Two-phase Flow Model Research Articles

An explicit approximation of the central angle for the curved interface in double-circle model for horizontal two-phase stratified flow

Stratified flow in horizontal tubes is frequently observed in gas-liquid two-phase flow system. In the two-fluid modeling, it is important to define the interface shape in solving the balance equations to determine the key parameters such as the interfacial transfer terms, void fraction, and pressure drop. A double-circle model is usually introduced to depict the concave-down interface in a horizontal circular tube under the stratified-wavy flow condition. However, calculation of the central angle in the double-circle model, which represents the interfacial curvature, requires an appropriate iterative numerical root-finding scheme to solve the implicit transcendental equation. In this study, an explicit approximate equation has been proposed without requirement of the iterative scheme and numerical instability, which is expected to improve the coding process and computation efficiency in the analysis code with the two-fluid model.

The die swell eliminating mechanism of hot air assisted 3D printing of GF/PP and its influence on the product performance

Abstract For eliminating the die swell phenomenon in 3D printing of GF/PP, a hot air assisted 3D printing method is proposed and its mechanism is studied. A two-phase flow model consisting of compressible gas and in-compressible melt is established, and the process of polymer filament extrusion is simulated. A series of experiments are conducted to compare the differences between traditional printing and gas-assisted printing in terms of extruded filament, temperature, and morphology. The simulation and experiment results show that the addition of gas effectively mitigates the melt die swell, and increases the extrusion filament temperature to more than 70°C. The extrusion pressure is reduced about two orders of magnitude, and the first normal stress is decreased from 400,000 to 20,000 Pa. The surface morphology of printed product is smoother and more refined. This study provides valuable information for understanding the principles of gas-assisted printing and demonstrates its potential for improving printing quality and efficiency.

On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness

Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn–Hilliard equation. We then analyse the resulting model and prove its well-posedness. A key to the analysis is the new concept of sigma-convergence in thin heterogeneous domains allowing to pass to the homogenization limit with respect to the heterogeneities and the domain thickness simultaneously.

The generalized Riemann problem scheme for a laminar two-phase flow model with two-velocities

In this paper, we propose a generalized Riemann problem (GRP) scheme for a laminar two-phase flow model. The model takes into account the distinctions between different densities and velocities, and is obtained by averaging vertical velocities across each layer for the two-phase flows. The rarefaction wave and the shock wave are analytically resolved by using the Riemann invariants and Rankine-Hugoniot condition, respectively. The source term is incorporated into the resolution of the GRP method. We further extend the GRP method to the two-dimensional (2-D) system, which is non-conservative. The Strang splitting method is applied, but it still can not provide explicit Riemann invariants and shock relations, which prevent us to apply the GRP method directly. Another splitting technique is also applied to the 2-D case, such that each split subsystem contains only one family of waves. Numerical experiments on some typical problems show that the proposed method achieves good performance.

Study of solid-liquid two-phase flow model of drilling fluids for analyzing mud cake formation

Mud cake is formed by the accumulation of particles on the surface and inside of the well wall during the filtration of drilling fluids, which is multiply affected by reservoir types, composition of drilling fluids, and wellbore conditions. Numerical simulation can provide a more comprehensive study than experiments, but the usual single-phase models of drilling fluid is difficult to simulate the non-homogeneous characteristics of mud cake. In this paper, the calculation method of interactions between particles and the drag force on particles with different sphericity in non-Newtonian fluid are derived. Therefore, a solid-liquid two-phase flow model of drilling fluid that describes the motion of solid and liquid phases, respectively, is constructed to investigate the influences of their properties on the dynamic non-homogeneous formation of mud cake in the real pore space of cores. The results show that the flow volume and velocity of the liquid phase are affected by the tortuosity of the pore channel, which in turn affects the entering number of particles. The influences of particle parameters on the entering number are radius > morphology > release velocity > free energy of the surface > density > release concentration. The solid-liquid two-phase flow model can refine the analysis to formulate the most applicable drilling fluids, which will significantly reduce the exploration and validation work of plugging experiments.

Reinvestigating the Kinetic Model for the Suspended Sediment Concentration in an Open Channel Flow

The prediction of sediment transport, related to different environmental and engineering problems, requires accurate mathematical models. Most available mathematical models for the concentrations of suspended sediments are based on the classical advection diffusion equation, which remains not efficient enough to describe the complete behavior related to sediment–water two-phase flows and the feedback between the turbulent unsteady flow and suspended sediments. The aim of this paper is to reinvestigate the kinetic model for turbulent two-phase flows, which accounts for both sediment–turbulence interactions and sediment–sediment collisions. The present study provides a detailed and rigorous derivation of the kinetic model equations, clarifications about the mathematical approach and more details about the main assumptions. An explicit link between the kinetic model and the classical advection diffusion equation is provided. Concentration profiles for suspended sediments in open channel flows show that the kinetic model is able to describe the near-bed behavior for coarse sediments.

Study of the mechanism of action of sand therapy on atherosclerosis based on the two-phase flow-Casson model.

Sand therapy is a non-pharmacological physiotherapy method that uses the natural environment and resources of Xinjiang to treat through the heat transfer and magnetic effects of sand. Employing the two-phase flow-Casson blood flow model, we investigate the mechanism of atherosclerosis prevention via sand therapy, offering a biomechanical theoretical rationale for the prevention of atherosclerosis through sand therapy via the prism of computational fluid dynamics (CFD). Sand therapy experiments were conducted to obtain popliteal artery blood flow velocity, and blood was considered as a two-phase flow composed of plasma and red blood cells, and CFD method was applied to analyze the hemodynamic effects of Casson's blood viscosity model before and after sand therapy. (1) The blood flow velocity increased by 0.24 m/s and 0.04 m/s at peak systolic and diastolic phases, respectively, after sand therapy; the axial velocity of blood vessels increased by 28.56% after sand therapy. (2) The average red blood cell viscosity decreased by 0.00014 Pa ⋅ s after sand therapy. (3) The low wall shear stress increased by 1.09Pa and the high wall shear stress reached 41.47Pa after sand therapy. (4) The time-averaged wall shear stress, shear oscillation index and relative retention time were reduced after sand therapy. The increase of blood flow velocity after sand therapy can reduce the excessive deposition of cholesterol and other substances, the decrease of erythrocyte viscosity is beneficial to the migration of erythrocytes to the vascular center, the increase of low wall shear stress has a positive effect on the prevention of atherosclerosis, and the decrease of time-averaged wall shear stress, shear oscillation index and relative retention time can reduce the occurrence of thrombosis.

Measuring and modeling of liquid water transport in a carbon paper with the aid of centrifuge experiment

In previous macroscopic average models of proton exchange membrane fuel cells (PEMFCs), liquid water was assumed to be continuous throughout the carbon paper. The transport of disconnected water drops in carbon paper has long been neglected in these models, which tend to underestimate water saturation in carbon paper. This study proposes a two-phase flow model that considers the transport of disconnected water drops to simulate the air-water transport in carbon paper. The proposed model was established based on the relationship between capillary force and liquid water saturation, and this relationship was obtained by conducting centrifuge experiments. In the centrifuge experiment, initially, the water saturation inside the carbon paper sample was one, and the centrifugal acceleration was zero. As the centrifugal acceleration increased, the water saturation decreased owing to the centrifugal force. After twenty seconds, the water saturation no longer decreases because the centrifugal force on the liquid water is balanced by the capillary force. Centrifugal acceleration was used to evaluate the capillary force. When the centrifugal acceleration was 185 ms−2, the saturation of the water drops in the balanced state was 32.0%. As the centrifugal acceleration increases to 739 ms−2, the saturation decreases to 6.5%. According to the experimental results, a function correlating the saturation and centrifugal acceleration, that is, the capillary force, was established. Finally, the results show that the centrifugal acceleration is more than 18.5 times that of the gravitational acceleration, indicating that the effect of gravity on the motion of water drops is negligible.

Flow regime classification using various dimensionality reduction methods and AutoML

Accurate identification of flow regimes is paramount in several industries, especially in chemical and hydrocarbon sectors. This paper describes a comprehensive data-driven workflow for flow regime identification. The workflow encompasses: i) the collection of dynamic pressure signals using an experimentally verified numerical two-phase flow model for three different flow regimes: stratified, slug and annular flow, ii) feature extraction from pressure signals using Discrete Wavelet Transformation (DWT), iii) Evaluation and testing of 12 different Dimensionality Reduction (DR) techniques, iv) the application of an AutoML framework for automated Machine Learning classifier selection among K-Nearest Neighbors, Artificial Neural Networks, Support Vector Machines, Gradient Boosting, Random Forest, and Logistic Regression, with hyper-parameter tuning. Kernel Fisher Discriminant Analysis (KFDA) is the best DR technique, exhibiting superior goodness of clustering, while KNN proved to be the top classifier with an accuracy of 92.5 % and excellent repeatability. The combination of DWT, KFDA and KNN was used to produce a virtual flow regime map. The proposed workflow represents a significant step forward in automating flow regime identification and enhancing the interpretability of ML classifiers, allowing its application to opaque pipes fitted with pressure sensors for achieving flow assurance and automatic monitoring of two-phase flow in various process industries.

Using X-ray computed tomography and pore-scale numerical modeling to study the role of heterogeneous rock surface wettability on hydrogen-brine two-phase flow in underground hydrogen storage

Underground hydrogen storage (UHS) is receiving increasing attention to address the challenges in hydrogen storage. A crucial aspect of UHS is understanding the transport of hydrogen in subsurface porous media. In this work, hydrogen core flooding experiments were conducted in a sandstone sample and then the pore-scale distribution of hydrogen and brine was visualized using high-resolution X-ray micro-computed tomography (micro-CT). After CT image processing, we measured the surface contact angles (CAs) on rock surfaces and found that the measured CAs followed a log-normal distribution. To investigate the influence of rock surface wettability on the transport properties in the hydrogen-brine-sandstone system, the lattice Boltzmann (LB) method was used to simulate two-phase flows with different surface CA distributions; hydrogen-brine relative permeability and capillary pressure curves through the primary drainage, imbibition, and secondary drainage processes were obtained by LB simulations. X-ray CT scanning showed that hydrogen resided in both large pores and small pores and pore throats after the primary drainage process (i.e., hydrogen displacing brine), whereas after the imbibition process (i.e., brine displacing hydrogen) hydrogen stayed primarily in large pores where the capillary pressure barriers were low. The LB two-phase flow modeling illustrated that water’s relative permeability increased whereas hydrogen’s relative permeability decreased when the core flooding moved from primary drainage to imbibition; in contrast, when the core flooding moved from imbibition to secondary drainage, water’s relative permeability decreased whereas hydrogen’s relative permeability increased. Decreasing the surface CA increased the capillary pressure and reduced the hydrogen residual rate, which indicates high hydrogen retrievability and thus is favorable for UHS practice. The change in CA’s standard deviation did not cause noticeable changes in water’s relative permeability curves, whereas it resulted in noticeable changes in hydrogen’s relative permeability curves. This work is the first study that utilizes X-ray micro-CT scanning and pore-scale multiphase flow modeling to quantitatively and comprehensively investigate hydrogen-brine two-phase flow properties under different rock surface wettability distributions. The research findings from this study will advance the understanding of hydrogen transport in an underground storage system and provide essential data for large-scale field studies in UHS.

Numerical simulation and analysis of a two-phase flow model considering bubble coverage for alkaline electrolytic water

The electrolysis of water to produce hydrogen is thought to be one of the most promising strategies to achieve carbon neutrality. However, the evolution of bubbles causes possible hindrances to its mass mobility between electrolytic solution and catalyst because they envelop the catalyst surface, which ultimately leads to a reduction in conversion efficiency. At present, the correlation between vigorous bubble evolution and electrolytic water performance has not been thoroughly investigated. Therefore, to quantitatively analyze this correlation, this work constructs an integrated model of the alkaline electrolytic cell based on COMSOL software that considers the effect of bubble coverage. The results show that increasing the bubble contact angle facilitates the generation and separation of bubbles and can decrease bubble coverage's effect on the electrolytic cell's current density at the same voltage. The current density can increase from 850 A/m2 to 1100 A/m2 with an increase in bubble contact angles from 90 ° to 140 ° at an electrolytic cell voltage of 1.83 V. In addition, although increasing the operating temperature (50–80 °C) enhances the negative effects due to bubble coverage, increasing the temperature still can increase the hydrogen production efficiency. Therefore, it can be believed that the work in this paper may guide the development and utilization of alkaline electrolytic cells.

The subdivision-based IGA-EIEQ numerical scheme for the Navier–Stokes equations coupled with Cahn–Hilliard phase-field model of two-phase incompressible flow on complex curved surfaces

We develop an accurate and robust numerical scheme for solving the incompressible hydrodynamically coupled Cahn–Hilliard system of the two-phase fluid flow system on complex surfaces. Our algorithm leverages a number of efficient techniques, including the subdivision-based isogeometric analysis (IGA) method for spatial discretization, the explicit Invariant Energy Quadratization (EIEQ) method for linearizing nonlinear potentials, the Zero-Energy-Contribution (ZEC) method for decoupling, and the projection method for the Navier–Stokes equation to facilitate fully decoupled type implementations. The integration of these methodologies results in a fully discrete scheme with desired properties such as linearity, second-order temporal accuracy, full decoupling, and unconditional energy stability. The implementation of the scheme is straightforward, requiring the solution of a few elliptic equations with constant coefficients at each time step. The rigorous stability proof of unconditional energy stability and the implementation procedure are given in detail. Numerous numerical simulations on complex curved surfaces are carried out to verify the effectiveness of the proposed numerical scheme.

Bridging the gap: Connecting pore-scale and continuum-scale simulations for immiscible multiphase flow in porous media

This study aims to bridge length scales in immiscible multiphase flow simulation by connecting two published governing equations at the pore-scale and continuum-scale through a novel validation framework. We employ Niessner and Hassnaizadeh's [“A model for two-phase flow in porous media including fluid-fluid interfacial area,” Water Resour. Res. 44(8), W08439 (2008)] continuum-scale model for multiphase flow in porous media, combined with the geometric equation of state of McClure et al. [“Modeling geometric state for fluids in porous media: Evolution of the Euler characteristic,” Transp. Porous Med. 133(2), 229–250 (2020)]. Pore-scale fluid configurations simulated with the lattice-Boltzmann method are used to validate the continuum-scale results. We propose a mapping from the continuum-scale to pore-scale utilizing a generalized additive model to predict non-wetting phase Euler characteristics during imbibition, effectively bridging the continuum-to-pore length scale gap. Continuum-scale simulated measures of specific interfacial area, saturation, and capillary pressure are directly compared to up-scaled pore-scale simulation results. This research develops a numerical framework capable of capturing multiscale flow equations establishing a connection between pore-scale and continuum-scale simulations.

A lattice Boltzmann model for incompressible gas and liquid two-phase flows combined with free-surface method

A novel lattice Boltzmann (LB) model is proposed to study the gas and liquid two-phase flows with large density and viscosity ratios. In the model, both the gas and liquid phases are considered as viscous incompressible fluids, which are governed separately by the two-relaxation-time LB equations. They are coupled by a momentum exchange method at the interface. The interaction between the gas and liquid phases is explicitly described and naturally involved in the model. The interfacial conditions in the model are validated by the benchmarks of the layered Poiseuille flow and the Laplace law. The feasibility of combining this model with the bubble model and the wetting scheme is proven through transient flow problems of single bubble rising and capillary intrusion. The validity of this model is confirmed by more complex flows including solid–liquid–gas coupling and droplet breaking problems by simulating shearing a droplet on a substrate and a droplet falling on a liquid film. The results demonstrate that the present model can be used to describe both the gas and the liquid flows. This work provides a solution to model the simulation of the dynamical behaviors of multi-phase flows.

The importance of the inertial coupling in the two-fluid model of two-phase flow

The new flux representation of the two-fluid model of two-phase flow, where the mixture is described in terms of the volumetric and drift fluxes, is currently the most consistent formulation to treat the inertial coupling between phases. In this representation, the dynamics of the relative motion between phases is revealed as a non-linear wave propagation equation. It is shown that the character and stability of this equation is determined by the balance between the inertial coupling and the interfacial drag. A novel stability criterion is derived that can be used to assess the interfacial closure laws and as a tool to determine the conditions under which a drift-flux correlation is stable. A family of inertial coupling functions for vertical two-phase flow, based on topologies of bubble's vortical wakes, is derived and the corresponding coupling parameters are assessed using available experimental data. The resulting stability maps reveal the occurrence of an unstable region at intermediate void fractions bound by a bistable condition at low and high void fractions, which can be associated with the slug flow-pattern regime.

Influence of embedded structure on two-phase reactive flow characteristics for a small combustion chamber with a moving boundary

In special launch scenarios such as armament and aerospace, the scale of the launch system is severely restricted, which causes unstable combustion of propellant. An embedded structure for the small propulsion system driven by solid propellant is proposed to overcome this problem. This study aims to demonstrate the two-phase flow behaviors and launch safety of the combustion chamber with an embedded structure. A two-dimensional two-phase flow model based on the modified two-fluid theory is developed to describe the detailed two-phase flow behaviors in the combustion chamber during launching. Different from most of the existing studies, the constitutive equations determined from actual physical conditions are used to close the system of continuity equations. The numerical results are compared with that of the experiment to verify the accuracy of the numerical model. On this basis, the launch performance of the embedded structure is investigated. The numerical results indicate that the embedded structure facilitates the ignition process and reduces the risk of excessive pressure, but decreases the muzzle velocity at the same time. In addition, the effect of design parameters on launch safety is further investigated. Design parameters directly affect the launch safety, and the selection of reasonable parameters is a useful method for enhancing the launch performance.

The Development of a Transient Analysis Platform of Near-Critical CO2 Thermodynamic Systems via an Enthalpy-Based Implicit Continuous Eulerian Approach

This work presents the development and validation of an enthalpy-based implicit continuous Eulerian (ICE) solver, termed the near-critical ICE solver (NICES), for the analysis of near-critical CO2 thermodynamic systems. Traditional approaches relying on pressure and temperature as main inputs for the analysis have limitations in handling CO2 near the critical point, which exhibits unique characteristics and frequent phase changes. To overcome these limitations, this study proposes using enthalpy as a more suitable mathematical modeling approach. The NICES methodology employs the homogeneous equilibrium model and the Span and Wagner equations of state for CO2. This solver demonstrates improved numerical stability and computational speed compared to explicit calculation methods, as validated by frictionless heated pipe scenarios involving phase transitions near the critical point. The enthalpy-based NICES platform can predict thermohydraulics, including multiphase flows, without requiring specialized two-phase flow models.

A ternary phase-field model for two-phase flows in complex geometries

In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn–Hilliard model is considered as the solid phase, and only one Cahn–Hilliard equation with degenerate mobility needs to be solved due to the condition of volume conservation, which is consistent with the standard phase-field model with a single-scalar variable for two-phase flows. To depict different wetting properties at the complex fluid–solid boundaries, the spreading parameters in ternary phase-field model are determined based on the Young’s law, in which the liquid–solid surface tension coefficient is assumed to be a linear function of gas–liquid surface tension coefficient and related to the contact angle and the minimum curvature of the solid surface. In addition, to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface, the phase-field variable of the solid phase is also used to derive the modified Navier–Stokes equations. To test the present model, we further develop a consistent and conservative Hermite-moment based lattice Boltzmann method where an adjustable scale factor is introduced to improve the numerical stability, and conduct the numerical simulations of several benchmark problems. The results illustrate that present model has the good capability in the study of the two-phase flows in complex geometries.

Heat transfer effect on the modeling of jets under supercritical and transcritical conditions

The injection of nitrogen under supercritical and transcritical conditions, where the injection temperature is below nitrogen’s critical point, but the pressure is above it, is considered in this paper. While the scientific community recognizes that the sharp gradients of the different thermophysical parameters make it inappropriate to employ a two-phase flow modeling at conditions above the critical point, the issue is not restrained to the mere representation of turbulence for a mono-phase flow. Instead, a quantitative similarity with gas-jet-like behavior led to proposing an incompressible but variable density hypothesis suitable for describing supercritical and sub/near-critical conditions. Presently, such an approach is extended and assessed for a configuration including injector heat transfer. As such, axial density and temperature decay rates and jet spreading rates of density and temperature are evaluated, indicating a higher mixing efficiency in the supercritical regime and an overall dominance of heat propagation over momentum transport, with a greater preponderance in the supercritical regime.

Discretization schemes for the two simplified global double porosity models of immiscible incompressible two-phase flow

We present the discretization schemes for the two simplified homogenized models of immiscible incompressible two-phase flow in double porosity media with thin fractures. The two models were derived previously by the authors by different linearizations of the nonlinear local problem called the imbibition equation which appears in the homogenized model after passage to the limit as ε → 0. The models are fully homogenized with the matrix-fracture source terms expressed as a convolution.