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Two-phase flow in inclined pipes frequently occurs in industrial applications such as oil and gas production, heat exchangers and nuclear reactors. Understanding liquid film thickness and interfacial friction coefficient is crucial for designing and optimizing these systems. This study investigates the effect of limited inclination angles on liquid film thickness and interfacial friction coefficient in two-phase flow within vertical pipes. An image recording and processing technique analyzes the counter-current flow of water and air, which forms an annular flow pattern in transparent pipes of various sizes. The results are segregated based on superficial velocities, Reynolds numbers and pipe diameters. A multivariate correlation is developed to determine the ratio of maximum to minimum film thickness and an equivalent film thickness correlation for inclined pipes. The interfacial friction coefficient is also evaluated, leading to a tri-variable correlation. The proposed correlations align closely with presented data and prior research ($R^2=0.96$ for film thickness ratio and $R^2=0.97$ for interfacial friction coefficient). The maximum deviation between data and proposed correlations is 2.86% for film thickness and 4.3% for the interfacial friction coefficient. These findings enhance the understanding of two-phase flow behavior in inclined pipes and offer valuable tools for industrial design and optimization.

This study undertakes a numerical investigation into the two-phase magnetohydrodynamic (MHD) flow of a novel Al₂O₃-Ag/ethylene glycol (30%)–water dusty Maxwell hybrid nanofluid within a porous stretched cylinder incorporates the influential factor of thermal radiation. Notably, it pioneers exploration into the flow characteristics of Maxwell nanofluids and hybrid nanofluids containing dust particles over a porous cylinder, an uncharted domain in the existing literature. By adeptly simplifying the governing partial differential equations into nonlinear ordinary differential equations (ODEs) using judiciously chosen similarity variables, our research employs MATLAB’s bvp4c scheme to obtain numerical solutions, presented both graphically and in tabular form. Our results unveil significant insights: the Maxwell fluid parameter and magnetic parameter exhibit a dual effect of enhancing heat transfer while mitigating velocity gradients. Moreover, increasing the curvature parameter exerts a favorable influence on the velocity and temperature profiles of both phases. Furthermore, the fluid-particle interaction parameter emerges as a pivotal factor shaping velocity and temperature profiles in the dust phase, while the radiation parameter notably amplifies heat transfer rates. Remarkably, our investigation reveals a notable 26% increase in total skin friction and a nearly 13.5% enhancement in heat transfer within the dusty Maxwell hybrid nanofluid configuration compared to the dusty Maxwell nanofluid arrangement. These findings hold profound practical implications for addressing real-life engineering challenges, offering invaluable insights into optimizing heat transfer and velocity profiles across diverse technical applications. They pave the way for the development of enhanced cooling mechanisms and highly efficient heat exchangers, crucial for tackling multifaceted engineering challenges.

In this paper, a lattice Boltzmann (LB) model is presented to study the two-phase hydrocarbon fluid systems. Based on the Peng–Robinson (P–R) free energy model, a Cahn–Hilliard type equation is derived to describe the interfacial properties. In the corresponding LB method, the gradient contribution of chemical potential is treated as source term, while the homogeneous part is put in the equilibrium distribution function, which guarantees its scale order in the Chapman–Enskog analysis. In the numerical experiments, the realistic hydrocarbon components of propane are numerically studied by the presented LB model in three dimensions. The numerical results show that the predicted surface tension and capillary pressure are in good agreement with laboratory data.

Slug flow is a two-phase fluid flow pattern, characterized by a series of liquid slugs dispersed by relatively large air bubbles. Air bubbles produced and trapped during the slug flow phenomenon conduct to interruption in flow which induces pressure and velocity fluctuations. These effects have destructive circumstances in conduits and conveyance structures. This paper deals with studying numerically two-phase flows using computational fluid dynamic (CFD) techniques performed in OpenFOAM (an open source software) by interFoam solver. Most of the previous concerning studies on slug flow were performed in micro-channels with small scales in which the expansion of the air bubbles was negligible. By contrast, we investigated the systems with large pressure drops which conduct to abrupt increases on the volume of air phase. The slug flow phenomenon could be created by introducing air and water with different velocities at inlet of a culvert with air to water velocity ratio varied from 1.1 to 34. First, this study focused on temporal and spatial variations of pressure and velocity along the culvert. After that, by dimensional analysis, the nondimensional parameters influencing the slug flow phenomenon are extracted and analyzed. Finally, different strategies for reducing the destructive effects of slug flow, including the shape and location of ribs, are evaluated and the best strategy is proposed.

In this study, phase field method of Lattice Boltzmann method (LBM) is employed to simulate the collision of a droplet with inclined dry walls under gravitational force. At first, dynamic behavior of moving droplet in a horizontal channel, through this method, has been investigated to verify convective boundary condition as the outlet one. Relatedly, falling of a droplet in vertical channel under gravity without any obstacle in certain Ohnesorge number (Oh) and Eotvos number (Eo), as related dimensionless numbers, is enquired. Then, breakup of a falling drop in the range of Eo $(11<\mathrm{\text{Eo}}<43)$, Oh $(0.2<\mathrm{\text{Oh}}<0.7)$, various angles of solid walls $(20<\theta <60)$, different sizes of the drop diameter $(2.2<\mathrm{\Delta }<4)$, influence of density ratio and parameter $K$ corresponding to surface tension are investigated. The results indicated that by increase in Eo, the breakup and deformation of droplet increased after collision while by growing Oh, the droplet retained its spherical shape. Change in the $\theta$ and $\mathrm{\Delta }$ has effect only on the size of generated fragments. Furthermore, higher density ratio reinforced gravitational force and resulted in more deformation of the droplet and its resistance was enhanced by higher parameter $K$.

This paper explores the interaction of different flow paths in a porous medium by observing the effect of having more than one drain in a simple model domain with a single source. The work is based on three-dimensional numerical simulations of the flow of injected water in a sandbox domain with porous volume completely filled by water and oil. The calculation uses the OpenFOAM library to solve Darcy’s equations for the dynamics of a two-phase flow: water as the wetting, oil as the nonwetting fluid. We observe the interactions of flows in different paths under changes of number of drains and their relative positions.

Slug flow is a flow pattern which occurs in conveyance systems containing a two phase-fluid flow. Large air bubbles entrapped along these systems interrupt the flow and conduct to undesirable pressures and their fluctuations. Most of the previous concerning studies on slug flow phenomenon were performed in micro-channels with small scales in which the expansion of the air bubbles was negligible. In contrast, we investigated the systems with large pressure drops which conduct to abrupt increases on the volume of air phase. In this research, the verification tests applying CFD techniques were performed in OpenFOAM software by interFoam solver. The performance of morning glory spillways is investigated under steady states. While during the occurrence of flood, by increasing the depth over the spillway crest, the discharge is augmented which conducts to entrap the air pockets with pressure and velocity fluctuations. These fluctuations influence on the life of structures and their performances. This study aimed on unsteady flow in a glory morning spillway and its consequences and proposing the measures for reducing the destructive effects of slug flow. The pressure and velocity fluctuation were considered as the indices for the performance of a hydraulic structure. Spatial and temporal variations of pressure and velocity along the spillway are evaluated. Also, the influences of spillway geometry on slug flow and the measures to attenuate its destructive effects are analyzed. The results showed that the better performances of morning glory spillway are coincided by the diameter of tunnel superior than the height of water above the crest.

In this study, numerical simulations are conducted to investigate droplet breakup in an asymmetric $T$-junction microchannel with different cross-section ratios. To this approach, a two-phase model based on the volume of fluid (VOF) method is adopted to study the three-dimensional feature of droplet motion inside $T$-junctions. The comparison reveals that the present results are in good agreement with previous studies. The effects of the capillary number (Ca), the non-dimensional droplet length ($L^{\ast }$), and the non-dimensional width ratio ($W^{\ast }$) on the breakup time and splitting ratio of daughter droplets are studied. Five distinct regimes are observed involving the non-breakup, breakup with tunnel, breakup without tunnel, asymmetric breakup, and sorting. Achieved results indicate that the time of breakup ($t_{\mathrm{\text{breakup}}}^{\ast }$) increases about 15% when the Ca is increased from 0.0134 to 0.0268 (about 100%). It is also found that the mass center of the mother droplet in the primary channel is shifted to a larger wide branch, which facilitates the asymmetric breakup of the droplet in a $T$-junction microchannel.

In this study, an incompressible and immiscible two-phase flow solver was employed to assess the accuracy of phase-interface capturing methods in simulating two-phase flows. Three benchmark investigations were conducted involving two dam break flows with deformable free surfaces and the upward motion of a gas bubble through a liquid column. Four phase-interface capturing schemes, namely, MULES, HRIC and CICSAM from the Color Function Volume of Fluid (CF-VoF), and Interface Reconstruction Volume of Fluid (IR-VoF), were utilized. Comparative analysis of the phase interfaces indicated that CICSAM and IsoAdvector consistently provided sharp interfaces across all cases when compared to MULES and HRIC. The mass conservation performance of all schemes excelled in the dam-break case with relatively simple free-surface development and the rising bubble case. An examination of the local pressure distribution over time revealed that methods yielding diffusive interfaces produced inaccurate results. Thus, the importance of employing denser grids or schemes that yield sharper interfaces, such as CICSAM and IsoAdvector, to enhance simulation accuracy was underscored. Overall, the results of this analysis confirm that the IsoAdvector scheme, which provides sharp interfaces, is a reliable option for simulating incompressible immiscible two-phase flows.

This paper reports the splitting morphology of low-viscous fingers in the microchannels that are associated with flat T-shaped, curved T-shaped, and Y-shaped junctions. The numerical simulations are based on the finite volume approach and the volume of the fluid model. In this study, microchannels are filled with silicon oil. Perfluorodecalin is used to displace silicon oil from the microchannels. Due to viscosity differences, the low-viscous finger (LVF)-shaped instability evolves at the interface of fluids. A single LVF propagates in the parent channel, and at the junction, it splits into two identical LVFs. It is noted that the splitting morphology of LVF depends upon the shape of the junction and its wettability. Therefore, there are three different junctions, i.e. flat T-shaped, curved T-shaped, and Y-shaped, with three different wettability conditions $(\theta )$, i.e. hydrophilic ($60^{\circ }$), hydrophobic ($120^{\circ }$), and superhydrophobic ($150^{\circ }$) are used for numerical investigation. It is found that a LVF splits symmetrically at all three different junctions but tips of LVFs are found to be convex in superhydrophobic conditions. The LVFs-shaped are curved in the limbs of curved T-shaped microchannel and straight in the limbs of flat T-shaped and Y-shaped microchannels. The findings of this paper may be used in lung biomechanics, respiratory diseases, biochemical testing, and many more.

The governing equations of two-phase flows have a safe operating range, and exceeding this range can negatively impact the results. To extend this safe range, one key strategy is to incorporate the momentum flux coefficient into the governing equations. This paper introduces the application of the momentum flux coefficient to no-pressure or free-pressure model equations for the first time, specifically evaluating its performance in downward co-current two-phase flows through numerical methods. A new and improved version of the no-pressure model is also presented. Findings suggest that the force approach method yields more accurate results compared to other methods, whereas the Richmeier method produces unrealistic outcomes at discontinuities. A comparison between the standard and the developed no-pressure models reveals that the latter does not prevent nonphysical mutations and even exacerbates their occurrence. However, the developed no-pressure model successfully reduces numerical distribution production.

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model¹ to rectangular grids (nine speeds) by using symbolic manipulation (Mathematica^TM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

It is quite meaningful in an engineering aspect to investigate liquid drop behaviors in two-phase flow, on which dispersive mixing or overall rheological characteristics heavily depend. There are two approaches numerically to deal with two-phase flow problems, which are the moving- and the fixed-grid methods: that is, interface tracking and interface capturing methods. In this study, we developed multiphase flow codes in both Lagrangian and Eulerian frameworks and compared each solution for the single drop problem in an axisymmetric channel flow. Deformation patterns of drops were observed by these two methods and we have discussed the characteristic features of two methods from the deformation of drop for the moving boundary problems.

The flow field plate is an important component of the fuel cell, and makes the flow state of the reactant gas produce obvious changes. In this paper, the method of computational fluid dynamics was used to study the influence of the waveform channel on the internal parameters of the fuel cell. Through analysis, the optimal cathode flow field waveform at different temperatures was determined. It was found that the waveform flow field plate is very limited in improving the average current density. The existence of the waveform would obviously change the distribution of liquid water. This paper has contributed to the full commercialization of fuel cells.

The study of multiphase flows gained much importance because of its extensive applications in nature and industry. These flows possess two or more thermodynamic phases, for example, one component phase (e.g., water vapors and water flow) or several components phase (e.g., water and oil flow). The most common example of multiphase flow in the context of the oil industry is petroleum. Further blood flow, porous structures, fluidized bed, bubbly flow in nuclear reactors, and fiber suspension in the paper industry are some significant examples of multiphase flows. In this paper, we considered the Couette flow of non-Newtonian (couple stress) fluid with variable magnetic field and thermal conductivity effects between parallel walls of the channel. The upper wall of the channel is in constant motion while the lower wall is in a fixed position. The variable viscosity effects with the suspension of hafnium particles are also discussed by taking Vogel’s viscosity case. The shooting method based on the R–K method is applied to obtain the numerical solution of the current problem. A comparison between Newtonian and non-Newtonian fluids is presented by sketching graphs. The variations in flow and temperature of fluid against various involved factors, including variable viscosity, wall temperature, thermal radiations, variable magnetic field, and thermal conductivity are sketched and also physically described. It is observed that variable viscosity parameter elevated both velocity and temperature profiles while wall temperature parameter decelerated both fields. Further, noticed that the variable thermal conductivity and variable magnetic field impede the velocity of the fluid and also retarded the temperature field. Our attempt is not just useful to investigate the mechanical and industrial multiphase flows but also delivers important results to fill the gap in the existing literature.

The axisymmetric unsteady two-phase flow problem is explored. The flow domain is defined by two co-axial circular cylinders and is axial symmetric. The Dirichlet-type boundary condition is used on the inner cylindrical surface, whereas the Robin-type boundary condition is used on the outer cylindrical surface. The velocities are computed analytically using a new form of the Weber transform that is suited for these boundary conditions. The effect of the slip parameter on velocities is investigated using numerical simulations and graphical representations. The studied problem is new in the literature because there do not exist any analytical studies regarding the problems with boundary conditions of Dirichlet type on the inner cylinder (the no-slip on the wall) and boundary conditions of Robin type on the outer cylinder (the mixture slipping on the wall). A new integral transform of Weber type has been employed to determine analytical solutions for such problems, together with the Laplace transform. The studied problem could generate analytical solutions for more two-phase flow problems in annular domains since the translational motions of the inner cylinder and the outer cylinder are given by arbitrary functions of the time t.

A two-phase solidification model was used that incorporates the descriptions of natural convection, heat transfer, solute transport and solid movement at macroscopic scale with microscopic relations for grain nucleation and growth. The implementation of the two-phase model was validated by comparisons with a consensus of previous numerical simulation for Sn-5wt.%Pb alloy and with experiment for Mg-4wt.%Y alloy cast in one-side-chilled resin sand mould. With free movement of globular grains in the bulk liquid, effects of melt superheat and nucleation density on fluid flow behavior and macrosegregation during solidification of Mg-4wt.%Y alloy were numerically investigated. It was found that a lower melt superheat and a higher nucleation density decrease the severity of macrosegregation by weakening the flotation of grains.

Using a drift flux representation for the two-phase flow, a new reduced order model has been developed to simulate density-wave oscillations (DWOs) in a heated channel. This model is then used to perform stability and semi-analytical bifurcation analysis, using the bifurcation code BIFDD, in which the stability boundary (SB) and the nature of Hopf bifurcation are determined in a suitable two-dimensional parameter space.

A comparative study is carried out to investigate the effects of the parameters in the drift flux model (DFM) — the radially void distribution parameter C₀ and the drift velocity V_gj — on the SB as well as on the nature of Hopf bifurcation. It is the first time that a systematic analysis has been carried out to investigate the effects of DFM parameters on the nature of Hopf bifurcation in a heated-channel two-phase flow.

The results obtained show that both sub- and super-critical Hopf bifurcations are encountered. In addition, it has been found that, while the SB is sensitive to both C₀ and V_gj, the nature of Hopf bifurcation for lower values of N_sub is more sensitive to V_gj than to C₀. Numerical integration of the set of ODEs is carried out to confirm the predictions of the semi-analytical bifurcation analysis.

We consider a two-phase model described by a pressureless gas system with unilateral constraint. We prove weak stability and the existence of weak solutions by passing to the limit in the sticky-blocks dynamics. We obtain the maximum principle on the velocity, the Oleinik entropy condition and local entropy inequalities. Initial data are taken in a very weak sense since the solution can jump initially in time.

A model describing two-phase, incompressible, immiscible flow in fractured media is discussed. A fractured medium is regarded as a porous medium consisting of two superimposed continua, a continuous fracture system and a discontinuous system of medium-sized matrix blocks. Transport of fluids through the medium is primarily within the fracture system. No flow is allowed between blocks, and only matrix-fracture flow is possible. Matrix block system plays the role of a global source distributed over the entire medium. Two-phase flow in a fractured medium is strongly related to phase mobilities and capillary pressures. In this work, four relations for these functions are presented, and the existence of weak solutions under each relation will also be shown.