Two-phase Flow Model Research Articles

A Mathematically Optimized Design Solution for Structure of PEMFC Catalyst Layer Based on a Two-Phase Flow Model

Abstract Proton exchange membrane fuel cells (PEMFCs) have emerged as a promising solution as the world is moving toward sustainable energy resources. However, in order to compete economically with existing technologies, further improvements in performance are necessary. Mathematical modeling and optimization are viable tools for designing better PEMFCs. This study aims to provide a framework for topological optimization of the electrode structure, with the ultimate goal of enhancing cell performance. To achieve this, a two-phase flow model of PEMFC is developed to characterize the cell performance. The model is then coupled with a topology optimization technique, which is the main focus of the present work, to seek an optimized constituent distribution in the catalyst layer. Results indicate that an electrode with a heterogeneous structure can enhance the overall cell performance by balancing various transport and rate processes. The optimized designs are investigated for various key factors, including effective diffusivity, effective conductivity, and liquid water management, to demonstrate how an optimized design can be advantageous.

Numerical Simulation of Flow Fields and Sediment-Induced Wear in the Francis Turbine

Based on the solid–liquid two-phase flow model and the Realizable k-ε Turbulence model, numerical simulations of the sediment–water flow in the flow components of the turbine were conducted. The distribution of sediment-induced wear within the turbine was obtained by analyzing the sediment volume fraction (SVF) and the erosion rate. The results revealed that sediment-induced wear on the stay and guide vanes was primarily distributed along the water inlet edge of the stay and guide vanes. For the runner blades, wear was predominantly localized along the water inlet edge and near the lower ring. The sediment-induced wear patterns on these flow components were found to be consistent with the sediment volume fractions (SVFs) on their surfaces.

Geometric flow control in lateral flow assays: Macroscopic two-phase modeling

Lateral flow assays (LFAs) are widely employed in a diverse range of applications, including clinical diagnostics, pharmaceutical research, forensics, biotechnology, agriculture, food safety, and environmental analysis. A pivotal component of LFAs is the porous polymeric membrane, which facilitates the capillary-driven movement of fluids, known as “imbibition,” in which a wetting fluid displaces a non-wetting fluid within the pore space of the membrane. This study presents a multi-scale modeling framework designed to investigate the imbibition process within LFAs. The framework integrates microscopic membrane characteristics into a macroscopic two-phase flow model, allowing the simulation of imbibition in membranes with different micro-scale properties and macro-scale profiles. The validity of the model was established through comparative analysis with documented case studies, a macro-scale single-phase flow model, and experimental observations, demonstrating its accuracy in simulating the imbibition process. The study also examines imbibition in various geometric configurations, including bifurcated (Y-shaped) and multi-branch geometries commonly found in multiplexed LFAs. The influence of geometric features such as length ratio, width ratio, branching angle, bifurcation point location, and asymmetry on fluid transport is investigated. Results indicate that membranes with larger branching angles exhibit slower imbibition. In addition, the influence of membrane type on macroscopic flow patterns is evaluated, showing that membranes with lower permeability require longer imbibition times. The insights gained from this research support a data-driven strategy for manipulating wetting behavior within LFAs. This approach can be leveraged to optimize the performance of LFAs and increase their effectiveness in various applications.

Lubrication optimization of high-speed train drive gearbox

The gears in the high-speed heavy-duty gearbox of the high-speed train are typical high-speed heavy-duty gears. Combined with the transmission principle and structural characteristics of the high-speed train drive gearbox, to ensure adequate lubrication of meshing gears and bearings, an optimization of the lubricating oil flow inside the gearbox was conducted. The oil and gas two-phase flow model inside the gearbox adopts the VOF model, and the turbulence model adopts the standard κ-ε model. Fluent is used for simulation calculation. The results show that the exhaust port position of the gearbox has little effect on the flow of lubricating oil inside the gearbox; the overall pressure distribution inside the gearbox is relatively uniform, with higher pressure only at the meshing gears; the distribution of lubricating oil inside the gearbox is related to the rotation of the gears, and the flow velocity of lubricating oil is mainly affected by the rotation of the gears, with the maximum flow velocity appearing around the gears; the flow of lubricating oil inside the gearbox meets the lubrication requirements of the gearbox. These results provide support for the lubrication design, flow channel structure improvement, and effectiveness evaluation of high-speed train transmission gearboxes.

Modelling pressure dynamics of oil–gas two-phase flow in double-porosity media formation with permeability-stress sensitivity

Pressure dynamics can reflect the basic characteristics of fluid flow through underground porous formation. In this research, the oil–gas two-phase flow model for a double-porosity media formation with permeability-stress sensitivity was first established for three kinds of outer boundaries. The unified governing equation was deduced by utilizing the H function. The nonlinear mathematical model in consideration of permeability-stress sensitivity was linearized by implementing the canonical perturbation transformation and then solved by using the Laplace transformation. After that, a sequence of typical log–log curves of pressure dynamics influenced by various model parameters were plotted and analyzed. These curves reflect the typical characteristic of a V shape caused by the inter-porosity fluid flow from matrix toward natural fractures. Oil saturation and permeability-stress sensitivity coefficient have much influence on the pressure dynamics. Ultimately, the established model of oil–gas two-phase flow was validated through a well-test fitting interpretation for a real condensate gas well in a sandstone formation. This research can offer insights into the pressure dynamics dominated by the oil–gas two-phase flow in naturally fractured formations and the permeability-stress sensitivity effect.

Two-group drift-flux model in tight lattice subchannel

Tight lattice rod bundles can increase equipment compactness and improve heat exchange efficiency, and they are widely adopted in heat exchange engineering. Understanding the flow characteristics of gas-liquid two-phase flow in tight lattice subchannels is essential for developing heat exchangers and fuel assemblies with these tight bundles. The drift-flux model (DFM) is a crucial two-phase flow model extensively used in subchannel analysis codes. Investigating the DFM in tight lattice subchannels benefits the advancement of these codes. For two-phase flow interfacial structures, significant two-group characteristics exist, with bubbles divided into small (group-one) and large (group-two) bubbles. The substantial differences in flow characteristics between these two groups provide a solid foundation for developing a two-group DFM. This study examined the two-group characteristics of two-phase flow in a tight lattice interior subchannel and developed a corresponding two-group DFM. The two-group correlations for the distribution parameters and drift velocities at the tight lattice interior subchannel level were proposed and verified using experimental data. The accuracy of the developed two-group DFM in predicting group-wise void fraction and gas velocity was also verified. The standard relative deviation between the model predictions and experimental data was 8.11 % and 13.1 % for group-one and group-two void fractions and 8.33 % and 11.7 % for group-one and group-two gas velocities, respectively. This indicates satisfactory accuracy for the newly developed two-group DFM in a tight lattice interior subchannel.

Analysis of heat generation and viscous dissipation with thermal radiation on unsteady hybrid nanofluid flow over a sphere with double-stratification: Case of modified Buongiorno's model

PurposeThis work uses entropy generation analysis to numerically analyze magnetohydrodynamics (MHD) unsteady flow, heat and mass transfer. The study considers changing viscosity, thermal radiation, viscous dissipation, mass suction, heat generation, and stratification processes in a hybrid nanofluid around a spinning sphere. A two-phase nanofluid flow model (Buongiorno model) is used to tackle the current challenge. Both the free stream velocity and the sphere's angular velocity changed over time. Design/methodology/approachThe case study's complicated partial differential equations are transformed into simpler ordinary differential equations utilizing similarity transformation. Implementing the fourth-order Runge-Kutta Fehlberg method with a shooting scheme in MATHEMATICA has allowed us to get numerical solutions for ordinary differential structures. FindingsThe many aspects of these regulated physical characteristics have been elucidated and thoroughly examined via the use of charts and tables. For increasing values of unsteadiness parameter, the velocity profiles in the x-direction grow while they decrease in the z-direction. On the other hand, the temperature profile exhibits a dual pattern, and the concentration profile decreases. As the chemical reaction parameter climbs from 0.25 to 1.0, the Sherwood number for the nanofluid rises by 6721.39% and for the hybrid nanofluid, 3818.9%. When Nr increases from 0.2 to 0.8, nanofluid Nusselt number climbs 22.5% and hybrid nanofluid's Nusselt number rises 21.9%. The Brinkmann number and nanoparticle volume percentage are strongly associated with entropy production. Entropy generation is dual for the temperature difference, magnetic, radiation, and changeable viscosity parameters. The findings are also compared to those from the existing literature and are in excellent agreement with them.

Development and validation of a 1D gas–liquid model for dissolved Mn(II) removal by oxidation process in a square bubble column

Modeling multiphase reactors requires an in-depth multidisciplinary analysis of various phenomena including the chemical kinetics, oxygen mass transfer, as well as the simulation of flows within these contactors. In this study, a 1D model of two-phase flow for Mn(II) removal from drinking water by aeration process is developed and validated. This model is based on the Eulerian description of two-phase gas–liquid flow with the comparison between a one-medium bubble size and a two-bubble class description to represent the bubble population in the heterogeneous flow regime. All the relevant chemical species are simulated by coupling hydrodynamics, gas–liquid mass transfer, and reaction kinetic. A pseudo-first-order model accounting for homogeneous and heterogeneous kinetics is considered for Mn(II) oxidation. The performance of the developed 1D model is compared and validated with experimental data. The 1D model was able to predict quantitatively Mn oxidation as a function of pH, initial Mn(II) and initial Mn(IV) concentrations.

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants

Construction of Solid-Liquid Two-Phase Flow and Wear Rate Prediction Model in Multiphase Pump Based on Mixture Model-Discrete Phase Model Combination Method

Blade wear is the critical problem in the operation of multiphase pump. This paper presents a numerical study of the multiphase flow of multiphase pump. The trajectory of particles in the pump is calculated by the discrete phase model. Then, the simulation results are compared with the model test results of the pump to verify the correctness of the simulation method. The results show that the particles in the impeller domain are mainly near the hub, and the particles in the diffuser domain form a agglomerated area in the middle of the flow channel. The average wear rate of the impeller is more affected by the particle size than that of the diffuser. The maximum wear rate of blade surface increases first and then decreases with the increase of particle size. According to the wear data under different particle sizes, the regression model between particle size and wear rate is fitted to predict the wear of mixed transport pump in actual operation. The research results have important reference value for the prediction of the wear performance of the multiphase pump.

Heat transfer performance and startup characteristics of separated gravity heat pipe

Separated gravity heat pipes, with distinct arrangements of evaporating and condensing sections, offer low thermal resistance, high heat transfer efficiency, and a simple structure, making them suitable for passive cooling of spent fuel pools through gravity-driven processes. In this study, a steady-state, one-dimensional, two-phase flow model is developed to analyze phase change heat transfer in a separated gravity heat pipe. The research investigates the impact of liquid filling rate and vacuum level on heat pipe operation. The findings reveal a notable increase in pressure drop inside the tube with higher liquid filling rates, which diminishes the adaptability of the heat pipe as pressure rises, resulting in a narrower range of effective liquid filling rates. Specifically, the liquid filling rate of the heat pipe ranges from 38 % to 72 % at P = 13.75 kPa and from 44 % to 68 % at P = 15.75 kPa. Additionally, a startup prediction model is formulated based on a thermal resistance network model using the ideal gas assumption. Two startup states—namely, the initial startup state and the subsequent startup state—are proposed for large-scale separated gravity heat pipe arrays. The heat pipe achieves the large-temperature-difference initial startup state at a 50 % liquid filling rate within 7 min before transitioning to the subsequent startup state. The vapor mass, heat transfer coefficient, and working fluid temperature initially increase and then decrease over time, with varying peak times. As the liquid filling rate increases, the maximum vapor mass also increases. The heat transfer coefficient peaks at a 60 % liquid filling rate before subsequently declining. The optimal liquid filling rate of 60 % is identified based on startup time, heat transfer coefficient, and overall heat transfer efficiency.

Study on the effect of Lorentz force on the nuclear reactor core melt stratification in electromagnetic cold crucible

To understand the effect of the Lorentz force on core melt stratification during experiments, a multi-physical field coupling model of electromagnetic induction, non-isothermal flow, and two-phase flow is established in this paper. The evolution of the layered core melt in the electromagnetic cold crucible is studied for different relative densities and phase volume fraction ratios between metal and oxide. The calculation results show that the coupling model can accurately describe the structural evolution of core melt. The Lorentz force cannot change the relative positions of the metal and oxide, but it can significantly affect the morphology of the core melt. If the density of the metal is less than that of the oxide, the Lorentz force causes the light metal with a small phase volume fraction to form a hemispherical shape in the top center of the crucible. As the phase volume fraction increases, the Lorentz force become weaker than those of gravity and buoyancy. The light metal is then flat. When the metal density is greater than the oxide density, the Lorentz force causes the heavy metal with a small phase volume fraction to appear as a hemisphere, but causes the heavy metal with a large phase volume fraction to appear as an ellipsoid in the lower part of the crucible.

Investigation of Backpressure Wave Propagation Properties during Gas Kicks in Managed Pressure Drilling

Summary It is often essential to provide backpressure to the wellbore by changing the opening size of the choke valve when a gas kick is detected during managed pressure drilling (MPD), which maintains the pressure in the bottom of the hole. In this study, a mathematical model was developed to explain how backpressure waves spread and weaken in a wellbore during MPD when there is a gas-liquid two-phase flow. The model is founded on a two-phase flow model, which thoroughly accounts for the gravity, shear force, and interphase interactions between the gas and liquid phases. The small perturbation theory was used to compute the backpressure wave’s propagation speed and attenuation coefficient. The outcome showed satisfactory agreement with other scholars’ experimental results. The model was used to study the impacts of the following variables on the backpressure wave propagation properties: void fraction, temperature, pressure, interphase resistance, shear force, density, invading gas composition, displacement of the drilling fluid, rate of intrusion of gas, gas-liquid surface tension, and drilling fluid viscosity. By using an example well, the laws of pressure wave propagation speed, attenuation coefficient, and propagation time with well depth were analyzed. Through evaluative methods in the field of economic management, the principal control variables governing the propagation of backpressure waves were determined. The conclusion is that, in terms of operational feasibility, lower drilling fluid density and reduced drilling fluid displacement are advantageous for a faster propagation of backpressure waves to the bottom of the well.

Numerical simulation of two-phase oil–water flow in fractured-vuggy reservoirs based on the coefficient of porous medium proportion and coupled regions

Based on the flow characteristics of fluids in various reservoir media, fractured-vuggy oil reservoirs can be classified into seepage zones and conduit flow zones. An interface exists between these two regions, where the movement of formation fluid near this interface is characterized by a coupling or transitional phenomenon between seepage and conduit flow. However, the complexity of this coupling interface poses challenges for traditional numerical simulations in accurately representing the intricate fluid dynamics within fractured-vuggy oil reservoirs. This limitation impacts the development planning and production adjustment strategies for fractured-vuggy oil reservoirs. Consequently, achieving accurate characterization and numerical simulation of these systems remains a critical challenge that requires urgent attention. A new mathematical model for oil-water two-phase flow in fractured-vuggy oil reservoirs is presented, which developed based on a novel coupling method. The model introduces the concept of the proportion coefficient of porous media within unit grids and defines a coupling region. It employs an enhanced Stokes–Brinkman equation to address the coupling issue by incorporating the proportion coefficient of porous media, thereby facilitating a more accurate description of the coupling interface through the use of the coupling region. Additionally, this proportion coefficient characterizes the unfilled cave boundary, simplifying the representation of model boundary conditions. The secondary development on the open-source fluid dynamics software is conducted by using matrix & laboratory (MATLAB). The governing equations of the mathematical model are discretized utilizing finite volume methods and applying staggered grid techniques along with a semi-implicit calculation format for pressure coupling—the Semi-Implicit Method for Pressure Linked Equations algorithm—to solve for both pressure and velocity fields. Under identical mechanism models, comparisons between simulation results from this two-phase flow program and those obtained from Eclipse reveal that our program demonstrates superior performance in accurately depicting flow states within unfilled caves, thus validating its numerical simulation outcomes for two-phase flow in fractured cave reservoirs. Utilizing the S48 fault-dipole unit as a case study, this research conducted numerical simulations to investigate the water-in-place (WIP) behavior in fractured-vuggy oil reservoirs. The primary focus was on analyzing the upward trend of WIP and its influencing factors during production across various combinations of fractures and dipoles, thereby validating the feasibility of the numerical modeling approach in real-world reservoirs. The simulation results indicated that when multiple dissolution cavities at different locations communicated with the well bottom sequentially, the WIP in the production well exhibited a staircase-like increase. Furthermore, as the distance between bottom water and well bottom increased, its effect on water intrusion into the well diminished, leading to a slower variation in the WIP curve. These characteristics manifested as sudden influxes of water flooding, rapid increases in water levels, and gradual rises—all consistent with actual field production observations. The newly established numerical simulation method for fractured-vuggy oil reservoirs quantitatively describes two-phase flow dynamics within these systems, thus effectively predicting their production behaviors and providing guidance aimed at enhancing recovery rates typically observed in fractured-vuggy oil reservoirs.

A pore-scale investigation of viscous coupling effect on immiscible two-phase flow in porous media

Viscous coupling effect plays a significant role in immiscible two-phase flow within porous media, while its influence on relative permeability remains uncertain. In this paper, an improved MRT-based viscosity-modified multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann model, capable of handling high viscosity ratio, is employed to simulate two-phase flow with different viscosities in a cross-array circular structure and a real rock structure, respectively. The applicability of this model for two-phase flow with various viscosity ratios has been verified by some typical tests. Systematically, the effects of viscosity ratio, structural configuration, and wetting condition on the relative permeability curves are investigated in conjunction with their component distributions and velocity fields at different two-phase saturations. These results indicate that due to the two-phase flow competition under different structural conditions, the viscous coupling effect has varying degrees of impacts on the mobility of thin phase and viscous phase. Further, the mechanism of two-phase lubricating effect is also discussed under different wetting conditions at Darcy flow regime.

Comparison of rotor hovering aerodynamic performance in free-surface and ground effects using numerical methods

The aerodynamic performance of the rotor hovering on the air–water free-surface, which is significant for cross-medium unmanned aerial vehicles, is merely studied. In this study, a compressible two-phase flow model is used to compare the aerodynamic performance in the free-surface effect (FSE) and the ground effect (GE) with various dimensionless distances, γ, between the rotor and the ground (or free-surface). According to the results, the vortex core in FSE moves further in both vertical and radial directions than in GE for the early stages. Additionally, the blade surface is separated into three parts. In zone I, the aerodynamic performance is mostly determined by proximity effects. For both FSE and GE, the downward induced velocity at the rotor disk rises with increasing γ, leading to a decrease in the sectional thrust coefficient CT,S. By the way, CT,S is larger in FSE. In zone III, the aerodynamic performance is mostly governed by the blade tip vortex. The trend of aerodynamic performance with γ is reversed compared with zone I. The above-mentioned two opposing tendencies result in a smaller rotor thrust in FSE than in GE within the range of 0.60≤γ≤3.00, but a higher rotor thrust in FSE within the range of γ≤0.60.

Numerical study on cavitation generation induced by the high-speed jet impact on the water surface

The complex interaction between shock waves and two-phase interfaces can generate cavitation. In this study, the cavitation induced by the high-speed jet impact on the water surface was investigated. The mixture fluid is modeled using the barotropic equation of state under the framework of the two-phase flow model, which can describe the mixture of air, water, and vapor with any proportion. Through constructing a 1D Riemann problem for the impact-induced cavitation phase transition, it indicates that the coupling effect of multiple rarefaction waves emitted from the two-phase interface is responsible for the cavitation phase transition inside the liquid. Then, a 3D (three-dimensional) simulation regarding the impact of a high-speed jet on the water surface was conducted and validated against previous experiments that captured the cavitation phase transition phenomenon in the central region after the jet impact. The 3D simulation results revealed the spatial structure and development process of shock waves in detail. The coupling effects of shock waves and two-phase interfaces generate a ring-shaped rarefaction wave, which develops radially inward and superimposes, resulting in the formation of acorn-shaped cavitation bubble nuclei inside the water. The 3D simulation can provide spatial shock/rarefaction wave structures and internal flow details that have never been obtained in experiments, such as shock generation and propagation, rarefaction wave generation and center convergence, and the internal structure of acorn-shaped cavitation nucleation. Furthermore, the influence of the jet velocity on the cavitation intensity was analyzed, and a quantitative relationship was provided.

Pore-scale simulation of two-phase flow in biporous media

Enhancing both permeability and capillary pumping in porous structures has emerged as a key focus for researchers, leading to the development of biporous media. While experimental studies on these structures have been conducted recently, there is a lack of numerical simulations due to difficulties in describing the geometry. To address this gap, the present study explores pore-scale numerical simulation of two-phase capillary flow in biporous media. A new simplified biporous structure is proposed, featuring a staggered arrangement of clusters, with each cluster composed of closely packed solid particles. For comparison, a monoporous media case is contrasted and represented using a conventional staggered arrangement of solid particles. Both passive and active capillary flow modes are considered in the present study. The numerical results align well with previous experimental findings on biporous media, indicating that the proposed biporous geometry effectively models two-phase flow in complex structures at a reasonable computational cost. The results show that capillary effects in biporous media are up to two times more effective than in monoporous structures. Simultaneously, permeability is enhanced by a factor of four in biporous media under similar circumstances, with most of the mass flow rate (more than 95%) passing through the larger pores between clusters. This combined impact of increased capillary action and higher permeability leads to enhanced wicking performance in biporous structures. The outcomes can help to understand two-phase flow physics in the biporous structure and develop reliable models for the simulation of biporous media on a macroscopic scale. Numerical modeling and comprehension of capillary structures play a crucial role in designing optimized geometries to enhance their performance.

On a Vlasov equation model for two-phase fluid flow

We consider the problem of water–air two-phase flow, which occurs during water aeration by air injection. We present and analyze a new model incorporating a nonlocal boundary condition, integrating the effect of the air phase through a source term applied to the water phase. This term is described using a kinetic approach based on the Vlasov equation. A numerical study is conducted, and numerical experiments are presented to demonstrate the effectiveness of the presented model

Analysis of the Effectiveness of Using a High-Accuracy Numerical Algorithm in the Simulation of Two-Phase Flow Problems

The continuous technical development of weapons and ammunition, as well as the growing requirements placed on new equipment, require the use of modern tools for their designing and testing. The analysis of the operation of powder propellant systems, which is the focus of interior ballistics, requires particularly specialised tools due to the complexity of the phenomena occurring during a shot. The development of numerical methods and the increase in the computing power of modern computers have enabled the modelling and simulation of highly complex physical problems and the development of numerical schemes with a theoretically arbitrary high order of accuracy. In this study, an attempt was made to develop a one-dimensional model of two-phase flows with a high order of solution accuracy in time, based on the finite volume method. The use of a two-phase flow model in the context of interior ballistics allows, among other things, the analysis of wave phenomena occurring during firing, which is crucial for safety reasons, especially in tank guns. The developed algorithm for solving two-phase systems was checked using recognised test problems for this type of model. The results of the work will be used to develop a numerical model to solve the main problem of interior ballistics.