## What is/are Multiphase Model?

Multiphase Model - The Volume of Fluid (VOF) multiphase model and laminar model were used to analyze wave propagation in offshore conditions.^{[1]}An ANSYS Fluent model for three different fill levels of tank was used for transient analysis in 2D, while a multiphase model was used to track the free surface of the liquid based on Volume of Fluid (VOF) and a dynamic meshing technique was used to simulate the excitation sources via a User Defined Function (UDF) code in the C++ environment.

^{[2]}The outcomes highlight the great importance of simulating debris flow entrainment processes adopting a multiphase model, which resulted particularly suitable for an accurate reproduction of the investigated event.

^{[3]}The simulations were conducted using FireStar2D, a complete physical 2D fire simulator based on a multiphase modelling approach.

^{[4]}In the current study, three-dimensional models were established to simulate the transient formation and dripping of droplets during Electroslag Remelting (ESR) of steel, combining the κ-ε two-equation turbulence model, Volume of Fraction (VOF) multiphase model, and Magnetohydrodynamics (MHD) model.

^{[5]}For multi-scale multiphase flow simulations, the particle model is combined with a level-set based multiphase model on a Cartesian grid.

^{[6]}The application of Computational Fluid Dynamics to aerobic fermentations faces several issues, such as validation of multiphase models at high gas holdup and with complex liquids under turbulent condition.

^{[7]}This staggered framework is based upon a multiphase model to account for salt transport and crystallization within the porous material and a plastic-damage model to account for the nonlinear mechanical behavior of the material.

^{[8]}This paper presents a study on the oil distribution within a screw compressor chamber using Computational Fluid Dynamics (CFD) with Volume of Fluid (VOF) multiphase model.

^{[9]}Compared to classical two-phase tumor growth models, the multiphase model can be used to describe a stratified tumor exhibiting several layers of tissue (e.

^{[10]}The energy density attenuation and correlative phenomena are numerically studied using a multiphase model.

^{[11]}Conclusion: The multiphase model using deep features presented in this paper provide 9% better results than the multiphase model without deep features based on TCF and FS metrics and 8% better results based on MT metric.

^{[12]}The multiphase model was applied on the hydrogenation of arabinose and galactose in a laboratory-scale open foam catalyst bed.

^{[13]}In this review, we elaborate on these applications and synthesize recent lattice Boltzmann methods (LBMs) including collision operators, boundary conditions, grid-refinement techniques, and multiphase models that have enabled the simulation of turbulence, thermodynamic phase change, and non-isothermal effects in a wide array of fluids, including cryogens.

^{[14]}This article combines aspects of reparameterized quadratic models and multiphase models to provide information on the timing of change.

^{[15]}The computational methodology is based on URANS equation with multiphase models for high-resolution interface capture between air and water.

^{[16]}The multiphase modeling provides a likely explanation—it is not “ablation cooling.

^{[17]}In this article, we show how to derive a multiphase model of Baer and Nunziato type with a simple stochastic model.

^{[18]}The volume of fraction (VOF) multiphase model and turbulence models (Realizable kε) were implemented to understand the gas and liquid holdup scenarios for flow in the horizontal annulus.

^{[19]}And a multiphase model was employed in this paper to build the design space for the products with initial voids.

^{[20]}Meanwhile, a multiphase model for the thermal conductivity of cement paste was proposed and used to study the influence of saturation and curing temperature on the thermal conductivity of cement paste.

^{[21]}These are conservativeness of spatial discretisation caused by the inappropriate grid generation, numerical instabilities and dissipations caused by misalignments and application of inappropriate discretisation of equations and the speed and accuracy of multiphase models used in CFD of positive displacement machines.

^{[22]}Hence, in the present study using the Volume of Fluid (VOF) based multiphase model, a detailed numerical understanding of breaking and making in interfaces during flow boiling in BWR is targeted.

^{[23]}This paper presents recent advances in multiphase modelling methods in Computational Fluid Dynamics (CFD).

^{[24]}The obtained accuracy in the validation tests and the good interphase definition in the instability cases, indicate an important improvement in the numerical results compared with single-phase and multiphase models where the shifting algorithm and the variable smoothing length formalism are not applied.

^{[25]}The consistent and conservative numerical framework is developed to preserve the physical properties of the multiphase model.

^{[26]}To clearly assess the significance of air in the multiphase model, four variants of the mixture are investigated (water; water and vapor; water and air; and water, vapor, and air together).

^{[27]}Particularly, the multiphase model that considered the effect of capillary pressure could predict specific aspects such as the water accumulation ahead of the drying front.

^{[28]}Two different numerical approaches are used—Passive scalar model and Multiphase model.

^{[29]}The purpose of this paper is to quantify the relative importance of the multiphase model for the simulation of a gas bubble impacted by a normal shock wave in water.

^{[30]}Our results support a multiphase model in which admixture between northeastern African–related peoples and eastern African foragers formed multiple pastoralist groups, including a genetically homogeneous PN cluster.

^{[31]},The multiphase model based on the Euler–Euler approach describing blood flow in the branched large vessel with a three-element Windkessel model in the coarcted geometry was not previously described in the literature.

^{[32]}The good agreement between the data for several different process conditions proves both the general validity of our multiphase model and the effectiveness.

^{[33]}In the multiphase model, the following equation is applied for each phase: (ximM/xjmM)P, T = const.

^{[34]}In this paper, the parameters of a multiphase model are calibrated based on a comprehensive set of experiments for a particular concrete of grade C30/37.

^{[35]}For both cases the Volume of Fluid (VOF) multiphase model was applied in the treatment of the water-air interaction.

^{[36]}A multiphase modelling scheme that covers various SCMs is therefore proposed in this study.

^{[37]}In this study, a multiphase model based on the kinetic theory of granular flow has been developed to study the mixing behaviour of biomass and sand particles in a bubbling fluidized bed.

^{[38]}A multiphase model was developed to simulate these results and was found to be a good agreement between experimental and numerical results.

^{[39]}This paper describes the first high-order accurate, fully compressible, multiphase model to simulate the expansion and collapse of a near-wall cavitation bubble in a low-frequency ultrasound field.

^{[40]}Several cavitation models and multiphase modeling approaches have been employed in the literature to predict the extent of cavitation in the fuel injection systems.

^{[41]}However, shortcomings of the formulation based on effective stress, which is usually employed in such multiphase models, were identified.

^{[42]}When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary.

^{[43]}A multiphase model for steam explosion is considered, with assumption of mechanical equilibrium between water and vapor phases in the mixture, but with non-equilibrium drag and heat exchange with high-temperature melt droplets taken into account.

^{[44]}The obtained accuracy in the validation tests and the good interphase definition in the instability cases, indicate an important improvement in the numerical results compared with single-phase and multiphase models where the shifting algorithm and the variable smoothing length formalism are not applied.

^{[45]}This study presents a theoretical and numerical analysis to derive a multiphase model of heat and mass transfer for low intensity/temperature convective drying of hygroscopic porous materials, with focus on food products.

^{[46]}To investigate the effects of a roof sprinkler on the heat environment of a greenhouse, a three-dimensional symmetrical model was built, in which a k-e (k-epsilon) turbulent model, a DO (Discrete Ordinates) irrational model, a Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm, and a multiphase model were used to simulate the effects of the roof sprinkler, at different flow rates.

^{[47]}tuning), and challenges associated with the multicomponent/multiphase modeling of core degradation phenomena.

^{[48]}In the present study, the multiphase modeling of centrifugal slurry pump is performed using two models, Mixture and Eulerian-Eulerian multiphase.

^{[49]}For the permanent requirement of producing clean steel, multiphase modelling has become a very important technology for process engineers, this tool is very useful to diagnose and control the refining operations in the ladle and the transfer operations from the ladle to the tundish and finally to the continuous casting mould.

^{[50]}

## two phase flow

A three-dimensional computational model, coupled with the Large Eddy Simulation (LES) model and Volume of Fluid (VOF) multiphase model, was established to investigate the two-phase flow and slag entrainment during steel bloom continuous casting.^{[1]}A computational fluid dynamic (CFD) study was conducted to understand the hydrodynamic behaviours of gas-solid two-phase flow in the regenerator of the CLC-FCC unit, based on a three-dimensional multiphase model (Eulerian-Eulerian) with the kinetic theory of granular flow.

^{[2]}In this study, computational fluid dynamics (CFD) simulations were conducted, using RNG k-e turbulence and Eulerian multiphase models, to investigate the gas–liquid two-phase flow characteristics in swirl meters.

^{[3]}In this study, the two-phase flow of liquid hydrogen spill is predicted with the mixture multiphase model, Lee model and Realizable k-e model, and the dispersion of hydrogen vapor cloud with the atmospheric inversion layer is numerically analyzed.

^{[4]}A coupled three-dimensional model, including Large Eddy Simulation model, Lagrangian Discrete Phase Model and VOF multiphase model was developed to investigate the transient two-phase flow and bubble distribution in continuous casting strand.

^{[5]}Homogenous Eulerian multiphase model including volume of fluid method was employed to solve two-phase flow field equations.

^{[6]}

## Eulerian Multiphase Model

The other was the "wall boiling model", which is suitable for nucleate boiling among the Eulerian multiphase models.^{[1]}Simultaneously, computational studies are performed using the Eulerian–Eulerian multiphase model with granular options adopted from literature.

^{[2]}The present numerical investigations employ the Eulerian multiphase model with renormalization (RNG) k–ε turbulence model to simulate the three-dimensional unsteady free-surface liquid–solid flow in a stirred tank.

^{[3]}The Eulerian–Eulerian multiphase model and k-ε were opted for simulating the two-phase hybrid MWCNT-Cu/water nanofluid and turbulence model in the collector.

^{[4]}The model is a continuum Eulerian multiphase model of the powder including models for the granular temperature; the effect of vibration can be included through appropriate wall boundaries for this granular temperature.

^{[5]}The Eulerian multiphase model was employed along with the renormalization (RNG) k-ε turbulence model to simulate liquid–solid flow with a free surface in a stirred tank.

^{[6]}Numerically, Computational Fluid Dynamics (CFD) simulations based on Discrete Phase Model (DPM), mixture and Eulerian multiphase model were conducted and compared.

^{[7]}In the numerical simulations, the Eulerian multiphase model, the population balance model, and the RSM turbulent model were coupled to simulate the droplet behavior in the swirling fluid field.

^{[8]}The research campaign has been conducted following the Eulerian multiphase model and the critical heat flux boiling model based on FLUENT software.

^{[9]}A three-dimensional Eulerian multiphase model was developed using the software ANSYS CFX to predict the gas-liquid flow in a simplified suction muffler geometry.

^{[10]}A steady-state model was created to simulate the HDVS, where the simulation of solid–liquid part flow within the HDVS was conducted by 3-D Eulerian–Eulerian multiphase model and Reynolds stress model combined with the kinetic theory of granular flow.

^{[11]}25 wt% of MWCNT–water nanofluid at the largest Reynolds number, while single-phase and Eulerian–Eulerian multiphase models accurately estimate the thermal fields of the diluted nanofluids at low Reynolds numbers, but overestimate the results for denser nanofluids at high Reynolds numbers.

^{[12]}The homogeneous Eulerian multiphase model was adopted to model the phase change process after LNG leaks to the ground.

^{[13]}In this study, computational fluid dynamics (CFD) simulations were conducted, using RNG k-e turbulence and Eulerian multiphase models, to investigate the gas–liquid two-phase flow characteristics in swirl meters.

^{[14]}In this study, blood flow in bifurcate channels that are pulmonary arteries after a novel surgery with Blalock–Taussig (B-T) shunt and intrapulmonary-artery fenestrated septation is investigated using Eulerian multiphase model.

^{[15]}Full loop 3D simulation of CFB with focusing on the furnace and cyclone by using computational fluid dynamic (CFD) program was implemented using Eulerian multiphase model to investigate sand volume of fraction, air, and sand velocity including pressure distribution around Cyclone.

^{[16]}The model is a continuum Eulerian multiphase model of the powder including models for the granular temperature; the effect of vibration can be included through appropriate wall boundaries for this granular temperature.

^{[17]}The results show the good prediction ability of Eulerian–Eulerian multiphase model, Reynolds stress model (RSM), and Tomiyama drag model.

^{[18]}The present numerical investigation, performed with the expert software Ansys® Fluent, Release 16, employs the Eulerian multiphase model along with the RNG k–ε turbulence model to simulate the free-surface liquid–solid flows in the baffled stirred reactor.

^{[19]}Simulations basing on the Eulerian multiphase model and a modified algebraic interface area density (AIAD) model are carried out to study the flooding mechanisms with liquid nitrogen (LN2) and its vapor (VN2) in an inclined pipe.

^{[20]}In present study, a numerical model has been developed to simulate steam–water interfacial characteristics in the injectors based on Eulerian–Eulerian multiphase model in ANSYS CFX software.

^{[21]}In this paper for the first time, WA model coupled with Eulerian multiphase model is successfully implemented to simulate the complex multiphase system RPB.

^{[22]}The Eulerian multiphase model is the closest to the experimental results, and the combination of the Eulerian multiphase model and Large Eddy Simulation can be applied to predict the mixing behavior in an industrial scale stirred-tank.

^{[23]}Numerical simulation of commercial CFD was used with Eulerian multiphase model implemented to analyzed sand volume of fraction, air and sand velocity including distribution of pressure around furnace.

^{[24]}For CFD simulations, the realizable k-e turbulence model with volume of fluid (VOF) and Eulerian-Eulerian multiphase models is successfully implemented in ANSYS Fluent solver.

^{[25]}Homogenous Eulerian multiphase model including volume of fluid method was employed to solve two-phase flow field equations.

^{[26]}In order to search for tools that allow facilitating the research in this type of pump, this study performs a CFD analysis of a centrifugal pump using OpenFOAM® free simulation software and uses the Eulerian-Eulerian multiphase model.

^{[27]}An Eulerian-Eulerian multiphase model with the Thermal Phase-Change criteria for two-phase heat, mass and momentum transfer has been used.

^{[28]}The WDR simulations are performed based on the large eddy simulation (LES) method together with the Eulerian multiphase model, and structural responses of the retractable roof subjected to WDR actions are determined by the dynamic analysis of the stadium in time domain.

^{[29]}The Eulerian multiphase model of Euler-Euler approach of Computational Fluid Dynamics (CFD) is used.

^{[30]}Eulerian multiphase model integrated with Rensselaer Polytechnic Institute (RPI) nucleate boiling model is adopted.

^{[31]}The numerical model was based on the Eulerian multiphase model and the population balance model (PBM) was used to calculate the bubble size distribution.

^{[32]}A classical Eulerian multiphase model and a modification of the standard k-ε eddy-viscosity turbulence model are adopted to simulate the dense solid–liquid suspension dynamics.

^{[33]}An Eulerian multiphase model and standard k-e turbulence model were employed to simulate the flow field inside the tank.

^{[34]}In this paper, the applicability of the WDR simulation method with the Eulerian multiphase model is verified for two tandem layout buildings under the complex WDR field.

^{[35]}Computational Fluid Dynamics (CFD) simulation was performed using the Euler-Lagrange approach with the Reynolds Stress Model (RSM) for turbulence and Eulerian Multiphase model for multiphase flow cases.

^{[36]}The Eulerian-Eulerian multiphase model was applied, along with the particle interfacial transfer model.

^{[37]}

## Mixture Multiphase Model

Thereby, an axial separator with multiple light phase outlets (LPOs) was introduced and three different structure designs of swirl chamber were investigated using the Mixture multiphase model and Reynolds stress turbulence model.^{[1]}The buoyancy was calculated by solving compressible governing equations, and the mixture multiphase model and improved compressible phase change model were used to calculate the boiling process.

^{[2]}The present study adopts the transient method to simulate the wind-induced snow distribution on embankment based on the mixture multiphase model and dynamic mesh technique.

^{[3]}In this study, the two-phase flow of liquid hydrogen spill is predicted with the mixture multiphase model, Lee model and Realizable k-e model, and the dispersion of hydrogen vapor cloud with the atmospheric inversion layer is numerically analyzed.

^{[4]}Algebraic slip mixture multiphase model coupled with turbulence model is employed to study the fluid dynamics of the venturi.

^{[5]}In addition, a CSAF fluid mechanic model is configured on the basis of the mixture multiphase model and cavitation model.

^{[6]}The governing equations and flow boiling models were added into FLUENT solver, and then worked with Mixture multiphase models by user defined functions (UDFs).

^{[7]}Numerical simulations are also carried out using the modified mixture multiphase model with additional shear lift, hindered settling drag law and slurry viscosity by solids and fines content.

^{[8]}

## Vof Multiphase Model

A three-dimensional computational model, combining the large eddy simulation (LES) turbulent model, VOF multiphase model for air phase, and discrete phase model (DPM) for injected bubbles, was established to evaluate the effects of drag force, lift force, pressure gradient force, virtual mass force, and wall lubrication force on the fluid flow and spatial distribution of bubbles in a continuous casting (CC) strand.^{[1]}A CFD study on horizontal oil-water flow with high viscosity ratio (O(103)) was conducted with the VOF multiphase model in conjunction with the SST k–ω turbulence scheme.

^{[2]}This paper established a CFD model for the fluid flow of oil in a refueling pipe based on FLUENT and applied a combined VOF multiphase model and Schnerr-Sauer cavitation model to simulate the cavitation behavior as the oil flows around obstacles in a pipe.

^{[3]}An experimentally verified simulation model was established by adopting a VOF multiphase model coupled with a realizable k−ε turbulence model.

^{[4]}A coupled three-dimensional model, including Large Eddy Simulation model, Lagrangian Discrete Phase Model and VOF multiphase model was developed to investigate the transient two-phase flow and bubble distribution in continuous casting strand.

^{[5]}Large eddy simulations using a VOF multiphase model were conducted for a plate length to height aspect ratio of 2.

^{[6]}

## Dimensional Multiphase Model

A computational fluid dynamic (CFD) study was conducted to understand the hydrodynamic behaviours of gas-solid two-phase flow in the regenerator of the CLC-FCC unit, based on a three-dimensional multiphase model (Eulerian-Eulerian) with the kinetic theory of granular flow.^{[1]}Here, using a three-dimensional multiphase model, we show that the initial temperature of PDCs linearly correlates to the percentage of collapsing mass, with a maximum temperature decrease of 45% in the case of low percentages of collapse (10%), owing to an efficient entrainment of air into the jet structure.

^{[2]}In this paper, a three-dimensional multiphase model of the polymer exchange membrane (PEM) fuel cell is simulated to study the effect of assembly pressure on the contact resistance between the gas diffusion layer (GDL) and bipolar plate (BP) interface.

^{[3]}In this paper, a single module of cross-flow membrane humidifier is evaluated as a three-dimensional multiphase model.

^{[4]}A validated two-dimensional multiphase model describing mass, momentum, turbulence and conjugate heat transfer between the bayonet tube and the ground is used to compare the effects of using a simplified fitted function to represent the ambient temperature with that of hourly temperature readings from a weather monitoring station.

^{[5]}

## Lagrangian Multiphase Model

The obtained numerical results from the applied Eulerian–Lagrangian multiphase model are also compared with experimental data from a linear shear flow apparatus with suspended buoyant particles, and good agreement was found.^{[1]}A three-dimensional Eulerian–Lagrangian multiphase model is applied to investigate the effect of solids outlet location, relative hot/cold airflow ratio, and droplet size on heat and mass transfer characteristics, G-acceleration, residence time, and separation efficiency of the product.

^{[2]}Lagrangian multiphase model was used to simulate the transport of sand and biomass particles, and the kinetic mechanism of biomass pyrolysis was adopted.

^{[3]}For selected turbulence models, deposition of particles with different Stokes numbers using Lagrangian multiphase model was enabled.

^{[4]}

## Fluid Multiphase Model

The volume of fluid multiphase model has been used to analyze the flow, and the simulation result reasonably predicts the wall temperature peaks.^{[1]}Therefore, this study aims the assessment of different sub-models of the interfacial heat transfer coefficient which is used as a closure relation in the two-fluid multiphase model.

^{[2]}The eulerian based model connected with two fluids multiphase model which emphasizes the dynamics of interaction between the nanoparticles and the base fluid.

^{[3]}The Realisable-k-ϵ turbulence model and the volume of fluid multiphase model were implemented, so as to simulate the effect of turbulent fluid flow on the shape of the top liquid steel meniscus.

^{[4]}

## Different Multiphase Model

This work aimed to use the computational fluid dynamics to study different multiphase models to represent the hydrocyclones, as well as modifications to its geometry to increase its efficiency.^{[1]}Firstly, a multiphase MPS method is developed by combining the single-phase improved MPS (IMPS) method proposed in our previous study with different multiphase models, including the improved density smoothing scheme, interparticle viscosity model, continuous acceleration model, surface tension model, incompressible-compressible model and multiphase collision model.

^{[2]}Code testing is performed using different multiphase modeling approches for processes relevant to magmatic systems: Rayleigh-Taylor instability, for buyoancy-driven magmatic processes; multiphase shock tube simulations, propedeutical to conduit dynamics studies; bubble growth and breakage in basaltic melts.

^{[3]}ABSTRACT The thermo-fluidic transport characteristics of the fly ash–water slurry flow in a straight horizontal pipe are predicted by deploying two different multiphase modeling strategies, viz.

^{[4]}

## Inhomogeneou Multiphase Model

An inhomogeneous multiphase model with shear stress transport turbulence was employed to validate the investigation by experimental results.^{[1]}To investigate the supercavity geometry and gas flow structure for the supercavities with two closure types under the different flow conditions, an inhomogeneous multiphase model with the SST turbulence model was established, and validated by experimental results.

^{[2]}The physics for the sloshing assessment were considered to identify the main aspects of the inhomogeneous multiphase model.

^{[3]}In present work, a three-dimensional steady numerical simulation is conducted to study the steam jet condensation in subcooled water flow in a vertical pipe with the presence of non-condensable gas based on inhomogeneous multiphase model.

^{[4]}

## Granular Multiphase Model

The simulation solved the reactive compressible Navier-Stokes equations coupled to an Eulerian kinetic-theory-based granular multiphase model.^{[1]}Three-dimensional full-loop computational fluid dynamics simulation using Euler granular multiphase model is carried out.

^{[2]}The complex LNG reactions were simplified and the Eulerian-Granular multiphase model was used to consider the behavior of bed materials and gas-solid interaction.

^{[3]}

## Pseudopotential Multiphase Model

The dynamic behavior of liquid droplets on a reconstructed real gas diffusion layer (GDL) surface with the inertial effect produced by the three dimensional (3D) flow channel is investigated using an improved pseudopotential multiphase model within the unified lattice Boltzmann model (ULBM) framework, which can realize thermodynamic consistency and tunable surface tension.^{[1]}In order to verify the applicability, the CST-LB model is combined with the pseudopotential multiphase model to simulate a series of benchmark cases, including concentration jump near the interface, gas dissolution in a closed system, species transport during drainage in a capillary tube, and multiphase species transport in the porous media.

^{[2]}The revised pseudopotential multiphase model is adopted to realize high-density ratio, good thermodynamic consistency, adjustable surface tension and high contact angle.

^{[3]}

## Euler Multiphase Model

The polishing mechanism is first introduced, then the Euler multiphase model is used to build the fluid mechanical model of the proposed method.^{[1]}The granular behaviors in rotating kilns have been investigated using a three-dimensional CFD model based on Euler-Euler multiphase model and the kinetic theory of granular flow.

^{[2]}Two phase Euler-Euler multiphase model was used while transfer of iodine from gaseous phase to liquid phase was modelled using species transport model.

^{[3]}

## Mechanical Multiphase Model

This study presents a hygro-thermo-mechanical multiphase model that describes the cyclic freeze-thaw behavior of partially saturated air-entrained concrete containing dissolved salt.^{[1]}Following this, we couple the mechanical multiphase model equations with a previously developed non-diffusional phase transformation kinetics model.

^{[2]}This paper presents an extension of a novel hygro-thermo-mechanical multiphase model for simulation of freezing of partially saturated air-entrained concrete on the structural scale to account for.

^{[3]}

## Coupled Multiphase Model

A coupled multiphase model based on computational fluid dynamics (CFD) and discrete element method (DEM) is developed to numerically investigate the extrusion-based 3D printing process of discontinuous carbon fibre reinforced polymer composites.^{[1]}The model is derived as a modified version of a fully-coupled multiphase model recently proposed by Gasch et al.

^{[2]}

## Developed Multiphase Model

Discharging performances of supercooled salt hydrate PCM (phase change material) in the rounded rectangular storage unit are numerically investigated with the developed multiphase model.^{[1]}The application of the FGM in combination with the Euler-Lagrange approach and specially developed multiphase model adaptions led to very precise results.

^{[2]}

## Atmospheric Multiphase Model

This will significantly facilitate the optimization of AOP and improve the predictive capabilities of atmospheric multiphase models in the future.^{[1]}In general, our results suggest that atmospheric multiphase models may be incomplete for highly soluble organics as biodegradation may represent an unrecognized efficient loss of such organics in cloud water.

^{[2]}

## Potential Multiphase Model

The proposed model combines a pseudo-potential multiphase model and a thermal single-component phase change model.^{[1]}In this paper, the improved Shan-Chen pseudo-potential multiphase model in lattice Boltzmann method was used to simulate the process of bubble passing through stenotic capillaries during the pathogenesis of decompression sickness, and the velocity variation of the fluid in the process of flow was studied.

^{[2]}

## Chen Multiphase Model

In this paper, a novel model to investigate leakage of gaseous working fluid in pressured devices with lubricating oil was created with Lattice Boltzmann method and Shan-Chen multiphase model.^{[1]}This paper presents an investigation into capillary rise dynamics in a vertical square micro-channel based on the lattice Boltzmann method with the Shan-Chen multiphase model.

^{[2]}

## Compressible Multiphase Model

A compressible multiphase model using the coupled Level Set with Volume of Fluid (VOF) model was adopted to investigate on the detail flow structure.^{[1]}In this case, the metals are in a pseudo-liquid state at the initial stages of the process, and from a mathematical point of view, a wave formation process can be described by compressible multiphase models.

^{[2]}

## Art Multiphase Model

Here, we analyzed the sulfate production rates using a state-of-art multiphase model constrained to the observed concentrations of transition metal ions (TMI), nitrogen dioxide, ozone, hydrogen peroxide, and other important parameters in winter and summer in the North China Plain.^{[1]}Here, we analyzed the sulfate production rates using a state-of-the-art multiphase model constrained to the observed concentrations of transition metal, nitrogen dioxide, ozone, hydrogen peroxide and other important parameters in winter and summer in the North China Plain.

^{[2]}

## Homogeneou Multiphase Model

The liquid motion inside the tanks can be described as sloshing with high amplitude, off-resonant roll excitation and was examined using a homogeneous multiphase model and VOF interface capturing approach as well as an experimental setup including piezoelectric pressure sensors and qualitative observation of the free surface.^{[1]}A series of computational fluid dynamics (CFD) simulations were carried out for the cavitating flows in two pumps, based on the RANS (Reynolds-Averaged Naiver-Stokes) solver with the turbulence model of k-ω shear stress transport and homogeneous multiphase model.

^{[2]}

## multiphase model coupled

An experimentally verified simulation model was established by adopting a VOF multiphase model coupled with a realizable k−ε turbulence model.^{[1]}Simulation of the gas–slag–matte three-phase flow in the furnace was performed by the volume of a fraction multiphase model coupled to a realizable k–e turbulence model.

^{[2]}Algebraic slip mixture multiphase model coupled with turbulence model is employed to study the fluid dynamics of the venturi.

^{[3]}

## multiphase model constrained

Here, we analyzed the sulfate production rates using a state-of-art multiphase model constrained to the observed concentrations of transition metal ions (TMI), nitrogen dioxide, ozone, hydrogen peroxide, and other important parameters in winter and summer in the North China Plain.^{[1]}Here, we analyzed the sulfate production rates using a state-of-the-art multiphase model constrained to the observed concentrations of transition metal, nitrogen dioxide, ozone, hydrogen peroxide and other important parameters in winter and summer in the North China Plain.

^{[2]}

## multiphase model volume

The multiphase model volume of fluid (VOF) is used to tackle the water–air mixture.^{[1]}For the numerical analysis, computational fluid dynamics ANSYS Fluent software was employed, and to tackle with water–air interaction, the nonlinear multiphase model volume of fluid (VOF) was applied.

^{[2]}