameters,physical fields,and vibration modes,demonstrating good reconstruction performance.Results concerning sensors show that 20 sensors(0.06%of total grids)achieve a balance between accuracy and cost,with superior accuracy obtained when arranged along the full length of the pipe compared to a dense arrangement at the front end.The models exhibited a signal-to-noise ratio tolerance of approximately 27 dB,with reconstruction accuracy being more affected by sensor failures at both ends of the pipeline.展开更多
The influence of the squeeze film between the tube and the support structure on flow-induced vibrations is a critical factor in tube bundles subjected to two-phase cross-flow.This aspect can significantly alter the th...The influence of the squeeze film between the tube and the support structure on flow-induced vibrations is a critical factor in tube bundles subjected to two-phase cross-flow.This aspect can significantly alter the threshold for fluidelastic instability and affect heat transfer efficiency.This paper presents a mathematical model incorporating the squeeze film force between the tube and the support structure.We aim to clarify the mechanisms underlying fluidelastic instability in tube bundle systems exposed to two-phase flow.Using a self-developed computer program,we performed numerical calculations to examine the influence of the squeeze film on the threshold of fluidelastic instability in the tube bundle system.Furthermore,we analyzed how the thickness and length of the squeeze film affect both the underlying mechanisms and the critical velocity of fluidelastic instability.展开更多
This work investigated the dynamic behavior of vertical pipes conveying gas-liquid two-phase flow when subjected to external excitations at both ends.Even with minimal excitation amplitude,resonance can occur when the...This work investigated the dynamic behavior of vertical pipes conveying gas-liquid two-phase flow when subjected to external excitations at both ends.Even with minimal excitation amplitude,resonance can occur when the excitation frequency aligns with the natural frequency of the pipe,significantly increasing the degree of operational risk.The governing equation of motion based on the Euler-Bernoulli beam is derived for the relative deflection with stationary simply supported ends,with the effects of the external excitations represented by source terms distributed along the pipe length.The fourth-order partial differential equation is solved via the generalized integral transform technique(GITT),with the solution successfully verified via comparison with results in the literature.A comprehensive analysis of the vibration phenomena and changes in the motion state of the pipe is conducted for three classes of external excitation conditions:same frequency and amplitude(SFSA),same frequency but different amplitudes(SFDA),and different frequencies and amplitudes(DFDA).The numerical results show that with increasing gas volume fraction,the position corresponding to the maximum vibration displacement shifts upward.Compared with conditions without external excitation,the vibration displacement of the pipe conveying two-phase flow under external excitation increases significantly.The frequency of external excitation has a significant effect on the dynamic behavior of a pipe conveying two-phase flow.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
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
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
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
By combining with an improved model on engraving process,a two-phase flow interior ballistic model has been proposed to accurately predict the flow and energy conversion behaviors of pyrotechnic actuators.Using comput...By combining with an improved model on engraving process,a two-phase flow interior ballistic model has been proposed to accurately predict the flow and energy conversion behaviors of pyrotechnic actuators.Using computational fluid dynamics(CFD),the two-phase flow and piston engraving characteristics of a pyrotechnic actuator are investigated.Initially,the current model was utilized to examine the intricate,multi-dimensional flow,and energy conversion characteristics of the propellant grains and combustion gas within the pyrotechnic actuator chamber.It was discovered that the combustion gas on the wall's constant transition from potential to kinetic energy,along with the combined effect of the propellant motion,are what create the pressure oscillation within the chamber.Additionally,a numerical analysis was conducted to determine the impact of various parameters on the pressure oscillation and piston motion,including pyrotechnic charge,pyrotechnic particle size,and chamber structural dimension.The findings show that decreasing the pyrotechnic charge will lower the terminal velocity,while increasing and decreasing the pyrotechnic particle size will reduce the pressure oscillation in the chamber.The pyrotechnic particle size has minimal bearing on the terminal velocity.The results of this investigation offer a trustworthy forecasting instrument for comprehending and creating pyrotechnic actuator designs.展开更多
In this study,we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network(EPINN),which is applied to simulate tw...In this study,we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network(EPINN),which is applied to simulate two-phase flow in heterogeneous porous media.Specifically,we first analyze the layerwise outputs of EPINN,and identify the distinct functions across layers,including dimensionality adjustment,pointwise construction of non-equilibrium potential,extraction of high-level features,and the establishment of long-range dependencies.Then,inspired by these distinct modules,we propose a novel constraint learning strategy based on regularization approaches,which improves neural network(NN)learning through layer-specific differentiated updates to enhance cross-timestep generalization.Since different neu ral network layers exhibit varying sensitivities to global generalization and local regression,we decrease the update frequency of layers more sensitive to local learning under this constraint learning strategy.In other words,the entire neural network is encouraged to extract more generalized features.The superior performance of the proposed learning strategy is validated through evaluations on numerical examples with varying computational complexities.Post hoc analysis reveals that gradie nt propagation exhibits more pronounced staged characte ristics,and the partial differential equation(PDE)residuals are more uniformly distributed under the constraint guidance.Interpretability analysis of the adaptive constraint process suggests that maintaining a stable information compression mode facilitates progressive convergence acceleration.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
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10972010,11028206,11371069,11372052,11402029,and 11472060)the Science and Technology Development Foundation of China Academy of Engineering Physics(CAEP),China(Grant No.2014B0201030)the Defense Industrial Technology Development Program of China(Grant No.B1520132012)
文摘Motivated by inconveniences of present hybrid methods,a gradient-augmented hybrid interface capturing method（GAHM） is presented for incompressible two-phase flow.A front tracking method（FTM） is used as the skeleton of the GAHM for low mass loss and resources.Smooth eulerian level set values are calculated from the FTM interface,and are used for a local interface reconstruction.The reconstruction avoids marker particle redistribution and enables an automatic treatment of interfacial topology change.The cubic Hermit interpolation is employed in all steps of the GAHM to capture subgrid structures within a single spacial cell.The performance of the GAHM is carefully evaluated in a benchmark test.Results show significant improvements of mass loss,clear subgrid structures,highly accurate derivatives（normals and curvatures） and low cost.The GAHM is further coupled with an incompressible multiphase flow solver,Super CE/SE,for more complex and practical applications.The updated solver is evaluated through comparison with an early droplet research.
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.
基金Iranian Offshore Oil Company (IOOC) for financial support of this work
文摘Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.
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.
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.
基金supports for this project from the National Natural Science Foundation of China(22378295).
文摘This study investigates the droplet formation for the liquid–liquid two-phase flow within a square T-junction microchannel through numerical simulation using volume of fluid method and experimental visualization using high-speed camera imaging.The T-junction microchannel has a cross-sectional width of 0.6 mm and a total length of 27.3 mm.The solution of cyclohexane with 2%and 3%mass concentrations of sorbitan trioleate surfactant were used as the continuous phase,and water was used as the dispersed phase.Slug flow,characteristic of squeezing regime,were predominantly observed.The effects of liquid–liquid two-phase flow rate ratio,and dimensionless number on droplet size,and pressure drop were investigated.The squeezing regime was mapped for 0.0005≤Ca_(c)≤0.0052(capillary number)and 0.1≤q≤10(flow rate ratio).The pressure drops of slugs were in the range from 40 Pa to 200 Pa.The slug lengths were measured between 1 mm and 9 mm.A universal flow map dependent on Ca_(c)Re_(d)^(0.5) are projected to investigate the droplet formation behavior in T-junction microchannel.Correlation expressions are proposed to predict pressure drops and the slug lengths for liquid–liquid two-phase flow in a square T-junction microchannel,using dimensionless numbers such as flow rate ratio and capillary number.The result shows that large continuous phase flow rates facilitate smaller slugs,whereas higher dispersed phase flow rates result in longer shorts.
基金The authors gratefully thank K.Tang and A.Beccantini fromthe Commissariata l’Energie Atomique for having provided the numerical solutions computed with their sevenequation model.The second author would like to particularly acknowledge the support provided by the German Jordanian University through the project SEED-SNRE 7-2014.
文摘A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of the one-fluid Euler solvers,differing from them by the presence of a void ratio transport-equation.The model and the system of equations to be simulated are presented.Results are displayed for shock and expansion tube problems,shock-bubble interaction and underwater explosion.Close agreement with reference solutions,obtained from explicit finite volume approaches,is demonstrated.Different numerical methods are additionally displayed to provide comparable and improved computational efficiency to the model and the system of equations.The overall procedure is therefore very well suited for use in general two-phase fluid flow simulations.
文摘The comparative study on seven equation models with two different six equations modelfor compressible two-phase flow analysis is proposed. The seven equations model isderived for compressible two-phase flow that is in the nonconservation form. In thepresent work, two different six equations model are derived for two pressures, two velocities and single temperature with the derivation of the equation of state. The closingequation for one of the six equations model is energy conservation equation while anotherone is closed by entropy balance equation. The partial differential form of governingequations is hyperbolic and written in the conservative form. At this point, the set ofgoverning equations are derived based on the principle of extended thermodynamics.The method of solving single temperature from both six equation models are simple anddirect solution can be obtained. Numerical simulation has been tried using one of the sixequation models for air–water shock tube problems. Explicit fourth order Runge–Kuttascheme is used with Finite Volume Shock Capturing method for solving the governingequations numerically. The pressure, velocity and volume fraction variations are captured along the shock tube length through flow solver. Experimental work is carried outto magnify the initial stage of liquid injection into a gas. The outcome of six equationsmodel for compressible two-phase flow has revealed the multi-phase flow characteristicsthat are similar to the actual conditions.
基金supported by the NSFC Grant no.12271492the Natural Science Foundation of Henan Province of China Grant no.222300420550+1 种基金supported by the NSFC Grant no.12271498the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
文摘Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.
基金supported by the Stable Support Fund forBasic Disciplines,China(No.3072024WD0201)。
文摘Underwater gas-liquid two-phase propulsion technology is an emerging propulsion method that offers high efficiency and unrestricted navigation speed.The integration of this technology into water ramjet engines can significantly enhance propulsion efficiency and holds substantial potential for broad applications.However,forming a gas-liquid two-phase flow within the nozzle requires introducing a large amount of rammed seawater.At this time,there is a complex phase transition problem of combustion products in the combustion chamber,which makes the thermodynamic calculation for gas-liquid two-phase water ramjet engines particularly challenging.This paper proposes a thermodynamic calculation method for gas-liquid two-phase water ramjet engines,based on the energy equation for gas-liquid two-phase flow and traditional thermodynamic principles,enabling thermodynamic calculations under conditions of ultra-high water-fuel ratios.Additionally,ground ignition tests of the gas-liquid two-phase engine were conducted,yielding critical engine test parameters.The results demonstrate that the gas-liquid two-phase water ramjet engine achieves a high specific impulse,with a theoretical maximum specific impulse of up to 7000(N s)/kg.The multiphase flow effects significantly impact engine performance,with specific impulse losses reaching up to 25.86%.The error between the thrust and specific impulse in the ground test and the theoretical values is within 10%,validating the proposed thermodynamic calculation method as a reliable reference for further research on gas-liquid two-phase water ramjet engines.
基金financial support by the National Natural Science Foundation of China (Nos.52471293 and 12372270)the National Youth Science Foundation of China (Nos.52101322 and 52108375)+3 种基金the Program for Intergovernmental International S&T Cooperation Projects of Shanghai Municipality, China (Nos.24510711100 and 22160710200)The Oceanic Interdisciplinary Program of Shanghai Jiao Tong University (No.SL2022PT101)funded by the Open Fund of the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology (No.LP2415)National Key R&D Program of China (No.2023YFC2811600)
文摘Deep-sea mineral resource transportation predominantly utilizes hydraulic pipeline methodology.Environmental factors induce vibrations in flexible pipelines,thereby affecting the internal flow characteristics.Therefore,real-time monitoring of solid–liquid two-phase flow in pipelines is crucial for system maintenance.This study develops an autoencoder-based deep learning framework to reconstruct three-dimensional solid–liquid two-phase flow within flexible vibrating pipelines utilizing sparse wall information from sensors.Within this framework,separate X-model and F-model with distinct hidden-layer structures are established to reconstruct the coordinates and flow field information on the computational domain grid of the pipeline under traveling wave vibration.Following hyperparameter optimization,the models achieved high reconstruction accuracy,demonstrating R^(2)values of 0.990 and 0.945,respectively.The models’robustness is evaluated across three aspects:vibration parameters,physical fields,and vibration modes,demonstrating good reconstruction performance.Results concerning sensors show that 20 sensors(0.06%of total grids)achieve a balance between accuracy and cost,with superior accuracy obtained when arranged along the full length of the pipe compared to a dense arrangement at the front end.The models exhibited a signal-to-noise ratio tolerance of approximately 27 dB,with reconstruction accuracy being more affected by sensor failures at both ends of the pipeline.
基金financially supported by the National Natural Science Foundation of China(Grant No.12072336).
文摘The influence of the squeeze film between the tube and the support structure on flow-induced vibrations is a critical factor in tube bundles subjected to two-phase cross-flow.This aspect can significantly alter the threshold for fluidelastic instability and affect heat transfer efficiency.This paper presents a mathematical model incorporating the squeeze film force between the tube and the support structure.We aim to clarify the mechanisms underlying fluidelastic instability in tube bundle systems exposed to two-phase flow.Using a self-developed computer program,we performed numerical calculations to examine the influence of the squeeze film on the threshold of fluidelastic instability in the tube bundle system.Furthermore,we analyzed how the thickness and length of the squeeze film affect both the underlying mechanisms and the critical velocity of fluidelastic instability.
基金financially supported by the Key Research and Development Program of Shandong Province(Grant Nos.2022CXGC020405,2023CXGC010415 and 2025TSGCCZZB0238)the National Natural Science Foundation of China(Grant No.52171288)the financial support from CNPq,FAPERJ,ANP,Embrapii,and China National Petroleum Corporation(CNPC).
文摘This work investigated the dynamic behavior of vertical pipes conveying gas-liquid two-phase flow when subjected to external excitations at both ends.Even with minimal excitation amplitude,resonance can occur when the excitation frequency aligns with the natural frequency of the pipe,significantly increasing the degree of operational risk.The governing equation of motion based on the Euler-Bernoulli beam is derived for the relative deflection with stationary simply supported ends,with the effects of the external excitations represented by source terms distributed along the pipe length.The fourth-order partial differential equation is solved via the generalized integral transform technique(GITT),with the solution successfully verified via comparison with results in the literature.A comprehensive analysis of the vibration phenomena and changes in the motion state of the pipe is conducted for three classes of external excitation conditions:same frequency and amplitude(SFSA),same frequency but different amplitudes(SFDA),and different frequencies and amplitudes(DFDA).The numerical results show that with increasing gas volume fraction,the position corresponding to the maximum vibration displacement shifts upward.Compared with conditions without external excitation,the vibration displacement of the pipe conveying two-phase flow under external excitation increases significantly.The frequency of external excitation has a significant effect on the dynamic behavior of a pipe conveying two-phase flow.
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 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.
基金supported by the National Natural Science Foundation of China(Grant No.11972194).
文摘By combining with an improved model on engraving process,a two-phase flow interior ballistic model has been proposed to accurately predict the flow and energy conversion behaviors of pyrotechnic actuators.Using computational fluid dynamics(CFD),the two-phase flow and piston engraving characteristics of a pyrotechnic actuator are investigated.Initially,the current model was utilized to examine the intricate,multi-dimensional flow,and energy conversion characteristics of the propellant grains and combustion gas within the pyrotechnic actuator chamber.It was discovered that the combustion gas on the wall's constant transition from potential to kinetic energy,along with the combined effect of the propellant motion,are what create the pressure oscillation within the chamber.Additionally,a numerical analysis was conducted to determine the impact of various parameters on the pressure oscillation and piston motion,including pyrotechnic charge,pyrotechnic particle size,and chamber structural dimension.The findings show that decreasing the pyrotechnic charge will lower the terminal velocity,while increasing and decreasing the pyrotechnic particle size will reduce the pressure oscillation in the chamber.The pyrotechnic particle size has minimal bearing on the terminal velocity.The results of this investigation offer a trustworthy forecasting instrument for comprehending and creating pyrotechnic actuator designs.
基金supported by the National Key R&D Program of China(No.2023YFB4104200)the National Natural Science Foundation of China(Nos.52474067,52441411,52325402,52034010,and12131014)+2 种基金the Natural Science Foundation of Shandong Province,China(No.ZR2024ME005)Fundamental Research Funds for the Central Universities(Nos.25CX02025A and 21CX06031A)the Youth Innovation and Technology Support Program for Higher Education Institutions of Shandong Province,China(No.2022KJ070)。
文摘In this study,we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network(EPINN),which is applied to simulate two-phase flow in heterogeneous porous media.Specifically,we first analyze the layerwise outputs of EPINN,and identify the distinct functions across layers,including dimensionality adjustment,pointwise construction of non-equilibrium potential,extraction of high-level features,and the establishment of long-range dependencies.Then,inspired by these distinct modules,we propose a novel constraint learning strategy based on regularization approaches,which improves neural network(NN)learning through layer-specific differentiated updates to enhance cross-timestep generalization.Since different neu ral network layers exhibit varying sensitivities to global generalization and local regression,we decrease the update frequency of layers more sensitive to local learning under this constraint learning strategy.In other words,the entire neural network is encouraged to extract more generalized features.The superior performance of the proposed learning strategy is validated through evaluations on numerical examples with varying computational complexities.Post hoc analysis reveals that gradie nt propagation exhibits more pronounced staged characte ristics,and the partial differential equation(PDE)residuals are more uniformly distributed under the constraint guidance.Interpretability analysis of the adaptive constraint process suggests that maintaining a stable information compression mode facilitates progressive convergence acceleration.
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.
