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• Methodology to estimate subchannel average flow parameters was developed. • Subchannel average two-phase flow parameters were obtained in an 8 × 8 rod bundle. • Operating parameter effects on the flow characteristics were found. • The distribution parameter model for the rod bundle was validated independently. • The drift velocity model for the rod bundle was validated independently. Two-phase flows in rod bundles or tube bundles appear in heat transfer systems. The bundle-average (or one-dimensional) void fraction is a critical parameter in overall system design, performance evaluation, and safety assessment. Accurate bundle-average void fraction prediction requires a precise interfacial momentum transfer term formulated using the distribution parameter and drift velocity, two essential drift-flux parameters in the drift-flux model. The currently utilized modeling approach is based on the distribution parameter and drift velocity determined together through drift-flux plots. This results in possible compensation errors between the distribution parameter and drift velocity in the model validation process. The independent validation of the constitutive equations for the distribution parameter and drift velocity has been challenging due to experimental difficulty in measuring detailed two-phase flow structures in rod bundles. The present study proposes an approximation methodology to obtain subchannel average two-phase flow parameters using local two-phase flow data measured at two local points: the subchannel center and minimum gap center in a rod bundle. The distributions of subchannel average two-phase flow parameters are invaluable in benchmarking subchannel analysis codes. Comprehensive subchannel average void fraction and gas velocity mappings are given to discuss the effects of gas and liquid velocities, pressure, spacer grid, and developing length on the two-phase flow characteristics in the rod bundle. The bundle-average distribution parameter values calculated by subchannel average two-phase flow parameters are used for independent validation of the constitutive equations of the distribution parameter. The bundle-average drift velocity values back-calculated using the distribution parameter values are also used for independent validation of the constitutive equation of the drift velocity. [ABSTRACT FROM AUTHOR]

Highlights • Heat transfer correlations of two-component two-phase flow in pipes were reviewed. • Heat transfer data of two-component two-phase flow in pipes were reviewed. • None of existing correlations could predict collected databases successfully. • The dependence of heat transfer coefficient on flow parameters was explained. • A heat transfer correlation was developed for two-component two-phase flow. Abstract The prediction of heat transfer coefficient for gas–liquid two-phase flows in vertical pipes is important for designing many industrial and engineering apparatuses such as nuclear power plants, solar collectors and petroleum pipelines. The mechanism of two-component two-phase heat transfer is more complicated than that of single-phase heat transfer. This study aims at developing a robust correlation of heat transfer coefficient for two-component two-phase slug flows in vertical pipes. The theoretical framework for the correlation development is inspired by considering classic Reynolds and Chilton–Colburn analogies. The framework demonstrates that the functional dependence of the two-component two-phase heat transfer coefficient on a void fraction or a two-phase multiplier is expressed by the Reynolds and Chilton–Colburn analogies. The correlation for the heat transfer coefficient of two-component two-phase slug flows in vertical pipes has been developed and validated by more than 200 existing data. The newly developed correlation predicts 95.1% of the collected two-phase heat transfer data within ± 30% error and the mean absolute relative deviation of the correlation is estimated to be 14.2%. The extended applicability of the newly developed correlation to other flow regimes such as bubbly, churn and annular flow regimes has been verified by the existing experimental data. The possible application of the newly developed correlation to large pipes is also discussed. In summary, it is expected that the newly developed correlation can predict the heat transfer coefficient of two-component two-phase flows under various conditions such as vertical upward and downward flows, developing and fully developed flows, laminar and turbulent flows and all two-phase flow regimes. The application of the correlation to vertical large pipes is also considered to be reasonable. [ABSTRACT FROM AUTHOR]

Steam submerged jet condensation has been widely used in many industry applications, especially in nuclear engineering. Since the heat and mass transfer varies with the condensation patterns as well as steam-water interface shapes, the identification and classification of the condensation regime is indispensable to conduct thermal-hydraulic analyses and to select adequate constitutive equations such as heat transfer coefficient. Different definitions and criteria have been used to classify the steam jet condensation regime. Due to the different transition criteria of condensation regime and multi-parameters’ effect, existing condensation regime maps do not agree each other. In this paper, unified criteria and definitions for each regimes have been proposed based on the dynamic behavior and geometrical shape of steam-water interface. The re-classified condensation regimes are chugging regime, hemispherical bubble oscillation regime, condensation oscillation regime, stable condensation regime and steam escape regime. The existing analytical model, empirical correlations and empirical map developed under different test section designs and test conditions failed to predict the existing experimental condensation regime transition boundaries. The discrepancy in the transition boundaries among existing experimental data is significant due partly to the subjective classification and complicated dependence on multiple parameters. Further efforts on both analytical and experimental researches are encouraged in the future. [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, and so, it is vital to have a thorough understanding of the flow mechanisms and regimes. With this point of view, flow regime transition criteria for vertical downward flow for a range of pipe diameters of 24–101.6 mm has been developed. Several models looked at the radial distribution of the bubbles and the wake effect of leading bubbles while others looked into the Kelvin-Helmholtz instability seen at the gas-liquid interface. The newly developed criteria have been compared to flow regime maps obtained via subjective and objective means, consisting of air-water data at atmospheric conditions as well as at an elevated pressure of 0.2 MPa. The new model is also compared to flow regime maps developed with different inlet conditions. Overall, the present model showed good agreements with the available data, with the exception of several 50.8 mm ID flow regime maps of different inlet conditions as well as a self-organizing neural network. This study also highlights the need for a more objective and consistent flow regime map data for large diameter pipes, the identification of cap-bubbly and churn-turbulent flows in these maps, and the deviations observed between a supervised and self-organizing neural network (SONN). [ABSTRACT FROM AUTHOR]

The demand of accurate prediction for two-phase flow behavior in a nuclear reactor core composed of fuel rod bundles or a heat exchanger composed of heat transfer tube bundles requires comprehensive understanding of flow regime, void fraction, heat transfer and pressure drop. In comparison with the great success in developing the two-phase flow regime transition criteria for simple geometries such as pipes, annulus and rectangular channels, limited researches have been performed for developing the flow regime transition criteria of upward two-phase flow in vertical rod bundles. In the vertical rod bundles, slug bubbles spanning the bundle casing cannot exist due to their surface instability and the two-phase flow characteristics in the vertical rod bundles are different from those in pipes, annulus or rectangular channels whose channel size are smaller than the length scale of the surface instability. This study has proposed a new flow regime transition criteria model based on the analysis on the underlying physics of the upward two-phase flow behavior in the vertical rod bundles. A reliable drift-flux correlation to predict void fraction in the vertical rod bundle developed recently has been used in modeling the flow regime transition criteria. This study has classified the flow regime into 6 distinct flow regime such as bubbly, finely dispersed bubbly, cap-bubbly, cap-turbulent, churn and annular flows. The newly developed flow regime transition criteria have been compared with existing 4 flow regime maps obtained in vertical rod bundles. The fluid systems include air-water and steam-water. A fairly good agreement with some discrepancies has been obtained between the newly developed transition criteria and the measured flow regime maps. [ABSTRACT FROM AUTHOR]

A steam generator thermal-hydraulic code based on homogeneous flow model has been useful based on its numerical stability and simpler formulation. One of key parameters for a steam generator thermal-hydraulic analysis is void fraction which determines two-phase mixture density and affects two-phase mixture velocity. These parameters are important for a heat transfer tube vibration analysis. A void fraction-quality correlation is very important to accurately convert the quality into the void fraction. The void fraction-quality correlation should preferably be applicable to parallel and cross flows in rod or tube bundles since two-phase flow in the steam generator encounters flow configuration change from the parallel flow along the tube bundle in the riser section of the steam generator to the cross flow in the U-bend section of the steam generator. A set of correlations depending on flow configuration such as parallel and cross flows, rod or tube array pattern and mass flux is developed based on legacy Smith correlation. The correlation agrees with the parallel and cross flow data with the mean absolute error (or bias) of 0.117% and the standard deviation (random error) of 2.26% and with the mean absolute error (or bias) of 0.760% and the standard deviation (random error) of 6.21%, respectively. The correlations are further simplified to a single correlation applicable for parallel and cross flow in rod or tube bundles. The Smith correlation with a modified constant entrainment parameter e being 0.5 is recommended for predicting void fraction in the steam generators. The Smith correlation with e = 0.5 is expected to be applicable for parallel and cross flows with various rod or tube array patterns including normal square, parallel triangular and normal triangular arrays. [ABSTRACT FROM AUTHOR]

Abstract: From the significance of three-dimensional simulation of dispersed flow systems in many engineering fields, extensive study was conducted for lift force in a single particle system as well as a multiparticle system. In this study, the lift force in a single particle system was modeled by considering the effect of bubble deformation on the lift force. The model was finalized based on existing data obtained in the range of particle Reynolds number from 3.68 to 78.8, viscous number from 0.0435 to 0.203 and Eötvös number from 1.40 to 5.83. The viscous number is defined by where , , , and are, respectively, fluid viscosity, fluid density, surface tension, gravitational acceleration and density difference between phases. The applicability of the model to higher particle Reynolds number system such as an air–water system was qualitatively examined. The lift force model developed in a single particle system was extended to a multiparticle system. The applicability of the extended lift force model was qualitatively examined. The similarity between drag and lift forces were also discussed. [Copyright &y& Elsevier]

Abstract: The interfacial area, which describes available area for the interfacial transfer of mass, momentum and energy, is a crucial parameter in a two-fluid model formulation. From this point of view, this study performed (i) extensive survey on existing models and correlations developed for boiling bubbly flows, (ii) extensive survey on existing interfacial area database for boiling bubbly flows, (iii) formulation of the physical model based on bubble number density transport equation, (iv) simplification of the model to identify the dominant parameters governing the interfacial area, and (v) finalization of the model based on the collected extensive data and development of the interfacial area correlation. The developed correlation of the interfacial area concentration agreed with 569 adiabatic flow data and 343 boiling flow data within averaged relative deviations of and , respectively. [Copyright &y& Elsevier]

In view of significance of a heat transfer correlation of flow boiling under the conditions of low liquid Reynolds number or liquid laminar flow, and very few correlations in principle suitable for such flow conditions, this study is aiming at developing a heat transfer correlation of flow boiling at low liquid Reynolds number for small diameter channels. The correlation is developed based on superimposition of two main flow boiling mechanisms, namely nucleate boiling and forced convection. In the correlation, two terms corresponding to nucleate boiling and forced convection are obtained from the pool boiling correlation by Forster and Zuber and the analytical annular flow model by Hewitt and Hall-Taylor, respectively. An extensive comparison with a collected database indicates that the developed correlation works satisfactorily with mean deviation and rms errors of 19.1% and 24.3%, respectively, under many experimental conditions such as different channel geometries (circular and rectangular) and flow orientations (vertical and horizontal)for some test fluids (water, R11, R12, and R113). A detailed discussion reveals that existing correlations for turbulent flow boiling such as Chen's correlation, Schrock and Grossman's correlation, and Dengler and Addoms's correlation may be derived from a generalized form of the newly developed correlation. [ABSTRACT FROM AUTHOR]

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. [Copyright &y& Elsevier]

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]

The effect of heated length on critical heat flux (CHF) in thin rectangular channels under atmospheric pressure has been studied. CHF in small channels has been widely studied in the last decades but most of the studies are based on flow in round tubes and number of studies focused on rectangular channels is relatively small. Although basic triggering mechanisms, which lead to CHF in thin rectangular channels, are similar to that of tubes, applicability of thermal hydraulic correlations developed for tubes to rectangular channels are questionable since heat transfer in rectangular channels are affected by the existence of nonheated walls and the noncircular geometry of channel circumference. Several studies of CHF in thin rectangular channels have been reported in relation to thermal hydraulic design of research reactors and neutron source targets and correlations have been proposed, but the studies mostly focus on geometrical conditions of the application of interest and therefore effect of channel parameters exceeding their interest is not fully understood. In his study, CHF data for thin rectangular channels have been collected from previous studies and the effect of heated length on CHF was examined. Existing correlations were verified with data with positive quality outlet flow but none of the correlations successfully reproduced the data for a wide range of heated lengths. A new CHF correlation for quality region applicable to a wide range of heated lengths has been developed based on the collected data. [ABSTRACT FROM AUTHOR]

Abstract: Axial developments of the local void fraction, interfacial area concentration and bubble Sauter mean diameter were measured in subcooled boiling flow of water in a vertical internally heated annulus using the double-sensor conductivity probe technique. Measurements were performed under varying conditions of heat flux, inlet liquid velocity and inlet liquid temperature. A total of 10 data sets were acquired. Based on these measurements with the previous data obtained in the present test loop, the influence of flow condition on the profiles of local two-phase flow parameters was discussed. The measured average void fraction and interfacial area concentration were compared with the predictions by existing correlations for drift-flux parameters and interfacial area concentration. Also, the recently proposed bubble layer thickness model in subcooled boiling was evaluated for the measurement data. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Accurate prediction of the interfacial area concentration is essential to successful development of the interfacial transfer terms in the two-fluid model. The interfacial area concentration in annular flow and annular-mist flow is especially relevant to the transition process to the liquid film dryout, which might lead to fatal problem in the safety and efficient operation of boiling heat transfer system. However, very few experimental and theoretical studies focusing on the interfacial area concentration in annular flow region have been conducted. From this point of view, measurements of annular flow parameters such as one-dimensional interfacial area concentration of liquid film and local interfacial area concentration profile of liquid film were performed by a laser focus displacement meter at 21 axial locations in vertical upward annular two-phase flow using a 3-m-long and 11-mm-diameter pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D =50–250. Data were collected for preset gas and liquid flow conditions and for Reynolds numbers ranging from 31,800 to 98,300 for the gas phase and 1050 to 9430 for the liquid phase. Axial development of the one-dimensional interfacial area concentration and the non-dimensional local interfacial area concentration profile of liquid film were examined with the data obtained in the experiment. Total interfacial area concentration including liquid film and droplets was also discussed with help of the existing drift-flux model, entrainment correlation, and droplet size correlation. [Copyright &y& Elsevier]

• Steam-Water Condensing-Injector (SI)'s pressure elevation mechanism was investigated through experiment • Experiments were carried out to obtain axial pressure and temperature profiles of central-water jet SI. • SI's heat transfer capability under steam-water direct contact condensation was assessed. • One-dimensional analytical model was implemented to assess SI's axial pressure distribution. The steam-water condensing injector (SI) is a device capable of producing high-pressure subcooled liquid streams by combining steam and subcooled liquid jet at a higher pressure than the inlet streams. The present study investigated the SI's pressure elevation mechanism using supersonic steam and a subcooled water jet. The experiment was carried out using central-water jet type SI equipped with an overflow port at the inlet steam pressures of 0.3 to 0.7 MPa and inlet liquid mass flow rates of 0.4 to 0.7 kg/s. Axial pressure and temperature distributions were measured at the mixing nozzle and diffuser sections to study the pressure elevation mechanism. Based on the analytical foundation laid by Grolmes (1968), the one-dimensional analytical model was implemented by treating SI's two-phase flow regimes as inverted annular and dispersed flows. For the current SI geometry and operating conditions, the present one-dimensional model could predict the axial pressure distribution of the SI and the maximum discharging pressure with reasonable accuracy for sufficiently high inlet flowrate ratio conditions. [ABSTRACT FROM AUTHOR]

In this paper, experimental investigation of the molten metal jet's colliding and spreading behaviors on the flat steel surface covered with water layer was carried out. High-frequency induction heating system was utilized to produce the molten metal sample and it was released to the wet surface from a fixed elevation. As the molten metal collides against the surface, it rapidly goes through solidification while spreading on the wet surface. High-speed thermo-camera was utilized to measure the molten metal's surface temperature during the spreading transient. Once the molten metal completely solidifies, molten metal's spread area and thickness were measured. From the obtained database, a dimensional analysis was conducted to investigate the key parameters responsible for the molten metal spreading on the wet surface. Based on the key non-dimensional parameters identified in the current analysis, the new empirical correlation was proposed. Its predictive capability was found to be 18.9% in mean absolute relative deviation. [ABSTRACT FROM AUTHOR]

A new interpretation of the characteristic area and frequency appearing in the wall nucleation source from the point of view of the stochastic nature of this phenomenon is presented in this paper. This analysis shows important drawbacks in the standard interpretation of these terms, such as a strong bias in the characteristic area and high sensitivity to experimental conditions for the frequency. Finally, methods to improve the measurement of the corresponding mean values as well as estimators for their uncertainties based on the definition of a generalized probability density function (PDF) are provided. [ABSTRACT FROM AUTHOR]

Abstract: In an effort to improve the prediction of void fraction and heat transfer characteristics in two-phase systems, closure relations to the one-dimensional modified two-fluid model are addressed. The drift-flux general expression is extended to two bubble groups in order to describe the void weighted mean gas velocities of spherical/distorted (group-1) bubbles and cap/slug/churn-turbulent (group-2) bubbles. Therefore, correlations for group-1 and group-2 distribution parameters and drift velocities are proposed and evaluated with experimental data. Furthermore, the covariance in the convective flux of the one-dimensional two-fluid model is addressed and interpreted with the available database. The dataset chosen for evaluation of the two-group drift-flux general expression contains 126 total data points taken in an annulus geometry. The proposed distribution parameters show an agreement within ±4.9% and ±1.2% for group-1 and group-2 data, respectively. The overall estimation of group-1 and group-2 void weighted mean gas velocity calculated with the newly proposed two-group drift-flux general expression shows an agreement of ±11.8% and ±17.7%, respectively. [Copyright &y& Elsevier]