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This paper develops and analyses a semi-discrete numerical method for the two-dimensional Vlasov–Stokes system with periodic boundary condition. The method is based on the coupling of the semi-discrete discontinuous Galerkin method for the Vlasov equation with discontinuous Galerkin scheme for the stationary incompressible Stokes equation. The proposed method is both mass and momentum conservative. Since it is difficult to establish non-negativity of the discrete local density, the generalized discrete Stokes operator become non-coercive and indefinite, and under the smallness condition on the discretization parameter, optimal error estimates are established with help of a modified the Stokes projection to deal with the Stokes part and, with the help of a special projection, to tackle the Vlasov part. Finally, numerical experiments based on the dG method combined with a splitting algorithm are performed. [ABSTRACT FROM AUTHOR]

We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for the volume averaged velocity field and a convective Cahn–Hilliard equation with dynamic boundary conditions for the phase field, which describes the location of the two fluids within the domain. The dynamic boundary conditions are incorporated to model the interaction of the fluids with the wall of the container more precisely. In particular, they allow for a dynamic evolution of the contact angle between the interface separating the fluids and the boundary, and for a convection-induced motion of the corresponding contact line. For our model, we first prove the existence of global-in-time weak solutions in the case where regular potentials are used in the Cahn–Hilliard subsystem. In this case, we can further show the uniqueness of the weak solution under suitable additional assumptions. We further prove the existence of weak solutions in the case of singular potentials. Therefore, we regularize such singular potentials by a Moreau–Yosida approximation, such that the results for regular potentials can be applied, and eventually pass to the limit in this approximation scheme. [ABSTRACT FROM AUTHOR]

Summary: We propose an implicit discontinuous Galerkin (DG) discretization for incompressible two‐phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L‐stable TR‐BDF2 method is adopted for the time discretization of the Navier‐Stokes equations and of the level set method. Adaptive mesh refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks. A specific analysis on the influence of different choices of the mixture viscosity is also carried out. [ABSTRACT FROM AUTHOR]

The current experimental investigation demonstrates the capability of neutron imaging to quantify cavitation, in terms of vapour content, within an orifice of an abruptly constricting geometry. The morphology of different cavitation regimes setting in was properly visualised owing to the high spatial resolution of 16 μm achieved, given the extensive field of view of 12.9 × 12.9 mm2 offered by the imaging set-up. At a second step, the method was proven capable of highlighting subtle differences between fluids of different rheological properties. More specifically, a reference liquid was comparatively assessed against a counterpart additised with a Quaternary Ammonium Salt (QAS) agent, thus obtaining a viscoelastic behaviour. In accordance with previous studies, it was verified, yet in a quantifiable manner, that the presence of viscoelastic additives affects the overall cavitation topology by promoting the formation of more localised vortical cavities rather than cloud-like structures occupying a larger portion of the orifice core. To the authors' best knowledge, the present work is the first to demonstrate that neutron imaging is suitable for quantifying in-nozzle cavitating flow at the micrometre level, consequently elucidating the distinct forms of vaporous structures that arise. The potential of incorporating neutron irradiation for the quantification of two-phase flows in metallic microfluidics devices has been established. [ABSTRACT FROM AUTHOR]

The current experimental investigation demonstrates the capability of neutron imaging to quantify cavitation, in terms of vapour content, within an orifice of an abruptly constricting geometry. The morphology of different cavitation regimes setting in was properly visualised owing to the high spatial resolution of 16 μm achieved, given the extensive field of view of 12.9 × 12.9 mm2 offered by the imaging set-up. At a second step, the method was proven capable of highlighting subtle differences between fluids of different rheological properties. More specifically, a reference liquid was comparatively assessed against a counterpart additised with a Quaternary Ammonium Salt (QAS) agent, thus obtaining a viscoelastic behaviour. In accordance with previous studies, it was verified, yet in a quantifiable manner, that the presence of viscoelastic additives affects the overall cavitation topology by promoting the formation of more localised vortical cavities rather than cloud-like structures occupying a larger portion of the orifice core. To the authors' best knowledge, the present work is the first to demonstrate that neutron imaging is suitable for quantifying in-nozzle cavitating flow at the micrometre level, consequently elucidating the distinct forms of vaporous structures that arise. The potential of incorporating neutron irradiation for the quantification of two-phase flows in metallic microfluidics devices has been established. [ABSTRACT FROM AUTHOR]

This review article highlights the critical impact of surface roughness in modifying the structure of two-phase flow within mini- and microchannels, particularly in processes such as boiling and condensation. Channel surface roughness enhances flow resistance, affects the distribution of vapor bubbles, and enhances heat transfer by providing additional nucleation sites. Several experiments have shown that while increased surface roughness enhances the efficiency of heat transfer, increased flow resistance may hurt system performance. This is so because too high a surface roughness negatively impacts flow resistance, a factor of importance in the optimization for a balance between heat transfer and flow resistance, especially in high-performance compact heat exchangers. Furthermore, the review identifies that higher-degree measurement and characterization techniques of the surface roughness are increasingly required, as traditional 2D parameters may not fully represent the actual physics of complex surface interactions in two-phase flow systems. Consequently, the article calls for further research that can examine the exact relationship between roughness, flow structure, and thermal performance with the aim of improving design strategies for future heat exchanger technologies. [ABSTRACT FROM AUTHOR]

We study the unique solvability of weak transmission problems in some unbounded domains containing at least one flat layer area, which is associated with the motion of two-phase fluids. In particular, we construct the solution to the transmission problem for the Laplace operator with non-homogeneous boundary conditions. As a direct consequence, the Helmholtz–Weyl decomposition for the two-phase problem is also proved. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier–Stokes–Cahn–Hilliard model with singular potential describing immiscible, viscous two-phase flows with matched densities, which is referred to as the Model H. This means that we show that the strong solutions to the nonlocal Model H converge to the strong solution to the local Model H as the weight function in the nonlocal interaction kernel approaches the delta distribution. Compared to previous results in the literature, our main novelty is to further establish corresponding convergence rates. Before investigating the nonlocal-to-local convergence, we first need to ensure the strong well-posedness of the nonlocal Model H. In two dimensions, this result can already be found in the literature, whereas in three dimensions, it will be shown in the present paper. Moreover, in both two and three dimensions, we establish suitable uniform bounds on the strong solutions of the nonlocal Model H, which are essential to prove the nonlocal-to-local convergence results. [ABSTRACT FROM AUTHOR]

Reactant gas and liquid water transport phenomena in the flow channels are complex and critical to the performance and durability of polymer electrolyte membrane fuel cells. The polymer membrane needs water at an optimum level for proton conductivity. Water management involves the prevention of dehydration, waterlogging, and the cell’s subsequent performance decline and degradation. This process requires the study and understanding of internal two-phase flows. Different experimental visualization techniques are used to study two-phase flows in polymer electrolyte membrane fuel cells. However, the experiments have limitations in in situ measurements; they are also expensive and time exhaustive. In contrast, numerical modeling is cheaper and faster, providing insights into the complex multiscale processes occurring across the components of the polymer electrolyte membrane fuel cells. This paper introduces the recent design of flow channels. It reviews the numerical modeling techniques adopted for the transport phenomena therein: the two-fluid, multiphase mixture, volume of fluid, lattice Boltzmann, and pressure drop models. Furthermore, this work describes, compares, and analyses the models’ approaches and reviews the representative results of some selected aspects. Finally, the paper summarizes the modeling perspectives, emphasizing future directions with some recommendations. [ABSTRACT FROM AUTHOR]

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In thermal spraying, molten YSZ (Yttria Stabilized Zirconia) drop impact is crucial to the understanding of formation of splats and hence coatings. However, existing studies hardly cast attention to the possible rebounding dynamics when successive molten YSZ drops impinge onto newly solidified splats whose temperature is still high so that freezing may be delayed. This work uses a newly developed numerical model based on the conservative level set method to probe into the rebounding dynamics of YSZ drops in practical thermal spraying conditions. The free-energy-based surface tension model in the phase field method was introduced to avoid the computing of curvature, which is however necessary in the continuum surface tension model. The projection method was invoked to solve the Navier–Stokes equations. The model was validated against an experiment of drop impact with rebounding, showing reasonable agreement. Moreover, the model was applied to both dense and hollow YSZ drop impact, with the details of fluid flow being analyzed. The maximum spread factor was found in agreement with existing scaling laws. [ABSTRACT FROM AUTHOR]

A numerical model was developed to investigate the behavior of round buoyancy-driven particle clouds in a quiescent ambient. The model was validated by comparing model simulations with prior experimental and numerical results and then applied the model to examine the difference between releases of positively and negatively buoyant particles. The particle cloud model used the entrainment assumption while approximating the flow field induced by the cloud as a Hill's spherical vortex. The motion of individual particles was resolved using a particle tracking equation that considered the forces acting on them and the induced velocity field. The simulation results showed that clouds with the same initial buoyancy magnitude and particle Reynolds number behaved differently depending on whether the particles were more dense or less dense than the ambient fluid. This was found even for very low initial buoyancy releases, suggesting that the sign of the buoyancy is always important and that, therefore, the Boussinesq assumption is never fully appropriate for such flows. [ABSTRACT FROM AUTHOR]

A snowdrift is a two-phase flow consisting of air and suspended particles. In the presence of snow particles in the air, additional stability appears in the surface layer due to the density gradient. The density gradient reduces turbulence and affects the properties of the surface layer. Therefore, to describe the properties of the flow with included snow particles, additional clarifications are required. A description of the surface layer parameterization with the presence of suspended snow particles is presented in this paper. The formulation of the effect of snow particles consists of the reformulation of the Obukhov turbulent length scale. The novel surface layer parameterization allows one to take into account the effect of snow particles on turbulent flow and may improve the estimates of friction velocity and boundary-layer height.The parameterization was successfully tested on the observational data. A description of snow particle influence has been included in the large eddy simulation (LES) model. The numerical experiments confirmed an increase in the stability of the surface layer. The mechanism of influence of suspended particles on the surface layer is analogous to a thermal stabilization of the turbulent flow, in which negative buoyancy acts to reduce the turbulent kinetic energy (TKE). [ABSTRACT FROM AUTHOR]

Pipe structures are commonly encountered in the geophysical context, and in particular in sedimentary basins, where they are associated with fluid migration structures. We investigate pipe formation through laboratory experiments by injecting water locally at a constant flow rate at the base of water-saturated sands in a Hele–Shaw cell (30 cm high, 35 cm wide, gap 2.3 mm). The originality of this work is to quantify the effect of a discontinuity. More precisely, bilayered structures are considered, where a layer of fine grains overlaps a layer of coarser grains. Different invasion structures are reported, with fluidization of the bilayered sediment over its whole height or over the finer grains only. The height and area of the region affected by the fluidization display a non-monotonous evolution, which can be interpreted in terms of fluid focusing vs. scattering. Theoretical considerations can predict the critical coarse grains height for the invasion pattern transition, as well as the maximum topography at the sediment free surface in the regime in which only the overlapping finer grains fluidize. These results have crucial geophysical implications, as they demonstrate that invasion patterns and pipe formation dynamics may control the fluid expulsion extent and localization at the seafloor. [ABSTRACT FROM AUTHOR]

In this work, different CFD models to compute flows inside a steam ejector were investigated. The results were compared to the analytical models as well as the experimental results from the literature. All the simulations gave realistic results from the hydrodynamic perspective with a relative error of the entrainment ratio between 25% and 40% compared to reference experimental data. However, an analysis of the temperature profiles showed that only realistic results from the thermodynamic perspective were given by multiphase calculations. The first multiphase model tested was the so-called Wet-Steam model from ANSYS Fluent. This model gave inconsistent results for the steam ejector CFD simulation due to the physical boundaries of this model. The second model tested was the Eulerian mixture model, which gave the most realistic results in terms of the physical conditions of the liquid and vapor phases inside the ejector. It also showed that the phase change could have a significant impact on the value of the critical output pressure as a way to improve the performance of the ejector. [ABSTRACT FROM AUTHOR]

In this paper, a thermodynamically consistent phase-field model is employed to simulate the thermocapillary migration of a droplet. The model equations consist of a general Navier–Stokes equation for the two-phase flows, a Cahn–Hilliard equation for the diffuse interface, and a heat equation, and meanwhile satisfy the balance laws of mass, energy and entropy. In particular, the total energy of the system includes kinetic energy, potential energy and internal energy, which leads to a highly coupled and nonlinear equation system. We therefore develop a linear mass and energy conserving, semi-decoupled numerical method for the numerical simulations. As the model contains a heat (energy) equation, a simple error term introduced by the temporal discretization of the momentum equation can be absorbed into the heat equation, such that the numerical solutions satisfy the conservation laws of mass and energy exactly at the temporal discrete level. Several numerical tests are carried out to validate our numerical method. [ABSTRACT FROM AUTHOR]

The work is devoted to the study of random statistical processes in two-phase flows. The objective is to obtain new computational and experimental data on the influence of previously undetermined factors on the trajectories of particle motion, their segregation, and the formation of a locally continuous flow field of the dispersed phase in supersonic turbulent two-phase flows. The results of computational and experimental study of the flow features of a two-phase supersonic flow are presented. A new experimental method was applied for analysis of influence of random statistical factors on the particle distribution in a high-speed carrier flow. The physical basis of the proposed method is to indicate the flow rate of the dispersed phase by means of particle adhesion to an obstacle installed in the flow. In order to analyze the segregation of the dispersed phase in the flow, the approach of quasi-continuumization of individual particle trajectories is applied. The method obtains a locally continuous flow stress field for dispersed phase flow. Empirical coefficients resulting from the influence of random statistical factors on the motion of dispersed particles in a two-phase flow are determined. The obtained computational and experimental data clarify the prediction of the distribution and segregation of dispersed phase particles with a size of 15–40 microns in a supersonic free flow. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical modeling of two-phase flows while using Baer–Nunziato type models. Focus is given here on the numerical treatment of source terms that involve three (or four) relaxation time scales. A new coupled approach relying on the continuous analysis of the system of ODEs is compared with a more widely used strategy grounded on the fractional step approach. Properties of schemes are given in both cases. Several numerical applications show that the coupled approach should be preferred for both stability and accuracy reasons. [ABSTRACT FROM AUTHOR]

Soft objects squeezing through small apertures are crucial for many in vivo and in vitro processes. Red blood cell transit time through splenic inter-endothelial slits (IESs) plays a crucial role in blood filtration and disease progression, while droplet velocity through constrictions in microfluidic devices is important for effective manipulation and separation processes. As these transit phenomena are not well understood, we sought to establish analytical and numerical solutions of viscous droplet transit through a rectangular slit. This study extends from our former theory of a circular pore because a rectangular slit is more realistic in many physiological and engineering applications. Here, we derived the ordinary differential equations (ODEs) of a droplet passing through a slit by combining planar Poiseuille flow, the Young–Laplace equations, and modifying them to consider the lubrication layer between the droplet and the slit wall. Compared to the pore case, we used the Roscoe solution instead of the Sampson one to account for the flow entering and exiting a rectangular slit. When the surface tension and lubrication layer were negligible, we derived the closed-form solutions of transit time. When the surface tension and lubrication layer were finite, the ODEs were solved numerically to study the impact of various parameters on the transit time. With our solutions, we identified the impact of prescribed pressure drop, slit dimensions, and droplet parameters such as surface tension, viscosity, and volume on transit time. In addition, we also considered the effect of pressure drop and surface tension near critical values. For this study, critical surface tension for a given pressure drop describes the threshold droplet surface tension that prevents transit, and critical pressure for a given surface tension describes the threshold pressure drop that prevents transit. Our solutions demonstrate that there is a linear relationship between pressure and the reciprocal of the transit time (referred to as inverse transit time), as well as a linear relationship between viscosity and transit time. Additionally, when the droplet size increases with respect to the slit dimensions, there is a corresponding increase in transit time. Most notably, we emphasize the initial antagonistic effect of surface tension which resists droplet passage but at the same time decreases the lubrication layer, thus facilitating passage. Our results provide quantitative calculations for understanding cells passing through slit-like constrictions and designing droplet microfluidic experiments. [ABSTRACT FROM AUTHOR]

The main theme of this paper is a numerical investigation of fluid-particle flow in a channel with aslant walls (divergent channel) by taking thermal slip and Ohmic heating into account. The shooting technique with the RK-4 method is exploited to solve the system of dimensionless equations. Graphical discussions of the effects of emerging factors have been conducted for both fluid and particle aspects of temperature and velocity profiles. A perfect match is found when the current results are compared to the previous ones. The results reveal that the fluid phase temperature diminishes but particle phase temperature improves with an augmentation of the thermal slip parameter. These types of flows are used by a variety of industries, including the processing of waste water, mines, petrochemical sectors. [ABSTRACT FROM AUTHOR]

This study reports the development of a numerical method to simulate two-phase flows of Newtonian fluids that are incompressible, immiscible, and isothermal. The interface in the simulation is located and reconstructed using the geometric volume of fluid (VOF) method. The implementation of the piecewise-linear interface calculation (PLIC) scheme of the VOF method is performed to solve the three-dimensional (3D) interface transport during the dynamics of two-phase flows. In this method, the interface is approximated by a line segment in each interfacial cell. The balance of forces at the interface is accounted for using the continuum interfacial force (CSF) model. To solve the Navier–Stokes equations, meshless finite difference schemes from the HiG-Flow computational fluid dynamics software are employed. The 3D PLIC-VOF HiG-Flow algorithm is used to simulate several benchmark two-phase flows for the purpose of validating the numerical implementation. First, the performance of the PLIC implementation is evaluated by conducting two standard advection numerical tests: the 3D shearing flow test and the 3D deforming field test. Good agreement is obtained for the 3D interface shape using both the 3D PLIC-VOF HiG-Flow algorithm and those found in the scientific literature, specifically, the piecewise-constant flux surface calculation, the volume of fluid method implemented in OpenFOAM, and the high-order finite-element software FEEL. In addition, the absolute error of the volume tracking advection calculation obtained by our 3D PLIC-VOF HiG-Flow algorithm is found to be smaller than the one found in the scientific literature for both the 3D shearing and 3D deforming flow tests. The volume fraction conservation absolute errors obtained using our algorithm are 4.48 × 10 − 5 and 9.41 × 10 − 6 for both shearing and deforming flow tests, respectively, being two orders lower than the results presented in the scientific literature at the same level of mesh refinement. Lastly, the 3D bubble rising problem is simulated for different fluid densities ( ρ 1 / ρ 2 = 10 and ρ 1 / ρ 2 = 1000 ) and viscosity ratios ( μ 1 / μ 2 = 10 and μ 1 / μ 2 = 100 ). Again, good agreement is obtained for the 3D interface shape using both the newly implemented algorithm and OpenFOAM, DROPS, and NaSt3D software. The 3D PLIC-VOF HiG-Flow algorithm predicted a stable ellipsoidal droplet shape for ρ 1 / ρ 2 = 10 and μ 1 / μ 2 = 10 , and a stable cap shape for ρ 1 / ρ 2 = 1000 and μ 1 / μ 2 = 100 . The bubble's rise velocity and evolution of the bubble's center of mass are also computed with the 3D PLIC-VOF HiG-Flow algorithm and found to be in agreement with those software. The rise velocity of the droplet for both the ellipsoidal and cap flow regime's is found, in the initial stages of the simulation, to gradually increase from its initial value of zero to a maximum magnitude; then, the steady-state velocity of the droplet decreases, being more accentuated for the cap regime. [ABSTRACT FROM AUTHOR]

The present work provides a detailed numerical investigation of a turbopump for waterjet applications in cavitating conditions. In particular, the study focuses on the complexities of cavitation modelling, serving as a pivotal reference for future computational research, especially in off-design hydro-jet scenarios, and it aims to extend current model assessments of the existing methods, by disputing their standard formulations. Thus, a computational domain of a single rotor-stator blade passage is solved using steady-state Reynolds-Averaged Navier–Stokes equations, coupled with one-, two-, and four-equation turbulence models, and compared with available measurements, encompassing both nominal and thrust breakdown conditions. Through grid dependency analysis, a medium refinement with the Shear Stress Transport turbulence model is chosen as the optimal configuration, reducing either computational time and relative error in breakdown efficiency to 1%. This arrangement is coupled with a systematic study of the Zwart cavitation model parameters through multipliers ranging from 10 − 2 to 10 2 . Results reveal that properly tuning these values allows for a more accurate reconstruction of the initial phases of cavitation up to breakdown. Notably, increasing the nucleation radius reduces the difference between the estimated head rise and experimental values near breakdown, reducing the maximum error by 4%. This variation constrains vapour concentration, promoting cavitation volume extension in the passage. A similar observation occurs when modifying the condensation coefficient, whereas altering the vaporization coefficient yields opposite effects. [ABSTRACT FROM AUTHOR]

This paper is the second of the series of two papers, which focuses on the derivation of an averaged 1D model for compressible bubbly flows. For this, we start from a microscopic description of the interactions between a large but finite number of small bubbles with a surrounding compressible fluid. This microscopic model has been derived and analysed in the first paper. In the present one, provided physical parameters scale according to the number of bubbles, we prove that solutions to the microscopic model exist on a timespan independent of the number of bubbles. Considering then that we have a large number of bubbles, we propose a construction of the macroscopic variables and derive the averaged system satisfied by these quantities. Our method is based on a compactness approach in a strong-solution setting. In the last section, we propose the derivation of the Williams–Boltzmann equation corresponding to our setting. [ABSTRACT FROM AUTHOR]

In this note, we introduce a microscopic model for the motion of gas bubbles in a viscous fluid. By interpreting a bubble as a compressible fluid with infinite shear viscosity, we derive a pde/ode system coupling the density/velocity/pressure in the surrounding fluid with the linear/angular velocities and radii of the bubbles. We provide a 1D analogue of the system and construct an existence theory for this simplified system in a natural regularity framework. The second part of the paper is a preparatory work for the derivation of an averaged or macroscopic model. [ABSTRACT FROM AUTHOR]

In this work, a conservative phase‐field lattice Boltzmann method (LBM) is proposed for incompressible two‐phase flows. In this method, two LB models are adopted to solve the nonlocal Allen–Cahn equation (ACE) and the Navier–Stokes equations, respectively. Unlike the previous models for the nonlocal ACE with a space‐time‐dependent Lagrange multiplier, a simple multiple‐relaxation time LB model is designed for the conservative and nonlocal ACE with a curvature‐dependent Lagrange multiplier, which can eliminate the problem of inherent coarsening process. Through the Chapman–Enskog analysis, the present LB model can correctly recover the ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LBM is validated by two tests, that is, the horizontal translation of two circular interfaces and a bubble rising under gravity, and the results show that the present LBM has a superior performance in capturing the large topological changes and small features of interfaces. [ABSTRACT FROM AUTHOR]

The immersed boundary method (IBM) is widely used in simulating multiphase flows. DCU (Deep Computing Unit) acceleration device is a kind of GPU-like device, which is developed by GPU technology authorised by AMD. To achieve an efficient numerical simulation of two-phase flows, we develop a parallel DCU-based immersed boundary method using the MPI+HIP programming model. To solve the slow convergence problem caused by domain partitioning in multigrid methods, a coarse grid aggregation (CGA) technique is effectively employed. We adopt a nonblocking communication approach with HIP streams to overlap computation and communication. To validate the proposed method running on DCU clusters, we conducted two numerical experiments of droplet deformation in shear flow and the rising bubble. Performance tests show that a speedup of 181 times more than the CPU version can be achieved with 32 DCUs in a $ 1024\times 512\times 512 $ 1024 × 512 × 512 mesh grid. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of a fully passive flapping foil device for energy harvesting in a free surface flow. The study uses numerical simulations to examine the effects of varying submergence depths and the impact of monochromatic waves on the foil's performance. For the numerical simulations, a in-house artificial compressibility two-phase solver is employed and coupled with a rigid body dynamic solver. The results show that the fully passive flapping foil device can achieve high efficiency for submergence depths between 4 and 9 chords, with an "optimum" submergence depth where the flapping foil performance is maximised. The effects of regular waves on the foil's performance were also investigated, showing that waves with a frequency close to that of the natural frequency of the flapping foil-aided energy harvesting. Overall, this study provides insights that could be useful for future design improvements for fully passive flapping foil devices for energy harvesting operating near the free surface. [ABSTRACT FROM AUTHOR]

We derive a novel thermodynamically consistent Navier–Stokes–Cahn–Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous models in the literature, our new model allows for surface diffusion, a variable contact angle between the diffuse interface and the boundary, and mass transfer between bulk and surface. In particular, this transfer of material is subject to a mass conservation law including both a bulk and a surface contribution. The derivation is carried out by means of local energy dissipation laws and the Lagrange multiplier approach. Next, in the case of fluids with matched densities, we show the existence of global weak solutions in two and three dimensions as well as the uniqueness of weak solutions in two dimensions. [ABSTRACT FROM AUTHOR]

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier–Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to model the behaviour of magnetic flows in the presence of a magnetic field. To this end, a rigorous implementation of a second-order two-phase solver for incompressible nonmagnetic flows is introduced first. This solver is implemented in the finite-difference framework, where a fifth-order conservative level set method is employed to capture the evolution of the interface, along with an incompressible solver based on the projection scheme to model the fluids. The solver demonstrates excellent performance even with high density ratios across the interface (Atwood number $ \approx 1 $ ≈ 1), while effectively preserving the mass conservation property. Subsequently, the numerical discretisation of Maxwell's equations under the magnetostatic assumption is described in detail, utilising the vector potential formulation. The primary second-order solver for two-phase flows is extended to the case of magnetic flows, by incorporating the Lorentz force into the momentum equation, accounting for high magnetic permeability ratios across the interface. The implemented solver is then utilised for examining the deformation of ferrofluid droplets in both quiescent and shear flow regimes across various susceptibility values of the droplets. The results suggest that increasing the susceptibility value of the ferrofluid droplet can affect its deformation and rotation in low capillary regimes. In higher capillary flows, increasing the magnetic permeability jump across the interface can further lead to droplet breakup as well. The effect of this property is also investigated for the Rayleigh–Taylor instability growth in magnetic fluids. [ABSTRACT FROM AUTHOR]

Transient flows in stormwater systems can lead to damaging and dangerous operational conditions, as exemplified by geysering events created by the uncontrolled release of entrapped air pockets. Extreme rain and associated rapid inflows may result in air pocket entrapment, which causes significant changes in flow conditions and potentially geysering. Stormwater geysers have been studied in different experimental and numerical modeling studies, as well as from limited data gathered within real systems. However, there is still no complete understanding of geysering events, as stormwater system geometries vary considerably. Most past studies involved releasing air from an intermediate shaft, in which a significant fraction of the entrapped air may bypass the release. This work advances the understanding of geysering by considering uncontrolled air release through an upstream shaft or manhole. In such cases, the entire air pocket is released upon reaching the shaft, worsening the occurrence of geysering. Pressure and water level measurements were performed for various combinations of initial water pressure, trapped air pocket volume, and vertical shaft geometries, indicating the higher severity of these geysering events. The results obtained also corroborate previous studies in that the measured pressure heads were lower than the grade elevation. Future studies should include larger-scale testing and the representation of this geometry using CFD. [ABSTRACT FROM AUTHOR]

Computer simulation of two-phase media flow in curvilinear channels and pipes of complex geometry is considered. The motion equations of a two-phase medium, simplified taking into account the features of the flow, which are written in an orthogonal coordinate system associated with the flow area, are solved by the method of surfaces of equal flow rates. An algorithm for calculating the flow for computer simulation has been constructed. Numerical calculations were carried out for channels of parabolic and conical shapes, taking into account the presence of the initial section of the flow and the influence of the centrifugal force field. Based on of computer simulation, various flow regimes and the influence of various parameters on the hydrodynamic situation in the flow area were studied. [ABSTRACT FROM AUTHOR]

An analysis of the current state of technology shows the prospects for the development of alternative electric heat energy sources for the operation of absorption refrigeration devices (ARDs). It is important in today's minds that the working body of the ARDs is a water-amonia mixture with the addition of inert gas (water, helium or their mixtures) to natural refrigerants and is also absolutely environmentally friendly (maybe zero the significance of the ozone potential and the potential of the “greenhouse” effect). Before achieving the ARDs, it is necessary to maintain minimal heat among the most common types of refrigeration equipment with low cooling capacity, which in many cases means their popularity among consumers. Of particular interest may be ARDs models that use alternative, non-electric thermal energy sources in their work. A series of experimental studies were carried out at the stationary centers of the ARDs. The object was monitored by the ARDs "Kiev" AC-35. The thermal energy supplied to the ARD generator was varied in the range of 50 W to 110 W at 10 W intervals. The lower range of thermal absorption of the generator indicates the effectiveness of the ARD in terms of starting the thermosyphon that is pumped. The upper boundary of the thermal zone of the generator is surrounded by increasing temperatures and the beginning of active corrosion processes. In order to find an algorithm for supplying combined thermal energy, an experimental study of the starting modes of the ARD from a non-operating mill was carried out. The duration of the start-up period in our investigations was punctuated by the entry into stationary mode of the ARD refrigeration chamber. The principle of stationary mode was determined due to the invariability of the temperature in the refrigerating chamber. It has been proven that in order to ensure the safety of the ARD cycle, it is sufficient to use a standard car electric battery with a 70 A·hours 12 V battery. [ABSTRACT FROM AUTHOR]

We propose a novel class of edge‐based interface‐tracking (EBIT) methods in the field of multiphase flows for advecting the interface. The position of the interface is tracked by marker points located on the edges of the underlying grid, making the method flexible with respect to the choice of spatial discretization and suitable for parallel computation. In this article we present a simple EBIT method based on two‐dimensional Cartesian grids and on a linear interface representation. [ABSTRACT FROM AUTHOR]

Two-phase flows are found in almost all areas of technology. For example, tubular evaporators, boiling water reactors, boiler blowdown systems, heaters, boilers, gas lift pumps, oil and geothermal wells, oil and gas pipelines, refrigerators, process pipelines, and condensers. Two-phase flows are classified as mixtures. According to the composition of the mixture are divided: (a) for single-component (or one-component) - vapor-liquid flows; (b) multicomponent - gas-liquid flows. One-component mixtures consist of the same substance in different states of aggregation. This can be not only vapor-liquid, but also a mixture of liquid or vapor with a solid phase, a water-ice mixture, or a vapor flow with ice particles, for example, in sublimation installations. Multicomponent mixtures are a combination of substances of different physical nature. These include not only gas-liquid flows, but also, for example, mixtures of air and sand, water and oil. The paper presents the main attention is paid to the movement of two-phase flows in the pipeline. [ABSTRACT FROM AUTHOR]

The aim of the present work is to account for polydisperse effects in a two-phase flow with a simple and fast method. Polydisperse two-phase flows arise in numerous applications. Fire sprinkler systems are relevant examples as they release clouds of polydisperse droplets. Another relevant example is the polydisperse two-phase flow created by the detonation of an explosive charge surrounded by a liquid layer. In such a situation, material interfaces are initially present and the created two-phase flow consists of a carrier gas phase and a liquid phase involving many droplets of various sizes. Spherical particles or droplets are usually assumed in two-phase flow computations. When dealing with explosion situations involving both dense and dilute flow regimes, multiple particle diameters can be addressed but at the price of introducing as many additional equations that describe mass, momentum and energy balance of the various particle classes. Consequently, the computation time needed to address numerical resolution increases tremendously. Under explosion situations involving many particle diameters, the method becomes intractable and is usually reduced to a single diameter, which is often insufficient. A simplified approach is developed in the present work to account for a substantial number of particles of different sizes with few extra computational cost. The approach is said to be simplified as a single velocity and a single temperature are considered for all the spherical particles, regardless of their diameters. This type of modeling seems apt for the target explosion situations. The focus is placed on the interfacial area, which is the main parameter involved in the coupling of the two phases. In the present work, Gamma-like continuous probability distributions are considered to address the various sizes of particles. The effects of the size distribution are only summarized in the specific interfacial area, yielding consequently few code modifications while taking into account the polydisperse aspect of the two-phase flow. [ABSTRACT FROM AUTHOR]

This paper concerns the application of the gamma radiation absorption method in the measurements of dispersed phase velocity in two-phase flows: liquid–gas flow in a horizontal pipeline and liquid–solid particles in a vertical pipe. Radiometric sets containing two linear 241Am gamma radiation sources and two NaI(Tl) scintillation detectors were used in the research. Due to the stochastic nature of the signals obtained from the scintillation probes, statistical methods were used for their analysis. The linear average velocity of the dispersed phase transportation was calculated using the phase of the cross-spectral density function of the signals registered by the scintillation detectors. It is shown that in the presented cases, the phase method can be more accurate than the most commonly used classical cross-correlation one. [ABSTRACT FROM AUTHOR]

The paper studies the segmented flow patterns of immiscible liquids in microchannels with T- and X-junction for 3D printing technologies. The flow visualization results serve to build the flow pattern maps with a distinguished area of stable plug flow. A fair agreement of the maps plotted using the superficial flow velocities is revealed, and the influence of the junction geometry on the boundaries of flow patterns is shown to be insignificant. When using a less viscous carrier phase, the region of a stable plug flow is demonstrated to expand towards higher superficial flow velocities. The separation of microdroplets from the trailing edges of plugs is investigated. It is found that the transition to the separation of microdroplets is described in terms of the capillary number, constructed from the bulk velocity of the phases, and the ratio of phase flow rates. Thus, a range of dimensionless parameters of microchannel devices, suitable for 3D printing of composite materials with specified properties is determined. [ABSTRACT FROM AUTHOR]

The importance of volumetric expanders has been increasing in the last decades because several studies confirmed that they lead to improved energy savings, limit the environmental impact, and reduce the energy intensity of industrial and domestic applications. In particular, several applications of the two-phase volumetric expanders, in which the operating fluid consists of liquid and vapor phases, were recently proposed. Nevertheless, the contributions in the scientific literature related to the overview of the state-of-the-art aspects of this technology are rare. For this reason, the present work discussed the potentialities and drawbacks of the available typologies of volumetric expanders that process a two-phase pure working fluid by analyzing a summary of leading studies in this field to go beyond previous efforts in the literature. The analysis revealed that twin-screw machines represent the best candidates, while reciprocating piston devices seemed the least well-adapted because of their reduced tolerance to droplets and high friction losses. Flash evaporation appeared to have the most significant impact on the expander because it affects both inlet and expansion phases, thus, determining the shape of the indicated cycle and the isentropic efficiency. [ABSTRACT FROM AUTHOR]

This study constructs a new diffuse-domain (DD) lattice Boltzmann (LB) method for two-phase flows in complex geometries. We first coupled the DD method with the consistent and conservative phase-field (CCPF) method which can be described by the DD-CC Navier--Stokes--Cahn--Hilliard (NSCH) equations with the consistency of reduction, the consistency of mass and momentum transport, and the consistency of mass conservation. Then we conducted a matched asymptotic analysis and found that the DD-CCNSCH equations would converge to the CCNSCH equations as the thickness of the DD interface approaches to zero. Since the boundary conditions imposed on the complex geometries are incorporated into the DD-CCNSCH equations as the source terms, the system can be implemented more readily in a large and regular domain, and there is no need to treat the complex boundary conditions specially. We further developed a DD-CCPFLB method, and through the Chapman--Enskog analysis, the DD-CCPFLB method can correctly recover the DD-CCNSCH equations for two-phase flows in complex geometries. To quantitatively validate the DD-CCPFLB method, three benchmark problems are considered, and the numerical results are in agreement with those obtained through directly solving the CCNSCH equations combined with the original boundary conditions, the analytical solution, or the reported data. Finally, the present method is used to study the problems of two-phase flows in complex geometries, including the droplet dynamics in the Y-shaped channel and a droplet passing through cylindrical obstacles. The effects of the wettability and viscosity ratio are mainly investigated, and it is found that these two factors have significant impacts on the droplet dynamics. [ABSTRACT FROM AUTHOR]

High fidelity spray flame modelling without ad-hoc tuning of the injection parameters is proposed for an Euler-Lagrangian LES description of turbulent combustion in swirled two-phase flow chambers. It is tested in a laboratory burner (SICCA-Spray rig from EM2C), which comprises both a simplex pressure swirl and an airblast atomiser. Relevant phenomena controlling the liquid spray inside the injector including primary and edge atomisation from a pressure swirl and an airblast atomiser respectively, secondary atomisation, evaporation and the formation and dynamics of the liquid film that forms on the inner injector wall are taken into account. Particular attention has been applied to understanding the shape of the droplet diameter probability distribution function and how each atomisation model contributes to it. Results show excellent agreement of the spray statistics measured experimentally with and without combustion. A sensitivity analysis of the model parameters shows that the models are sufficiently insensitive to user chosen parameters, which, together with their relatively low computational cost, make these models ideal candidates for industrial applications. [ABSTRACT FROM AUTHOR]

Entropy is a key notion in the analysis of properties of mass systems. This notion was first formulated in thermodynamics and then expanded to gas systems. In the previous paper, the author has formulated the notion of entropy for two-phase flows. The analysis of properties of this kind of entropy made it possible to formulate the conditions of invariance of the behavior of narrow-size-class particles in a two-phase flow. In addition, this analysis has revealed a universal dimensionless parameter of affinization of separation curves, which makes it possible to control the process of bulk materials separation into fractions by particle sizes and densities. The use of this parameter will enable solving a number of challenging problems related to specific technological processes. [ABSTRACT FROM AUTHOR]

Two-phase flow is very important in many areas of science, engineering, and industry. Two-phase flow comprising gas and liquid phases is a common occurrence in oil and gas related industries. This study considers three flow regimes, including homogeneous, annular, and stratified regimes ranging from 5–90% of void fractions simulated via the Mont Carlo N-Particle (MCNP) Code. In the proposed model, two NaI detectors were used for recording the emitted photons of a cesium 137 source that pass through the pipe. Following that, fast Fourier transform (FFT), which aims to transfer recorded signals to frequency domain, was adopted. By analyzing signals in the frequency domain, it is possible to extract some hidden features that are not visible in the time domain analysis. Four distinctive features of registered signals, including average value, the amplitude of dominant frequency, standard deviation (STD), and skewness were extracted. These features were compared to each other to determine the best feature that can offer the best separation. Furthermore, artificial neural network (ANN) was utilized to increase the efficiency of two-phase flowmeters. Additionally, two multi-layer perceptron (MLP) neural networks were adopted for classifying the considered regimes and estimating the volumetric percentages. Applying the proposed model, the outlined flow regimes were accurately classified, resulting in volumetric percentages with a low root mean square error (RMSE) of 1.1%. [ABSTRACT FROM AUTHOR]

The pressure losses during the supply of a vertical two-phase flow of a mixture of water and abrasive particles were studied experimentally. The experimental data are used to calculate the flow friction coefficient, which should be taken into account in theoretical calculations. [ABSTRACT FROM AUTHOR]

A modified form of BGK source terms is proposed for modeling two-phase flows with thermodynamical disequilibrium. The novelty is that three independent time-scales allow to manage the return to the thermodynamical equilibrium while remaining in agreement with the second law of thermodynamics. This is achieved thanks to the definition of a "local-in-time" equilibrium state which tends toward the asymptotic equilibrium state when time increases. The thermodynamical paths of the system are then modified with respect to the classical BGK source terms used for two-phase flow modeling, and the relaxation process of the system toward the asymptotic equilibrium state can be defined with additional degrees of freedom. In a numerical point of view, both the classical and the modified BGK source terms have advantages. The choice between these two forms strongly depends on the numerical strategy used to perform simulations. [ABSTRACT FROM AUTHOR]

A three‐dimensional adaptive mesh refinement‐multiphase lattice Boltzmann flux solver (3D‐AMR‐MLBFS) is developed for effectively simulating complex multiphase flows with large density ratio and high Reynolds number. In the method, the multiphase lattice Boltzmann flux solver (MLBFS) is used to solve the flow field and the level set method is adopted to capture the interface. In addition, a free energy‐based continuum surface tension force (FE‐CSF) model, which has a clear physical basis and does not need to introduce a regularization function, is applied to calculate the surface tension force. In order to improve the computational efficiency and at the same time ensure accuracy, the adaptive mesh refinement technology is introduced. This method is used to simulate three‐dimensional collision of two equal‐sized droplets for a wide range of parametric conditions. We not only verify the developed method by comparing with available literature data but also successfully reproduce four typical outcomes of droplet collision, namely coalescence, reflexive separation, stretching separation, and liquid membrane shattering, for which the evolutions of droplet morphologies and various energies are revealed. [ABSTRACT FROM AUTHOR]

The authors performed 3D numerical simulation of the unsteady outflow of a two-phase liquid-vapor flow from a tube with spherical monodisperse filling. The numerical model was developed by the smoothed particle method, and its verification was carried out using experimental data on the motion of a bubble flow in a tube. The minimum size of smoothed particles and their required number to build a correct computational model have been determined. Structural and hydraulic characteristics of the flow in the presence of phase transitions have been obtained. The calculated data on the three-dimensional spatial distribution of the vapor phase and pressure losses both over the cross section of the unit cell formed by the dispersed backfill and along the entire length of the channel are given. The analysis of the dynamics of changes in pressure losses along the length of the tube has been carried out; two characteristic sections with different dynamics of the growth of pressure losses have been found. Data were obtained on the distribution of the volumetric steam content in the tube at its various positions: horizontal, vertical, and with an inclination of 45°. The influence of the angle of inclination of the tube on the character of the distribution of steam over its cross section is shown. In this case, the greatest difference in the structure is observed between the vertical and horizontal positions. It has also been demonstrated that its structure tends to be homogeneous as the flow moves. The calculation model used made it possible to determine pressure loss in the working section from the inlet of the vapor-liquid flow into the tube to the outlet under conditions corresponding to the onset of the critical flow regime. Comparison of the results of numerical calculations, including the critical mass flow rates at the outflow of a vapor-liquid flow from the tube, with the available experimental data and previously obtained results of analytical studies, noted their good match. [ABSTRACT FROM AUTHOR]

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An investigation of the effect of capillary and viscous forces on the dynamics of the development of two types of interfacial contacts "injected fluid–ejected fluid" and "injected fluid–solid body" in the case of two-phase flows in porous media with different heterogeneities of the pore structure is carried out. The connection between the dynamics of development of interfaces, distribution of fluids in the pore space of samples and the average size of pore channels filled with the injected fluid is being established. To simulate a two-phase flow the present work resorts to the lattice Boltzmann equations together with the multirelaxation time collision operator, as well as the color field gradient model for describing the effects of interfacial interaction. The relationship between the capillary and viscous forces is controlled by flow velocity and interfacial tension. Computational experiments are carried out on artificial digital models of porous media with the use of the Monte Carlo algorithm. The heterogeneity of porous structures is described numerically with the aid of the randomness coefficient calculated as the standard deviation of local porosity measured in Voronoi′s cells. A linear law of the development of the specific length of interfacial "fluid–fluid" and "fluid–solid body" contacts has been established. The two-phase flow parameters and the heterogeneity of the pore structure exert their effect only on the dynamics of the growth of the interface length. An increase in the heterogeneity of the pore structure contributes to the growth of the mean size of pore channels filled with injected fluid. The randomness coefficient exerts an insignificant effect on the dynamics of the development of the "fluid–fluid" contact and a negative effect on the dynamics of the development of the "fluid–solid body" interface. In transition from flow with viscous fingers to a regime with capillary fingers, a significant decrease in the dynamics of development of the "fluid–fluid" contact and an increase in the dynamics of the development of the "fluid–solid body" interface are observed. [ABSTRACT FROM AUTHOR]