Experimental study on interfacial area transport in vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, and interfacial velocity of vertical upward bubbly flows in an annulus with the hydraulic equivalent diameter of 19.1 mm were measured by the double-sensor conductivity probe. A total of 20 data were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The obtained data will be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flow systems.     

Interfacial area transport of vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation in a subcooled boiling flow, the one-dimensional interfacial area transport equation was evaluated by the data taken in the hydrodynamic separate effect tests without phase change, or an adiabatic air-water bubbly flow in a vertical annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Twenty data sets consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s were used for the evaluation of the one-dimensional interfacial area transport equation. The one-dimensional interfacial area transport equation agreed with the data with an average relative deviation of ±8.96%. Sensitivity analysis was also performed to investigate the effect of the initial bubble size on the interfacial area transport. It was shown that the dominant mechanism of the interfacial area transport was strongly dependent on the initial bubble size.     

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.     

Volumetric interfacial area prediction in upward bubbly two-phase flow

In two-phase flow studies, a volumetric interfacial area balance equation is often used in addition to the multidimensional two-fluid model to describe the geometrical structure of the two-phase flow. In the particular case of bubbly flows, numerous works have been done by different authors on the subject. Our work concerns two main modifications of this balance equation: (1) new time scales are proposed for turbulence induced coalescence and breakup, (2) modeling of the nucleation of new bubbles on the volumetric interfacial area. The 3D module of the CATHARE code is used to evaluate our new model, in comparison to three other models for interfacial area found in the literature, on two different experiments. First, we use the DEBORA experimental data base for the comparison in the case of boiling bubbly flow. The comparison of the different volumetric interfacial area models to the DEBORA experimental data shows that even though the theoretical values of the coefficients are adopted in our modified model, this model has a quite good capability to predict the local two-phase geometrical parameters in the boiling flow conditions. Secondly, we compare the predictions obtained with the same models to the DEDALE experimental data base, for the case of adiabatic bubbly flow. In comparison to the other models tested, our model also gives quite good predictions of the bubble diameter in the case of adiabatic conditions.     

Interfacial area transport equation: model development and benchmark experiments

The interfacial area transport equation dynamically models two-phase flow regime transitions and predicts continuous changes of the interfacial area concentration along the flow field. It replaces the flow regime-dependent correlations for the interfacial area concentration in thermal-hydraulic system analysis. In the present study, detailed formulation of the interfacial area transport equation is presented along with its evaluation results based on the detailed benchmark experiments. In view of model evaluation, the equation is simplified into one-dimensional steady state one-group interfacial area transport equation. The prediction made by model agrees well with the experimental data obtained in round pipes of various diameters. The framework for the two-group transport equation and the necessary constitutive relations are also presented in view of bubble transport of various sizes and shapes.     

Local flow measurements of vertical upward bubbly flow in an annulus

Local measurements of flow parameters were performed for vertical upward bubbly flows in an annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Double-sensor conductivity probe was used for measuring void fraction, interfacial area concentration, and interfacial velocity, and laser Doppler anemometer was utilized for measuring liquid velocity and turbulence intensity. A total of 20 data sets for void fraction, interfacial area concentration, and interfacial velocity were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. A total of eight data sets for liquid velocity and turbulence intensity were acquired consisting of two void fractions, about 0.050, and 0.10, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter namely interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment using the annulus.     

Modeling of the condensation sink term in an interfacial area transport equation

A model for the condensation sink term in an interfacial area transport equation (IATE) was developed. In the model, a bubble nucleation due to a wall surface boiling and a bubble collapse due to a condensation were assumed to be symmetric phenomena. Based on this consideration the condensing region for a subcooled condition can be divided into two regions: the heat transfer-controlled region and the inertia-controlled region. In the heat transfer-controlled region, the condensation Nusselt number approach is appropriate. On the other hand, in the inertia-controlled region, the resultant mechanical force may be balanced through an interface between a bubble and an ambient liquid. The modeled condensation sink term in an IATE in this study was evaluated against existing data which had been obtained from a bubble condensation in a subcooled water flow through a non-heated annulus. The evaluation result showed that the present model could predict the axial distribution of the interfacial area concentration accurately.     

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.     

Active nucleation site density in boiling systems

Realizing the significance of the active nucleation site density as an important parameter for predicting the interfacial area concentration in a two-fluid model formulation, the active nucleation site density has been modeled mechanistically by knowledge of the size and cone angle distributions of cavities that are actually present on the surface. The newly developed model has been validated by various active nucleation site density data taken in pool boiling and convective flow boiling systems. The newly developed model clearly shows that the active nucleation site density is a function of the critical cavity size and the contact angle, and the model can explain the dependence of the active nucleation site density on the wall superheat reported by various investigators. The newly developed model can give fairly good predictions over rather wide range of the flow conditions (0 kg/m² s ? mass velocity ? 886 kg/m² s; 0.101 MPa ? pressure ? 19.8 MPa; 5° ? contact angle ? 90°; 1.00×10⁴ sites/m² ? active nucleation site density ? 1.51×10¹⁰ sites/m²).     

One-dimensional drift-flux model for two-phase flow in a large diameter pipe

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 vertical upward two-phase flow in a large diameter pipe. One of the important flow characteristics in a large diameter pipe is a liquid recirculation induced at low mixture volumetric flux. Since the liquid recirculation may affect the liquid velocity profile and promote the formation of cap or slug bubbles, the distribution parameter and the drift velocity in a large diameter pipe can be quite different from those in a small diameter pipe where the liquid recirculation may not be significant. A flow regime at a test section inlet may also affect the liquid recirculation pattern, resulting in the inlet-flow-regime dependent distribution parameter and drift velocity. Based on the above detailed discussions, two types of inlet-flow-regime dependent drift-flux correlations have been developed for two-phase flow in a large diameter pipe at low mixture volumetric flux. A comparison of the newly developed correlations with various data at low mixture volumetric flux shows a satisfactory agreement. As the drift-flux correlations in a large diameter pipe at high mixture volumetric flux, the drift-flux correlations developed by Kataoka-Ishii, and Ishii have been recommended for cap bubbly flow, and churn and annular flows, respectively, based on the comparisons of the correlations with existing experimental data.     

Flow structure of subcooled boiling flow in an internally heated annulus

Local measurements of flow parameters were performed for vertical upward subcooled boiling flows in an internally heated annulus. The annulus channel consisted of an inner heater rod with a diameter of 19.1 mm and an outer round pipe with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. The double-sensor conductivity probe method was used for measuring local void fraction, interfacial area concentration, and interfacial velocity. A total of 11 data were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s and two inlet liquid temperatures, 95.0 and 98.0 °C. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter, namely, interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment.     

Pore-scale numerical study of multiphase reactive transport processes in cathode catalyst layers of proton exchange membrane fuel cells

understanding interactions between multiphase flow and reactive transport processes in catalyst layers (CL) of proton exchange membrane fuel cells is crucial for obtaining better performance and lower cost. In this study, a pore-scale model is developed to simulate coupled processes occurring in CLs, including oxygen diffusion, electrochemical reaction, and air-liquid two phase flow. Simulation conducted in an idealized local CL structures shows that the pore-scale model successfully captures dynamic behaviors of liquid water including generation, growth and subsequent migration, as well as the interaction between multiphase flow and reactive transport. Pore-scale simulation is then conducted in hydrophobic CLs with complicated structures where carbon, platinum, ionomer and pores are resolved. It is found that filling modes of the liquid water in the CLs are different. Before forming the continuous flow paths in CLs, liquid water presents as tiny droplets in pores surrounding relative large pores. After the continuous flow paths are formed, liquid water dynamic behaviors follow the capillary fingering mechanism. The multiphase flow and reactive transport processes are closely coupled with each other, and as liquid water saturation increases the reaction rate decreases. Increasing the hydrophobicity can alleviate the water flooding, accelerate the water breakthrough, and facilitate the water evaporation.     

A linear and non-linear analysis on interfacial instability of gas-liquid two-phase flow through a circular pipe

A linear instability analysis was conducted firstly on the interface of a stratified gas-liquid two-phase flow in a circular piper employing a two-fluid model. The constitutive equations simulation technique was discussed, and the dispersive equation of interfacial waves was derived. The effects of flow rates of gas and liquid, liquid viscosity, surface tension and tube inclination on the stability of interface were investigated. A set of non-linear hyperbolic governing equations was deduced from the complete two-fluid model equation by omitting the effect of the surface tension and assuming a quasi-steady-state for the gas phase. Using characteristic line and finite difference, the propagation and growth of the interfacial disturbances were investigated in terms of gas and liquid superficial velocities. Then the results of the non-linear stability analysis were compared with those obtained by the linear stability analysis and experimental data. The non-linear stability analysis not only confirms the conclusions reached by the linear instability analysis, but also gives an insight into the growth and propagation of the interfacial disturbances on the interface of a gas-liquid two-phase flow.     

A molecular dynamics study of interfacial thermal transport in heterogeneous systems

Non-equilibrium molecular dynamics software was developed to study thermal transport at the nanoscale. Lennard–Jones parameters of pure argon (mass and bond strength) were systematically modified to create heterogeneous thin film systems, including layered systems and nanocomposites, to investigate the influence of interfaces on thermal conductivity. Results were analyzed using combinations of kinetic theory and a thermal resistance network model together with the acoustic mismatch model (AMM). The introduction of a second material into an argon film generally decreased its overall thermal conductivity. Moreover, the presence of a nanoparticle was less influential in reducing thermal conductivity than the addition of a thin layer.     

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

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 kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equations that specify the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, the shear stresses, the interfacial momentum transfer and the wall friction, since these macroscopic effects govern the relative velocity between phases. A comparison of the models with existing experimental data shows a satisfactory agreement.     

Numerical simulation of two-fluid electroosmotic flow in microchannels

This paper presents a numerical scheme for stratified two-liquid electroosmotic flows. The simulation results highlight that using the electroosmotic effects can control the interface location of a pressure-driven two-liquid flow. A finite volume method is used to solve the coupled electric potential equation and Navier–Stokes equation together.The validity of the numerical scheme is evaluated by comparing its predictions with the results of the analytical solutions in the fully developed regions. The liquid–liquid interface developments due to the favorably and adversely applied electric field are examined.     

Numerical studies of interfacial phenomena in liquid water transport in polymer electrolyte membrane fuel cells using the lattice Boltzmann method

Water management is an important issue in the polymer electrolyte membrane (PEM) fuel cell, which is considered as a promising alternative power source for future automotive applications. In this article, lattice Boltzmann simulations are conducted to examine the interfacial phenomena in liquid water transport in porous materials of a PEM fuel cell. Numerical results clearly indicate that large perforated pores through the porous diffusion layers can serve as a convenient liquid water transport pathway and thus assist in liquid water removal. An interconnected horizontal and vertical pore combination is especially beneficial to liquid water transport through the porous layers in flooding conditions. Therefore, liquid water transport in a PEM fuel cell may be effectively managed through well engineered interfacial structures in porous materials.     

Numerical study of two-phase flow patterns in the gas channel of PEM fuel cells with tapered flow field design

In this study the air–water two-phase flow in a tapered channel of a PEMFC was numerically simulated using the volume of fluid (VOF) method. In particular, a 3D mathematical model of the fuel cell flow channel was used to obtain a reliable evaluation of the fuel cell performance for different taper angles and different temperatures and to calculate the total amount of water produced. This information was then used as boundary conditions to simulate the two-phase flow in the cell channel through a 2D VOF model. Typical operating conditions were assigned and the numerical mesh was constructed to represent the real fuel cell configuration. The results show that tapering the channel downstream enhances the water removal due to increased airflow velocity. In the rectangular channel no film formation is noted with a marked predominance of slug flow. In contrast, as the taper angle is increased the predominant two-phase flow pattern is film flow. Finally many contact angles have been used to simulate the effect of the hydrophobicity of a GDL surface on the motion of the water. As the hydrophobicity of a GDL surface is decreased the presence of film is more evident even for less tapered channels.     

Numerical study of cell performance and local transport phenomena in PEM fuel cells with various flow channel area ratios

Three-dimensional models of proton exchange membrane fuel cells (PEMFCs) with parallel and interdigitated flow channel designs were developed including the effects of liquid water formation on the reactant gas transport. The models were used to investigate the effects of the flow channel area ratio and the cathode flow rate on the cell performance and local transport characteristics. The results reveal that at high operating voltages, the cell performance is independent of the flow channel designs and operating parameters, while at low operating voltages, both significantly affect cell performance. For the parallel flow channel design, as the flow channel area ratio increases the cell performance improves because fuel is transported into the diffusion layer and the catalyst layer mainly by diffusion. A larger flow channel area ratio increases the contact area between the fuel and the diffusion layer, which allows more fuel to directly diffuse into the porous layers to participate in the electrochemical reaction which enhances the reaction rates. For the interdigitated flow channel design, the baffle forces more fuel to enter the cell and participate in the electrochemical reaction, so the flow channel area ratio has less effect. Forced convection not only increases the fuel transport rates but also enhances the liquid water removal, thus interdigitated flow channel design has higher performance than the parallel flow channel design. The optimal performance for the interdigitated flow channel design occurs for a flow channel area ratio of 0.4. The cell performance also improves as the cathode flow rate increases. The effects of the flow channel area ratio and the cathode flow rate on cell performance are analyzed based on the local current densities, oxygen flow rates and liquid water concentrations inside the cell.