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The prediction capability of the two-fluid model for gas–liquid dispersed two-phase flow depends on the accuracy of the closure relations for the interfacial forces. In previous studies of two-phase flow Computational Fluid Dynamics (CFD), interfacial force models for a single isolated bubble has been extended to disperse two-phase flow assuming the effect in a swarm of bubbles is similar. Limited studies have been performed investigating the effect of the bubble concentration on the lateral phase distribution. Bubbles, while moving through the liquid phase, may undergo turbulence-driven random collision with neighboring bubbles without significant coalescence. The rate of these collisions depends upon the bubble approach velocity and bubble spacing. The bubble collision frequency is expected to be higher in locations with higher bubble concentrations, i.e., volume fraction. This turbulence-driven random collision causes the diffusion of the bubbles from high concentration to low concentration. Based on experimental observations, a phenomenological model has been developed for a “turbulence-induced bubble collision force” for use in the two-fluid model. For testing the validity of the model, two-phase flow data measured at Purdue University are utilized. The geometry is a 10 mm × 200 mm cross section channel. Experimentally, non-uniform inlet boundary conditions are applied with different sparger combinations to vary the volume fraction distribution across the wider dimension. Examining uniform and non-uniform inlet data allows for the influence of the volume fraction to be studied as a separate effect. The turbulence-induced bubble collision force has been implemented in ANSYS CFX. The assessment results show agreement with the measured data, correctly capturing the redistribution of volume fraction downstream with uniform and non-uniform inlet profiles. In particular, for the non-uniform data, the transverse redistribution of volume fraction at downstream locations is captured. This signifies the importance of bubble–bubble collision phenomena in correctly predicting volume fraction distributions. [ABSTRACT FROM AUTHOR]

In view of the practical importance of the interfacial area transport equation in flow analysis based on the two-fluid model, especially for flow analysis in a reactor core which has a relatively small channel configuration, the dominant mechanism in the interfacial area transport in small diameter pipes was firstly identified by evaluating the experimental data obtained for pressurized bubbly flows under microgravity, where the source and sink terms of the interfacial area concentration due to bubble expansion and wake entrainment collision are negligible. The sink term of the interfacial area concentration of bubbly flow in small diameter pipe was modeled in terms of the shear collision mechanism. The one-dimensional interfacial area transport equation with the developed sink term was evaluated by using 74 datasets obtained for adiabatic gas-liquid bubbly flows, including upward flows and microgravity flows in pipes with inside diameters of 9.0, 5.0 and 3.0 mm. A detailed discussion was provided on the interfacial area transport mechanism in small-diameter pipe. The overall standard deviation of the absolute error between predicted and measured interfacial area concentrations was 11.8%. The present model will reproduce the interfacial area transport of bubbly two-phase flows in small-diameter pipes with inside diameters of 3.0–9.0 mm, at superficial liquid and gas velocities over the ranges 〈 j f 〉 = 0.073–0.949 m/s, and 〈 j g 〉 = 0.00434–0.0500 m/s, and also over a wide range of axial distances, z / D = 5–188. [ABSTRACT FROM AUTHOR]

Downward two-phase flow is observed in light water reactor accident scenarios such as loss of coolant accident (LOCA) and loss of heat sink accident (LOHS) due to loss of feed water or a secondary pipe break. Hence, a comprehensive literature review has been performed for the co-current downward two-phase flow with information on the flow regime transitions and flow characteristics for each regime in the downward flow. The review compares the experimental data of the flow regime map and the current available transition models. Objectivity of the data varies on the method utilized as a certain degree of subjectivity is still present in the most objective method. Nevertheless, experimental data through subjective methods such as direct visualization or analysis of a wire mesh sensor (WMS) data were still studied in this review. Despite the wide range of flow regime data for numerous pipe sizes, a consensus was not reached for the effect of pipe sizes on flow regime transition. However, it is known that a larger pipe results in greater degree of coalescence at lower gas flow rates ( Hibiki et al., 2004 ). The introduction of a flow straightener at the inlet led to less coring and fluid rotation and inevitably, reduced bubble coalescence. This also resulted in the disappearance of the kinematic shock wave phenomenon, contrary to an inlet without a flow straightener. The effect of flow inlet, flow location, pipe diameter and bubble interfacial forces on the radial distribution as well as bubble coalescence and breakup rate are studied. Moreover, the interfacial area concentration and the bubble coalescence and breakup mechanisms are shown to vary in the axial direction as well as with flow rate, flow area and pressure drop. The liquid velocity field, bubble shape and shear stress are studied for a stationary slug bubble with downward liquid flow. Furthermore, the relationship between the plug and foam flow shape profiles, relative velocity, void fraction and gas slug velocity at an elevated pressure of 0.2 MPa studied by Sekoguchi et al. (1996) are also analyzed, together with the five plug flow sub-regime groups located in the low slip and high slip velocity regions. For the annular flow, the relationship between liquid film thickness, entrainment mechanisms, film velocity and shear stress are studied as well. Alike to plug flow, five sub-regimes in the annular flow are also examined along with the bubble and droplet entrainment mechanisms. The paper also discusses the pressure drop for bubbly, slug, foam, falling film and annular flow regimes, with a particular focus on the most accurate interfacial friction factor correlation for annular flow and its applicability for a wide range of pipe diameters. The flow instability of a system such as static and dynamic instability in the presence of a downcomer, for both single and parallel heated channels are examined too. Finally, the most accurate and versatile drift-flux correlation applicable to all downward flow regimes is highlighted and compared to drift-flux type correlations as it will be a stepping stone to attain a more accurate co-current downward flow transition model. Further experimental effort is essential to achieve a strong foothold in the understanding of co-current downward two-phase flow, as it is vital for nuclear engineering applications. [ABSTRACT FROM AUTHOR]

Highlights: [•] A scaled experimental facility is designed based on the sound scaling approach. [•] Starts up transients are performed to identify the instability phenomena. [•] Four heater rods are used to simulate the chaotic flashing phenomena. [•] Experiments are performed with and without void-reactivity feedback. [•] Modify power scaling is used for transient tests. [Copyright &y& Elsevier]

Highlights: [•] A scaled experimental facility is designed based on the sound scaling approach. [•] Experiments are performed to identify the instability phenomena. [•] Four heater rods are used to simulate the chaotic flashing phenomena. [•] Experiments are performed with and without void-reactivity feedback. [•] Stability maps are obtained at different system pressures. [Copyright &y& Elsevier]

Abstract: Time–volume averaged two-fluid model considering structural materials in a control volume (porous media approach) is formulated for two-phase flow analyses. The time–volume averaged two-fluid model is obtained rigorously by averaging local time-averaged two-fluid model over a control volume including structural materials. The volume porosity based model obtained by the simple time–volume averaging is converted into the surface porosity based model by introducing the directional surface porosity concept. The covariance approach is adopted to consider distributions of various variables in the control volume. The obtained porous media formulation is consistent with existing two-fluid model. Existing constitutive equations may be applicable to the porous media formulation provided they are properly time–volume averaged in the control volume. The strategy to obtain time–volume averaged constitutive equations is briefly discussed. [Copyright &y& Elsevier]

• Two-group interfacial area concentration models are implemented into TRAC-BF1 code. • Large and small interfacial area concentration models are developed for sensitivity analyses. • Sensitivity analyses of interfacial area effect on code predictions are conducted. • Sensitivity analyses include steady-state and transient flows and flow regime transition. • Interfacial area concentration has a minor effect on void fraction prediction in adiabatic flow. In one-dimensional two-fluid model-based codes, an interfacial drag force appears in a momentum conservation equation. The interfacial drag force is an essential parameter in predicting a void fraction. The accurate modeling of the interfacial drag force is indispensable for evaluating thermal–hydraulic characteristics in a nuclear reactor core. The interfacial drag force is formulated as the product of an 'overall' drag coefficient and the square of the relative velocity between gas and liquid phases. The 'overall' drag coefficient is expressed by the product of a drag coefficient, interfacial area concentration, and density of continuous phase. The rigorous model of the drag coefficient depending on a bubble shape regime has been established. The modeling of the interfacial area concentration depending on a flow regime is one of the weakest links in thermal–hydraulic analysis. The interfacial area transport equation was proposed to predict the dynamic change of the interfacial area concentration but has not reached a level accurate enough to predict the interfacial area concentration. Due to its incomplete development situation, an alternative way to predict the interfacial area concentration through a semi-theoretical interfacial area correlation has been proposed. This study aims to elucidate the effect of the interfacial area concentration on void fraction prediction in a one-dimensional thermal–hydraulic analysis. A one-dimensional two-fluid model-based code, such as TRAC-BF1, has been modified by implementing two existing constitutive equations of the interfacial area concentration into the code. This study also introduces large and small interfacial area concentration models of the interfacial area concentrations. The large and small interfacial area concentration models are designed to intentionally provide hypothetical large and small interfacial area concentrations within physically possible ranges. A total of four interfacial area concentration models is tested under adiabatic two-phase flow conditions. Code calculations with the four different models under steady-state and transient-state conditions and flow regime transitions have identified that the effect of the interfacial area concentration on the void fraction is insignificant for the adiabatic two-phase flows. The findings obtained in this study suggest that a simple interfacial area correlation is sufficient in modeling the interfacial drag force for adiabatic two-phase flows. However, robust and accurate modeling of the interfacial area concentration is still indispensable for two-phase flows with phase change because the interfacial heat transfer term in an energy conservation equation includes the interfacial area concentration. [ABSTRACT FROM AUTHOR]

• A two-phase flow structure in large-sized square channels (LSCs) was discussed. • Drift-flux analysis was performed with bubbly flow data in LSCs. • Correlations of void fraction and interfacial area in LSCs were recommended. • Frictional pressure drop calculation procedure in LSCs was recommended. • A criterion of developing length was recommended. Economic Simplified Boiling Water Reactor (ESBWR) concept has been proposed to improve the reactor safety feature. The core flow in ESBWR is driven by natural circulation induced by the difference between two-phase flow density in a partitioned chimney and single-phase flow density in a downcomer. The accurate prediction of the void fraction in the chimney is the key to calculate the two-phase flow density. The geometry of the partitioned chimney is a square channel with 0.61 m in the current ESBWR design, which is considered a large-sized square channel. Extensive research has been conducted for two-phase flows in large-sized circular channels, but the research for two-phase flows in large-sized square channels is very limited. In view of this, the current paper summarized the current understanding of the two-phase flow behavior in large-sized square channels and reviewed existing data collected in large-sized square channels. The two-phase flow parameters considered in the assessment were critical channel size at the boundary between medium and large-sized channels, developing length, void fraction, interfacial area concentration, flow regime transition, and frictional pressure drop. The assessment clearly indicated that experimental study in large-sized channels was very limited. Most datasets were collected in atmospheric air–water bubbly flows. Thus, the constitutive equations of two-phase flows were not fully evaluated. Some analytical studies for critical channel size and distribution parameter were introduced to give insight into the geometrical effect on the two-phase flow parameters. This paper strongly recommended collecting fundamental data. [ABSTRACT FROM AUTHOR]

• Downward two-phase flows were focused in relation to nuclear safety analyses. • Void fraction data and correlations of vertical downward two-phase flows were reviewed. • The predictive performance of existing correlations was evaluated with the collected databases. • A new drift-flux correlation was developed for vertical downward two-phase flows. • The new correlation achieved superior predictive performance to existing correlations. The two-fluid model has been adopted as a platform of nuclear thermal–hydraulic system analysis code because it can treat the mechanical and thermal non-equilibrium between phases through the interfacial transfer terms. Precise modeling of the area-averaged interfacial drag force in the interfacial momentum transfer term is essential in predicting void fraction accurately. The drift-flux parameters, such as the distribution parameter and drift velocity, play an essential role in formulating the area-averaged interfacial drag force. This study aims at developing a drift-flux correlation with a wide application range for vertical downward two-phase flows. First, over 1200 experimental void fraction data of vertical downward two-phase flows were collected from 13 sources. Then, the existing correlations of the distribution parameter and drift velocity were reviewed and examined. Finally, a new drift-flux correlation was developed based on a large amount of experimental data and state-of-the-art knowledge of two-phase flow behaviors. The comparison between the experimental and calculated void fractions by the newly-developed correlation demonstrated that the new correlation could achieve superior performance to the existing correlations. More than 93% of the predicted void fractions were predicted within ± 20% error with the mean relative deviation and mean absolute relative deviation of 0.609% and 9.93%, respectively. [ABSTRACT FROM AUTHOR]

Highlights • This paper provides several flow regime maps. • The development of flow regime along axial direction was studied. • The effect of two kinds of spacer grids on flow regime transition was investigated. • The existing flow regime transition criteria were verified by the obtained flow regime maps. • Some discrepancies have been discussed. Abstract In relation to the development of flow regime criteria for rod bundle geometry, this paper provides several experimental flow regime maps at different axial locations with simple and prototypic spacer grids, respectively. Experiments with vertical adiabatic air-water flow were conducted under an atmospheric pressure condition. The experiment facility was composed of 5 × 5 rod arranged on a square pitch in a square casing with 9.5 mm outside diameter and 12.6 mm pitch. The inlet superficial gas velocities range from 0.01 to 8.69 m/s, while inlet superficial liquid velocities range from 0.06 to 2.51 m/s. New flow regime maps were acquired at three axial locations of z / D H = 21.9, 58.4 and 107 through high-speed camera images. The experimental maps obtained were compared with the existing analytical models of flow regime transition criteria for vertical rod bundles. A reasonable agreement has been obtained between measured flow regime maps and models of the existing flow regime transition criteria for rod bundles at fully developed flow conditions. The different effects of two types of spacer grids on the flow regime transition were also discussed in this paper. [ABSTRACT FROM AUTHOR]

In engineering fields such as power generation systems (nuclear and thermal power plants), chemical processing, oil industry and so on, large-diameter channels have been extensively used to increase the mass, momentum and heat transport capability of the working fluid. Compared with small-diameter pipes, two-phase flow in the large-diameter channels shows more complicated flow characteristics. Much larger cap bubbles can exist and the interfacial instability prevents the large cap bubbles from forming large stable Taylor bubbles. So, the flow regimes and the radial void fraction profiles are different and the relative velocities between the two phases are significantly increased compared to those in small-diameter pipes. This paper reviews the recent progress in the research on two-phase flows in large-diameter channels. Recent progress on the state-of-the-art tool of four-sensor probe is explained and the necessary two-group bubbles can be classified through the measured bubble diameter, instead of the present method using bubble chord length, in 3-dimensional two-phase flow. The databases on the flows in large-diameter channels are presented and their typical multi-dimensional characteristics are discussed in detail. The most updated constitutive equations covering flow regime transition criteria, drift-flux correlations, interfacial area concentration (IAC) correlations and one- and two-group interfacial area transport equation(s) (IATE(s)) are summarized and their merits and drawbacks are analyzed. The important assumption that the area-averaged interfacial velocity weighted by IAC is equal to the area-averaged gas velocity weighted by void fraction in the 1D IATE has been confirmed by the present newly-obtained experimental data. The 1D numerical simulations of multi-dimensional two-phase flows in large-diameter channel are reviewed. Finally, the future research directions are suggested. [ABSTRACT FROM AUTHOR]

• Evaluated void prediction sensitivity to changes in interfacial area modeling method. • Evaluated interfacial area prediction sensitivity to changes in modeling method. • Updated constitutive models for IATE using surface response method. • New model improved IATE total interfacial area predictive accuracy. The nuclear industry requires accurate modeling efforts to ensure safety standards are consistently achieved. To that end, the sensitivity of void fraction and interfacial area concentration predictions to changes in the interfacial area concentration modeling methods was evaluated. Several interfacial area concentration correlations and interfacial area transport equation coalescence and breakup models have been compared to the data of Schlegel et al. and Shen et al. using a computational tool developed in MATLAB. Bubble coalescence and breakup empirical constants were optimized for the group void fractions and interfacial area concentrations using the computational tool and the surface response method. The results indicate that the transport equation approach has a higher accuracy for both the void fraction and interfacial area concentration predictions than the correlation approach. The Smith et al. model is shown to have the highest void fraction predictive accuracy. The optimized model is shown to successfully increase accuracy of the interfacial area concentration prediction. This is also the highest accuracy observed for interfacial area concentration predictions. [ABSTRACT FROM AUTHOR]

Highlights: [•] Discussion of boiling and wall nucleation dataset obtained in a vertical annulus. [•] Overview of the interfacial area transport equation modeling in boiling flow. [•] Comparison of bubble departure diameter and frequency with existing models. [•] Evaluation of the interfacial area transport equation prediction in boiling flow. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents experimental and modeling approaches in characterizing interfacial structures in gas–liquid two-phase flow. For the modeling of the interfacial structure characterization, the interfacial area transport equation proposed earlier has been studied to provide a dynamic and mechanistic prediction tool for two-phase flow analysis. A state-of-the-art four-sensor conductivity probe technique has been developed to obtain detailed local interfacial structure information in a wide range of flow regimes spanning from bubbly to churn-turbulent flows. Newly obtained interfacial area data in 8×8 rod-bundle test section are also presented. This paper also reviews available models of the interfacial area sink and source terms and existing databases. The interfacial area transport equation has been benchmarked using condensation bubbly flow data. [Copyright &y& Elsevier]

Abstract: A counterpart test to the Passive Nachwärmeabfuhr und Druckabbau Test Anlage (Passive Decay Heat Removal and Depressurization Test Facility, PANDA) International Standard Problem (ISP)-42 test was conducted at the Purdue University Multi-Dimensional Integral Test Assembly (PUMA) facility. Aimed to support code validation on a range of light water reactor (LWR) containment issues, the ISP-42 test consists of six sequential phases (Phases A–F) with separately defined initial and boundary conditions, addressing different stages of anticipated accident scenario and system responses. The counterpart test was performed from Phases A to D, which are within the scope of the normal integral tests performed on the PUMA facility. A scaling methodology was developed by using the PANDA facility as prototype and PUMA facility as test model, and an engineering scaling has been applied to the PUMA facility. The counterpart test results indicated that functions of passive safety systems, such as passive containment cooling system (PCCS) start-up, gravity-driven cooling system (GDCS) discharge, PCCS normal operation and overload function were confirmed in both the PANDA and PUMA facilities with qualitative similarities. [Copyright &y& Elsevier]

Abstract: An integral test simulating a postulated Small Break Loss Of Coolant Accident (SB LOCA) has been conducted on a scaled-down test facility, Purdue University Multi-Dimensional Integral Test Assembly (PUMA). This test aims to simulate the hypothetical Bottom Drain Line Break (BDLB) accident initialized by an instantaneous guillotine rupture of the vessel Bottom Drain Line (BDL) in a generic design of natural circulation BWR equipped with passive safety systems. The objective of this research is to evaluate the ability of passive safety systems in this BWR to keep core from uncover and containment from overpressure during a SB LOCA transient by reproducing the LOCA transient in the test facility. The integral test simulates the interaction of reactor components and demonstrates the functionality of passive safety systems, such as Emergency Core Cooling System (ECCS) and Passive Containment Cooling System (PCCS). The experimental results showed that the two most important safety criteria were satisfied: the core coolant level was always higher than the Top of Active Fuel (TAF) and containment pressure did not exceed the design limit during this SB LOCA. The scaling principle of the test facility and RELAP5/Mod3.3 code capability were evaluated through the comparison between the experimental data and the code simulation. [Copyright &y& Elsevier]