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Metallic foams have become a cutting-edge solution for many thermal management problems. These are of interest by thermal research community because of the cellular structure and have gas-filled pores inside a metal matrix. Due to the uniqueness in their structure, they exhibit good performance in boiling heat transfer because of the properties such as higher specific surface area, large number of nucleation sites, wettability characteristics, and capillary action. The boiling heat transfer over metal foam is a complex phenomenon, greatly affected by the thickness, porosity, and pores per inch (PPI) of metal foam along with the thermo-physical properties of the foam and boiling liquid. By thoroughly examining recent research investigations, the paper explains the impact of open-cell metal foams on pool boiling of different liquids such as water, refrigerants, organic liquids, and dielectric liquids. This paper reviews the complexity and various influencing factors involved in flow boiling through metal foam in tubes. It also highlights findings that show metal foam significantly enhances jet impingement boiling heat transfer. Moreover, the discussion on gradient metal foams, offering insights into their potential to enhance boiling heat transfer. The comprehensive review also encompasses numerical modeling studies, such as the lattice Boltzmann method, contributing to a deeper understanding of the intricate flow and heat transfer characteristics within channels filled with metal foam. [ABSTRACT FROM AUTHOR]

Counter-current imbibition can improve the recovery efficiency of complex fractured reservoirs, but there are few studies on the pore-scale mechanism and the factors affecting the recovery efficiency. This paper attempts to track the microscopic oil–water imbibition process through phase field method simulation, revealing the distribution characteristics of oil and water phases at different stages, as well as the sudden change characteristics of pressure and velocity at the instant of oil film rupture. Then, the influence of fracture aperture, capillary number and viscosity ratio on oil recovery efficiency is discussed. Results indicate that the microscopic imbibition process can be divided into 4 stages: the oil film forms after oil–water contact, then the oil film ruptures to form oil droplets, then the oil–water line moves outward from the large pore, and finally the oil droplets gather to discharge from the fracture. It is also found that there will be sudden changes at the moment of oil film rupture, the pressure drops sharply and the velocity increases sharply. Moreover, there exists a critical fracture aperture which is approximately 10 times the average pore size, and if the fracture is smaller than the critical fracture aperture, a dead oil zone occurs, which affects recovery. Additionally, LogM-LogCa stability diagram is constructed which is mainly dominated by viscous forces, capillary forces. As the capillary number increases, the recovery efficiency shows an overall decreasing trend. When the viscosity ratio was greater than 10, there was no significant change in the recovery efficiency, influenced by the weakening of the dominant role of viscous forces. New findings are beneficial to enhancing the recovery efficiency of low permeability reservoirs. [ABSTRACT FROM AUTHOR]

The Rothman-Keller colour gradient Lattice Boltzmann Method (LBM) provides a means to simulate two phase flow of immiscible fluids by modelling number densities of two fluids, plus a "recoloring" step that ensures separation of the two fluids. Here, we model an additional number density representing the concentration of an additive to fluid 1 which affects the viscosity of this fluid. The Peclet number – rate of advection to diffusion – is used to set the diffusion coefficient of the concentration. We present tests to demonstrate the method including flow and merging of two adjacent droplets with different additive concentrations, and two-phase flow tests in a 2D porous matrix involving injection of fluid with an additive that increases the viscosity and thus decreases viscous fingering (e.g. a polymer additive). We demonstrate that use of polymers from the start of waterflooding leads to a high saturation of 90% much sooner than when polymers are applied after breakthrough. This work demonstrates that the RK color gradient multiphase LBM can be used to study viscous fingering behavior in porous media in which the injected low viscosity fluid can have its viscosity varied with time by use of an additive. This is both of scientific interest and has economic implications to Enhanced Oil Recovery, in which water–potentially with a polymer additive to increase viscosity– is injected from an injection well into a rock layer saturated with a high viscosity fluid (oil) to help push out the oil into a production well. [ABSTRACT FROM AUTHOR]

Fluid flow through layered materials with different wetting behavior is observed in a wide range of applications in biological, environmental and technical systems. Therefore, it is necessary to understand the occuring transport mechanisms of the fluids at the interface between the layered constituents. Of special interest is the water transport in polymer electrolyte membrane fuel cells. Here, it is necessary to understand the transport mechanisms of water throughout the cell constituents especially on the cathode side, where the excess water has to be removed. This is crucial to choose optimal operating conditions and improve the overall cell performance. Pore-scale modeling of gas diffusion layers (GDLs) and gas distributor has been established as a favorable technique to investigate the ongoing processes. Investigating the interface between the hydrophobic porous GDL and the hydrophilic gas distributor, a particular challenge is the combination and interaction of the different material structures and wetting properties at the interface and its influence on the flow. In this paper, a modeling approach is presented which captures the influence of a hydrophilic domain on the flow in a hydrophobic porous domain at the interface between the two domains. A pore-network model is used as the basis of the developed concept which is extended to allow the modeling of mixed-wet interactions at the interface. The functionality of the model is demonstrated using basic example configurations with one and several interface pores and it is applied to a realistic GDL representation in contact with a channel-land structured gas distributor. [ABSTRACT FROM AUTHOR]

Two phase flows are of particular importance in various research fields. In the current article, a novel system consists of an X-ray tube and one sodium iodide crystal detector with ability of determining type of flow regime as well as void fraction percentage of a two phase flow, is proposed. MCNP-X code was used for physical modelling of the proposed system and its performance. Radial basis function (RBF) was also implemented for analyzing and classifying the obtained data from the proposed system. Counts in each 1 keV energy bin of photon energy spectra in the detector were inserted in RBF as inputs data set and flow regime and void fraction percentage were obtained as the two outputs. After training the RBF network, the system could simultaneously recognize all the flow regimes and predict the void fraction percentage of a modelled liquid–gas two-phase flow with an acceptable error. The proposed methodology in the present paper has three main novelties and advantages over former studies. Firstly, in this system an X-ray tube is used compared to previous studies where one or more radioisotope sources served as radiation source in a radiation based multi-phase flow meter. Secondly, in former works at least two detectors were used to recognize type of flow pattern and meter volume fractions simultaneously, while in this study only one detector is utilized. Thirdly, in this study just one neural network is used, while in other studies more than one network was used. [ABSTRACT FROM AUTHOR]

The performance of the air-trapping mechanism to suppress sloshing impact pressure in a prismatic tank was numerically evaluated. In order to implement the air-trapping mechanism, a short horizontal baffle array was installed on either side of the tank to collect air by the sloshing flow. The impact pressure change was analyzed by setting the ratio of the baffle length to the tank width as a parameter, and the pressure distribution on the wall was observed through eight calculation points (CPs) set between the baffles in the direction of tank height. The suppression performance of impact pressure was evaluated using Eulerian- Eulerian multiphase model to consider the water-air two-phase flow. The visualization results show the generation of sloshing impact pressure and the effects of the air-trapping mechanism. Quantitative comparisons of time series results of pressure were performed using peak pressure comparison and fast Fourier transform (FFT) analysis. The overall sloshing impact pressure reduction was 58.2 % in the FFT analysis and the maximum reduction rate was 70.4 %. [ABSTRACT FROM AUTHOR]

The calculation of pressure drop in pipes two-phase flow is essential in different areas. Even though several studies concerning this issue have been conducted, an accurate correlation is still required. The objective of the paper is to develop correlations for two-phase friction pressure drop and mixture viscosity. The new correlation can be used to compute the friction pressure drop for two phase flow in homogenous approach modeling. The original equation is generated from a similitude between the mixture viscosity for two-phase flows and the thermal conductivity of the porous structure. The new correlation is evaluated against 846 experimental data of friction pressure drop collected from literature on circular pipes; the experimental data including different working fluids such as R1234ze (E), R32, R-600a R717, R134a, R410A and carbon dioxide (CO2) at different hydraulic inner diameters and mass flux. Models are assessed based on the relative percentage error and the probability density function (PDF). The predictions by the new correlation and other correlations from the literature are compared based on some experimental data. It is found that new correlation has a mean absolute relative deviation (MARD) of 30%. It is proved that these new correlations of two-phase flow pressure drop can be used to predict the experiment measurements of pressure drop, on circular pipes, minichannels and microchannels. [ABSTRACT FROM AUTHOR]

This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a time-discrete Cahn-Hilliard-Navier-Stokes system with variable densities. The free energy density associated with the Cahn-Hilliard system incorporates the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier-Stokes equation. A dual-weighted residual approach for goal-oriented adaptive finite elements is presented which is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Details of the numerical realization of the adaptive concept and a report on the numerical tests are given. [ABSTRACT FROM AUTHOR]

The mold filling behavior of gradual expansion structure in low pressure casting was studied by two phase flow model using the Volume of Fluid method, and was verified by water simulation with a Plexiglas mold. To get smooth mold filling process and provide a guide for the pressurizing speed design in the producing practice, the mathematical model with the pressurizing speed, expansion angle and height of the gradual expansion structure was established. For validation experiments, ZL205A alloy castings were produced under two different pressurizing speeds. Weibull probability plots were used to assess the fracture mechanisms under different pressurizing speeds. Mechanical properties of ZL205A alloy were applied to assess the entrainment of oxide film. The results show that the filling process of a gradual expansion structure in a low pressure casting can be divided into the spreading stage and filling stage by gate velocity. The gate velocity continues to increase in the gradual expansion structure, and increases with the increase of pressurizing speed or expansion angle. Under the effect of the falling fluid raised by the jet flow along the sidewall, the fluid velocity decreases in the jet zone from ingate to free surface. As such, oxide film entrainment does not occur when the gate velocity is greater than the critical velocity, and the gate velocity no longer reflects the real state of the free surface. The scatter of the mechanical properties is strongly affected by the entrainment of oxide films. [ABSTRACT FROM AUTHOR]

In this paper a two-phase Lattice Boltzmann model, capable of handling large density jumps, is used to simulate the vapor filmwise condensation and dew drop sprinkling, outside different horizontal geometries. These geometries include circle, rectangle, square, and a bank of circular and rectangular tubes. In order to calculate the temperature field a passive scalar approach is combined with the Lattice Boltzmann framework and the flow field is assumed to be affected by temperature under the hypothesis of Boussinesq. Additionally, the effect of phase-change on velocity field is taken into account by adding a suitable source term to the pressure-momentum distribution equation. To simplify the model, it is assumed that the vapor remains at the saturation temperature and the amount of heat transferred through the interface is the only driving force for condensation. To demonstrate the validity of the model, the results are compared with a variety of analytical, numerical and experimental data. The validated model then is employed to study the influence of different parameters such as vapor temperature, Stefan number and Archimedes number on vapor condensation outside multiple cross sections. Finally, the condensate inundation and mean heat transfer coefficients are analyzed in horizontal tube banks. [ABSTRACT FROM AUTHOR]

In this experimental study a new flow regime map for gas-liquid two-phase flow regime detection is presented based on interpretation of transient flow pressure signals and utilizing neural networks. In this regard, the pressure signals of an air-water two phase flow at different location on a vertical pipe with an inside diameter of 50 mm and a total length of 6 m are measured. Averaged pressure and pressure fluctuation data were analyzed in different flow regimes along the upriser pipe to recognize the effects of flow regimes on pressure response. A set of pressure parameters are introduced based on averaged pressure data to present meaningful criteria for flow regime identification. Pressure fluctuations also used for flow regime recognition by applying two common signal processing methods. The processed signals are used as the inputs of a feed forward back propagation neural network to predict the flow regime. The neural network outputs are then used to present a flow regime map. The proposed neural network flow map is compared with the experimental data by photographic flow visualization technique. This comparison shows an acceptable agreement between the neural network outputs and experimental results. [ABSTRACT FROM AUTHOR]

Riemann problems for the full set of Euler equations for two phases with phase transition are considered. Based on the assumptions across the phase boundary kinetic relations to describe the mass transfer between the phase are derived from the second law of thermodynamics. Self-similar as well as singular solutions can be constructed. For both cases the structure of the solution is discussed. [ABSTRACT FROM AUTHOR]

In this work, the saturation equation in the two phase flow model is transformed into quadratic bilinear form by introducing auxiliary variables. This new formulation is the first step for applying training-free reduced order modeling. There is no approximation involved in this transformation and it only increases the size of the problem linearly, before applying any model order reduction technique. Although this might seem counterintuitive to increase the size of the system, it can improve the basis selection and consequently the reduced system. Also, this formulation allows certain properties of the original model to be preserved in the reduced-order model, such as stability and passivity. A projection-based model order reduction on this form of system will yield a reduced-order model without the need to use anymore approximation such as discrete empirical interpolation method for evaluating nonlinear terms. Although in this work only the proper orthogonal decomposition is applied, this formulation is the first step for training free model order reduction after addressing the existing challenges. One of the main challenges is the dependency of the saturation equation on flux which is changing at different time steps, and thus makes the saturation equation time varying. The numerical results of applying the proposed formulation with POD model order reduction on a two-phase immiscible flow show a substantial reduction in the computational complexity. [ABSTRACT FROM AUTHOR]

KAERI (Korea Atomic Energy Research Institute) has been developing a multi-dimensional two-phase flow code named CUPID for multi-physics and multi-scale thermal hydraulics analysis of Light water reactors (LWRs). The CUPID code has been validated against a set of conceptual problems and experimental data. In this work, the CUPID code has been parallelized based on the domain decomposition method with Message passing interface (MPI) library. For domain decomposition, the CUPID code provides both manual and automatic methods with METIS library. For the effective memory management, the Compressed sparse row (CSR) format is adopted, which is one of the methods to represent the sparse asymmetric matrix. CSR format saves only non-zero value and its position (row and column). By performing the verification for the fundamental problem set, the parallelization of the CUPID has been successfully confirmed. Since the scalability of a parallel simulation is generally known to be better for fine mesh system, three different scales of mesh system are considered: 40000 meshes for coarse mesh system, 320000 meshes for mid-size mesh system, and 2560000 meshes for fine mesh system. In the given geometry, both single- and two-phase calculations were conducted. In addition, two types of preconditioners for a matrix solver were compared: Diagonal and incomplete LU preconditioner. In terms of enhancement of the parallel performance, the OpenMP & MPI hybrid parallel computing for a pressure solver was examined. It is revealed that the scalability of hybrid calculation was enhanced for the multi-core parallel computation. [ABSTRACT FROM AUTHOR]

This article presents the results of experimental investigation of heat transfer process, carried out using the model of heat exchanger. Two-phase statically stable foam flow was used as a heat transfer fluid. Heat exchanger model consisted of staggered tube bank. Experimental results are presented with the focus on influence of tube position in the line of the bank, volumetric void component and velocity of gas component of the foam. The phenomena of liquid draining in cellular foam flow and its influence on heat transfer rate has also been discussed. The experimental results have been generalized by relationship between Nusselt, Reynolds and Prandtl numbers. [ABSTRACT FROM AUTHOR]

The measurement and study of liquid films in the case of two phase flows is significant in many heat transfer and mass transfer applications, such as chemical process industries, micro reactors, coating processes and in boilers. The focus of the present study was to measure and characterize the thickness of the liquid films for various two phase flow regimes in conventional and in mini channels using a non-intrusive technique. Experiments were performed on tubes of diameters 0.6, 1.5, 2.6 and 3.4mm. The superficial velocities of gas and liquid are in the range of 0.01-50 and 0.01-3m/s, respectively. The flow patterns were recorded with a high speed camera. A method to determine the two phase flow velocity using image registration has been discussed. Morphological processing and gray scale analysis were used to determine the liquid film thickness and characterize the flow regimes. The flow patterns identified are bubbly, dispersed bubbly, slug, slug-annular, wavy-annular, stratified, and annular. The flow regimes were validated with flow maps available in the literature. The liquid film thickness was identified by distance transform technique in image processing. The magnitude of film thickness varied with liquid and gas flow velocities. The film thickness was represented in terms of capillary number. The variation in film thickness along the length of the flow regime has been discussed. A relation between the liquid film thicknesses measured using the non-intrusive image processing technique and capillary number for the conventional and mini tubes is proposed based on the analysis. It is concluded from the proposed correlation that the variation in liquid film thickness is different for conventional and mini channels because of the effect of inertial dominance in conventional channels and viscous dominance in mini channels. [ABSTRACT FROM AUTHOR]

The objective of this study was to understand fluid heat and mass transfer processes in porous media with different pore structures. High-resolution Magnetic Resonance Imaging was used to measure fluid flow velocity and temperature maps in porous media. Firstly, three orthogonal velocity components ( V, V, and V) of single phase flow measurement were evaluated. The flow distribution in porous media is rather heterogeneous, and it is consistent with heterogeneous pore structure, and the velocity in large pore is high. Then we presented initial results from the extension of this work to two-phase flow. The CO channeling phenomena were obvious. And the CO velocity was calculated from saturation of water. Finally, the linearity relationship between temperature and the MRI parameter was determined for porous media, and we measured the temperature distribution of water saturated porous media. The study provides useful data for heat and mass process during CO storage. [ABSTRACT FROM AUTHOR]

Numerical simulations have been carried out to investigate the formation and motion of single bubble in liquids using volume-of-fluid (VOF) method using the software platform of FLUENT 6.3. Transient conservation mass and momentum equations with considering the effects of surface tension and gravitational force were solved by the pressure implicit splitting operator (PISO) algorithm to simulate the behavior of gas-liquid interface movements in the VOF method. The simulation results of bubble formation and characteristics were in reasonable agreement with experimental observations and available literature results. Effects of fluid physical properties, operation conditions such as orifice diameter on bubble behavior, detachment time, bubble formation frequency and bubble diameter were numerically studied. The simulations showed that bubble size and bubble detachment times are linear functions of surface tension and decrease exponentially with the increase in liquid density. In contrast, only a small influence of the fluid viscosity on bubble size and detachment time was observed. Bubble collapse at a free surface simulation with VOF method was also investigated. [ABSTRACT FROM AUTHOR]

This paper presents simplified forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The simplified jump relations for the pressure, the temperature, the density, the velocity of the mixture and the speed of sound have been derived in terms of the upstream Mach number. The expressions for the adiabatic compressibility of the mixture and the change-in-entropy across the shock front have also been derived in terms of the upstream Mach number. Further, the handy forms of shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. The simplified shock jump relations reduce to the Rankine-Hugoniot conditions for shock waves in an ideal gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. Finally, the effects due to the mass fraction of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas are studied on the pressure, the temperature, the density, the velocity of the mixture, the speed of sound, the adiabatic compressibility of the mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of dust particles affects the flow field behind the shock front. The aim of this paper is to contribute to the understanding of how the shock waves behave in the gas-solid particle two-phase flows. [ABSTRACT FROM AUTHOR]

The injection of supercritical carbon dioxide ( $$\text{ CO}_{2})$$ in deep saline aquifers leads to the formation of a $$\text{ CO}_{2}$$ rich phase plume that tends to float over the resident brine. As pressure builds up, $$\text{ CO}_{2}$$ density will increase because of its high compressibility. Current analytical solutions do not account for $$\text{ CO}_{2}$$ compressibility and consider a volumetric injection rate that is uniformly distributed along the whole thickness of the aquifer, which is unrealistic. Furthermore, the slope of the $$\text{ CO}_{2}$$ pressure with respect to the logarithm of distance obtained from these solutions differs from that of numerical solutions. We develop a semianalytical solution for the $$\text{ CO}_{2}$$ plume geometry and fluid pressure evolution, accounting for $$\text{ CO}_{2}$$ compressibility and buoyancy effects in the injection well, so $$\text{ CO}_{2}$$ is not uniformly injected along the aquifer thickness. We formulate the problem in terms of a $$\text{ CO}_{2}$$ potential that facilitates solution in horizontal layers, with which we discretize the aquifer. Capillary pressure is considered at the interface between the $$\text{ CO}_{2}$$ rich phase and the aqueous phase. When a prescribed $$\text{ CO}_{2}$$ mass flow rate is injected, $$\text{ CO}_{2}$$ advances initially through the top portion of the aquifer. As $$\text{ CO}_{2}$$ is being injected, the $$\text{ CO}_{2}$$ plume advances not only laterally, but also vertically downwards. However, the $$\text{ CO}_{2}$$ plume does not necessarily occupy the whole thickness of the aquifer. We found that even in the cases in which the $$\text{ CO}_{2}$$ plume reaches the bottom of the aquifer, most of the injected $$\text{ CO}_{2}$$ enters the aquifer through the layers at the top. Both $$\text{ CO}_{2}$$ plume position and fluid pressure compare well with numerical simulations. This solution permits quick evaluations of the $$\text{ CO}_{2}$$ plume position and fluid pressure distribution when injecting supercritical $$\text{ CO}_{2}$$ in a deep saline aquifer. [ABSTRACT FROM AUTHOR]

We develop a simplified model of choked flow in pipes for CO-water solutions as an important step in the modelling of a whole hydraulic system with the intention of eliminating the carbon dioxide generated in air-independent submarine propulsion. The model is based on an approximate fitting of the homogeneous isentropic solution upstream of a valve (or any other area restriction), for given fluid conditions at the entrance. The relative maximum choking back-pressure is computed as a function of area restriction ratio. Although the procedure is generic for gas solutions, numeric values for the non-dimensional parameters in the analysis are developed only for choking in the case of carbon dioxide solutions up to the pure-water limit. [ABSTRACT FROM AUTHOR]

This article describes a semi-analytical model for two-phase immiscible flow in porous media. The model incorporates the effect of capillary pressure gradient on fluid displacement. It also includes a correction to the capillarity-free Buckley-Leverett saturation profile for the stabilized-zone around the displacement front and the end-effects near the core outlet. The model is valid for both drainage and imbibition oil-water displacements in porous media with different wettability conditions. A stepwise procedure is presented to derive relative permeabilities from coreflood displacements using the proposed semi-analytical model. The procedure can be utilized for both before and after breakthrough data and hence is capable to generate a continuous relative permeability curve unlike other analytical/semi-analytical approaches. The model predictions are compared with numerical simulations and laboratory experiments. The comparison shows that the model predictions for drainage process agree well with the numerical simulations for different capillary numbers, whereas there is mismatch between the relative permeability derived using the Johnson-Bossler-Naumann (JBN) method and the simulations. The coreflood experiments carried out on a Berea sandstone core suggest that the proposed model works better than the JBN method for a drainage process in strongly wet rocks. Both methods give similar results for imbibition processes. [ABSTRACT FROM AUTHOR]

We benchmark a family of hybrid finite element-node-centered finite volume discretization methods (FEFV) for single- and two-phase flow/transport through porous media with discrete fracture representations. Special emphasis is placed on a new method we call DFEFVM in which the mesh is split along fracture-matrix interfaces so that discontinuities in concentration or saturation can evolve rather than being suppressed by nodal averaging of these variables. The main objective is to illustrate differences among three discretization schemes suitable for discrete fracture modeling: (a) FEFVM with volumetric finite elements for both fractures and porous rock matrix, (b) FEFVM with lower dimensional finite elements for fractures and volumetric finite elements for the matrix, and (c) DFEFVM with a mesh that is split along material discontinuities. Fracture discontinuities strongly influence single- and multi-phase fluid flow. Continuum methods, when used to model transport across such interfaces, smear out concentration/saturation. We show that the new DFEFVM addresses this problem producing significantly more accurate results. Sealed and open single fractures as well as a realistic fracture geometry are used to conduct tracer and water-flooding numerical experiments. The benchmarking results also reveal the limitations/mesh refinement requirements of FE node-centered FV hybrid methods. We show that the DFEFVM method produces more accurate results even for much coarser meshes. [ABSTRACT FROM AUTHOR]

The injection of supercritical CO in deep saline aquifers leads to the formation of a CO plume that tends to float above the formation brine. As pressure builds up, CO properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO-rich phase and the formation brine. We introduce a correction to account for CO compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection. [ABSTRACT FROM AUTHOR]

The influence of baffle position on liquid sloshing during the braking and turning of a tank truck was studied using a volume of fluid (VOF) model. The forces, their positions and weight distribution during braking and the forces and rolling moment during turning were calculated. The reliability of the calculation method was validated by comparisons with experimental results. The results showed that during braking, liquid splashes in the tank and the maximum forces and G (the ratio of weight acting on the front axle to the rear axle) are large when A (the ratio of the arch area above the baffle to the area of cross section)≤0.1. When A≥0.2, as the position of the baffle is lowered, the maximum of F (the force in direction x) first decreases then increases, and the maximum of F (the force in direction y) and G increase. During turning, liquid splashes in the tank and the maximum forces and M (the rolling moment) are large when D (the ratio of the arch area above the baffle to the area of cross section)≤0.2. When D≥0.3, as the position of the baffle is lowered, the maximums of F, F (the force in direction z) and M increase. [ABSTRACT FROM AUTHOR]

The flow pattern and hydraulics of a Mini V-Grid valve (MVG) tray is predicted by using computational fluid dynamics simulation. A 3-D CFD model in the Eulerian framework was used. The simulation results for MVG tray are compared with that of sieve tray. The sieve tray geometry and operating conditions are based on the Solari and Bell’s sieve tray [1]. The MVG tray differs from that of Solari and Bell’s sieve tray solely by the difference in design of available openings for the flow of gas. The simulation results show that the clear liquid height and the pressure drop of MVG tray are lower than that of sieve tray whereas the liquid velocity is higher and contacts of phases are good. The simulation results of sieve tray are in agreement with the experimental data of Solari and Bell [1]. [ABSTRACT FROM AUTHOR]

Boiling heat transfer at water flow with low mass flux in heat sink which contained rectangular microchannels was studied. The stainless steel heat sink contained ten parallel microchannels with a size of 640 × 2050 μm in cross-section with typical wall roughness of 10–15 μm. The local flow boiling heat transfer coefficients were measured at mass velocity of 17 and 51 kg/m2s, heat flux on 30 to 150 kW/m2 and vapor quality of up to 0.8 at pressure in the channels closed to atmospheric one. It was observed that Kandlikar nucleate boiling correlation is in good agreement with the experimental data at mass flow velocity of 85 kg/m2s. At smaller mass flux the Kandlikar model and Zhang, Hibiki and Mishima model demonstrate incorrect trend of heat transfer coefficients variation with vapor quality. [ABSTRACT FROM AUTHOR]

Effervescent atomization is one of the twin-fluid atomization methods while it has better performance in terms of smaller drop sizes and/or lower injection pressures. In order to investigate the effects of the internal flow patterns on droplet characteristics, a new kind of effervescent atomizer was designed and manufactured. The bubble forming process was visualized with a high-speed camera, while the droplet size was characterized with a LDV/PDA system. The experimental results show that there are three regimes of the two-phase flows inside the discharge orifice, one is bubbly flow, another is annular flow while the other is the intermittent flow. The flow patterns transfered from bubbly flow to intermittent flow and then to annular flow with decreasing of the water flow rate. In addition, with increasing of the working pressure or decreasing of the water flow rate, the SMD (Sauter mean diameter) of the droplets decreased and the axial mean velocity increased. [ABSTRACT FROM AUTHOR]

This study investigates droplet formation in a micro-channel using the lattice Boltzmann (LB) method. A cross-junction micro-channel and two immiscible, water and oil phase fluids, were used to form the micro-droplets. Droplets are formed by the hydrodynamic instability on the interface between two immiscible fluids when two immiscible fluids are imported simultaneously in a cross-junction micro-channel. The Shan & Chen model, which is a lattice Boltzmann model of two-phase flows, is used to treat the interaction between immiscible fluids. The detailed process of the droplet formation in the cross-junction micro-channel was illustrated. The results of the droplet formation by the LBM predicted well the experimental data by PIV (particle image velocimetry). The effect of the surface tension and the flow rate of water phase fluid on the droplet length and the interval between droplets was also investigated. As the surface tension increased, the droplet length and the interval between droplets were increased. On the other hand, when we increased the flow rate of the water phase fluid under the condition of the fixed oil-phase fluid flow rate, the droplet size was increased while the interval between droplets was decreased. [ABSTRACT FROM AUTHOR]

In this article, the unified mathematical model for splash droplets and suspended mist of atomized flow was established, which classifies the atomized sources into the splash source and the suspended source. For the splash source, the Lagrangian method was used to simulate the random motion of splash water droplets, and for the suspended source the theory of air-water two-phase flow was used to simulate the mist flow moving in particle clouds. The rainfall intensity of the atomized flow was obtained by summarizing the rainfall intensities relative to the above two types of atomized sources. Both experimental data and prototype observation data were used for the verification of the mathematical model. For both the distribution of rainfall intensity, and the outer edge of the atomized flow, the simulation results are in agreement with the experimental data or prototype observation data. [ABSTRACT FROM AUTHOR]

Experiments of dense-phase pneumatic conveying of pulverized coal were carried out in a test facility with a conveying pressure up to 4 MPa. The influence of fluidization nitrogen flow rate, the flow rate of supplementary nitrogen, and the pressure difference between sending hopper and receiving hopper on the solids to gas ratio and the solid mass flow rate was investigated. Test results indicate that with the increase in fluidization nitrogen flow rate, the solid mass flow rate increases, and the solids to gas ratio increases at first and then declines. When the fluidization of pulverized coal in the sending vessel becomes intensive, with the increase in supplementary nitrogen flow rate, the solids to gas ratio declines and the solid mass flow rate increases. And the solid mass flow rate increases linearly with the increase in pressure difference between two hoppers. The experimental results provide a database for the design and operation of a dense-phase pneumatic conveying system. [ABSTRACT FROM AUTHOR]

Spreadsheet optimization using a range of nonlinear error functions was utilized for parameter estimation of the two-phase pressure–saturation models developed by van Genuchten, Brutsaert, Russo and Kosugi. The data was obtained from the UNSODA database (US Salinity Laboratory, Riverside, California). Results show that spreadsheet optimization is a practical platform for evaluations based on minimizing nonlinear error functions, consequently allowing for a broader mathematical approach to parameter estimation. An error function representing the sum of the squares of errors provided the best fit for a majority of the soils evaluated, although the fractional error function provided the best fit for silts and loams. Outcomes indicated that the van Genuchten parameters m and n may also be estimated individually as opposed to following the published relationship of m=1−1/ n. [ABSTRACT FROM AUTHOR]

In the present study, the unsteady Couette flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponential decaying pressure gradient is studied without neglecting the Hall effect. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field is applied perpendicular to the plates. The governing equations are solved numerically using finite differences to yield the velocity and temperature distributions for both the fluid and dust particles. [ABSTRACT FROM AUTHOR]

In the present study, the unsteady Hartmann flow of a dusty viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied without neglecting the ion slip. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below. The fluid is acted upon by an external uniform magnetic field which is applied perpendicular to the plates. An analytical solution for the governing equations of motion is obtained to yield the velocity distributions for both the fluid and dust particles. [ABSTRACT FROM AUTHOR]

As part of our work on the absorption solar refrigeration cycle and with the objective of optimizing the efficiency of flat plate solar collectors in the generation phase, an experimental study has been conducted on the forced convective boiling heat transfer of NH3-H2O mixtures flowing inside a 6 mm inner diameter vertical smooth tube. Using a water-heated double pipe type generator, the local heat transfer coefficients are measured inside the inner tube for a range of heat flux (8.211-18.521 kW/m ²), mass flux (707-2688 kg/m ².s), mass flow rate (0.02 -0.076 kg/s), and ammonia mass concentration (42%, 55%, and 61%). Three theoretical models are used to predict the boiling heat transfer coefficients. Experimental data were compared with the available correlations. The obtained results confirm the good performance of Mishra et al. and Bennett and Chen's models in predicting the convective boiling heat transfer coefficient of ammonia water mixtures. These models are able to predict the boiling heat transfer data within an accuracy of ±20 %. [ABSTRACT FROM AUTHOR]

The successful application of Electrical Capacitance Tomography (ECT) depends heavily on the image reconstruction speed and quality. The two requirements usually cannot be satisfied simultaneously. Also, for a large number of acquired 2D ECT images, a 3D presentation of them is much desired to track the variations of the material distribution in a third dimension. To facilitate ECT for practical flow analyses in process engineering, the authors have recently developed algorithms for 3D image presentation and for online iterative image reconstruction that only takes the same time as a linear back projection method but yields good image qualities as the Landweber iterative method does. The new methods have been successfully applied to visualize several classes of two phase flows, namely fluidization, cyclone separation, circulating rate determination in circulating fluidized beds, pneumatic conveying, rotating drum mixing. Special characteristics in each case have been discussed and valuable results are obtained, which are reported in this paper. [ABSTRACT FROM AUTHOR]

Vapor-liquid two phase flow behavior of R123 inside herringbone microfin tubes has been studied. Herringbone microfin tube is a kind of internally finned tube in which microfins are installed inside the tube where the microfins form multi-V-shape in flow direction. For the present experiment three different types of herringbone microfin tubes with helix angle β=8°, 14° and 28° are used. Experimental observations showed how flow diverges and converges inside herringbone microfin tube due to fin arrangement. The effect is more remarkable for larger helix angle. From the measurements of the cross-sectional liquid flow rate distribution, the liquid removal and collection and the entrained droplet are discussed. Quantity of liquid droplets is increased with increase of helix angle. The tube with helix angle β=28° shows higher quantity of liquid droplets than others. [ABSTRACT FROM AUTHOR]

The boundary integral technique is used to study the effect of deformation on the steady, creeping, thermocapillary migration of a fluid particle under conditions of axisymmetry, negligible thermal convection and an insulated tube wall. The spherical radius of the fluid particle (i.e. the radius as if the particle were a sphere, a ′= (3V/4π)1/3, V is the particle volume) and that of the tube are denoted, respectively, by a′and b′. For small capillary number Ca = 0.05, only for a large fluid particle ( a′/ b′ = 0.8) is deformation significant. For a′/ b′= 0.8, hydrodynamic stresses squeeze the particle, reduce the interaction of the particle with the wall and thereby increase the terminal velocity. For small particles a′/b′< 0.8 and Ca = 0.05 the fluid particles translate as spheres, due to the fact that the fluid particle is too far away from the wall to be subject to distending hydrodynamic stresses. The deformable particle moves faster than a spherical one in the thermocapillary migration. The increase in velocity with capillary number is larger for thermocapillary motion than for buoyancy. [ABSTRACT FROM AUTHOR]

A k-ε-k multi-fluid model was used to simulate confined swirling gas-solid two phase jet comprised of particle-laden flow from a center tube and a swirling air stream entering the test section from the coaxial annular. After considering the drag force between the two phases and gravity, a series of numerical simulations of the two-phase flow of 30μm, 45μm, 60μm diameter particles were performed on a x × r = 50 × 50 mesh grid respectively. The results showed that the k-ε-k multi-fluid model can be applied to predict moderate swirling multi-phase flow. When the particle diameter is large, the collision of the particles with the wall will influence the prediction accuracy. The bigger the diameter of the particles, the stronger the collision with the wall, and the more obvious the difference between measured and calculated results. [ABSTRACT FROM AUTHOR]

This paper presents a k-ε-k p multi-fluid model for simulating confined swirling gas-solid two phase jet comprised of particle-laden flow from a center tube and a swirling air stream entering the test section from the coaxial annular. A series of numerical simulations of the two-phase flow of 30 μm, 45 μm, 60 μm diameter particles respectively yielded results fitting well with published experimental data. [ABSTRACT FROM AUTHOR]

In this paper we compare two models for flow in porous media. The first is the well known Richards' equation, which is based on the assumption that the air in the unsaturated zone has infinite mobility. This means that it models a single phase. In the second and more general full two-phase approach, the air is considered as a separate phase. Here, we use the fractional flow equation. We study the difference between the two models numerically by varying the relative contribution of the different physical terms (the gravity and the total velocity) in the fractional flow equation. Richards' equation is considered as the limit of the fractional flow approach when the mobility of the air-phase tends to infinity. In particular, we are interested in determining the parameter intervals where the two models differ significantly, and we will quantify the asymptotic behavior. The equations are studied in the two-dimensional (2D) case. The study is based on a relative permeability depending quadratically on the saturation, and a capillary pressure expressed by a cubic function of the saturation. [ABSTRACT FROM AUTHOR]

A k- ε -k p multi-fluid model is stated and adopted to simulate swirling gas-solid two phase flow. A particle-laden flow from a center tube and a swirling air stream from the coaxial annular enter the test section. A series of numerical simulations of the two-phase flow are performed based on 30 µ m, 45 µ m, 60 µ m diameter particles respectively. The results fit well with published experimental data. [ABSTRACT FROM AUTHOR]

The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached. [ABSTRACT FROM AUTHOR]

A numerical model is developed to study the hopping motion of sand grains (saltation) in neutral atmospheric surface layers. Saltation is considered as a self-limiting process governed by the interaction of four components: aerodynamic entrainment, particle motion, splash entrainment and wind modification. The model comprises a large eddy simulation model for atmospheric surface-layer flows, a Lagrangian model for particle trajectories and a statistical description for aerodynamic entrainment and splash entrainment. The numerical simulation is focused on the aspects of saltation that are not well understood from experimental studies, including the role of splash, the evolution of wind and momentum flux profiles, and the effective roughness length, z$\_0s$. It is shown that for splash to be effective, the surface friction velocity must exceed a critical value for a given particle size. The numerically estimated z$\_0s$ is compared with the analytical model of Raupach and the experimental data of Gillette et al. The model is also used to calculate the streamwise sand drift and the numerical results found to be in agreement with the existing wind-tunnel measurements. [ABSTRACT FROM AUTHOR]

The bubble visualization in two-phase flow using the E1T (Electrical Impedance Tomography) technique requires an image reconstruction process. When the conventional iterative image reconstruction algorithms are used, the processing time increases rapidly and the convergence characteristics become very poor as the spatial resolution increases. In order to overcome this problem, this study proposes an adaptive mesh grouping method utilizing the genetic algorithm and the fuzzy set theory. Computer simulations using the improved Newton-Raphson method combined with the proposed method show promising results that mesh grouping may become a useful way to mitigate the ill-conditioning phenomenon which makes the EIT inverse problem difficult. [ABSTRACT FROM AUTHOR]

Immiscible two phase flow in porous media can be described by the fractional flow model. If capillary forces are neglected, then the saturation equation is a non linear hyperbolic conservation law, known as the Buckley–Leverett equation. This equation can be numerically solved by the method of Godunov, in which the saturation is computed from the solution of Riemann problems at cell interfaces. At a discontinuity of permeability this solution has to be constructed from two flux functions. In order to determine a unique solution an entropy inequality is needed. In this article an entropy inequality is derived from a regularisation procedure, where the physical capillary pressure term is added to the Buckley Leverett equation. This entropy inequality determines unique solutions of Riemann problems for all initial conditions. It leads to a simple recipe for the computation of interface fluxes for the method of Godunov. [ABSTRACT FROM AUTHOR]

In the article, the boundary integral technique is used to solve the hydrodynamic movement of a train of deformable fluid particles in a tube. When a fluid particle is in a tube, the total normal stress difference is not constant any more, this fore tends to distend and elongate the particle. We find that the difference between the velocity of a deformable fluid particle and a sphere (with the same radius) increases as the distance between the particles decreases, and that the increase in velocity with L′/a′ is greater the capillary number, and this increase becomes less pronounced as radius decreases. [ABSTRACT FROM AUTHOR]