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A multiphase mathematic model based on realizable k-e turbulence model for subsonic flow was presented to investigate the mixing flow behaviors between gas and water in the gas-liquid ejector. The simulation was carried out to predict the pumping performance of the ejector by a commercial computational code ANSYS-FLUENT 15.0. General agreements between the predicted results and experimental data validated the present theoretical model. Using the present approach, the pressure, velocity, and turbulence intensity distribution along center-line and contours of gas and liquid volume fraction profiles were predicted. It is found that the mixing process between gas and water in ejector can be divided into three periods, co-axial flow, mixing shock flow, and bubble flow. The prediction results show that the mixing shock is a dominant position in affecting the mixing flow behavior in gas-liquid ejector and the ejector’s performances.

Foams are of great importance as a result of their expansive presence in everyday life—they are used in the food, cosmetic, and process industries, and in detergency, oil recovery, and firefighting. There is a little understanding of foam formation using soft porous media in terms of the quality of foam and foam formation. Interaction of foams with porous media has recently been investigated in a study by Arjmandi-Tash et al., where three different regimes of foam drainage in contact with porous media were observed. In this study, the amount of foam generated using porous media with surfactant solutions is investigated. The aim is to understand the quality of foam produced using porous media. The effect of capillary sizes and arrangement of porous in porous media has on the quality of foam is investigated. This is then followed by the use of soft porous media for foam formation to understand how the foam is generated on the surface of the porous media and the effect that different conditions (such as concentration) have on the quality of the foam. The quality of foam is a blanket term for bubble size, liquid volume fraction, and stability of the foam. The liquid volume fraction is calculated using a homemade dynamic foam analyser, which is used to obtain the distribution of liquid volume fraction along with the foam height. Soft porous media does not influence substantially the rate of decay of foam produced, however, it decreases the average diameter of the bubbles, whilst increasing the range of bubble sizes due to the wide range of pore sizes present in the soft porous media. The foam analyser showed the expected behaviour that, as the foam decays and becomes drier, the liquid volume fraction of the foam falls, and therefore the conductivity of foam also decreases, indicating the usefulness of the home-made device for future investigations.

Accurate prediction of the local liquid volume fraction ( e L ) distribution, an important process parameter that governs the performance of Trickle Bed Reactors (TBRs), is still a challenge. In the present work, Eulerian multi-fluid simulations of local e L distribution were performed in a laboratory-scale pseudo-3D (rectangular) and cylindrical TBR and the predictions were compared with the Electrical Resistance Tomography (ERT) measurements of Singh et al. (2017). The effect of formulation of capillary pressure force ( F ‾ C ) was investigated and it was found that - P C ∇ e L definition of F ‾ C preserved the functional relation between the capillary pressure ( P C ) and e L , and that e L ∇ P C definition of F ‾ C reversed the same. Through the simulations performed for the pseudo-3D column, we showed that the alteration in the functional relation severely affects the ability of F ‾ C = e L ∇ P C definition to predict the effects of particle diameter, gas and liquid flow rates. It was elucidated that such an alteration underpredicts F ‾ C and could necessitate the inclusion of additional dispersion forces for particles with small diameters. F ‾ C implemented as - P C ∇ e L provided satisfactory predictions of the steady-state local e L distribution for the bed pre-wetted with the pseudo-Kan pre-wetting method. However, the P C model required an empirical correction ( [ ( d P / d thr ) ( e S ) 0.6 ] - 13.957 ) to predict the steady-state local e L distribution in the bed pre-wetted using the Levec method. While the modified F ‾ C predicted the time-averaged local e L distribution satisfactorily for different liquid flow rates and liquid distributor configurations, it was seen that further reduction in F ‾ C was required to predict the dynamic liquid spreading behavior under synthetically created pulsing flow conditions.

Experiments on air–water two-phase swirling annular flows in a vertical pipe of 40 mm diameter were carried out at atmospheric pressure and room temperature to investigate interfacial and wall friction factors, fi and fw. The friction factors were evaluated using measured pressure drops and void fractions. Measurements of liquid film thickness and flow observation were also conducted. The ranges of the gas and liquid volume fluxes, JG and JL, were 12.5 ≤ JG ≤ 20.0 m/s and 0.03 ≤ JL ≤ 0.11 m/s, respectively. The main conclusions obtained are as follows: (1) fi and fw in swirling annular flows are several times larger than those in non-swirling flows, (2) fi is well correlated in terms of the liquid volume fraction and the gas Reynolds number, ReG, (3) ReG and the liquid Reynolds number, ReL, are required for correlating fw, and (4) the liquid film thicknesses in two-phase swirling flows in a one-fifth model of a BWR separator are well predicted using the two-fluid model and the correlations of fi and fw developed based on the experimental data.

Interstitial flows at the middle height of a freely draining foam column were measured by microparticle image velocimetry (μPIV), and superficial flow was measured from the bottom of the foam by a digital weighing scale. In addition, Plateau border widths were measured from the μPIV images. Plateau borders were selected for μPIV particle-tracking analysis based on their orientation being nearly vertical. Interstitial liquid velocity in the vertically oriented Plateau borders was found to depend linearly on the square of the width consistent with Poiseuille flow. Three foams were examined including a commercial fluorinated Aqueous Film Forming Foam (AFFF), a commercial non-fluorinated firefighting foam (Re-healing Foam Type 6; RF6), and a simple lab-mixed foam composed from sodium dodecyl sulfate (SDS) in water. The interstitial velocity and superficial velocity measurements were compared with theoretical models that assumed either channel-dominated (CD) or node-dominated (ND) viscous dissipation, i.e. rigid or mobile interfaces. The measurements were found to fall in between the two limiting cases for AFFF and RF6, with RF6 showing closer agreement with the CD case than the ND case. Flow measurements in SDS foam agreed approximately with the ND model, as expected, prior to foam breakdown. An approximate liquid volume fraction at the middle height of the foam column was also obtained from the ratio of interstitial flow to superficial flow.

Encapsulated phase change materials (EPCM) are the most common way to integrate with thermal systems for energy storage applications. Encapsulation greatly alters the thermal response of phase change materials (PCM) in terms of phase change temperatures and thermal hysteresis. Existing numerical schemes; however, can only simulate bulk PCM behavior and ignore the influence of encapsulation on the thermal response of EPCM. In this study, novel computational fluid dynamics (CFD)-based conduction dominant numerical schemes are developed for the first time to model the thermal response of EPCM and validated with the experimental DSC curve of the in-house fabricated EPCM capsules. The proposed heat source/sink scheme successfully predicts the heat-temperature responses and liquid volume fraction of EPCM with thermal hysteresis. It is recommended that the CFD-based conduction dominant heat source/sink scheme developed for EPCM in current study should be incorporated into energy simulation softwares for accurate performance predication when EPCM capsules are expected to be used in thermal energy storage systems and applications.

Hydrate blockages impose a serious flow assurance problem on gas transportation pipelines. Regular inspections for the formation of hydrate blockages are imperative along with the use of an effective blockage removal method. In this study, the processes of hydrate blockage formation and removal were investigated using a fully visual flow loop. Comprehensive analysis of the pressure drop was performed along with a discussion of the acquired visual images of the hydrates to describe the phenomena. Hydrate blockage first occurred in no through-flow zone of the pipeline, specifically in deadleg. The results showed that higher LL (liquid loading: the initial liquid volume fraction) caused a blockage in the inlet, while lower LL caused a faster and more widespread blockage. Moreover, shut-in and restart operations also caused blockages due to the temperature decrease and annealing of hydrate. The experiments showed that blockages formed more quickly as a result of lower LL during the shut-in operation. This necessitated the reduction of shut-in duration and maintenance of the temperature at phase equilibrium condition. In addition, the depressurization method was used to decompose bulk hydrate in order to remove the blockage. The results confirmed that stepwise depressurization could be applied to prevent hydrate reformation at a higher LL and water conversion rate, while a lower backpressure could be used at lower LL to efficiently remove blockages.

Two-phase liquid-gas flows are common in several industrial processes. Since oil and gas are simultaneously produced in most petroleum reservoirs, the two-phase flow occurs in petroleum transport as well. Depending on the petroleum viscosity, a large amount of energy is needed to move the oil-gas mixture, resulting in significant expenses. The present work aims to investigate the influence of oil viscosity on pressure drop and liquid volume fraction of the upward two-phase flow of different types of oil in a vertical pipe. This study was accomplished using Computational Fluid Dynamic techniques, and Beggs and Brill correlation. The numerical simulations were performed using the application Ansys CFX 13.0, in which governing equations were solved utilizing the finite volume method. The results of pressure drop and liquid volume fraction obtained by both methods were analyzed and discussed. The numerical results for the pressure drop show that the CFX value was approximately 24% lower than that predicted by the Beggs and Brill correlation in the worst case. The liquid volume fraction decreased along the pipe length due to the viscosity effects of the oil.

The drainage of foams created using emulsions has been investigated from both experimental and theoretical point of view. The drainage of emulsion foam is investigated using mixture of sodium dodecyl sulphate and oil, which were prepared using the double syringe method. For the preparation of each emulsion, SDS solution and oil are passed from one syringe into the other through a plastic tube leading to thorough mixing. In the course of drainage both the foam height and the thickness of the free liquid layer accumulated at the bottom of the foam were measured. A theoretical model was developed, taking into account both surface viscosity and non-Newtonian behaviour of the foamed emulsion to describe the time evolution of both the foam height and the thickness of the free liquid layer. The model is based on consideration of drainage of non-Newtonian liquid through the Plateau borders and the mobility of the gas/liquid interface is taken into account. Both experiments and theoretical predictions show no measurable change of the foam height while a free liquid layer starts to accumulate at the bottom boundary of the foam after an initial rapid increase of liquid volume fraction to the maximum value at the bottom of the foam. Theoretical predictions of rate of drainage, free liquid layer formation, foam height and liquid volume fraction for foamed emulsion systems of various oil volume fractions are compared with experimental observations. Comparison of the predicted and the experimentally measured time dependences showed a reasonable agreement.

Free drainage in egg-white foams with a variety of gas volume fractions was investigated by an electrical resistivity technique. Changes in resistivity at different heights in the foam were monitored as a function of time thus giving information on the local liquid volume fraction (or content) and therefore the rate of foam drainage. The wettest egg-white foam was the most unstable, with changes in liquid volume fraction observed within minutes of foam aging. Because bubble sizes are very small, a huge effect of capillary forces confers egg-white foams with a very good stability to drainage. The complex nature of the egg-white liquid (bulk and interfacial properties), the likely presence of denatured-aggregate complexes in the Plateau borders, and very small bubble sizes are key parameters for understanding the stability of egg-white foams that makes them excellent foaming materials for food science and culinary purposes.

We present an overview of recent advances in the understanding of foam structure and energy and their dependence on liquid volume fraction. We consider liquid foams in equilibrium for which the relevant energy is surface energy. Measurements of osmotic pressure can be used to determine this as a function of liquid fraction in good agreement with results from computer simulations. This approach is particularly useful in the description of foams with high liquid content, so-called wet foams. For such foams X-ray tomography proves to be an important technique in analysing order and disorder. Much of the discussion in this article is also relevant to bi-liquid foams, i.e. emulsions, and to solid foams, provided that the solidification preserves the structure of the initially liquid foam template.

In the present paper, a numerical model for the simulation of wet-steam flows has been developed and implemented within a commercial CFD code (ANSYS Fluent) via user defined functions. The scheme is based on a single-fluid approach and solves the transport equations for a homogeneous mixture coupled with conservation equations for the droplets number and liquid volume fraction. The model is validated against a steam nozzle test-case and then compared with experimental data from a steam ejector with a significant amount of generated liquid phase. The simulations show a good agreement both in terms of mass flow rates and pressure profile data. Some of the modeling assumptions are also reviewed and discussed.

International audience; The interaction between oil and foam has been the subject of various studies. Indeed, oil can be an efficient defoaming agent, which can be highly valuable in various industrial applications where undesired foaming may occur, as seen in jet-dyeing processes or waste water treatment plant. However, oil and foam can also constructively interact as observed in detergency, fire-fighting, food and petroleum industries, where oil can be in the foam structure or put into contact with the foam without observing a catastrophic break-up of the foam. Under specific physico-chemistry conditions, the oil phase can even be trapped inside the aqueous network of the foam, thus providing interesting complex materials made of three different fluid phases that we name oil-laden foam (OLF). In this review, we focus on such systems, with a special emphasis on dry OLF, i.e. with a total liquid volume fraction, smaller than 5%. We first try to clarify the physical and chemical conditions for these systems to appear, we review the different techniques of the literature to obtain them. Then we discuss their structure and identify two different OLF morphologies, named foamed emulsion, in which small oil globules are comprised within the network of the aqueous foam and biliquid foams, where the oil also comprised in the aqueous foam network is continuous at the scale of several bubbles. Last, we review the state of the art of their evolution in particular concerning topological changes, coalescence, coarsening and drainage.

Computational fluid dynamic models (CFD) have been used for the description of hydraulic characteristics of packed sieve tray (PST). PST is a conventional sieve tray combined with a slice thickness of packing on the tray deck. Eulerian-Eulerian framework has been used to solve the equations of both liquid and gas phases assumed as two interpenetrating phases. A commercial scaled sieve tray has been simulated based on a three-dimensional unsteady state model. Comparison with experimental data proves good agreement for the simulation results under the studied conditions. Effects of the packing on the liquid velocity distribution, clear liquid height and vertical liquid volume fraction distribution have been investigated. The simulation results show that 3.08 cm of packing thickness could increase the clear liquid height up to 17 percent and froth height up to 10 percent as well as promoting froth density by 6 percent with the only drawback of increasing wet pressure drop up to 16 percent in froth regime.

International audience; Tabulated chemistry is a popular technique to account for detailed chemical effects with an affordable computational cost in gaseous combustion systems. How- ever its performances for spray combustion have not completely been identified. The present article discusses the chemical structure modeling of spray flames us- ing tabulated chemistry methods under the hypothesis that the chemical subspace accessed by a two-phase reactive flow can be mapped by a collection of gaseous flamelets. It is shown that tabulated chemistry methods based either on pure pre- mixed flamelets or on pure non-premixed flamelets fail to capture the structure of spray combustion. The reason is the complexity of the chemical structure of spray flames which exhibits both premixed-like and non-premixed-like reaction zones. To overcome this issue, a new multi-regime flamelet combustion model (called Partially-Premixed Flamelet Tabulation 2PFT) is presented in this paper. Information from premixed, partially-premixed and diffusion flames are stored in a 3-D look-up table parametrized as function of the progress variable Yc, de- scribing the progress of the reaction, the mixture fraction Yz, denoting the local equivalence ratio, and the scalar dissipation, which identifies the combustion regime. The performances of the 2PFT method are evaluated on counterflow laminar spray flames for different injection conditions of droplet diameter, liquid volume fraction and velocity. The 2PFT tabulation method better describes the chemical structure of spray flames compared to the classical techniques based on single archetypal flamelets. These results also confirm that the chemical structure of laminar spray flame can be modeled by a multi-regime flamelet combustion model based on gaseous flamelets.

We observed and calculated the solid and liquid volumes and mass parameters of canine vocal fold thyroarytenoid (TA) muscle at tissue dehydration levels of 30% and 70% followed by a complete rehydration to examine the effects of hydration recovery with respect to biphasic properties of the TA muscle in relation to the vocal fold lamina propria. Twenty samples of TA muscle were harvested from 10 canine larynges. Each sample group was subjected to either 30% or 70% dehydration. Following dehydration, the samples rehydrated until the tissue mass stabilized. The solid volume and mass fraction, liquid volume and mass fraction, liquid–solid volume and mass ratios, and degree of hydration recovery were calculated. Median liquid–solid volume ratios were significantly different between the 30% and 70% groups after rehydration and between the medians of 30% and 70% liquid–solid mass ratios after rehydration. The means of solid mass fraction, liquid mass fraction, solid volume fraction, and liquid volume fraction all displayed statistically significant differences. Irreversible tissue damage undergone via severe dehydration of the TA muscle indicates the anatomical and physiological similarity between the TA muscle and the lamina propria. The results imply the significance of the biphasic theory in the construction of biomechanical models.

The coarsening of polyhedral grains in a liquid matrix was calculated using crystal growth and dissolution equations used in crystal growth theories for faceted crystals. The coarsening behavior was principally governed by the relative value of the maximum driving force for growth (Δgmax), which is determined by the average size and size distribution, to the critical driving force for appreciable growth (Δgc). When Δgmax was much larger than Δgc, pseudonormal grain coarsening occurred. With a reduction of Δgmax relative to Δgc, abnormal grain coarsening (AGC, when Δgmax ≥ Δgc) and stagnant grain coarsening (SGC, when Δgmax < Δgc) were predicted. The observed cyclic AGC and incubation for AGC in real systems with faceted grains were explained in terms of the relative value between Δgmax and Δgc. The effects of various processing and physical parameters, such as the initial grain size and distribution, the liquid volume fraction, step free energy, and temperature, were also evaluated. The calculated results were in good agreement with previous experimental observations.

The microgravity phases of parabolic flights were used to perform experiments with soap films trapped in wire frames, a variation of the wire frame experiments originally designed by the nineteenth century Belgian scientist Joseph Plateau. We considered the formation of an eightfold vertex of Plateau borders within a cubic frame. In terrestrial experiments such a vertex can only be formed when liquid is forced through the Plateau borders, but in microgravity we found this vertex to be stable under equilibrium (non-flow) conditions once the liquid volume fraction exceeds 0.022 ± 0.005. This is consistent with the theoretical value for the transition, which for our experiment we estimate to be 0.0192.

The gas-phase relative electric permittivities, densities, and liquid drop out volumes within the two-phase envelope have been determined from measurements of the resonance frequency of the lowest order inductive−capacitance mode of a re-entrant cavity for (0.4026 CH4 + 0.5974 C3H8); the dew temperatures between (315.5 and 340.4) K that correspond to dew pressures of (2.87 to 6.83) MPa for this mixture along with a description of the apparatus were reported by Kandil et al. (J. Chem. Thermodyn. 2005, 37, 684−691). The relative permittivity of the gas was determined with an uncertainty of 0.01 %. These results differed by between −(0.02 and 0.4) % from estimates obtained from the correlation reported by Harvey and Lemmon (Int. J. Thermophys. 2005, 26, 31−46) and the precise measurements of Schmidt and Moldover (Int. J. Thermophys. 2003, 24, 375− 403) for the pure components when the Oster (J. Am. Chem. Soc. 1946, 68, 2036−2041) mixing rule for total molar polarizabilities was applied. Gas densities were ob...

We studied the stability of foams containing small bubbles (radius ≲ 50 μm). The foams are made from aqueous surfactant solutions containing various amounts of glycerol. The foams start breaking at their top, when the liquid volume fraction has decreased sufficiently during liquid drainage. Unlike in foams with larger bubbles, the liquid fraction at which the foam destabilizes is surprisingly high. In order to interpret this observation we propose that film rupture occurs during reorganization events (T1) induced by bubble coarsening, which is particularly rapid in the case of small bubbles. New films are therefore formed rapidly and if their thickness is too small, they cannot be sufficiently covered by surfactant and they break. Using literature data for the duration of T1 events and the thickness of the new films, we show that this mechanism is consistent with the behavior of the foams studied.

A model for drainage/imbibition of a foam placed on the top of a porous substrate is presented. The equation of liquid imbibition into the porous substrate is coupled with a foam drainage equation at the foam/porous substrate interface. The deduced dimensionless equations are solved using a finite element method. It was found that the kinetics of foam drainage/imbibition depends on three dimensionless numbers and the initial liquid volume fraction. The result shows that there are three different regimes of the process. Each regime starts after initial rapid decrease of a liquid volume fraction at the foam/porous substrate interface: (i) rapid imbibition: the liquid volume fraction inside the foam at the foam/porous substrate interface remains constant close to a final liquid volume fraction; (ii) intermediate imbibition: the liquid volume fraction at the interface with the porous substrate experiences a peak point and imbibition into the porous substrate is slower as compared with the drainage; (iii) slow imbibition: the liquid volume fraction at the foam/porous substrate interface increases to a maximum limiting value and a free liquid layer is formed between the foam and the porous substrate. However, the free liquid layer disappears after some time. The transition points between these three different drainage/imbibition regimes were delineated by introducing two dimensionless numbers.

A simple graphical method of calculating the liquid volume fraction, or wetness, of a rising pneumatic foam is presented that is deterministic, given system properties (such as the bubble size distribution and the rate at which gas is sparged to the column) and the kinematic viscosity of the interstitial fluid along with some information about the drainage behavior of the stationary foam analogue. Thus, it is shown that data for the wetness of rising columns of SDS foam (Stevenson, P.; Stevanov, C. Ind. Eng. Chem. Res. 2004, 43, 6187) can be well-predicted using an equation (Neethling, S. J.; Lee, H. T.; Cilliers, J. J. J. Phys.: Condensed Matter 2002, 14, 331) for the drainage of liquid through stationary columns of SDS foam. Further, the liquid overflow rate can be well-predicted once the liquid volume fraction is calculated. The effects of washwater added to the top of the column and bubble bursting on the equilibrium volumetric fraction have been considered theoretically. It is shown that the volumet...

The main objectives of the present article are in developing and evaluating a new model for the droplet collision, and in discussing the physical feature for the mutual impinging sprays. The new model is originally devised to be capable of predicting the droplet collision-induced breakup accompanied with the formation of satellite droplets. From the well-established conservation equations, the several formulae are newly proposed by consideration of some important regimes such as bounce, coalescence, and stretching and reflexive separation. This formulation makes it possible to predict the number of satellite droplets, and the droplet sizes and velocities. The extensive experiments are conducted for the inter-spray impingement systems under the various conditions to investigate the influence of impinging angle and impingement distance upon the spray characteristics. The droplet sizes and velocities are measured by the phase Doppler particle analyzer system and the distribution of liquid volume fraction is also measured by the self-manufactured patternator. In addition, numerical predictions by the new model and the O’Rourke model are compared with experimental data for the various parameters. It is found that the SMD (Sauter mean diameter) measured in the downstream region after inter-spray impingement are 40% smaller than those for the case of single nozzle. The new model shows vigorous breakup during collision, which is no longer seen in the O’Rourke model.

In this paper, the general multimaterial formulation of Kashiwa and Rauenzahn [1] is used to derive an appropriate hydrodynamic model for a trickle-bed reactor operating under trickling flow conditions. Using some realistic assumptions, the resulting model consists of two equations in two unknowns, i.e., liquid volume fraction and pressure. Moreover, the equations exhibit elliptic (pressure) and hyperbolic (volume fraction) behaviours, which require the use of different numerical methods in order to correctly handle these different numerical behaviours. Thus, the finite volume method, the Crank–Nicholson scheme and the second order Godunov's method combined with the solution of Riemann problem were implemented. The numerical results of pressure drops derived from the model solution are shown to be in good agreement with the values measured in the same operating conditions or previously published in the literature.

In this paper, effects of liquid volume fraction, temperature and work pressure in cryogenic vessels on the pressure rise rates in cryogenic vessels are analyzed. Graphs of the relation between storage-pressure and heat flow received by the container per unit of volume for various volume fractions are proposed, and also graphs of the relation between time and pressure of non-loss storage for various volume fractions are presented. The best volume fraction is defined. Also, the graphs of the relation between environmental temperature and the performance of non-loss storage are proposed. In addition, the phenomenon of liquid-temperature layering is analyzed and methods to reduce this layering are suggested. These results have significance in the design, usage and selection of cryogenic vessels.

A theoretical model for gas–liquid annular/dispersed flow through a venturi meter is reported. It is based on an earlier model developed for venturi scrubbers. Changes implemented are based on new research and on the different physics between the two cases. The predictions of the model have been tested using information from recent experiments on venturi meters employed for measuring wet-gas flows with a liquid volume fraction up to 10%. The model gives good predictions with appropriate values of a small set of input variables.