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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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

A six-equation Baer–Nunziato model at pressure equilibrium for two ideal gases is derived from a full non-equilibrium model by applying an asymptotic pressure expansion. Conditions on the interfacial pressure are provided that ensure hyperbolicity of the reduced model. Closure conditions for the relaxation terms are given that ensure consistency of the model with the second law of thermodynamics. [ABSTRACT FROM AUTHOR]

We present a fully coupled level set and volume of fluid method for free surface flow simulations on unstructured grids in two- and three-dimensions. The evolution of the level set function and the volume fraction are updated at each time step. The level set advection equation is solved by a least squares weighted residual method while the volume fraction advection is solved using an unsplit Eulerian-Lagrangian scheme. The reconstruction of the interface in the volume of fluid method is performed using the volume fraction information together with the normal vector obtained from the level set function. The reconstructed interface is then used to reinitialize the level set function. Thanks to the fully coupling of the two methods, the interface reconstruction is carried out efficiently and the mass conservation is preserved exactly. The proposed method is validated against several benchmarks and is coupled with the incompressible Navier-Stokes solver to solve two-phase flow problems. Numerical results show that the method is capable of resolving complex interface changes efficiently and accurately. [ABSTRACT FROM AUTHOR]

Experience gained from the operation of nuclear power plants shows that emergencies or incorrect actions of the personnel may give rise to water hammer phenomena, which exert additional impacts on the pipelines and equipment. Condensation-induced water hammer (CIWH) is one of the most destructive kinds of water hammer. Experimental studies of CIWH were carried out in a number of scientific organizations around the world. The main features of the experimental facilities used in the world are considered. For studying the CIWH phenomena occurring in a horizontal channel, a special experimental test facility was set up in 2018 at the Elektrogorsk Research and Engineering Center for Nuclear Power Plants' Safety (EREC). The facility's test section and the parameters of experimental regimes are described. Fifty-two experiments were carried out on the facility under different initial and boundary conditions for three values of the water flowrate supplied to the facility (1, 3, and 5 t/h), two values of water temperature (30 and 60°С), and two values of vapor pressure in the test section (0.6 and 1.0 MPa). In all experiments, CIWH phenomena were recorded. As an example, one experimental regime was considered in detail, and the CIWH occurrence mechanism is described proceeding from the readings of pressure and level gages and temperature sensors. The described experimental regime was modeled using the RELAP5 and WAHA thermal-hydraulic codes. The effect that the size of nodalization diagram cells and the integration time step have on the computation results is analyzed. The significant amount of experimental points obtained from the study can be used for setting up a database for validating computer codes. [ABSTRACT FROM AUTHOR]

We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three-dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input for lattice Boltzmann simulations. We perform a quantitative analysis of the multiphase pore-scale dynamics, and we identify the dominant fluid structures governing mass transport. The results show the existence of three different regimes of transport: a fast inertial dynamics at short times, characterised by a compact uniform front, a viscous-capillary regime at intermediate times, where liquid is transported along a gradually increasing number of preferential flow paths of the size of one–two pores, and a third regime at longer times, where liquid, after having reached the outlet, is exclusively flowing along such flow paths and the two-phase fluid structures are stabilised. We observe that the fibrous layer presents significant variations in its microscopic morphology, which have an important effect on the pore invasion dynamics, and counteract the stabilising viscous force. Liquid transport is indeed affected by the presence of microstructure-induced capillary pressures acting adversely to the flow, leading to capillary fingering transport mechanism and unstable front displacement, even in the absence of hydrophobic treatments of the porous material. We propose a macroscopic model based on an effective contact angle that mimics the effects of the such a dynamic capillary pressure. Finally, we underline the significance of the results for the optimal design of face masks in an effort to mitigate the current COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Air entrainment within water is a common feature of flows over hydraulic works – spill over a dam, wave breaking on a dike, etc. – and its accurate modeling is a key to better design such structures. The Smoothed Particle Hydrodynamics (SPH) method appears as a natural way to model such highly distorted flows. To avoid computationally prohibitive costs related to the full discretization of bubbles or drops, a mixture model for high density ratio flows relying on a volume-based formulation with relative velocity between phases has first been developed and validated in Fonty et al. (Proceedings of 13th international SPHERIC workshop. Galway, Ireland, 2018; Int J Multiph Flow 111:158–174, 2019. 10.1016/j.ijmultiphaseflow.2018.11.007). Instead of having a once and for all assigned phase as in multifluid SPH, each particle now carries both phases through their respective volume fractions. In the present work, in order to handle practical air entrainment application cases, the open boundary formulation described in Ferrand et al. (Comput Phys Commun 210:29–44, 2017. 10.1016/j.cpc.2016.09.009) is adapted to this mixture model. Then, after introducing turbulence through a k - ϵ model, a specific closure on the air bubbles relative velocity is proposed including a Stokesian drag term and turbulent diffusion. This model is then applied to two cases of air entrainment: a stepped spillway for interfacial aeration and a plunging jet for local aeration. Finally a 3D industrial test case of discharge-control structure at the La Coche power plant (France) is considered. While valuable insights are obtained for the volume fraction field, further investigations are required to improve the modeling of the flow dynamics. [ABSTRACT FROM AUTHOR]

Dynamic mode decomposition (DMD) and deep learning are data-driven approaches that allow a description of the target phenomena in new representation spaces. This fact motivates their comparison in the analysis of flow data, generated through experimental setups and numerical simulations. The focused application is the processing of high-speed videos of horizontal two-phase stratified and slug flows regimes. Henceforth, in this work, we consider the traditional DMD, the sparsity-promoting DMD (SPDMD) and, in the deep learning context, we select an unsupervised convolutional autoencoder (CAE). In this avenue, it becomes imperative to compare DMD and deep learning with respect to: computational complexity of target techniques; reduced order modeling versus data representation; data set necessary to compute the dynamic modes and deep learning training; the preservation of the phase interface in the DMD and CAE space; data synthesis. In general, the results favor DMD in the considered applications. [ABSTRACT FROM AUTHOR]

An accurate numerical approach is presented for computing two-phase flows with surface tension at low-Mach regime. To develop such a model, where slight compressible effects are taken into account as well as correct thermodynamical closures, both the liquid and the gas are considered compressible and described by a precise compressible solver. A low-Mach correction has been implemented to eliminate excessive numerical dissipation. The interface between two-phase flows is captured by the level set method that is considered to be sharp. The interface capturing issue of the level set method within the Eulerian framework is the key point of the two-phase flow simulations, and in this work we propose a high-order coupled time-space approach for interface advection. Several numerical test-cases have been employed to validate the present numerical approach and enlighten its good performance. [ABSTRACT FROM AUTHOR]

We present a novel mathematical model of two-phase interfacial flows. It is based on the Entropically Damped Artificial Compressibility (EDAC) model, coupled with a diffuse-interface (DI) variant of the so-called one-fluid formulation for interface capturing. The proposed EDAC-DI model conserves mass and momentum. We find appropriate values of the model parameters, in particular the numerical interface width, the interface mobility and the speed of sound. The EDAC-DI governing equations are of the mixed parabolic–hyperbolic type. For such models, the local spatial schemes along with an explicit time integration provide a convenient numerical handling together with straightforward and efficient parallelisation of the solution algorithm. The weakly-compressible approach to flow modelling, although computationally advantageous, introduces some difficulties that are not present in the truly incompressible approaches to interfacial flows. These issues are covered in detail. We propose a robust numerical solution methodology which significantly limits spurious deformations of the interface and provides oscillation-free behaviour of the flow fields. The EDAC-DI solver is verified quantitatively in the case of a single, steady water droplet immersed in gas. The pressure jump across the interface is in good agreement with the theoretical prediction. Then, a study of binary droplets coalescence and break-up in two chosen collision regimes is performed. The topological changes are solved correctly without numerical side effects. The computational cost incurred by the stiffness of the governing equations (due to the finite speed of sound and the interface diffusion term) can be overcome by a massively parallel execution of the solver. We achieved an attractively short computation time when our EDAC-DI code is executed on a single, desktop-type Graphics Processing Unit. [ABSTRACT FROM AUTHOR]

A study is made of the influence of surface tension on two-phase drainage flows in a porous medium. Computational filtration experiments are conducted in a three-dimensional digital microtomographic model of sandstone. To simulate two-phase flows, use is made of lattice Boltzmann equations; interfacial phenomena and wetting effects are described using the color-gradient-based method. Calculations are carried out at the same rate of injection of a nonwetting fluid and at a ratio of the viscosities of nonwetting and wetting phases of 1:10. Results are obtained according to which growth in the interfacial tension contributes to the rise in the efficiency of displacement of the wetting fluid, which is recorded at the moment the injected phase breaks through, and to the decrease in the efficiency after its breakthrough. It is established that distinctive features of flows with capillary fingering that arise at high surface tensions are the stepwise character of travel of the leading front and the growth of displacement channels in directions different from the hydrodynamic pressure difference. It is shown that interfacial tension is a parameter whose variation enables us to change the type of two-phase flow. Increase in the interfacial tension contributes to the transition of the flow with viscous fingering to a flow with capillary fingering. The efficiency of displacement of the wetting fluid in the transition crossover zone is the lowest. [ABSTRACT FROM AUTHOR]

Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier–Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh–Taylor instability, and a film flowing down a vertical wall in an extended region. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the time-periodic solution to a coupled compressible Navier- Stokes/Allen-Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in ℝN. The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory, and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force. [ABSTRACT FROM AUTHOR]

The focus of this work is to investigate and to apply, for the first time, a very high-resolution correction procedure via reconstruction (CPR) numerical discretization technique for the hyperbolic saturation equation that describes 1-D oil-water displacement through heterogeneous porous media. The CPR method can achieve high-order accuracy via a compact stencil consisting of the current cell and its immediate neighbors; in addition, the CPR recovers simplified versions of nodal discontinuous Galerkin (NDG), spectral volume (SV), and spectral difference (SD) methods using an adequate polynomial reconstruction function, whose coefficients are preprocessed and stored. Indeed the CPR versions of NDG and SV/SD are highly efficient. In order to suppress numerical oscillations near shocks, which are typical from higher-order schemes, a hierarchical MLP (multi-dimensional limiting process) is used in the reconstruction stage. The integration in time is carried out using a third-order RK (Runge-Kutta) method. A number of 1-D two-phase flow benchmark problems are solved, to verify the accuracy, efficiency, and shock-capturing capability of the adopted methodology. [ABSTRACT FROM AUTHOR]

The dynamics of evaporation from the confined surface of a horizontal layer of liquid (ethanol) under the action of a gas (air) flow has been experimentally studied. The influence of the longitudinal dimension of the interface (0.01–0.03 m) on the specific mass rate of evaporation was studied. It was found that the specific mass evaporation rate decreases with an increase in the interface length due to a decrease in the vapor concentration gradient in the boundary layer. [ABSTRACT FROM AUTHOR]

Modeling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of two Cahn–Hilliard-type equations and incompressible Navier–Stokes equation. With the introduction of two auxiliary variables, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. By certain subtle explicit-implicit treatments to stress and convective terms, we construct first and second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving only a sequence of linear elliptic equations, and computations of phase-field variables, velocity and pressure are fully decoupled. We further establish a rigorous proof of unconditional energy stability for the first-order scheme. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow, where the increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence. [ABSTRACT FROM AUTHOR]

The crisis of heat transfer in a FC-72 liquid film moving under the action of a gas flow along a smooth or micro-finned heater was experimentally investigated. It is shown that the use of micro-finning leads to an increase in the critical heat flux, since additional washing of the heated surface occurs due to the capillary effect. [ABSTRACT FROM AUTHOR]

The structure of convective flows in a horizontal evaporating layer of liquid (ethanol) was studied experimentally depending on the velocity of gas (air) flowing near the interface. Using the PIV method, we measured distribution of the two-dimensional velocity field and visualized the convective flows in a liquid layer. The existence of a vortex flow structure in an evaporating liquid layer, when the interface moves towards the gas flow, was proved. [ABSTRACT FROM AUTHOR]

Consideration is given to the regimes of water flow in a hydrodynamic-flow plant with cavitation and hydraulic shock. Calculations are carried out by the CFX hydrodynamic unit of the general physical computational system ANSYS and are compared with experimentally measured values of pressure; flow velocities are also computed. It is shown that the hydraulic shock ensures a growth of the order of 5 atm in the external pressure on a vapor bubble. The possibility of the nanodiamond forming in flows of carbon-containing fluids in such regimes is discussed. [ABSTRACT FROM AUTHOR]

The joint steady-state motion of a rivulet of incompressible liquid and a gas flow in a microchannel was studied taking into account the action of gravity forces, tangential stress at the gas-liquid interface, and Van der Waals forces. The values of contact angle are calculated for various values of liquid and gas flow rates. It is shown that for a constant liquid flow rate, an increase in gas velocity leads to a decrease in the height of rivulet, and the surface of rivulet becomes flatter. A significant deforming effect of rivulet on the velocity distribution in gas is found. [ABSTRACT FROM AUTHOR]

Self-aeration in high-speed free surface flows occurs commonly and is of interest to ocean engineering, hydraulic engineering, and environmental engineering. For two-phase air-water flows, macroscopic air-water flow properties develop gradually, accompanied by the change of microscopic air-water structures. In this article, representational experimental studies on macroscopic and microscopic characteristics of self-aerated open-channel flows are summarized and compared. The isolated effect of the flow Reynolds number and air quantity on the differences in air count rate and chord size are analyzed and discussed. The results show that the characterized flow depth y50, affected by the turbulence transfer, is a specific criterion to distinguish the interior air-water structure development. Two distinct linear trends of self-aeration are found, depending on the y50/y90 variation with a breaking point at Cmean = 0.50. The air count rate and size scale in self-aerated flows are affected by the air quantity of self-aerated flows, even with identical flow Reynolds numbers. Thus, a specific parameter is proposed to assess the air-water structures and a series of self-similarity relationships in self-aeration properties are obtained. The link between macroscopic and microscopic air-water properties results in significant scale effect on air-water structures in self-aerated flows. [ABSTRACT FROM AUTHOR]

The results of numerical simulation of the processes of two-phase flow through a porous medium in three-dimensional digital models of the porous space of three natural sandstone samples are given. The calculations are carried out using the lattice Boltzmann equations and the digital field gradient model over a wide range of the capillary numbers and the viscosity ratios of injected and displaced fluids. The conditions of flow through a porous medium with capillary fingering, viscous fingering and with stable displacement front are revealed. [ABSTRACT FROM AUTHOR]

We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in RN, and the Navier-Stokes-Korteweg equations is used in the upper domain and the Navier-Stokes equations is used in the lower domain. We prove the existence of R-bounded solution operator families for a resolvent problem arising from its model problem. According to Göts and Shibata (Asymptot Anal 90(3-4):207-236, 2014), the regularity of ρ+ is Wq1 in space, but to solve the kinetic equation: uΓ·nt=[[ρu]]·nt/[[ρ]] on Γt we need Wq2-1/q regularity of ρ+ on Γt, which means the regularity loss. Since the regularity of ρ+ dominated by the Navier-Stokes-Korteweg equations is Wq3 in space, we eliminate the problem by using the Navier-Stokes-Korteweg equations instead of the compressible Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

In this work, we study the influence of the contact angle boundary condition on 3D CFD simulations of the bubble generation process occurring in a capillary T-junction. Numerical simulations have been performed with the commercial Computational Fluid Dynamics solver ANSYS Fluent v15.0.7. Experimental results serve as a reference to validate numerical results for four independent parameters: the bubble generation frequency, volume, velocity and length. CFD simulations accurately reproduce experimental results both from qualitative and quantitative points of view. Numerical results are very sensitive to the gas-liquid-wall contact angle boundary conditions, confirming that this is a fundamental parameter to obtain accurate CFD results for simulations of this kind of problems. [ABSTRACT FROM AUTHOR]

A single velocity model of one-component media for calculating two-phase flows is presented. The model is based on conservation laws with minimal additional assumptions. The model and numerical method are intended for the direct numerical simulation (DNS) of complex two-phase flows with high-performance computing systems (exascale computing). The closed set of governing equations is written for nonaveraged parameters (so-called microparameters) and for a medium with a complex equation of state. It is assumed that each point of the flow is completely characterized by a single density, single velocity, and single internal energy. The diffused interface model is used for describing an interphase boundary. A method for generating the relationship between thermodynamic functions and all possible values of density and internal energy is presented. The real functions for the pure phases are used. The hydrodynamic basis of the model consists of Navier-Stokes equations or Euler equations that take heat conductivity processes into consideration. The reliability of the model is tested on a 1D problem for real water, in particular, on the Stefan problem and on the problem on the formation and coalescence of bubbles. [ABSTRACT FROM AUTHOR]

The aim of this work is the development of the lattice Boltzmann model for simulation of the mold filling process. The authors present a simplified approach to the modeling of liquid metal-gas flows with particular emphasis on the interactions between these phases. The boundary condition for momentum transfer of the moving free surface to the gaseous phase is shown. Simultaneously, the method for modeling influence of gas back pressure on a position and shape of the interfacial boundary is explained in details. The problem of the lattice Boltzmann method (LBM) stability is also analyzed. Since large differences in viscosity of both fluids are a source of the model instability, the so-called fractional step (FS) method allowing to improve the computation stability is applied. The presented solution is verified on the bases of the available reference data and the results of experiments. It is shown that the model describes properly such effects as: gas bubbles formation and air back pressure, accompanying liquid-gas flows in the casting mold. At the same time the proposed approach is easy to be implemented and characterized by a lower demand of operating memory as compared to typical LBM models of two-phase flows. [ABSTRACT FROM AUTHOR]

Moving contact line problem plays an important role in fluid-fluid interface motion on solid surfaces. The problem can be described by a phase-field model consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition (GNBC). Accurate simulation of the interface and contact line motion requires very fine meshes, and the computation in 3D is even more challenging. Thus, the use of high performance computers and scalable parallel algorithms are indispensable. In this paper, we generalize the GNBC to surfaces with complex geometry and introduce a finite element method on unstructured 3D meshes with a semi-implicit time integration scheme. A highly parallel solution strategy using different solvers for different components of the discretization is presented. More precisely, we apply a restricted additive Schwarz preconditioned GMRES method to solve the systems arising from implicit discretization of the Cahn-Hilliard equation and the velocity equation, and an algebraic multigrid preconditioned CG method to solve the pressure Poisson system. Numerical experiments show that the strategy is efficient and scalable for 3D problems with complex geometry and on a supercomputer with a large number of processors. [ABSTRACT FROM AUTHOR]

Numerical methods for solving equations of two-phase hydrodynamics, which describe the flow of a dispersed solid and gas mixture are considered. The Godunov method is applied as the main approach to approximate numerical fluxes in solutions of the relevant Riemann problems. The formulations of these problems for the solid and gas phases are given, their exact analytical solution is described, and possible simplified approximate solutions are discussed. The obtained theoretical results are applied to the construction of a discrete model, which results in the generalization of the well-known Godunov-type and Rusanov-type methods to the case of nonequilibrium two-phase media. The numerical results involve the verification of the constructed methods on the analytical solutions of two-phase equations. [ABSTRACT FROM AUTHOR]

The paper reviews a number of the physical features of tropical cyclones, including the important reaction of the sea induced by the hurricane itself. Indeed, the sea-atmosphere interface is a critical aspect in attempting to predict a hurricane's behaviour and one to which researchers in engineering fluid mechanucs may be able to make a significant contribution. The known sensitivity of the atmosphere to increasing temperature differences implies that over the coming decades, with global warming, there will be corresponding effects on the intensity, size, and the geographical distribution of hurricanes. Finally, some of the outline strategies suggested for reducing such occurrences are exmined. [ABSTRACT FROM AUTHOR]

The first results from a study of the motion of liquid-phase particles in the interblade channel of an isolated nozzle array of a steam turbine are reported. Some features of the formation of secondary droplets produced by the interaction of primary moisture with the blade walls are examined. The influence of the moisture content of the main flow on the formation of the steam-droplet layer near the convex blade surface is established. [ABSTRACT FROM AUTHOR]

Research results of Russian and foreign scientists of heat and mass transfer in whirling flows, swirling effect, superficial vortex generators, thermodynamics and hydrodynamics at micro- and nanoscales, burning at swirl of the flow, and technologies and apparatuses with the use of whirling currents for industry and power generation were presented and discussed at the 'Heat and Mass Transfer in Whirling Currents' 5th International Conference. The choice of rational forms of the equipment flow parts when using whirling and swirling flows to increase efficiency of the heat-power equipment and of flow regimes and burning on the basis of deep study of the flow and heat transfer local parameters was set as the main research prospect. In this regard, there is noticeable progress in research methods of whirling and swirling flows. The number of computational treatments of swirling flows' local parameters has been increased. Development and advancement of the up to date computing models and national productivity software are very important for this process. All experimental works are carried out with up to date research methods of the local thermoshydraulic parameters, which enable one to reveal physical mechanisms of processes: PIV and LIV visualization techniques, high-speed and infrared photography, high speed registration of parameters of high-speed processes, etc. There is a problem of improvement of researchers' professional skills in the field of fluid mechanics to set adequately mathematics and physics problems of aerohydrodynamics for whirling and swirling flows and numerical and pilot investigations. It has been pointed out that issues of improvement of the cooling system and thermal protection effectiveness of heat-power and heat-transfer equipment units are still actual. It can be solved successfully using whirling and swirling flows as simple low power consumption exposing on the flow method and heat transfer augmentation. [ABSTRACT FROM AUTHOR]

Two dimensional axisymmetric and three-dimensional VOF simulations of gas/liquid transient flow were performed using a multiphase flow algorithm based on the finite-volume method. The results for motion of a multiple bubbles of a heterogeneous sizes aligned horizontally and perpendicular to a hot surface incorporating thermocapillary forces in a rotating liquid in a zero-gravity environment have been presented for the first time. No bubbles broke in any of the cases observed. The results also show that collision and agglomeration of bubbles of unequal sizes diameter are different from those of similar size diameters presented from earlier research work of Alhendal et al. Acta Astronaut. 117, 484-496 (2015). Different flow patterns such as thermocapillary bubble migration, collision, and stream function were observed and presented for the 2-D and 3-D models. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Riemann problem for a five-equation, two-pressure (5E2P) model proposed by Ransom and Hicks for an isentropic compressible gas-liquid two-phase flows. The model is given by a strictly hyperbolic, non-conservative system of five partial differential equations (PDEs). We investigate the structure of the Riemann problem and construct an approximate solution for it. We solve the Riemann problem for this model approximately assuming that all waves corresponding to the genuinely nonlinear characteristic fields are rarefaction and discuss their properties. To verify the solver, a series of test problems selected from the literature are presented. [ABSTRACT FROM AUTHOR]

A model for polydisperse particle clouds has been developed in this study. We extended the monodisperse particle cloud model of Lai et al. (Environ Fluid Mech 13(5):435-463, ) to the case of polydisperse particles. The particle cloud is first considered to be a thermal or buoyant vortex ring, with the thermal induced velocity field modeled by an expanding spherical Hill's vortex. The buoyancy of the composite thermal is assumed to be the sum of buoyancy contributed by the all particles inside the thermal. Individual particles (of different particle properties) in the cloud are then tracked by the particle tracking equation using the computed induced velocity field. The turbulent dispersion effect is also accounted for by using a random walk model. Experiments of polydisperse particle clouds were carried out to validate the model. The agreement between model predictions and experiments was reasonable. We further validate our model by comparing it with the LES study of Wang et al. (J Hydraul Eng ASCE 141(7):06015006, ). The limitations of our model are then discussed with reference to the comparison. Overall, although some flow details are not captured by our model, the simplicity and generality of the model makes it useful in engineering applications. [ABSTRACT FROM AUTHOR]

The results of a calculation and experimental research of the influence of nonuniformity of the submerged perforated sheet on steam demand leveling on the evaporation surface are published in the current article. A short description of the PGV test facility and a measuring system whose test section is a transverse 'cut' of an actual PGV-1000 steam generator with the internals is presented. The methods of experimental starts are explained and instrumentations are described. A uniformly perforated sheet with the flow section of 5.7% and a nonuniformly perforated sheet with the flow section of 4.3% on the cold half and 8.1% on the hot half were used in the experiments. The system pressure was approximately 7 MPa, the inlet steam flow rate was varied between 4.23 and 7.94 t/h, i.e., the steam velocity on the evaporation surface was 0.15-0.29 m/s. The experimental results were analyzed with (1) the engineering method based on estimating the flow rates of steam on hot and cold half by the experimental values of the pressure drop on submerged list and (2) the STEG code, which was developed for three-dimensional mathematical modeling of the two-phase thermohydraulics in the heat exchanger volume and upgraded. It was established that changing the perforation from a uniform to a nonuniform one increases the residual nonuniformity coefficient, which characterizes the flow of steam from the hot side to the cold side under the sheet. However, the steam separation becomes worse because of a high local residual nonuniformity coefficients near the border of two plates with different perforation levels. [ABSTRACT FROM AUTHOR]