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The modeling of interphase forces plays a significant role in the numerical simulation of gas–liquid flow in a rotodynamic multiphase pump, which deserves detailed study.

Numerical analysis is conducted to estimate the influence of interphase forces, including drag force, lift force, virtual mass force, wall lubrication force and turbulent dispersion force.

The results show that the magnitude of the interphase forces can be sorted by: drag force > virtual mass force > lift force > turbulent dispersion force > wall lubrication force. The relations between interphase forces and velocity difference of gas–liquid flow and also the interphase forces and gas volume fraction are revealed. The distribution characteristics of interphase forces in the passages from impeller inlet to diffuser outlet are illustrated and analyzed. According to the results, apart from the drag force, the virtual mass force, lift force and turbulent dispersion force are required, whereas wall lubrication force can be neglected for numerical simulation of gas–liquid flow in a rotodynamic multiphase pump. Compared with the conventional numerical method which considers drag force only, the relative errors of predicted pressure rise and efficiency based on the proposed numerical method in account of four major forces can be reduced by 4.95 per cent and 3.00 per cent, respectively.

The numerical analysis reveals the magnitude and distribution of interphase forces inside multiphase pump, which is meaningful for the simulation and design of multiphase pump.

This paper investigates the multi‐phase behaviour of droplets injected into a nozzle at two separate wall locations. The physical features of the droplets (rate of mass, density and radius) at each injector location are identical. This system can be described by a two‐phase Eulerian—Eulerian approach that yields classical systems of equations: three for the gaseous phase and three for the dispersed droplet phase. An underlying assumption in the two phase model is that no interaction occurs between droplets. The numerical solution of the model (using the MacCormack scheme) indicates however that the opposite jets do interact to form one jet. This inconsistency is overcome in the current paper by associating the droplets from a given injection location with a separate phase and subsequently solving equations describing a multiphase system (here, three‐phase system). Comparison of numerical predications between the two‐phase and the multiphase model shows significantly different results. In particular the multiphase model shows no jet interaction.

This paper aims to present an efficient IMPES algorithm based on a global model order reduction method, proper orthogonal decomposition (POD), to achieve the fast solution and prediction of two-phase flows in porous media.

The key point of the proposed algorithm is to establish an accurate POD reduced-order model (ROM) for two-phase porous flows. To this end, two projection methods including projecting the original governing equations (Method I) and projecting the discrete form of original governing equations (Method II) are respectively applied to construct the POD-ROM, and their distinctions are compared and analyzed in detail. It is found the POD-ROM established by Method I is inapplicable to multiphase porous flows due to its failed introduction of fluid saturation and permeability that locate on the edge of grid cell, which would lead to unphysical results.

By using Method II, an efficient IMPES algorithm that can substantially speed up the simulation of two-phase porous flows is developed based on the POD-ROM. The computational efficiency and numerical accuracy of the proposed algorithm are validated through three numerical examples, and simulation results illustrate that the proposed algorithm displays satisfactory computational speed-up (one to two orders of magnitude) without sacrificing numerical accuracy obviously when comparing to the standard IMPES algorithm that without any acceleration technique. In addition, the determination of POD modes number, the relative errors of wetting phase pressure and saturation, and the influence of POD modes number on the overall performances of the proposed algorithm, are investigated.

1. Two projection methods are applied to establish the POD-ROM for two-phase porous flows and their distinctions are analyzed. The reason why POD-ROM is difficult to be applied to multiphase porous flows is clarified firstly in this study. 2. A highly efficient IMPES algorithm based on the POD-ROM is proposed to accelerate the simulation of two-phase porous flows. 3. Satisfactory computational speed-up (one to two orders of magnitude) and prediction accuracy of the proposed algorithm are observed under different conditions.

Interphase forces between the gas and liquid phases determine many phenomena in bubbly flow. For the interphase forces in a multiphase rotodynamic pump, the magnitude analysis was carried out within the framework of two-fluid model. The purpose of this paper is to clarify the relative importance of various interphase forces on the mixed transport process, and the findings herein will be a base for the future study on the mechanism of the gas blockage phenomenon, which is the most challenging issue for such pumps.

Four types of interphase forces, i.e. drag force, lift force, virtual mass force and turbulent dispersion force (TDF) were taken into account. By comparing with the experiment in the respect of the head performance, the effectiveness of the numerical model was validated. In conditions of different inlet gas void fractions, bubble diameters and rotational speeds, the magnitude analyses were made for the interphase forces.

The results demonstrate that the TDF can be neglected in the running of the multiphase rotodynamic pump; the drag force is dominant in the impeller region and the outlet extended region. The sensitivity analyses of the bubble diameter and the rotational speed were also performed. It is found that larger bubble size is accompanied by smaller predicted drag but larger predicted lift and virtual mass, while the increase of the rotational speed can raise all the interphase forces mentioned above.

This paper has revealed the magnitude information and the relative importance of the interphase forces in a multiphase rotodynamic pump.

This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model.

The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used.

This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results.

The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow.

The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.

In this paper, the flow of multiphase fluids in a one-dimensional homogeneous porous media involving the gravity effects is numerically studied using the dominant wave method. The paper aims to discuss these issues.

The numerical scheme used for solving the pressure equations, obtained for the black-oil model, is a backward Euler scheme while the hyperbolic mass conservation equations, derived for both black-oil and Buckley-Leverett models, are solved using the dominant wave method. Higher-order schemes are achieved using either variable derivatives along with the minmod limiter or a MUSCL type interface construction scheme using the Fromm's limiter. The mass conservation equations are solved using the first-order forward Euler method in time. Harten's entropy correction procedure is employed to avoid non-physical expansion shocks.

It was found that the dominant wave method can accurately solve multiphase flow equations involving gravity effects. Numerical experiments also show that both minmod and Fromm's limiters can be successfully used to construct higher-order schemes while the minmod limiter gives slightly more diffuse solutions.

The flow models considered here include two- and three-phase Buckley-Leverett and the black-oil models and the capillary effects are neglected.

The proposed scheme can be efficiently used for solving problems involving non-convex flux functions especially those experienced during gravity drainage process in hydrocarbon reservoirs.

To the best of authors knowledge, this is the first time that the dominant wave method has been used to tackle multiphase flow problems involving gravity effect.

The purpose of this paper is the application of the computational fluid dynamics model simulating the blood flow within the aorta of an eight-year-old patient with Coarctation of Aorta.

The numerical model, based on commercial code ANSYS Fluent, was built using the multifluid Euler–Euler approach with the interaction between the phases described by the kinetic theory of granular flow (KTGF).

A model of the blood flow in the arches of the main aorta branches has been presented. The model was built using the multifluid Euler–Euler approach with the interaction between the phases described by the KTGF. The flow and pressure patterns, as well as the volumetric concentration of the blood components, were calculated. The lumped parameter model was implemented to couple the interaction of the computational domain with the remaining portion of the vascular bed.

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.

The purpose of this paper is to study a multiphase-flow instrumentation for film thickness measurement, especially impedance-based, not only for gas–liquid flow but also for mixtures of immiscible and more viscous substances such as oil and water. Conductance and capacitive planar sensors were compared to select the most suitable option for oil – water dispersed flow.

A study of techniques for measurement of film thickness in oil – water pipe flow is presented. In the first part, some measurement techniques used for the investigation of multiphase flows are described, with their advantages and disadvantages. Next, examinations of conductive and capacitive techniques with planar sensors are presented.

Film thickness measurement techniques for oil–water flow are scanty in the literature. Some techniques have been used in studies of annular flow (gas–liquid and liquid–liquid flows), but applications in other flow patterns were not encountered. The methods based on conductive or capacitive measurements and planar sensor are promising solutions for measuring time-averaged film thicknesses in oil–water flows. A capacitive system may be more appropriate for oil–water flows.

This paper provides a review of film thickness measurements in pipes. There are many reviews on gas – liquid flow measurement but not many about liquid – liquid flow.

This paper aims to introduce a two-dimensional smoothed particle hydrodynamics (SPH) framework for simulating the evaporation and combustion process of fuel droplets.

To solve the gas–liquid two-phase flow problem, a multiphase SPH method capable of handling high density-ratio problems is established. Based on the Fourier heat conduction equation and Fick’s law of diffusion, the SPH discrete equations are derived. To effectively characterize the phase transition problem, inspired by volume of fluid method, the concept of liquid phase mass fraction of the SPH particles is proposed. The one-step global reaction model of n-hexane is used for the vapor combustion.

The evaporation and combustion process of single droplet conforms to the law. The framework works out well when the evaporation of multiple droplets involves coalescence process. Three different kinds of flames are observed in succession in the combustion process of a single droplet at different inflow velocity, which agree well with the results of the experiment.

To the best of the authors’ knowledge, this is the first computational framework that has the capability to simulate evaporation and combustion with SPH method. Based on the particle nature of SPH method, the framework has natural advantages in interface tracking.

The purpose of this paper is to investigate oil-gas slug formation in horizontal straight pipe and its associated pressure gradient, slug liquid holdup and slug frequency.

The abrupt change in gas/liquid velocities, which causes transition of flow patterns, was analyzed using incompressible volume of fluid method to capture the dynamic gas-liquid interface. The validity of present model and its methodology was validated using Baker’s flow regime chart for 3.15 inches diameter horizontal pipe and with existing experimental data to ensure its correctness.

The present paper proposes simplified correlations for liquid holdup and slug frequency by comparison with numerous existing models. The paper also identified correlations that can be used in operational oil and gas industry and several outlier models that may not be applicable.

The correlation may be limited to the range of material properties used in this paper.

Numerically derived liquid holdup and holdup frequency agreed reasonably with the experimentally derived correlations.

The models could be used to design pipeline and piping systems for oil and gas production.

The paper simulated all the seven flow regimes with superior results compared to existing methodology. New correlations derived numerically are compared to published experimental correlations to understand the difference between models.