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This study focusses on investigating the effect of flow orientation on global and local two-phase flow parameters under two-phase flow conditions. Flow visualization, pressure measurement, and conductivity probe measurements are performed in a test facility made of 50.8 mm inner diameter acrylic pipes with flow visualization, pressure measurement, and conductivity probe measurement. Characteristics of flow regimes and interfacial structures, and frictional pressure drop prediction in the vertical upward and vertical downward two-phase flows are compared and analyzed. The results show that unique coring phenomenon and slug bubbles with off-centered noses appear in the vertical downward flow. The flow regime transition boundaries shift to the lower gas superficial velocities in the vertical downward flow compared to that in the vertical upward flow. Furthermore, the distribution and one-dimensional transport of the void fraction, interfacial area concentration, bubble velocity, bubble Sauter-mean diameter, and bubble frequency are acquired and compared to study the effect of flow orientation on interfacial structures. The interfacial structure and its development are found to be mainly affected by the lift force and the turbulence related bubble interactions. The frictional pressure drop is acquired and modeled by the Lockhart–Martinelli correlation. The frictional pressure drop is found to be larger in the vertical upward flow than that in the vertical downward flow. The recommended C value for both vertical upward and vertical downward flows are proposed.

The current work performs air-water experiments in three different pipe sizes of 38 mm, 51mm, and 102 mm to investigate the frequencies of plug and slug bubbles in horizontal flows. The local four-sensor conductivity probe is used to establish experimental data for large elongated bubbles. The investigated conditions focus on a relatively high superficial liquid velocity region (1.0 m/s ≤ jf ≤ 4.0 m/s), where limited experimental data are available in the literature. The investigated superficial gas velocity (jg) ranges from 0.19 m/s to 3.0 m/s. In total, 19 conditions are studied. To identify the elongated plugs and slugs, the local four-sensor conductivity probe is located near the top wall. Based on the flow visualization study, the stable plug and slug bubbles cannot be shorter than a pipe diameter. Therefore, a chord length greater than a pipe size is used as a criterion to pick up the elongated plug and slug bubbles. Using the obtained data, the frequencies of plug and slug bubbles are analyzed. For the investigated conditions, the Strouhal number (St) ranges from 0.03 to 1.68, while the St of the existing data in the literature are generally below 0.1. It is found that the frequency of elongated bubbles increases as jf increases, but first increases then decreases as jg increases. This indicates that large elongated bubbles start to coalesce once jg reaches a certain value. This threshold has a higher value of jg than the plug to slug transition point. In addition, the frequency decreases as pipe size increases. The existing correlations in the literature are evaluated using the newly collected data. It is found that the St number-based correlations can predict the data with higher accuracy. New correlations are developed using the new data and they can predict the frequency with an absolute average percentage difference of ±20%.

The current work seeks to perform the one-dimensional drift-flux analysis for horizontal gas-dispersed flow, to provide closure models for void fraction and to investigate the relative motion between gas and liquid phases. A reliable experimental database for void fraction and bubble velocity is first established over a wide range of flow conditions for bubbly, plug and slug flows in different pipe sizes, due to the limitations of existing database. It is found that the effects of flow regime and pipe size on the drift-flux analysis are insignificant. The drift velocity is found to be negative in horizontal bubbly flow. This is consistent with the conclusion by the 〈α〉–〈β〉 analysis, where the slope is found to be greater than one. This indicates that the gas phase moves slower than the liquid phase in horizontal bubbly flow. The analysis also indicates that the horizontal plug and slug flows are relatively more homogeneous than horizontal bubbly flow. As such, the homogeneous flow model can predict the void fraction better for plug and slug flows. The current drift-flux analysis provides closure relations for C0 and 〈〈Vgj〉〉 that can be employed in TRACE, while existing closure relations are developed for vertical flow and cannot be used for horizontal flow prediction. In addition, various void fraction models in literature are evaluated. It is found that the correlations modified from vertical flow generally cannot predict the void fraction well for horizontal flow. The correlations for plug and slug flows by Franca and Lahey, and Lamari underestimate the void fraction, which may be because these correlations are developed for relatively low jf conditions, while the current work focuses on conditions at jf greater than 2.0 m/s.

This paper performs experimental studies to investigate the effects of pipe size on horizontal air–water two-phase flow in a wide range of flow configurations. Some of the major characteristic two-phase flow phenomena of interest include flow regime transitions, two-phase frictional pressure drop, local interfacial structures, and drift-flux analysis. Based on the experimental results obtained in two pipe sizes, the flow regime maps and the correlations for two-phase frictional pressure drop employed in conventional nuclear reactor system analysis codes (TRACE and RELAP) are evaluated. It is found that the flow regime maps in the codes incorrectly predict plug and slug flows as bubbly flow. Effects of pipe size on flow regime transitions are observed, while these effects are not reflected on the maps employed in the codes. The frictional pressure drop analysis suggests that the closure relations used in both TRACE and RELAP can be improved for horizontal two-phase flow. The local time-averaged two-phase flow parameters acquired by a four-sensor conductivity probe including void fraction, interfacial area concentration, bubble velocity, and bubble Sauter-mean diameter provide quantitative descriptions for the interfacial structures in different pipe sizes. It is found that increasing the pipe size tends to cause bubbles to be more concentrated near the top wall in bubbly flow. As a result, the bubble layer occupies a smaller portion of the flow area as pipe diameter increases. Based on the experimental database, drift-flux analysis using both the 〈〈vg〉〉 vs. 〈 j〉 and 〈α〉 vs. 〈β〉 methods is performed. The effect of pipe size on drift-flux analysis is found to be negligible. The global slip is found to be less than one, indicating that the gas phase moves slower than the liquid phase in horizontal bubbly flow. This analysis also provides a predictive method to estimate the void-weighted bubble velocity and void fraction, which can be predicted with an average percent difference of ±3.3% and ±3.1%, respectively.

This study performs an experimental investigation of frictional pressure drop in air–water two-phase flows in straight pipes. A reliable experimental database for the two-phase pressure drop and void fraction is established with a differential pressure transducer and a four-sensor conductivity probe, respectively. The two-phase flow investigated focuses on gas-dispersed flow regimes in different pipe diameters of 38.1 mm, 50.8 mm, and 101.6 mm. Systematic study on the effects of flow orientation, flow regime and pipe size is performed. The most commonly used predictive models for the two-phase frictional pressure drop are evaluated with the newly established database and the existing databases found in the literature. It is demonstrated that both the conventional Lockhart-Martinelli approach and the ϕ f – correlation can generally predict the two-phase frictional pressure drop very well with different suggested values of coefficients C and n for different flow orientations, based on the established data. Meanwhile, the results show that the values of C and n are independent of the pipe size and the flow regime. The homogeneous flow model is evaluated with four β (ratio of volumetric flow rates) based mixture viscosity correlations. The predictions with the Beattie and Whalley mixture viscosity correlation are found to be the best regardless of the flow orientation. The Lockhart-Martinelli approach with the coefficient C calculated by correlation employed in the nuclear system analysis code RELAP5-3D and the Muller-Steinhagen and Heck correlation are also evaluated. It is found that these two modeling approaches as well as the homogeneous flow model tend to underestimate most of the experimental data. Improvements for pressure drop prediction in nuclear reactor safety analysis codes are observed.

The current work seeks to investigate the interfacial structure and establish an extensive experimental database in horizontal air–water two-phase flow in a 101.6 mm inner diameter pipe. A wide range of flow configurations are studied including bubbly, plug and slug flows. A flow visualization study using the high-speed video camera enables qualitative description of bubbly-to-plug and bubbly-to-slug transitions, while the database of local time-averaged two-phase flow parameters obtained by the four-sensor conductivity probe enables quantitative study on the evolution of the flow. Detailed measurements across the flow area are performed for nine test conditions at three different axial locations downstream of the inlet. Using this database, the effects of superficial liquid and gas velocities, and development length on the evolution of interfacial structure are investigated. Similar characteristics are observed as in a counterpart 38 mm ID horizontal two-phase flow facility, which include (1) the bubbles are found to be more concentrated near the top wall in bubbly flow as superficial liquid velocity decreases at a constant superficial gas velocity, while increasing superficial gas velocity promotes the growth of bubble layer thickness; (2) in bubbly-to-plug transition, the void fraction of small bubbles decreases and the size of small bubbles increases, while in bubbly-to-slug transition, opposite trends are observed. Meanwhile, different characteristics on the evolution of the interfacial structure are also observed, which indicates the effect of increasing pipe diameter. The bubbly-to-plug/slug transition is found to shift to higher superficial liquid velocities as pipe diameter increases. It is observed that the gas phase is more concentrated near the top wall in the large diameter pipe. As a result, the distance between bubbles is smaller and there is a higher chance for bubbles to coalesce into large bubbles. The critical void fraction where the bubbly-to-plug/slug transition initiates decreases as pipe size increases.

The present study seeks to investigate horizontal bubbly-to-plug and bubbly-to-slug transition flows. The two-phase flow structures and transition mechanisms in these transition flows are studied based on experimental database established using the local four-sensor conductivity probe in a 3.81 cm inner diameter pipe. While slug flow needs to be distinguished from plug flow due to the presence of large number of small bubbles (and thus, large interfacial area concentration), both differences and similarities are observed in the evolution of interfacial structures in bubbly-to-plug and bubbly-to-slug transitions. The bubbly-to-plug transition is studied by decreasing the liquid flow rate at a fixed gas flow rate. It is found that as the liquid flow rate is lowered, bubbles pack near the top wall of the pipe due to the diminished role of turbulent mixing. As the flow rate is lowered further, bubbles begin to coalesce and form the large bubbles characteristic of plug flow. Bubble size increases while bubble velocity decreases as liquid flow rate decreases, and the profile of the bubble velocity changes its shape due to the changing interfacial structure. The bubbly-to-slug transition is investigated by increasing the gas flow rate at a fixed liquid flow rate. In this transition, gas phase becomes more uniformly distributed throughout the cross-section due to the formation of large bubbles and the increasing bubble-induced turbulence. The size of small bubbles decreases while bubble velocity increases as gas flow rate increases. The distributions of bubble size and bubble velocity become more symmetric in this transition. While differences are observed in these two transitions, similarities are also noticed. As bubbly-to-plug or bubbly-to-slug transition occurs, the formation of large elongated bubbles is observed not in the uppermost region of bubble layer, but in a lower region. At the beginning of transitions, relative differences in phase velocities near the top of the pipe cross-section to those near the pipe center become larger for both gas and liquid phases, because more densely packed bubbles introduce more resistance to both phases.

This paper focuses on investigating the geometric effects of inlets on global and local two-phase flow parameters in vertical-downward air–water two-phase flow. Flow visualization, frictional pressure loss analysis, and local experiments are performed in a test facility constructed from 50.8 mm inner diameter acrylic pipes. Three types of inlets of interest are studied: (1) two-phase flow injector without a flow straightener (Type A), (2) two-phase flow injector with a flow straightener (Type B), and (3) injection through a horizontal-to-vertical-downward 90° vertical elbow (Type C). A detailed flow visualization study is performed to characterize flow regimes including bubbly, slug, churn-turbulent, and annular flow. Flow regime maps for each inlet are developed and compared to identify the effects of each inlet. Frictional pressure loss analysis shows that the Lockhart–Martinelli method is capable of correlating the frictional loss data acquired for Type B and Type C inlets with a coefficient value of C = 25, but additional data may be needed to model the Type A inlet. Local two-phase flow parameters measured by a four-sensor conductivity probe in four bubbly and near bubbly flow conditions are analyzed. It is observed that vertical-downward two-phase flow has a characteristic center-peaked void profile as opposed to a wall-peaked profile as seen in vertical-upward flow. Furthermore, it is shown that the Type A inlet results in the most pronounced center-peaked void fraction profile, due to the coring phenomenon. Type B and Type C inlets provide a more uniform distribution of the void fraction profile with a reduced coring effect.

This paper presents experimental studies performed to characterize horizontal air–water two-phase flow in a round pipe with an inner diameter of 3.81 cm. A detailed flow visualization study is performed using a high-speed video camera in a wide range of two-phase flow conditions to verify previous flow regime maps. Two-phase flows are classified into bubbly, plug, slug, stratified, stratified-wavy, and annular flow regimes. While the transition boundaries identified in the present study compare well with the existing ones (Mandhane et al., 1974) in general, some discrepancies are observed for bubbly-to-plug/slug, and plug-to-slug transition boundaries. Based on the new transition boundaries, three additional test conditions are determined in horizontal bubbly flow to extend the database by Talley et al. (2015a). Various local two-phase flow parameters including void fraction, interfacial area concentration, bubble velocity, and bubble Sauter mean diameter are obtained. The effects of increasing gas flow rate on void fraction, bubble Sauter mean diameter, and bubble velocity are discussed. Bubbles begin to coalesce near the gas–liquid layer instead of in the highly packed region when gas flow rate increases. Using all the current experimental data, two-phase frictional pressure loss analysis is performed using the Lockhart–Martinelli method. It is found that the coefficient C = 24 yields the best agreement with the data with the minimum average difference. Moreover, drift flux analysis is performed to predict void-weighted area-averaged bubble velocity and area-averaged void fraction. Based on the current database, functional relations for ≪ v g ≫ vs. j > and α > vs. j g >/ j > have been studied. It is found that ≪ v g ≫ – j > method predicts the void-weighted area-averaged bubble velocity and area-averaged void fraction better compared to α > – j g >/ j > method.

This study develops a one-group interfacial area transport equation (IATE) for vertical-upward-to-horizontal air–water bubbly two-phase flows through a 90° elbow with a non-dimensional centerline radius of curvature of three. In order to develop the model, an extensive database is established by acquiring local two-phase flow parameters using a four-sensor conductivity probe upstream and downstream of the elbow. The data show there exist three characteristic regions in void distribution, including a bimodal-to-bimodal region, a bimodal-to-single-peaked region, and a developed horizontal flow region with void accumulated at the top of the pipe cross-section. Using the database, the preliminary dissipation length model developed by Yadav et al. (2014b) is improved by including the transition region near the exit of the elbow in addition to the dissipation region. To close the IATE model, the bubble velocity advection term and bubble interaction terms in the IATE are correlated with the parameter characterizing the “elbow-strength”. The two-phase pressure drop across the elbow is modeled using the modified Lockhart–Martinelli correlation which takes into account the minor loss effect. The closed IATE model is implemented to predict interfacial area transport in vertical-upward-to-horizontal two-phase flow. It is found that the developed model is capable of predicting interfacial area concentration with an average percent difference of less than ±6%.

While significant efforts have been made to investigate two-phase flows in vertical upward channels, limited work has been performed to study the effects stemming from geometric configurations on two-phase flow transport, such as flow restrictions and change in flow orientation. This presents significant shortcomings in the application of predictive models to practical systems, including nuclear power reactors. It has been well observed that geometric restrictions (e.g., elbows, spacer-grid, and inlet configurations) and change in flow orientation (e.g., upward-to-horizontal, horizontal-to-downward) can cause significant effects on the hydrodynamics of two-phase flow. In view of these, high-resolution separate-effect experiments have been performed to establish a two-phase flow database that is accurate, extensive and good enough for multi-phase CFD codes development, to develop predictive models accounting for geometric effects, and to improve the performance of nuclear reactor system analysis codes. Recent studies on the effects of the vertical-upward and vertical-downward 90-degree elbows, spacer grid, inlet configurations, and change in flow orientation are summarized. Some of the major two-phase flow phenomena investigated in the present study include flow regime transition, pressure loss, two-phase flow parameters, flow development, and interfacial drag. To demonstrate the functionality of the newly developed models, the one-dimensional steady-state one-group interfacial area transport equation is employed to predict two-phase flow transport under geometric effects.

As a part of characterizing the bubble interaction mechanisms and flow regime transition processes in horizontal gas–liquid two-phase flow, a flow visualization study is performed in an air–water test facility constructed from 3.81 cm inner diameter clear acrylic round pipes. The test section is approximately 250 diameters in length to allow for development of the flow. Flow visualizations are performed using a high-speed video camera at 80 and 245 diameters downstream of the inlet to observe the development of the flow structures. A total of 27 flow conditions including bubbly, plug, slug, stratified, wavy, and annular flows are characterized in the present study. In highly turbulent bubbly flow conditions it is found that the distribution becomes more uniform with increasing development length through a turbulence penetration process that counters the effect of buoyancy. It is also found that plug bubbles form below a layer of small bubbles rather than at the upper pipe wall where the bubbles are most packed. In fact, it is consistently found that turbulence-based bubble interactions do not occur in the most densely packed regions as the eddies there are not large enough to effect the bubbles. Rather, bubble packing-induced coalescence occurs in these regions and contributes to the formation of plug bubbles. The newly formed plug bubbles move faster than, and ultimately pass, the smaller bubbles above due to the effect of the wall. These small bubbles are subsequently overtaken by the following plug bubble and coalesce with the nose region through a process denoted as drag-induced coalescence.

The current work seeks to develop an additional database in air–water horizontal bubbly flow through a 3.81 cm inner diameter test section with a total development length of approximately 250 diameters. The experimental conditions are chosen to cover a wide range of the bubbly flow regime based upon flow visualization using a high-speed video camera. A database of local time-averaged void fraction, bubble velocity, interfacial area concentration, and bubble Sauter mean diameter are acquired throughout the entire pipe cross-section using a four-sensor conductivity probe for nine flow conditions. To investigate the evolution of the flow, measurements are made at axial locations of 44, 116, and 244 diameters downstream of the inlet. Using this database, the effects of gas flow rate, liquid flow rate, and development length on the local and area-averaged two-phase flow parameters are presented. From the local profiles, it is found that highly turbulent liquid flow conditions cause the void fraction profile to become more uniform with increasing development length through a turbulent mixing process which counters the effect of buoyancy. Bubble interactions are also observed to play a significant role in the evolution of the flow such that the area-averaged void fraction and interfacial area concentration can have different axial trends.

This study investigates two issues in the practical application of the local conductivity probe for two-phase flow measurements. First, the effects of signal “ghosting,” an electrical interference ...

Understanding the effects of spacer grids on the coolant flow through a nuclear reactor core is required for best-estimate design and analysis of the plant. The impact of a spacer grid on two-phase...

This study investigates the geometric effects of a 90-degree vertical-upward elbow on local two-phase flow-parameters in an air–water system, and develops an experimental database for interfacial area transport modeling. The experimental facility is constructed from 5.08 cm inner diameter acrylic pipes and includes vertical and horizontal sections interconnected by a 90-degree vertical glass elbow. The elbow has a radius of curvature of 15.24 cm and is installed at L / D = 63 from the inlet. A four-sensor conductivity probe is used to measure time-averaged local two-phase flow parameters including: void fraction, bubble velocity, interfacial area concentration, and bubble frequency at ten axial locations along the test section. It is observed that the bubbles moving through the vertical-upward elbow are entrained by the secondary flow leading to a bimodal distribution in bubbly flow conditions. For the flow conditions investigated within the study, this bimodal distribution occurs regardless of the bubble distribution upstream of the elbow. It is found that the change in bubble distribution downstream of the elbow is strongly correlated to the dissipation of the elbow effects. Furthermore, the dissipation characteristics as well as the length of dissipation region for the vertical-upward elbow are found to be a strong function of the liquid-phase flow rate.

The conventional thermal-hydraulic nuclear reactor system analysis codes utilize a two-field, two-fluid formulation for two-phase flows. To provide closure, static flow regime transition criteria and algebraic relations are employed to estimate the interfacial area concentration (ai). To better reflect the dynamic evolution of two-phase flow, an experimental version of TRACE is developed to estimate the ai using the one-group interfacial area transport equation (IATE), which includes mechanistic models for bubble coalescence and disintegration. These models account for: (1) bubble break-up due to impact of a turbulent eddy, (2) bubble coalescence due to random collision driven by turbulent eddies, and (3) bubble coalescence due to the acceleration of a bubble in the wake region of a preceding bubble. To assess the impact of including bubble interaction models in TRACE, code predictions of experimental data measured by a multi-sensor conductivity probe are compared to both the IATE and flow regime based predictions. In total, 50 air–water vertical co-current upward and downward bubbly flow conditions in pipes with diameters ranging from 2.54 to 20.32 cm are evaluated. It is found that TRACE, using the conventional flow regime relation, always underestimates ai by predicting a larger bubble size than observed in the experimental data. Additionally, the axial trend of the ai prediction is always linear because ai in the conventional code is predominantly determined by the pressure. However, TRACE with the one-group IATE significantly improves the prediction results, yielding a ±13.0% difference with the data. It is found that the non-linear developments observed in the experimental data, which reflect bubble interactions, are predicted well using the IATE. Moreover, in several conditions dominated by bubble interactions, the ai trend displayed is opposite to the effect of pressure. In these cases, the conventional TRACE relation predicts an incorrect trend in ai, while the IATE predicts the experimental data well.

The present study implements the one-dimensional interfacial area transport equation into the TRACE code, being developed by the U.S. Nuclear Regulatory Commission. The interfacial area transport equation replaces the conventional flow regime dependent correlations and the regime transition criteria for furnishing the interfacial area concentration in the two-fluid model. This approach allows dynamic tracking of the interfacial area concentration by mechanistically modeling bubble coalescence and disintegration mechanisms. Thus, it eliminates potential artificial bifurcations or numerical oscillations stemming from the use of conventional static correlations. To implement the interfacial area transport equation, a three-field version of TRACE is utilized, which is capable of tracking both the continuous liquid and gas fields as well as a dispersed gas field. To demonstrate the feasibility of the present approach, the steady-state one-group interfacial area transport equation applicable to adiabatic air–water bubbly two-phase flow is first tested in the present study. Data obtained in 18 different flow conditions from two vertical co-current upward air–water bubbly two-phase flow experiments performed in round pipes (25.4 mm and 48.3 mm) are used to help evaluate the implementation. Results obtained from TRACE with the interfacial area transport equation (TRACE-T) and those from TRACE without the transport equation (TRACE-NT) are compared to demonstrate the enhancement in prediction accuracy. The predictions made by TRACE-T agree well with the data with an average percent difference of approximately ±8%. It is also evident from the results that while TRACE-T accounts for dynamic interaction of bubbles along the flow field, the predictions made by TRACE-NT are attributed primarily to the pressure change.

Present study investigates the geometric effects of flow obstruction on the distribution of local two-phase flow parameters and their transport characteristics in horizontal bubbly flow. The round glass tubes of 50.3 mm in inner diameter are employed as test sections, along which a 90-degree Elbow is located at L/D = 206.6 from the two-phase mixture inlet. In total, 15 different flow conditions are examined within the air–water bubbly flow regime. The detailed local two-phase flow parameters are acquired by the double-sensor conductivity probe at four different axial locations. The effect of elbow is found to be evident in both the distribution of local parameters and their development. The elbow clearly promotes bubble interactions resulting in significant changes in interfacial area concentration. It is also found that the elbow-effect propagates to be more significant further downstream (L/D = 250) than immediate downstream (L/D = 225) of the elbow. Furthermore, it is shown that the elbow induces significant oscillations in the flow in both vertical and horizontal directions of the tube cross-section. Characteristic geometric effects due to the existence of elbow are also shown clearly in the transport of one-dimensional interfacial area concentration and void fraction along the flow.

The objective of the current study is to better understand the interfacial structure and its development in an air–water planar bubble jet, as well as to provide a unique benchmark data set for a 3D thermal-hydraulic analysis code. Both flow visualization and local measurements were performed in three characteristic flow conditions at four elevations along a test section with a cross section of 200 mm in width and 10 mm in gap. A high-speed digital video camera was applied in the flow visualization study to capture the flow structures and bubble interaction phenomena, while a miniaturized four-sensor conductivity probe was used to acquire the time-averaged local void fraction, interfacial velocity, and bubble number frequency. Also, the interfacial area concentration and the averaged bubble Sauter mean diameter were obtained from the local measurements. The lateral bubble transport and bubble interaction mechanisms were clearly demonstrated in the acquired data.

Accurate prediction of the interfacial area concentration is essential to successful development of the interfacial transfer terms in the two-fluid model. Mechanistic modeling of the interfacial area concentration entirely relies on accurate local flow measurements over extensive flow conditions and channel geometries. From this point of view, accurate measurements of flow parameters such as void fraction, interfacial area concentration, and interfacial velocity were performed by a multi-sensor probe at three axial locations as well as seven radial locations in vertical downward bubbly flows using a 25.4 mm-diameter pipe. In the experiment, the superficial liquid velocity and the void fraction ranged from −1.25 to −3.11 m/s and from 1.61% to 21.0%, respectively.

This paper presents an experimental study of local liquid velocity measurement in downward air-water bubbly and slug flows in a 50.8 mm inner-diameter round pipe. The axial liquid velocity and its fluctuations were measured by a laser Doppler anemometry (LDA) system. It was found that the maximum liquid velocity in a downward two-phase flow could occur off the pipe centerline at relatively low liquid flow rates and this observation is consistent with other researchers’ results. The comparisons between the liquid flow rates measured by a magnetic flow meter and those obtained from the local LDA and multi-sensor conductivity probe measurements showed good agreement. In addition, based on the local measurements the distribution parameter and the drift velocity in the drift-flux model were obtained for the current downward flow tests.

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.

In view of the great importance to two-fluid model, structure of downward bubbly flows in vertical pipes has been discussed intensively based on available data sets of local flow parameters including extensive air–water data sets recently measured by the authors. In this study, an approximate radial phase distribution pattern map has been proposed based on available data sets, and radial profiles of local flow parameters such as void fraction, interfacial area concentration, interfacial velocity, and bubble Sauter mean diameter have been discussed in detail. The one-dimensional drift-flux model for a downward two-phase flow and the correlation of the interfacial area concentration have been compared with the downward flow data. The correlations applicable to the predictions of one-dimensional void fraction and interfacial area concentration for a downward bubbly flow have been recommended by the comparison.

A dynamic approach employing the interfacial area transport equation is presented to replace the static flow regime dependent correlations for the interfacial area concentration. The current study ...

Local characteristics of the liquid phase in upward and downward air–water two-phase flows were experimentally investigated in a 50.8-mm inner-diameter round pipe. An integral laser Doppler anemometry (LDA) system was used to measure the axial liquid velocity and its fluctuations. No effect of the flow direction on the liquid velocity radial profile was observed in single-phase liquid benchmark experiments. Local multi-sensor conductivity probes were used to measure the radial profiles of the bubble velocity and the void fraction. The measurement results in the upward and downward two-phase flows are compared and discussed. The results in the downward flow demonstrated that the presence of the bubbles tended to flatten the liquid velocity radial profile, and the maximum liquid velocity could occur off the pipe centerline, in particular at relatively low flow rates. However, the maximum liquid velocity always occurred at the pipe center in the upward flow. Also, noticeable turbulence enhancement due to the bubbles in the two-phase flows was observed in the current experimental flow conditions. Furthermore, the distribution parameter and the void-weighted area-averaged drift velocity were obtained based on the definitions.

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.

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 downward two-phase flows. The constitutive equation that specifies the distribution parameter in the downward flow has been derived by taking into account the effect of the downward mixture volumetric flux on the phase distribution. It was assumed that the constitutive equation for the drift velocity developed by Ishii for a vertical upward churn-turbulent flow determined the drift velocity for the downward flow over all of flow regimes. To evaluate the drift-flux model with newly developed constitutive equations, area-averaged void fraction measurement has been extensively performed by employing an impedance void meter for an adiabatic vertical co-current downward air–water two-phase flow in 25.4-mm and 50.8-mm inner diameter round tubes. The newly developed drift-flux model has been validated by 462 data sets obtained in the present study and literatures under various experimental conditions. These data sets cover extensive experimental conditions such as flow system (air–water and steam–water), channel diameter (16–102.3 mm), pressure (0.1–1.5 MPa), and mixture volumetric flux (−0.45 to −24.6 m/s). An excellent agreement has been obtained between the newly developed drift-flux model and the data within an average relative deviation of ±15.4%.

This paper presents the general strategy for modeling the source and sink terms in the two-group interfacial area transport equation. The two-group transport equation is applicable in bubbly, cap bubbly, slug, and churn-turbulent flow regimes to predict the change of the interfacial area concentration. This dynamic approach has an advantage of flow regime-independence over the conventional empirical correlation approach for the interfacial area concentration in the applications with the two-fluid model. In the two-group interfacial area transport equation, 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. Based upon a detailed literature review of the research on the bubble interactions, five major bubble interaction mechanisms are identified for the gas–liquid two-phase flow of interest. A systematic integral approach, in which the significant variations of bubble volume and shape are accounted for, is suggested for the modeling of two-group bubble interactions. To obtain analytical forms for the various bubble interactions, a simplification is made for the bubble number density distribution function.

In relation to the development of the interfacial area transport equation, local flow measurements of vertical downward air–water flows in a pipe with an inner diameter of 50.8 mm were performed at three axial locations of z/D=6.50, 34.0, and 66.5 as well as ten radial locations from r/R=0 to r/R=0.9 using a multi-sensor probe. In the experiment, the superficial liquid velocity and the void fraction ranged from −0.620 m/s to −2.49 m/s and from 0.21% to 8.4%, respectively. The dependence of the interfacial area transport on the liquid velocity, void fraction, and bubble size is discussed in detail.

This paper presents the local measurement results of interfacial parameters in a vertical air–water upward two-phase bubbly flow. The measured parameters are local time-averaged void fraction, interfacial area concentration, bubble Sauter mean diameter, and interfacial velocity. The measurements are performed in a 101.6-mm inner diameter pipe by four-sensor conductivity probes. These data are further used to evaluate the one-dimensional, steady state, one-group interfacial area transport equation (IATE), which can serve as one of the constitutive relations for the two-fluid model. The agreement between the predictions from the transport equation and the experimental measurements is reasonably good. The resulting deviation is carefully examined. As a conclusion, the two-group IATE is recommended for general gas–liquid two-phase flow in various flow regimes.

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.

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.

A miniaturized four-sensor conductivity probe is designed to effectively minimize the reported limitations of the previous designs. The new probe is capable of measuring both large and small bubbles. The signal processing scheme is constructed for the probe in such a way that the two-phase parameters of different types of bubbles can be identified and categorized. Image analysis is employed to benchmark the new probe. A good agreement between the experimental data and the theoretical calculation is obtained, which assesses both the measurement principle and the capability of the signal processing scheme. The experimental data are obtained in a 5.08-cm ID vertical co-current air/water loop at two different axial locations of L/D=32 and 64 in slug flow conditions. The local time-averaged two-phase parameters obtained by the probe include the interfacial area concentration, void fraction, interface velocity, chord length, and Sauter mean diameter for various types of bubbles. The measured parameters are categorized in two groups in view of the development of a two-group interfacial transport equation. The development of geometric two-phase flow parameters of each group along the axial direction of the flow duct is well demonstrated.

The objective of the present study is to develop a miniaturized four-sensor conductivity probe, applicable to a wide range of two-phase flows to obtain the time-averaged local two-phase flow parameters of various types of bubbles. Experimental data acquired by the probe are categorized into two groups in view of two-group interfacial area transport: namely spherical/distorted bubbles as Group 1 and cap/Taylor bubbles as Group 2. Benchmark experiment employing the image analysis method is performed. The results from the benchmark experiment assess both the measurement principle and signal processing scheme of the newly developed four-sensor conductivity probe method.

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.

This study presents a comparison of the geometric effects of 90 deg and 45 deg elbows in horizontal two-phase air-water bubbly flow. Two separate experiments were performed in the horizontal test section made out of 50.3 mm inner diameter glass tubes. The first set of data was collected with a 90 deg elbow installed, and then a 45 deg elbow was added to the existing facility to acquire the second set of data. A total of 15 different flow conditions, all within the bubbly flow regime, were identified for the 90 deg experiment, and very similar flow conditions were extended to the 45 deg experiment. A double-sensor conductivity probe was employed to acquire the local data at seven different axial positions along the test section, out of which four measurement locations are associated with the 90 deg experiment and three with the 45 deg experiment. The data show that the elbows have a significant effect on the development of interfacial structures as well as the bubble interaction mechanisms. Furthermore, there are characteristic similarities and differences between the effects of the two elbows. While the effect of the 45 deg elbow is evident immediately after the elbow, the 90 deg elbow effect tends to propagate further downstream of the elbow rather than immediately after the elbow. Moreover, it is shown that both elbows induce spatial oscillations in the interfacial structures and two-phase flow parameters, but the degree and the nature of oscillations differ. The effects of the elbows are also compared for the axial transport of the two-phase flow parameters.

A dynamic treatment of interfacial area concentration has been studied over the last decade by employing the interfacial area transport equation. When coupled with the two-fluid model, the interfacial area transport equation replaces the flow regime dependent correlations for interfacial area concentration and eliminates potential artificial bifurcation or numerical oscillations stemming from these static correlations. An extensive database has been established to evaluate the model under various two-phase flow conditions. These include adiabatic and heated conditions, vertical and horizontal flow orientations, round, rectangular, annulus, and 8×8 rod-bundle channel geometries, and normal-gravity and reduced-gravity conditions. Currently, a two-group interfacial area transport equation is available and applicable to comprehensive two-phase flow conditions spanning from bubbly to churn-turbulent flow regimes. A framework to couple the two-group interfacial area transport equation with the modified two-fluid model is established in view of multiphase computational fluid dynamics code applications as well as reactor system analysis code applications. The present study reviews the current state-of-the-art in the development of the interfacial area transport equation, available experimental databases, and the analytical methods to incorporate the interfacial area transport equation into the two-fluid model.

Present study investigates the geometric effects of flow obstruction on the distribution of local two-phase flow parameters and their transport characteristics in horizontal two-phase flow. The round glass tubes of 50.3mm in inner diameter are employed as test sections, along which a 90-degee elbow is located at L/D = 206.6 from the two-phase mixture inlet. In total, 15 different flow conditions are examined within the air-water bubbly flow regime. The detailed local two-phase flow parameters are acquired by the double-sensor conductivity probe at four different axial locations. The effect of elbow is found to be evident in both the distribution of local parameters and their development. The elbow clearly promotes bubble interactions resulting in significant changes in interfacial area concentration. It is also found that the elbow-effect propagates to be more significant further downstream (L/D = 250) than immediate downstream (L/D = 225) of the elbow. Furthermore, it is shown that the elbow induces significant oscillations in the flow in both vertical and horizontal directions of the tube cross-section. Characteristic geometric effects due to the existence of elbow are also shown clearly on the axial development of one-dimensional interfacial area concentration and void fraction.Copyright © 2006 by ASME

The two-phase pressure drop due to the minor loss in horizontal bubbly two-phase flow is studied. In particular, geometric effects of a 90-degree elbow is of interest in the present study. Experiments are performed in air-water two-phase flow near atmospheric pressure condition in round glass tube with inner diameter of 50.3mm. Along the test section, 90-degee elbow is installed at L/D = 206.6 from the two-phase mixture inlet. Experiments are performed in 15 different flow conditions and the local static pressures are measured at five axial locations. Characteristic pressure drop due to the elbow is clearly demonstrated in the profiles of local pressure data along the axial direction. It is also found that the elbow effect propagates and is more significant further downstream than immediate downstream of the elbow. The overall two-phase frictional pressure loss between L/D = 0 and 329 can be predicted well with the Lockhart-Martinelli correlation with parameter C = 25, which is higher than the generally accepted value of C = 20. A correlation for the two-phase pressure loss, including the minor loss due to the 90-degree elbow is developed by employing the approach analogous to that of Lockhart-Martinelli’s. The newly developed correlation suggests that the modified parameter, C = 65 fits best with the experimental data. In addition, the two-phase minor loss factor for the 90-degree elbow is found to be k = 0.58, 50% higher than that recommended for single-phase flow.Copyright © 2006 by ASME

The vertical co-current downward air-water two-phase flow was studied under adiabatic condition. In view of studying the effect of flow area on interfacial structure and regime transition, round tubes of 25.4-mm ID and 50.8-mm ID were employed as test sections. The flow regime map was constructed for each test section by employing a newer approach. Unlike the conventional flow visualization method, the present approach minimizes the subjective judgment in determining the flow regimes. It was found that the flow regime in the co-current downward flow strongly depend on the channel size. The local two-phase flow parameters were acquired by the multi-sensor miniaturized conductivity probe in bubbly flow. They include: the local time-averaged void fraction, interfacial area concentration, bubble velocity and bubble Sauter mean diameter. The area-averaged data acquired by the impedance void meter were analyzed by the drift flux model. Three different distributions parameters were developed for the different ranges of non-dimensional superficial velocity, defined by the ration of total superficial velocity to the drift velocity. The new correlations can be applied to a co-current downward two-phase flow in a wide range of flow regime spanning from bubbly to annular flow.Copyright © 2003 by ASME

In the two-fluid model, the field equations are expressed by the six conservation equations consisting of mass, momentum and energy equations for each phase. The existence of the interfacial transfer terms is one of the most important characteristics of the two-fluid model formulation. The interfacial transfer terms are strongly related to the interfacial area concentration and to the local transfer mechanisms such as the degree of turbulence near interfaces. This study focuses on the development of a closure relation for the interfacial area concentration. A brief summary of several problems of the current closure relation for the interfacial area concentration and a new concept to overcome the problem are given.

The objective of the present work is to study and model the interfacial structure development of air-water two-phase flow in a confined test section. Experiments of a total of 9 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. The bubbles 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 parameters are time-averaged local void fraction, interfacial velocity, bubble number frequency, interfacial area concentration, and bubble Sauter mean diameter for both groups of bubbles. Also, the line-averaged and area-averaged data are presented and discussed. The comparisons of these parameters at different elevations demonstrate the development of interfacial structure along the flow direction due to bubble interactions.

The local interfacial structure for vertical air-water co-current downward two-phase flow was investigated under adiabatic conditions. A multi-sensor conductivity probe was utilized in order to acquire the local two-phase flow parameters. The present experimental loop consisted of 25.4 mm and 50.8 mm ID round tubes as test sections. The measurement was performed at three axial locations: L/D = 13, 68 and 133 for the 25.4 mm ID loop and L/D = 7, 34, 67 for the 50.8 mm ID loop, in order to study the axial development of the flow. A total of 7 and 10 local measurement points along the tube radius were chosen for the 25.4 mm ID loop and the 50.8 mm ID loop, respectively. The experimental flow conditions were determined within bubbly flow regime. The acquired local parameters included the void fraction, interfacial area concentration, bubble interface frequency, bubble Sauter mean diameter, and interfacial velocity.Copyright © 2002 by ASME

The objective of the present research is to study the flow regime map, the detailed interfacial structures, and the bubble transport in an adiabatic air-water two-phase flow mixture, flowing upward through a vertical round pipe having 1.27 cm. inner diameter. The flow regime map is obtained by processing the characteristic signals acquired from an impedance void meter, using a self-organized neural network. The local two-phase flow parameters are measured by the state-of-the-art four-sensor conductivity probe at three axial locations in the pipe. The measured local parameters include void fraction (α), interfacial area concentration (ai ), bubble frequency (fb ), bubble velocity (Ub ) and bubble Sauter mean diameter (Dsm ). The radial profiles of these parameters and their development along the axial direction reveals the structure of the two phase mixture and the bubble interaction mechanisms.Copyright © 2002 by ASME

Flow regime identification for an adiabatic vertical co-current downward air-water two-phase flow in the 25.4 mm ID and the 50.8 mm ID round tubes was performed by employing an impedance void meter coupled with the neural network classification approach. This approach minimizes the subjective judgment in determining the flow regimes. The signals obtained by an impedance void meter were applied to train the self-organizing neural network to categorize these impedance signals into a certain number of groups. The characteristic parameters set into the neural network classification included the mean, standard deviation and skewness of impedance signals in the present experiment. The classification categories adopted in the present investigation were four widely accepted flow regimes, viz. bubbly, slug, churn-turbulent, and annular flows. These four flow regimes were recognized based upon the conventional flow visualization approach by a high-speed motion analyzer. The resulting flow regime maps classified by the neural network were compared with the results obtained through the flow visualization method, and consequently the efficiency of the neural network classification for flow regime identification was demonstrated.Copyright © 2002 by ASME

Experiments are performed in a scaled 1x3 rod bundle adiabatic air-water test facility to investigate the effects of a spacer grid on singleand two-phase flows. A four-sensor conductivity probe is used to obtain detailed measurements of local time-averaged two-phase flow parameters, including the void fraction and interfacial area concentration, throughout the flow cross-section at four axial locations. The local two-phase flow data indicates that the spacer grid causes redistribution of the bubbles. In the transition from bubbly to slug flows, the spacer grid is found to promote bubble coalescence. In the slug to churn-turbulent transition, however, the grid breaks up the larger bubbles, causing an increase in the interfacial area concentration across the spacer grid. Additionally, local velocity measurements in single-phase liquid flow are performed with a laser Doppler anemometer to investigate the change in the turbulence structure across the grid. The axial turbulence intensity measurements show the influence of the spacer grid dimples, indicating an increased mixing effect from these structures.

This communication introduces a non-intrusive method for void fraction measurement and identification of two-phase flow regimes, based on ultrasonic sensing. The underlying algorithm is built upon the recently reported theory of a statistical pattern recognition method called symbolic dynamic filtering (SDF). The results of experimental validation, generated on a laboratory test apparatus, show a one-to-one correspondence between the flow measure derived from SDF and the void fraction measured by a conductivity probe. A sharp change in the slope of flow measure is found to be in agreement with a transition from fully bubbly flow to cap-bubbly flow.