Numerical modeling of three-dimensional two-phase gas–liquid flow in the flow field plate of a PEM electrolysis cell

Numerical simulations were performed for three-dimensional two-phase water/oxygen flow in the flow field plate at the anode side of a PEM electrolysis cell. The mixture model was used to simulate two phases for the purpose of examining flow features in the flow field plate in order to effectively guide the design of electrolysis cells. The water flow rate was maintained as a constant of 260 mL/min, while the flow rate of oxygen generation was assumed to change from 0 to 14 mg/s. The obtained results including the velocity, pressure, and volume fraction distributions are presented and discussed. It is found that the obtained results for single-phase flow cases cannot be linearly extrapolated into the two-phase flow cases. The irregular velocity profile (locally low velocity magnitude near the exit port section) is not observed when the flow rate of oxygen generation is relatively low. As the mass flow rate of oxygen generation increases, reverse flow develops inside the flow channels.     

Flow and heat transfer in a micro-cylindrical gas–liquid Couette flow

Analytic solutions for the gas and liquid velocity and temperature distribution are determined for steady state one-dimensional microchannel cylindrical Couette flow between a shaft and a concentric cylinder. The solution is based on the continuum model and takes into consideration the velocity slip and temperature jump in the gaseous phase defined by the Knudsen number range of 0.001 < Kn < 0.1. The two fluids are assumed immiscible. The gas layer is adjacent to the shaft which rotates with angular velocity ω_s and is thermally insulated. The outer cylinder rotates with angular velocity ω_o and is maintained at uniform temperature. The governing parameters are identified and the effects of the Knudsen number and accommodation coefficients on the velocity and temperature profiles, reduction in the overall temperature rise due to the gas layer, the Nusselt number and shear reduction are examined. It was found that the required torque to rotate the liquid in the annular space is significantly reduced by introducing a thin gas layer adjacent to the shaft. Also, reduction in shaft temperature is enhanced through a combination of high energy accommodation coefficient and low momentum accommodation coefficients. Results also indicate that the gas layer becomes more effective in reducing the shaft temperature when the housing angular velocity is much larger than the shaft angular velocity.     

Three-dimensional measurement of gas dissolution process in gas–liquid microchannel flow

The three-dimensional CO₂ dissolution process through a gas–liquid interface in microfluidic devices was investigated experimentally, for the precise control of CO₂ dissolution. The gas dissolution was evaluated by using confocal micron-resolution particle image velocimetry (micro-PIV) combined with laser induced fluorescence (LIF), which has the ability to measure the velocity and dissolved CO₂ concentration distribution in a liquid flow field. The measurement system is based on the confocal microscope, which has excellent depth resolution and enables visualization of the three-dimensional distributions of velocity and dissolved CO₂ concentration by rendering two-dimensional data. The device is comprised of a polydimethylsiloxane chip, whose microchannels were fabricated by using a cryogenic micromachining system. The width and depth of the liquid flow channel are larger than those of the gas flow channel. This is due to the need for decreasing the width of the gas–liquid interface and increasing the hydraulic diameter of the liquid channel, whose conditions generate a static gas–liquid interface. The experiments were performed for three different liquid flow conditions corresponding to Reynolds numbers of 1.0 × 10^?2, 1.2 × 10^?2 and 1.7 × 10^?2, and the gas flow rate was set to be constant at 150 μL/min. The LIF measurements indicate that an increase in the Reynolds number yields a decrease in dissolved gas in the spanwise directions. Furthermore, molar fluxes by convection and diffusion were evaluated from the experimental data. The molar fluxes in the streamwise direction were at least 20 times as large as those in the spanwise and depthwise directions. This reveals that an increase in momentum transport in the spanwise and depthwise directions is an important factor for enhancing mass transfer in the gas–liquid microchannel flow.     

Physical modelling and advanced simulations of gas–liquid two-phase jet flows in atomization and sprays

This review attempts to summarize the physical models and advanced methods used in computational studies of gas–liquid two-phase jet flows encountered in atomization and spray processes. In traditional computational fluid dynamics (CFD) based on Reynolds-averaged Navier–Stokes (RANS) approach, physical modelling of atomization and sprays is an essential part of the two-phase flow computation. In more advanced CFD such as direct numerical simulation (DNS) and large-eddy simulation (LES), physical modelling of atomization and sprays is still inevitable. For multiphase flows, there is no model-free DNS since the interactions between different phases need to be modelled. DNS of multiphase flows based on the one-fluid formalism coupled with interface tracking algorithms seems to be a promising way forward, due to the advantageous lower costs compared with a multi-fluid approach. In LES of gas–liquid two-phase jet flows, subgrid-scale (SGS) models for complex multiphase flows are very immature. There is a lack of well-established SGS models to account for the interactions between the different phases. In this paper, physical modelling of atomization and sprays in the context of CFD is reviewed with modelling assumptions and limitations discussed. In addition, numerical methods used in advanced CFD of atomization and sprays are discussed, including high-order numerical schemes. Other relevant issues of modelling and simulation of atomization and sprays such as nozzle internal flow, dense spray, and multiscale modelling are also briefly reviewed.     

Thermo-hydrodynamics analysis of vapor–liquid two-phase flow in the flat-plate pulsating heat pipe

A three-dimensional unsteady model of vapor–liquid two-phase flow and heat transfer in a flat-plate pulsating heat pipe (FP-PHP) is developed and numerically analyzed to study the thermal-hydrodynamic characteristics in two different configurations of FP-PHPs. The thermo-hydrodynamics characteristics under steady unidirectional circulation condition of the studied FP-PHPs are numerically investigated and discussed. The results indicate that the bubbly flow, slug flow and semi-annular/annular flow occur in the FP-PHP under the condition of steady unidirectional circulation, when the adjacent tubes of the FP-PHP become ‘upheaders’ and ‘downcomers’ of working fluid. The periodical oscillations of fluid temperature and vapor volume fraction are observed to be synchronous, while the temperature oscillation amplitude at adiabatic section is larger than that at condenser section but less than that at evaporator section. The increases in the heat load lead to the high temperature level and small integral equivalent thermal resistance of the FP-PHP. Additionally, compared with the traditional FP-PHP with uniform channels, the FP-PHP with micro grooves incorporated in the evaporator section is effective for the heat transfer enhancement and possesses a smaller thermal resistance at high heat loads.     

Investigation on the void fraction of gas–liquid two-phase flows in vertically-downward pipes

A special experimental loop is designed and constructed to study the characteristics of the void fraction of gas–liquid two-phase flow in vertically-downward pipes. The test section is made of transparent pipe with a length of 6 m and an internal diameter of 25 mm. The void fraction ranging from 0.1 to 0.98 widely is measured using quick-closing valve method. It is found that the range of the void fraction could be divided into three regions with different flow patterns and different relationships between the void fraction and the gas–liquid volumetric flow rate ratio. Moreover, 39 correlations for calculating the void fraction collected from present literature, are classified, and evaluated using the experimental data obtained in this study. The prediction of correlations in the literature needs to be improved when the void fraction is small.     

VOF modelling of gas–liquid flow in PEM water electrolysis cell micro-channels

In this study, the gas–liquid flow through an interdigitated anode flow field of a PEM water electrolysis cell (PEMEC) is analysed using a three-dimensional, transient, computational fluid dynamics (CFD) model. To account for two-phase flow, the volume of fluid (VOF) method in ANSYS Fluent 17.2 is used. The modelled geometry consists of the anode channels and the anode transport layer (ATL). To reduce the complexity of the phenomena governing PEMEC operation, the dependence upon electro-chemistry is disregarded. Instead, a fixed source of the gas is applied at the interface between the ATL and the catalyst layer. An important phenomenon that the model is able to capture is the gas–liquid contact angle on both the channel wall and ATL-channel interface. Particularly, the latter interface is crucial in capturing bubble entrainment into the channel. To validate the numerical simulation, photos taken of the gas–liquid flow in a transparent micro-channel, are qualitative compared against the simulation results. The experimental observations confirm the models prediction of long Taylor bubbles with small bubbles in between. From the simulation results, further intriguing details of the flow are revealed. From the bottom to the top of the outgoing channel, the film thickness gradually increases from zero to 200 μm. This increase in the film thickness is due to the particular superficial velocity field that develops in an interdigitated flow. Here both the superficial velocities change along the length of the channel. The model is capable of revealing effect of different bubble shapes/lengths in the outgoing channel. Shape and the sequence of the bubbles affect the water flow distribution in the ATL. The model presented in this work is the first step in the development of a comprehensive CFD model that comprises multiphase flow in porous media and micro-channel, electro-chemistry in catalyst layers, ion transport in membrane, hydrogen evolution, etc. The model can aid in the study of gas–liquid flow and its impact on the performance of a PEMEC.     

Numerical study of liquid-gas and liquid-liquid Taylor flows using a two-phase flow model based on Arbitrary-Lagrangian–Eulerian (ALE) formulation

The liquid-gas and liquid-liquid Taylor flows in circular capillary tubes are numerically studied using a mathematical model developed in the frame of Arbitrary-Lagrangian–Eulerian (ALE), where the interface is tracked so that the important interfacial curvature and forces for Taylor flow can be accurately estimated. It is found that for liquid-gas Taylor flow, thin film thickness predicted by the present numerical model agrees very well with the benchmark experimental data both in visco-capillary and visco-inertia flow regimes. Thin film thicknesses decreases first and then increases as Reynolds number (Re) increases at relatively large capillary numbers (Ca). With the increase of Ca, classical pressure drop correlations become inaccurate, because of strong internal circulation inside liquid slug, the appearance of waves at rear meniscus, as well as the deviation from semi-spherical shape of head meniscus. For liquid-liquid flow, when Ca is small, thin film thickness correlations for liquid-gas flow can be used since the disperse phase has negligible effects, while when Ca is relatively large, the viscosity ratio and density ratio of continuous phase to disperse phase become two additional influencing factors. The larger are the viscosity ratio and the density ratio, the thicker is the film thickness. Different from stagnant thin film in liquid-gas flow, the flow in thin film of liquid-liquid flow is not stagnant and has a large contribution to pressure drop. The numerical model developed in this study is shown to be a powerful and accurate tool to study both the liquid-gas and liquid-liquid Taylor flows.     

Capillary pressure of a continuous gas–oil–water flow in a horizontal micron capillary

Capillary pressure is one of the most important factors in characterizing the fluid behavior in a wide variety of processes with environmental and energy concerns. In this paper, Washburn equation is extended to describe the displacement kinetics of the continuous gas–oil–water flow in a single horizontal tube. Experimental investigations of the continuous two- and three-phase flows in capillaries with diameters of 2–10 μm were performed to study the effect of the capillary pressure on their fluid behavior. The results indicate that the total capillary pressure of a continuous three-phase flow is affected by the combined action of the two fluid interfaces presented: gas–liquid and liquid–liquid interfaces.     

New prediction methods for CO2 evaporation inside tubes: Part I – A two-phase flow pattern map and a flow pattern based phenomenological model for two-phase flow frictional pressure drops

An updated flow pattern map was developed for CO₂ on the basis of the previous Cheng–Ribatski–Wojtan–Thome CO₂ flow pattern map [1], [2] to extend the flow pattern map to a wider range of conditions. A new annular flow to dryout transition (A–D) and a new dryout to mist flow transition (D–M) were proposed here. In addition, a bubbly flow region which generally occurs at high mass velocities and low vapor qualities was added to the updated flow pattern map. The updated flow pattern map is applicable to a much wider range of conditions: tube diameters from 0.6 to 10 mm, mass velocities from 50 to 1500 kg/m² s, heat fluxes from 1.8 to 46 kW/m² and saturation temperatures from ?28 to +25 °C (reduced pressures from 0.21 to 0.87). The updated flow pattern map was compared to independent experimental data of flow patterns for CO₂ in the literature and it predicts the flow patterns well. Then, a database of CO₂ two-phase flow pressure drop results from the literature was set up and the database was compared to the leading empirical pressure drop models: the correlations by Chisholm [3], Friedel [4], Grönnerud [5] and Müller-Steinhagen and Heck [6], a modified Chisholm correlation by Yoon et al. [7] and the flow pattern based model of Moreno Quibén and Thome [8], [9], [10]. None of these models was able to predict the CO₂ pressure drop data well. Therefore, a new flow pattern based phenomenological model of two-phase flow frictional pressure drop for CO₂ was developed by modifying the model of Moreno Quibén and Thome using the updated flow pattern map in this study and it predicts the CO₂ pressure drop database quite well overall.     

Distribution of particle resident time in a combined coaxial gas–solid two-phase impinging stream

Gas–solid two-phase impinging stream technology is the process of strengthening the interphase reaction. Short resident time of particles in the impingement region directly leads to inadequate engineering reaction. Therefore, improving the particle resident time in the impingement region can promote engineering application efficiently and adequately. In order to improve the particle resident time in the impingement region, this paper presents a new type of impinging stream technology, named the combined impinging stream (CIS). Flow characteristics of the CIS are studied by means of CFD-DEM at different L/D of impinging stream reactor. Besides, the particle motion behavior and the particle resident time in the impingement region are also studied. The results show that the impingement region of the CIS is instantaneously moving in the collision chamber. The CIS shortens the particle resident time in the jet region and increases the number of passing through the impingement region; the particle does the oscillatory movement in the impingement region, which greatly improves the particle resident time in the impingement region. Therefore, reasonably setting inlet fluid velocity can greatly improve the particle resident time in the impingement region at different L/D.     

Mass and heat transport impact on the peristaltic flow of a Ree–Eyring liquid through variable properties for hemodynamic flow

Variable properties play a prominent role in analyzing the blood flow in narrow arteries. Specifically, considering the variation of thermal conductivity and viscosity helps in the understanding of the rheological behavior of blood and other biological fluids, such as urine, spermatozoa, and eye drops. Inspired by these applications, the current study incorporates the impact of variable thermal conductivity and viscosity for modeling the peristaltic flow of a Ree–Eyring liquid through a uniform compliant channel. The governing equations are nondimensionalized with the assistance of similarity transformations. The long-wavelength and small Reynolds wide variety approximation are utilized for solving the governing differential equations. Furthermore, the series solution method (perturbation technique) is utilized for solving the nonlinear temperature equation. The obtained results show that the velocity is greater in the case of the Newtonian liquid than that of the non-Newtonian liquid.     

Influence of the particle–turbulence modulation modelling in the simulation of a non-isothermal gas–solid flow

A gas–solid suspension upward flowing in a heated vertical pipe has been simulated numerically using both Eulerian–Eulerian and Eulerian–Lagrangian approaches. Particular attention has been paid to the influence of the modelling of the particle–turbulence interactions. A model based on a source-term formulation derived from a study by Crowe (Int. J. Multiphase Flow 26 (5) (2000) 719) allows predicting turbulence enhancement due to a strong particle influence in the core of the pipe flow. Calculations of suspension Nusselt numbers, characterizing the heat transfer between the pipe wall and the flow, have therefore been performed, with a satisfactory level of accuracy, compared with available experimental data. Some numerical difficulty remains however, especially due to the near-wall layer interactions which seem very difficult to simulate.     

Numerical investigations of catalyst–liquid slurry flow in the photocatalytic reactor for hydrogen production based on algebraic slip model

A new device of photocatalytic reactor with solar concentrator for hydrogen production was introduced in this paper. In order to investigate the effects of the slurry flow and catalyst distributions in the reactor on photocatalysis for hydrogen production, an algebraic slip mixture model (ASM) was used to simulate the dynamics of the catalyst–water slurry flow. A block-structured non-uniform grid was applied to discretize the entire domain and an algebraic multi-grid (AMG) method was used to solve the pressure field. The mean slurry pressure gradients obtained by the model were in agreement with the experimental data in former literature. Based on this verification, catalyst particle distributions, slurry velocity distributions and inter-phase slip velocity distributions in photocatalytic reactor pipe were investigated. The results show that the catalyst tends to distribute near the bottom of the pipe in the reactor, leading to a concentration gradient along the vertical direction of cross section. But due to the effects of turbulence force against the gravity, a heterogeneous suspending state will be achieved in a fully developed flow.     

Solvothermal synthesis,nanostructural characterization and gas cryo-adsorption studies in a metal–organic framework (IRMOF-1) material

A nanoporous metal–organic framework material, exhibiting an IRMOF-1 type crystalline structure, was prepared by following a direct solvothermal synthesis approach, using zinc nitrate and terephthalic acid as precursors and dimethylformamide as solvent, combined with supercritical CO₂ activation and vacuum outgassing procedures. A series of advanced characterization methods were employed, including scanning electron microscopy, Fourier-transform infrared radiation spectroscopy and X-ray diffraction, in order to study the morphology, surface chemistry and structure of the IRMOF-1 material directly upon its synthesis. Porosity properties, such as Brunauer–Emmet–Teller (BET) specific area (～520 m²/g) and micropore volume (～0.2 cm³/g), were calculated for the activated sample based on N₂ gas sorption data collected at 77 K. The H₂ storage performance was preliminary assessed by low-pressure (0–1 bar) H₂ gas adsorption and desorption measurements at 77 K. The activated IRMOF-1 material of this study demonstrated a fully reversible H₂ sorption behavior combined with an adequate gravimetric H₂ uptake relative to its BET specific area, thus achieving a value of ～1 wt.% under close-to-atmospheric pressure conditions.     

Langmuir–Maxwell and Langmuir–Smoluchowski boundary conditions for thermal gas flow simulations in hypersonic aerodynamics

The simulation of nonequilibrium thermal gas flow is important for the aerothermodynamic design of re-entry and other high-altitude vehicles. In computational fluid dynamics, the accuracy of the solution to the Navier–Stokes–Fourier (N–S–F) equations depends on the accuracy of the surface boundary conditions. We propose new boundary conditions (called the Langmuir–Maxwell and the Langmuir–Smoluchowski conditions), for use with the N–S–F equations, which combine the Langmuir surface adsorption isotherm with the Maxwell/Smoluchowski slip/jump conditions in order to capture some of the physical processes involved in gas flow over a surface. These new conditions are validated for flat plate flow, circular cylinder in cross-flow, and the flow over a sharp wedge for Mach numbers ranging from 6 to 24, and for argon and nitrogen as the working gases. Our simulation results show that the new boundary conditions give better predictions for the surface pressures, compared with published experimental and DSMC data.     

Linear stability analysis of Poiseuille–Bénard–Marangoni flow in a horizontal infinite liquid film

We present the first linear stability analysis of a Poiseuille–Bénard–Marangoni flow, which refers to a horizontal infinite liquid film flowing in one direction with uniform heating from below. This study concerns the two limiting cases of pure buoyancy effect (Ma = 0) and pure thermocapillary effect (Ra = 0). The stability thresholds of the flow and their variation with the control parameters (Biot, Reynolds and Prandtl numbers) are given and compared with those for a Poiseuille–Rayleigh–Bénard flow. The spatial structures of the flow are presented, and it is shown that the centers of the rolls are shifted upwards compared to the PRB case and that there is a loss of symmetry with respect to the vertical axis for the transverse rolls. These effects are directly linked to thermocapillary convection.     

Heat transfer enhancement in a small pipe by spinodal decomposition of a low viscosity,liquid–liquid,strongly non-regular mixture

We report experimental evidence of a 20–40 % enhancement of the effective heat transfer coefficient for laminar flow of a partially miscible binary liquid–liquid mixture in a small diameter horizontal tube that obtains when phase separation occurs in the tube. A mixture of acetone–hexadecane is quenched into the two-phase region so as to induce spinodal decomposition. The heat transfer rate is enhanced by self-induced convective effects sustained by the free energy liberated during phase separation. The experimental heat transfer coefficients obtained when separation occurs are compared to the corresponding values predicted for flow of a hypothetic mixture with identical properties but undergoing separation. For such comparison, the energy balance equation must carefully take into account both the sensible heat and the excess enthalpy difference between the inlet and the outlet streams because our liquid–liquid binary mixture is a very asymmetric system with large excess enthalpies. The non-ideal mixture thermodynamic properties needed for the energy balance are obtained by an empirical procedure from the experimental data available in the literature for our mixture. The experimental setup and calculation procedure is tested by experiments performed using single-phase water flow and single-phase mixture flow (above the critical point). The convective heat transfer augmentation that results in the presence of liquid–liquid phase separation may be exploited in the cooling or heating of small scale systems where turbulent convection cannot be achieved.