Traveling void wave in horizontal two-phase flow

In the framework of pattern dynamics approach, the discrete bubble model was developed for simulating inherent fluctuation of void fraction in a horizontal two-phase flow. Then flow patterns were identified based on the statistical properties of void fraction fluctuation, and the flow pattern map agreed with the experimental observation of high-pressure two-phase flow of CO₂ in horizontal tubes. The time-averaged pressure drop and the void fraction obtained in the simulation agreed reasonably with the existing correlations. Thus the horizontal flow version of the discrete bubble model demonstrates its relevance in simulating inherent fluctuation of two-phase flow.     

Simulation of Convective Heat Transfer of Gas–Liquid Bubble Train Flow in Wet Microtube

In this paper, a direct numerical simulation of a two‐phase incompressible gas–liquid flow for simulation of bubble motion and convective heat transfer in a microtube is presented. The microtube radius is 10 μm. The interface between the two phases is tracked by the volume of fluid method with the continuous surface force model. Newtonian flows are solved using a finite volume scheme based on the PISO algorithm. Numerical simulation is done on an axisymmetric domain with a periodic boundary condition for different values of pressure gradient, void fraction, and bubble period. Mean pressure gradient is fixed for each simulation. The superficial Reynolds numbers of gas and liquid phases studied are 0.3 to 7 and 5 to 210, respectively. Numerical results are coincident with the Serizawa regime map, and there is a linear relation between the void fraction and gas flow ratio. Simulation shows local Nusselt number increases in the presence of a gas bubble.     

The “tornado” effect induced by magnetohydrodynamic convection in an electrolytic cell with a wire-electrode

High energy consumption is the key problem to be solved in water electrolysis for hydrogen production. Imposing magnetic field during electrolysis is proved to be a research-worthy method to reduce the required electrical energy, since the magnetohydrodynamic convection can be induced without additional energy input. Considering the structure of commercial electrolyzers, the magnetic field perpendicular to the electrode surface is most likely to be applied in practical engineering. But there is still a lack of research on the gas-liquid two-phase flow in the electrolytic cell under this condition. To avoid mutual blocking between a large number of bubbles and obtain clear two-phase flow images of the electrolysis process, a wire electrode is used as cathode to generate hydrogen bubbles in this work. The cell voltage is obviously reduced by external magnetic field, and an interesting “bubble tornado” is formed under the action of induced magnetohydrodynamic convection. The numerical simulation results and theoretical analysis indicate that: (1) the formation of the bubble chain is caused by low-pressure region along the vertical axis; (2) the unstable low-pressure region is the key factor leading to the formation of continuously deformed bubble chain; (3) the bubble dispersion may be related to Kelvin-Helmholtz flow instability. We anticipate our work being a starting point for the application of magnetic field in practical engineering.     

Mechanistic study for the interfacial area transport phenomena in an air/water flow condition by using fine-size bubble group model

A set of number density transport equations based on the bubble size are used to predict the void fraction and the interfacial area concentration in an air/water flow conditions. As the closure relations for the number density transport equations, a coalescence due to random collisions and a breakup due to an impact of the turbulent eddies are modified based on previous studies. The bubble expansion term due to a pressure reduction and a coalescence due to a wake entrainment are modeled for the number density transport equation. In order to predict the local experimental data, a computational fluid dynamic (CFD) code coupling the two-fluid model and number density transport equations are developed in this study. As for the results of the numerical analysis, the developed model predicts well the void fraction and interfacial area concentration although some deviations between the prediction and the experiment are shown for the high void fraction conditions.     

Numerical and experimental investigation of two-phase flow in an electrochemical cell

In this study, a two-phase mathematical model is adapted to study void fraction distribution, flow field and characteristics of electrolysis process. The model involves transport equations for both liquid and gaseous phases. An experimental set-up is established to collect data to validate and improve the mathematical model. The void fraction is determined from measurement of resistivity changes in the system due to the presence of bubbles. It is observed that there is a good agreement between the numerical results and the experimental data.     

Distribution parameter and drift velocity of drift-flux model in bubbly flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for bubbly flow regime. The constitutive equation that specifies the distribution parameter in the bubbly flow has been derived by taking into account the effect of the bubble size on the phase distribution, since the bubble size would govern the distribution of the void fraction. A comparison of the newly developed model with various fully developed bubbly flow data over a wide range of flow parameters shows a satisfactory agreement. The constitutive equation for the drift velocity developed by Ishii has been reevaluated by the drift velocity calculated by local flow parameters such as void fraction, gas velocity and liquid velocity measured under steady fully developed bubbly flow conditions. It has been confirmed that the newly developed model of the distribution parameter and the drift velocity correlation developed by Ishii can also be applicable to developing bubbly flows.     

Application of a two-phase flow model for natural convection in an electrochemical cell

A two-phase mathematical model is applied to natural convection in an electrochemical cell. The model solves transport equations for both phases with an allowance of interphase mass and momentum exchange. The effect of current density and bubble size on the gas release rate, velocity field and void fraction distribution are investigated in a range of parameter. The flow in the system was generated due to the density difference between gas and liquid phases. It is found that both current density and bubble size significantly affect the gas release rate and velocity field. At an intermediate current density two circulation patterns form at the vicinity of the free surface. The circulations rotating opposite directions enhance lateral diffusion of gas phase. The gas evolution is enhanced with higher current density and lower bubble diameters.     

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.     

Single-phase and two-phase heat transfer characteristics of low temperature hybrid micro-channel/micro-jet impingement cooling module

This study examines the single-phase and two-phase cooling performance of a hybrid micro-channel/micro-jet impingement cooling scheme using HFE 7100 as working fluid. This scheme consists of supplying coolant from a series of jets that deposit liquid into the micro-channels. A single-phase numerical scheme that utilizes the k–ε turbulent model and a method for determining the extent of the laminarized wall layer shows very good predictions of measured wall temperatures. It is shown jet velocity has a profound influence on single-phase cooling performance. High jet velocities enable jet fluid to penetrate the axial micro-channel flow and produce a strong impingement effect at the wall. On the other hand, the influence of jets at low jet velocities is greatly compromised compared to the micro-channel flow. During nucleate boiling, vapor layer development along the micro-channel in the hybrid module is fundamentally different from that encountered in conventional micro-channels. Here, subcooled jet fluid produces repeated regions of bubble growth followed by bubble collapse, rather than the continuous growth common to conventional micro-channel flow. By reducing void fraction along the micro-channel, the hybrid scheme contributes greater wall temperature uniformity. Increasing subcooling and/or flow rate delay the onset of boiling to higher heat fluxes and higher wall temperatures, and also increase critical heat flux considerably. A nucleate boiling heat transfer coefficient correlation is developed that fits the present data with a mean absolute error of 6.10%.     

Modeling of bubble-layer thickness for formulation of one-dimensional interfacial area transport equation in subcooled boiling two-phase flow

In relation to the formulation of one-dimensional interfacial area transport equation in a subcooled boiling flow, the bubble-layer thickness model was introduced to avoid many covariances in cross-sectional averaged interfacial area transport equation in the subcooled boiling flow. The one-dimensional interfacial area transport equation in the subcooled boiling flow was formulated by partitioning a flow region into two regions; boiling two-phase (bubble layer) region and liquid single-phase region. The bubble-layer thickness model assuming the square void peak in the bubble-layer region was developed to predict the bubble-layer thickness of the subcooled boiling flow. The obtained model was evaluated by void fraction profile measured in an internally heated annulus. It was shown that the bubble-layer thickness model could be applied to predict the bubble-layer thickness as well as the void fraction profile. In addition, the constitutive equation for the distribution parameter of the boiling flow in the internally heated annulus, which was used for formulating the bubble-layer thickness model, was developed based on the measured data. The model developed in this study will eventually be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flows.     

Single-phase and two-phase magnetohydrodynamic pipe flow

Experimental results are presented for a range of measured temperatures and other parameters of vertically downward flows, both single-phase (sodium) and two-phase (sodium-nitrogen), in a conducting-wall pipe in the presence of a transverse magnetic field. Existing MHD theory predicted, to within experimental error, all single-phase pressure differences for magnetic interaction parameter values of up to approximately 100, beyond which the single-phase normalized resistance coefficients were noticeably lower than the laminar-flow predictions. The magnetic interaction parameter at which such deviation occurred was governed by the conductivity ratio. Two-phase pressure differences were obtained across a range of void fractions, approximately 0.3-0.8, where two distinct flow regimes were encountered. For those two regimes, the normalized resistance coefficients of pressure difference were predicted to within experimental error by the corresponding two-phase MHD pressure-difference models. In half of the two-phase cases examined, decreases were observed in normalized resistance coefficients at high values of the magnetic interaction parameter, a trend similar to that found in single-phase flow. The wall-voltage profiles of single-phase flows were symmetric with respect to the center of the applied magnetic field region; two-phase wall-voltage profiles were asymmetric because of the expansion of the gaseous nitrogen along the length of the test section. The influence of temperature and other system parameters upon pressure differences and wall voltages, and the possible effect of ‘M-shaped’ velocity profiles in the two types of flow are discussed.     

Error reduction,evaluation and correction for the intrusive optical four-sensor probe measurement in multi-dimensional two-phase flow

The objective of the present study is to increase the reliability of multi-dimensional two-phase flow measurement using an intrusive optical four-sensor probe. We investigated the error reducing ways in fabricating an optical conical four-sensor probe from its basic principles and sought for a control technique to sharpen the optical fiber tip and a sensor assembling method for a four-sensor probe. According to the measuring process by a multi-sensor probe, measurement errors were classified into signal processing errors and hydrodynamic errors. The signal processing errors in the void fraction due to the threshold setting and those in the interfacial area concentration (IAC) due to the interface-pairing scheme and the threshold setting were analyzed and concluded to be tiny and negligible in the measurement by an optical four-sensor probe. The hydrodynamic errors were classified into oncoming bubble errors, receding bubble errors and transversal or missing bubble errors according to the bubble motion relative to the probe. The maximum errors in both IAC and void fraction due to oncoming bubbles in a four-sensor probe measurement were estimated to be 10%. The maximum underestimation for IAC in the traditional transversal bubble recovering way of a four-sensor probe was reported up to 30% when the intensity of bubble velocity fluctuation equaled to 1 and the bubble size was close to the probe separations between sensor tips. The maximum measurement errors in IAC and void fraction for the receding bubbles were valued at 31% and 38%, respectively, at low liquid and high gas flow rates conditions by performing evaluation experiments using downward-facing and upward-facing probes. To overcome the unsatisfactory measurement errors for the receding and transversal bubbles, we proposed expressions for the correction of IAC and void fraction in the four-sensor probe measurement in a multi-dimensional two-phase flow by adding the contribution of escaped bubbles due to the hindrance of the probe rear parts and that of transversal bubbles due to the existence of finite distance separation between the sensor tips.     

Heat transfer analysis for particle–fluid suspension thermomagnetohydrodynamic peristaltic flow with Darcy–Forchheimer medium

This theoretical analysis explores the effect of heat and mass transfer on particle–fluid suspension for the Rabinowitsch fluid model with the stiffness and dynamic damping effects through Darcy–Brinkman–Forchheimer porous medium. In this study, we also incorporate slip and transverse magnetic field effects. Using low Reynolds number, to neglect inertial forces and to keep the pressure constant during the flow, channel height is used largely as compared with the ratio of length of the wave. A numerical technique is used to solve flow governing system of differential equations. Particular attention is paid to viscous damping force parameter, stiffness parameter, and rigidity parameter; also, the numerical data for thermal profile, momentum, and concentration distribution are presented graphically. Outcomes are deliberated in detail for different fluid models (thinning, thickening, and viscous models). It is found that velocity profile increases for greater values of viscous damping effect and stiffness and rigidity parameter for shear thinning, but conflicting comportment is showed for thickening nature model. Viscous dissipation effects increases the thermal profile for all cases of fluid models. The scope of the present article is valuable in explaining the blood transport dynamics in small vessels while considering the important wall features with chemical reaction characteristics. The current analysis has extensive applications in biomedical engineering field, that is, peristaltic pumps.     

Modeling and numerical investigation of hydrogen nucleate flow boiling heat transfer

Liquid hydrogen flow boiling heat transfer in tubes is of great importance in the hydrogen applications such as superconductor cooling, hydrogen fueling. In the present study, a numerical model for hydrogen nucleate flow boiling based on the wall partition heat flux model is established. The key parameters in the model such as active nucleation site density, bubble departure diameter and frequency are carefully discussed and determined to facilitate the modeling and simulation of hydrogen flow boiling. Simulation results of the numerical model show reasonably well agreement with experimental data from different research groups in a wide operation condition range with the means absolute error (MAE) of 10.6% for saturated and 5.3% for subcooled flow boiling. Based on the model, wall heat flux components and void fraction distribution of hydrogen flow boiling are studied. Effects of mass flow rate and wall heat flux on the flow boiling heat transfer performance are investigated. It is found that in the hydrogen nucleate flow boiling, the predominated factor is the Boiling number, rather than the vapor quality. A new simple correlation is proposed for predicting hydrogen saturated nucleate flow boiling Nusselt number. The MAE between the correlation predicted and experimentally measured Nusselt number is 13.6% for circular tubes and 12.5% for rectangular tubes. The new correlation is applicable in the range of channel diameter 4–6.35 mm, Reynolds number 64000–660,000, saturation temperature 22–29 K, Boiling number 8.37 × 10^?5–2.33 × 10^?3.     

Influence of hydrodynamic parameters on the critical current density at water electrolysis: Mass flux,channel inclination and inlet void fraction

Hydrogen production rate increases as current density increases in a water electrolysis. At a certain high current density, the cell potential abruptly increases due to the hydrogen film formed at the cathode, which is known as the critical current density (CCD). Hence, it is imperative to increase the CCD for effective hydrogen production. However, the investigations regarding hydrodynamic parameters, which affect the CCD have hardly been performed. This work investigated the influence of the hydrodynamic parameters such as mass flux, inclination of cathode channel and inlet void fraction on the CCD in water electrolysis. The increase in the mass flux increased the CCD regardless of the channel inclination and the inlet void fraction due to the enhanced hydrogen bubble elimination near the surface, which retards hydrogen film formation. The influence of the inlet void fraction showed different trend according to the channel inclination. Monotonically decreasing trend was measured in the vertical channel due to reduced flow rate near the surface as the void fraction increased. Meanwhile, a peak was measured in the inclined channels. The inlet voids at bubbly flow regime dispersed the hydrogen bubbles from the cathode, while those at the slug flow regime aided and enhanced the hydrogen film formation at the cathode. It is concluded that the inlet void fraction either enhances or impairs the CCD depending on the flow regime. The authors expect that this work would shed light on the roles of hydrodynamic parameters for efficient hydrogen production.     

Mass transfer-controlled bubble growth during rapid decompression of a liquid

An analysis based on the integral method is presented for the solution of mass transfercontrolled bubble growth during a rapid decompression of a liquid-gas solution. Predicted results are in very good agreement with experimental measurements on an ethyl alcohol-CO₂ solution at 25°C and initial pressures of 0.44–1.12 MPa. An outline of the way in which the bubble growth model could be combined with a bubble nucleation model to predict void fractions in one-dimensional two-phase flow passages is given. Specific results for bubble growth and void fraction calculations are presented for the flow of monoethanolamine-CO₂ solution at an initial pressure of 8.8 MPa and 150°C through a singlestage turbine and a five-stage reverse pump.     

Numerical simulation of bubbly two-phase flow in a narrow channel

An advanced numerical simulation method on fluid dynamics - lattice-Boltzmann (LB) method is employed to simulate the movement of Taylor bubbles in a narrow channel, and to investigate the flow regimes of two-phase flow in narrow channels under adiabatic conditions. The calculated average thickness of the fluid film between the Taylor bubble and the channel wall agree well with the classical analytical correlation developed by Bretherton. The numerical simulation of the behavior of the flow regime transition in a narrow channel shows that the body force has significant effect on the movement of bubbles with different sizes. Smaller body force always leads to the later coalescence of the bubbles, and decreases the flow regime transition time. The calculations show that the surface tension of the fluid has little effect on the flow regime transition behavior within the assumed range of the surface tension. The bubbly flow with different bubble sizes will gradually change into the slug flow regime. However, the bubbly flow regime with the same bubble size may be maintained if no perturbations on the bubble movement occur. The slug flow regime will not change if no phase change occurs at the two-phase interface.     

A void fraction model for annular flow in horizontal tubes

An important feature of detailed system simulation models for unitary air conditioners is the calculation of charge inventory. Void fraction determination in the two-phase regions of the heat exchangers is the primary challenge associated with charge inventory calculations. Annular flow is one of the predominant flow regimes encountered in horizontal heat exchangers. Analytical annular flow models typically fail to accurately represent void fraction. Thus, many of the available void fraction models are empirically based. To improve the prediction capabilities of void fraction models, a mechanistic void fraction model has been developed for annular flow in horizontal tubes. The present model considers the effect of momentum eddy diffusivity damping at the liquid-vapor interface. Two approaches are presented for determining the wall shear stress. The modeling results are compared to predictions from various void fraction models found in the literature. The present model is found to work well at moderate mass fluxes.     

Numerical prediction of a two-phase fluid driving system using cavitating flow of magnetic fluid

A new concept of a two-phase fluid driving system using cavitating flow of a magnetic fluid is proposed, and the driving and acceleration performance of the system is numerically predicted. A typical computational model for cavitating flow of a magnetic fluid is proposed and several flow characteristics, taking into account the strong nonuniform magnetic field, are numerically investigated to realize the further development and high performance of the proposed new type of two-phase fluid driving system using magnetic fluids. Based on numerical results, the two-dimensional structure of the cavitating flow as well as the cloud cavity formation of the magnetic fluid through a vertical converging–diverging channel are shown in detail. The numerical results demonstrate that an effective two-phase magnetic driving force and fluid acceleration can be obtained by the practical use of magnetization of the working fluid. Also clarified is the cavitation number in the case of a strong magnetic field with a larger value than that in the case of a nonmagnetic field. Magnetic control for suppression of cavitation bubbles is remarkably enhanced in the condition of high Reynolds number. Further clarified is the precise control of the cavitating flow of magnetic fluid that is possible by effective use of the magnetic body force that acts on cavitation bubbles.     

Thermal slip and radiative heat transfer effects on electro‐osmotic magnetonanoliquid peristaltic propulsion through a microchannel

A mathematical study is described to examine the concurrent influence of thermal radiation and thermal wall slip on the dissipative magnetohydrodynamic electro‐osmotic peristaltic propulsion of a viscous nanoliquid in an asymmetric microchannel under the action of an axial electric field and transverse magnetic field. Convective boundary conditions are incorporated in the model and the case of forced convection is studied, that is, thermal and species (nanoparticle volume fraction) buoyancy forces neglected. The heat source and sink effects are also included and the diffusion flux approximation is employed for radiative heat transfer. The transport model comprises the continuity, momentum, energy, nanoparticle volume fraction, and electric potential equations with appropriate boundary conditions. These are simplified by negating the inertial forces and invoking the Debye–Hückel linearization. The resulting governing equations are reduced into a system of nondimensional simultaneous ordinary differential equations, which are solved analytically. Numerical evaluation is conducted with symbolic software (MATLAB). The impact of different control parameters (Hartmann number, electro‐osmosis parameter, slip parameter, Helmholtz–Smoluchowski velocity, Biot numbers, Brinkman number, thermal radiation, and Prandtl number) on the heat, mass, and momentum characteristics (velocity, temperature, Nusselt number, etc) are presented graphically. Increasing Brinkman number is found to elevate temperature magnitudes. For positive Helmholtz–Smoluchowski velocity (reverse axial electrical field) temperature is strongly reduced, whereas for negative Helmholtz–Smoluchowski velocity (aligned axial electrical field), it is significantly elevated. With increasing thermal slip, nanoparticle volume fraction is also increased. Heat source elevates temperatures, whereas heat sink depresses them, across the microchannel span. Conversely, heat sink elevates nanoparticle volume fraction, whereas heat source decreases it. Increasing Hartmann (magnetic) parameter and Prandtl number enhance the nanoparticle volume fraction. Furthermore, with increasing radiation parameter, the Nusselt number is reduced at the extremities of the microchannel, whereas it is elevated at intermediate distances. The results reported provide a good insight into biomimetic energy systems exploiting electromagnetics and nanotechnology, and, furthermore, they furnish a useful benchmark for experimental and more advanced computational multiphysics simulations.