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This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas–liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas–liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equation in the confined flow. These models include both intra-group and inter-group bubble interactions.

The bubble interaction mechanisms have been analytically modeled in the first paper of this series to provide mechanistic constitutive relations for the two-group interfacial area transport equation (IATE), which was proposed to dynamically solve the interfacial area concentration in the two-fluid model. This paper presents the evaluation approach and results of the two-group IATE based on available experimental data obtained in confined upward flow, namely, 11 data sets in or near bubbly flow and 13 sets in cap-turbulent and churn-turbulent flows. The two-group IATE is evaluated in steady-state, one-dimensional (1D) form. To account for the inter-group bubble transport, the void fraction transport equation for Group-2 bubbles is also used to predict the void fraction for Group-2 bubbles. Agreement between the data and the model predictions is reasonably good and the average relative difference for the total interfacial area concentration between the 24 data sets and predictions is within 7%. The model evaluation demonstrates the capability of the two-group IATE focused on the current confined flow to predict the interfacial area concentration over a wide range of flow regimes.

The objective of the present work is to study and model the interfacial structure development of air–water two-phase flow in a confined flow passage. Experiments of a total of 13 flow conditions in cap-turbulent and churn-turbulent flow regimes are carried out in a vertical air–water upward two-phase flow experimental loop with a test section of 200 mm in width and 10 mm in gap. Miniaturized four-sensor conductivity probes are used to measure local two-phase parameters at three different elevations for each flow condition. Bubble characteristics captured by the probes are categorized into two groups in view of the two-group interfacial area transport equation, i.e., spherical/distorted bubbles as Group 1 and cap/churn-turbulent bubbles as Group 2. The acquired local parameters are time-averaged void fraction, interfacial velocity, bubble number frequency, interfacial area concentration, and bubble Sauter mean diameter for each group of bubbles. Also, the line-averaged and area-averaged data are presented and discussed in detail. The comparisons of these parameters at different elevations demonstrate the development of interfacial structures along the flow direction due to bubble interactions and the hydrodynamic effects. Furthermore, these data can serve as one part of the experimental data for investigation of the interfacial area transport in a confined two-phase flow.

The interfacial area transport equation applicable to the bubbly flow is presented. The model is evaluated against data acquired by a state-of-the-art miniaturized double-sensor conductivity probe in an adiabatic air–water co-current vertical test loop under atmospheric pressure condition. In general, a good agreement, within the measurement error of ±10%, is observed for a wide range in the bubbly flow regime. The evaluation of the individual particle interaction mechanisms demonstrates the active interactions between the bubbles and highlights the mechanisms playing the dominant role in interfacial area transport. The analysis employing the drift flux model is also performed for the data acquired. Under the given flow conditions, the distribution parameter of 1.076 yields the best fit to the data.

The interfacial structure of the two-phase flows is of great importance in view of theoretical modeling and practical applications. In the present study, the focus is made on obtaining detailed local two-phase flow parameters in the air–water bubbly flow in an adiabatic rectangular vertical duct using the double-sensor conductivity probe. The characteristic wall peak is observed in the profiles of the interfacial area concentration and the void fraction. The development of the interfacial area concentration along the axial direction of the flow is studied in view of the interfacial area transport and bubble interactions. The experimental data is compared with the drift flux model with C0=1.35.

Two-fluid model predictions of film dryout in annular flow are limited by the uncertainties in the entrainment rate of droplets from the liquid film. The main cause of these uncertainties is the lack of separate effects experimental data in the range of the operating conditions in industrial applications. Air–water and Freon-113 entrainment rate data have been obtained in 10 mm tubes using the double film extraction technique. These experiments have been scaled to approach high-pressure steam–water flow conditions. The effects of surface tension and density ratio, missing from most previous data sets, have been systematically tested. The entrainment rate mechanism is scaled by the Kelvin–Helmholtz instability at the film surface. Based on this analysis and the new data, a new correlation is proposed that is valid for low-viscosity fluids in small ducts in the ripple-annular regime.

High pressure steam–water annular flow was simulated with scaled air–water and Freon-113 experiments. A unique Freon-113 loop was built to obtain low surface tension and high vapor density data on entrainment fraction. The results were compared with two correlations available in the open literature. The Ishii and Mishima correlation was capable to collapse the data for air–water, Freon-113 and steam–water experiments satisfactorily. However the correlation needs to be adjusted for high Weber numbers of the gas phase. The data was limited to the ripple-annular regime because the film extraction technique is not reliable when the film becomes frothy.

In the two-fluid model, interfacial concentration is one of the important parameters. The objective of this study is to develop an interfacial area equation with the source and sink terms being properly modeled. For bubble coalescence, the random collisions between bubbles due to turbulence, and the wake entrainment process due to the relative motions of the bubbles, were included. For bubble breakup, the impact of turbulent eddies is considered. Compared with measured axial distributions of the interfacial area concentration under various flow conditions, the adjustable parameters in the source/sink terms were obtained for the simplified one-dimensional transport equation.

Two-fluid model predictions of film dryout in annular flow, leading to nuclear reactor fuel failure, are limited by the uncertainties in the constitutive relations for the entrainment rate of droplets from the liquid film. The main cause of these uncertainties is the lack of separate-effects experimental data in the range of the operating conditions in nuclear power reactors. An air–water experiment has been performed to measure the entrainment rate in a small pipe. The current data extend the available database in the literature to higher gas and liquid flows and also to higher pressures. The measurements were made with the film extraction technique. A mechanistic model was obtained based on Kelvin–Helmholtz' instability theory. The dimensionless model includes the Weber number of the gas and the liquid film Reynolds number. Kataoka and Ishii's correlation (Kataoka, I., Ishii, M., 1982. NUREG/CR-2885, ANL-82-44) is modified based on this model and the new data. The new correlation collapses the present air–water data and Cousins and Hewitt's data (Cousins, L.B., Hewitt, G.F., 1968. UKAEA Report AERE-R5657) The effects of pressure and surface tension were considered in the derivation so it may be applied for boiling water reactor operating conditions.