Two-group Interfacial Area Transport Equation Research Articles

Validation of two-group interfacial area transport equation in boiling flow

The Two-Fluid Model is the backbone of thermal-hydraulics and system-analysis codes for nuclear design. The Two-Fluid Model tracks the transfer of conserved quantities—mass, momentum, and energy—without the need for bubble interface tracking. However, two-phase flows are characterized by their different flow regimes which change as more vapor is present in the flow, from bubbly flow to cap/slug flow to annular flow. The two-group Two-Fluid Model can track the progression of boiling flows beyond the bubbly region without the need for flow-regime maps. A two-group wall-boiling model is implemented and coupled with the two-group Interfacial Area Transport Equation. The resulting model is compared against experimental data and predicts the growth in cap/slug bubbles through interaction models rather than through flow-regime maps. The coupled model can predict the growth in void fraction and interfacial area concentration beyond the capability of the one-group model, demonstrating the applicability of a coupled two-group approach to modeling boiling flow.

Two-group drift-flux model for dispersed gas-liquid flows in annuli

Interfacial area concentration (IAC) plays a vital role in mass, momentum, and heat transfers between gas and liquid phases in two-phase flows. The IAC of group-one bubbles, including spherical and distorted bubbles, differs from the IAC of group-two bubbles, including cap, slug and churn-turbulent bubbles. The two-group interfacial area transport equation (IATE) can be used as a mechanistic model to obtain the IAC of each group. The equation demands the two-group gas velocity fields, leading to the need to solve an extra momentum equation, which is complicated. The two-group drift-flux model can prevent this complexity by providing two-group gas velocities without introducing the extra momentum equation. Despite the importance of gas-liquid flows in annuli, the drift-flux model for gas-liquid flows is not well-developed like it is for pipe flows. The main objective of this study is to develop a two-group drift-flux model for dispersed vertical flows in annuli. The two-group drift-flux model provides the flow characteristics of group-one and group-two bubbles, such as void fractions and velocities, which strongly affect the prediction of the available interfacial area concentration of the group-one and group-two bubbles for heat and mass transfer. Hence, after comprehensively investigating the available experimental data, this study first improves a one-group drift-flux model for dispersed gas and low-viscosity liquid upward flows in annuli and proposes a new two-group drift-flux model. Then, the models are evaluated using the respective group experimental data. The consistency between one-group and two-group drift-flux models is also investigated. This consistency helps to reduce the two gas momentum equations to one gas mixture momentum equation. The results of the comparison between model predictions and experimental data are satisfactory.

Two-group drift-flux model for dispersed gas-liquid flows in rod bundles

Interfacial transfer terms in gas-liquid two-phase flows are formulated as the product of interfacial area concentration (IAC) and flux. The interfacial area transport equation (IATE) is essential for obtaining IAC in transient and developing two-phase flows. Two-group IATE was developed to account for the difference in the interfacial drag force between two groups of bubbles, where spherical and distorted bubbles are categorized as group one, while cap, slug, and churn turbulent bubbles are categorized as group two. The rigorous two-group approach requires two-group gas momentum equations, resulting in one additional momentum equation in the two-fluid model. The mixture gas momentum equation is considered to avoid the additional momentum equation. The two-group drift-flux model is necessary to calculate the two-group gas velocity from the mixture velocity. The present study develops an approximation methodology to acquire subchannel average and rod bundle average two-group two-phase flow parameters based on the validated power law assumption and a limited number of local data. The two-group model is developed for the distribution parameter and drift velocity for dispersed two-phase flows in rod bundles. The total performance of the newly developed two-group drift-flux model is evaluated by two-phase flow data in rod bundles. The results show that the developed two-group drift-flux model could well predict two-group gas velocities in rod bundles. This model is useful for subchannel thermal hydraulic analysis codes as a complement to the conventional one-group drift-flux model.

Two-group drift-flux model for dispersed gas-liquid flow in large-diameter pipes

Interfacial heat and mass transfer are prevalent in industrial processes. The interfacial transfer rate can be obtained by the product of their fluxes and interfacial area concentration (IAC) calculated by the interfacial area transport equation (IATE). Bubbles show different behavior according to their sizes. Hence, bubbles are classified into two groups. Consequently, two-group IATE is required causing to use of two gas momentum equations leading to more complexity. The present study suggests a new reliable two-group drift-flux modeling to reduce the two gas momentum equations to one gas mixture momentum equation for gas-liquid flow in large-diameter pipes. The model is developed based on the drift-flux model concept and experimental data. Group-one and group-two distribution parameters and drift velocities are validated through experimental data. The results show that the proposed two-group drift-flux model can support the concept of drift velocity from the bubbly to beyond the bubbly flow and consistency between the one-group and two-group drift-flux models. Moreover, steam-water data are used to validate the applicability of the model in steam-water flows condition. The developed two-group drift-flux model is indispensable for reducing the two gas momentum equations to one gas mixture momentum equation when two-group IATE is implemented into thermal-hydraulic codes to improve the prediction accuracy of IAC.

Comparison of bubbles interaction mechanisms of two-group Interfacial Area Transport Equation model

This work deals with 3D simulations of complex bubbly, cap-bubbly and churn regimes exhibiting bubbles of different shapes and with broad bubble size distribution. The first contribution of this work is to investigate and compare several bubble interaction mechanisms of coalescence and fragmentation for the 2-Group Interfacial Area Transport Equation (IATE) model. For two of these models, this is the first time their performances are assessed within a CFD code. The second contribution is to propose and assess a novel model of fragmentation and coalescence. Finally, a validation versus experimental data on three different configurations and three different regimes is performed. In particular, the interaction mechanisms are analyzed for one specific regime. The implementation of the two-group IATE model has been systematically performed in the 3D NEPTUNE CFD code.

Comparison of Intergroup Mass Transfer Coefficient Correlations in Two-Group IATE for Subcooled Boiling Flow

The interfacial area concentration (IAC) is of vital importance in determining the interfacial transfer terms of mass, momentum, and energy between phases in the two-fluid model. The two-group (2-G) interfacial area transport equation (IATE) dynamically models the IAC evolution of large and small bubbles, and the intergroup transfer bookkeeps the mass transferring between two groups. Different intergroup mass transfer coefficient correlations are employed in the 2-G IATE model, which include one old correlation and three new correlations previously developed by the authors. The two-group IATE is benchmarked with subcooled boiling experimental dataset. The group-1 interfacial area concentration results show that the three modified correlations improve the physically incorrect prediction by the old correlation. With the modified correlations, the 2-G IATE is foundationally capable of predicting the group-1 interfacial area concentration in subcooled boiling flow.

Two-phase interfacial structure development in vertical narrow rectangular channels

This study has experimentally investigated flow characteristics of two group bubbles in upward two-phase flows in a vertical narrow rectangular channel with 0.993 mm in gap, 40 mm in width, 2000 mm in height, and 1.94 mm in equivalent hydraulic diameter, Dh. The local measurements are performed at seven axial positions (z/Dh =52, 104, 155, 207, 415, 622, 829 (z: the axial distance from the inlet) using a high-speed camera. The database of the locally evolving parameters has been established by processing the images from the high-speed camera measurements. The measured parameters include the void fraction, interfacial area concentration (IAC), Sauter mean diameter and number density of group-1 and -2 bubbles, and gas-phase velocity of all bubbles. A total of 14 flow conditions are set at four different superficial liquid velocities ranging from 0.214 m/s to 2.08 m/s and different superficial gas velocities ranging from 0.0755 m/s to 1.70 m/s at the inlet. The observed flow regimes cover the bubbly, cap-bubbly, and slug flows. The measured void fraction ranges from 3.92 % to 42.6 %. The axially developing features of the two-phase flows are analyzed for the three flow regimes. Abrupt and gradual axial two-group bubble evolutions with intensive bubble coalescence at the flow regime transition are, respectively, observed at low and high superficial liquid velocity conditions. The newly-obtained experimental database has been used to evaluate the existing two-group interfacial area transport equation (IATE) and its corresponding source and sink models for the two-phase flow in the vertical narrow rectangular channel. Group-1 bubble IAC mean relative error of 21.1% and group-2 bubble IAC mean relative error of 33.4% have been obtained in the evaluations. The existing two-group IATE cannot satisfactorily predict the intensive bubble coalescence and the intragroup transport of the two-group bubbles at the transition from bubbly to slug flow in the vertical narrow rectangular channel. Therefore, it is necessary to improve the existing models of the intergroup and intragroup bubble interactions in the existing two-group IATE in the future.

Comparison of Bubbles Interaction Mechanisms of Two-Group Interfacial Area Transport Equation Model

Comparison of Bubbles Interaction Mechanisms of Two-Group Interfacial Area Transport Equation Model

Two-group interfacial area transport equation coupled with void transport equation in adiabatic steam water flows

The two-group coupled model with IATE is benchmarked with the recently available adiabatic phase-change flow datasets. The current state of adiabatic phase-change data is extensively discussed, followed by a thorough review of the two-group two-fluid model and the two-group IATE. The interfacial mass generation models from RELAP5/MOD3.3 are benchmarked and are observed to underpredict the group-2 interfacial mass generation rate which then causes underprediction of void fraction under flashing conditions. A new group-2 interfacial mass generation model is proposed using the mass-energy balance approach where slug bubbles are assumed as a cylinder with a constant width that only grows in the lengthwise direction. The proposed model is implemented to the two-group coupled model with IATE and benchmarked with the flashing datasets where the accuracy of the predicted values is significantly improved. Similar benchmark is carried out for flashing conditions with a near-zero initial void faction and adiabatic phase-change flows with an initial condensing phase followed by a flashing phase. It is observed that due to the lack of interfacial area concentration, the interfacial mass generation model is unable to produce a significant enough interfacial mass generation rate to allow the growth of bubbles. Bubble generation models are implemented to the simulations at flashing inception where improved results are obtained.

Comprehensive evaluation of two-group interfacial area transport equation and new intergroup transfer model

Interfacial Area Transport Equation (IATE) is developed to dynamically capture the flow structure change and predict Interfacial area concentration (IAC) for various flow regimes. Some recent experimental results show developing flows with intensive bubble coalescence at bubbly to slug transition in small pipes. The drastic IAC decreasing due to bubble coalescence under such conditions has not been well studied in previous IATE benchmark efforts, therefore it may not be captured by the current constitutive models for IATE. In this work, a comprehensive evaluation of the state-of-the-art two-group IATE models is performed using the small pipe data collected at bubbly and slug flow with a focus on transition. The evaluation result shows unsatisfactory performance in predicting the developing flow with intensive bubble coalescence at bubbly to slug transition. The reason is the underestimation of intergroup transfer from group I bubbles to group II bubbles. To improve the IATE performance, a new intergroup wake-entrainment model is developed to enhance the prediction capability for the intergroup void and IAC transfer. The new model incorporates a transition function derived based on the log-normal bubble size distribution and the lift force effect on bubble movement for group I bubbles, which allows for a smooth transition from bubbly to slug flow. The new intergroup transfer model significantly improves the IATE prediction capability in the 25.4 mm ID pipe and its applicability on other types of flow channels including 50.8 mm ID pipe and 200 × 10 mm duct is also verified.

Progress in two-phase flow modeling: Interfacial area transport

The interfacial area transport equation (IATE) employs a dynamic approach to predict interfacial area concentration (IAC) in two-phase flows. It eliminates the need for the static flow regime transition criteria and flow regime dependent IAC correlations used in closing the two-fluid model and therefore any potential artificial bifurcation or numerical oscillations stemming from these static correlations. The efforts to develop the IATE are reviewed in this work, focusing on studies within the past decade. The current state-of-the-art in IATE is a two-group interfacial area transport equation that is applicable to predict interfacial area concentration from bubbly to churn-turbulent flows. An extensive experimental database has been established in literature for various two-phase flow conditions. The database is used to develop constitutive models to close the IATE and to validate its performance. These include adiabatic and heated conditions, vertical and horizontal flow orientations, channels with flow restrictions, round, rectangular, annulus, and rod-bundle geometries, and normal-gravity and reduced-gravity conditions. IATE has been implemented into practical system analysis codes such as TRACE and computational fluid dynamics (CFD) codes such as CFX and Fluent to evaluate its performance. In addition, the recent efforts of extending the IATE beyond churn-turbulent flow to churn-annular transition and annular flows are also reviewed. These include the new instrumentation, experimental database, and additional constitutive models to predict annular flows.

Two-phase interfacial area characteristics and transport under the transition from subcooled boiling to saturated boiling flows

This study focuses on the analysis of the transition from the subcooled boiling to saturated boiling flow. During this process, vapor generates drastically in a short developing length, which makes it difficult to predict the interfacial characteristics of two-phase flow. To investigate the characteristics of this process, experiments were performed in a vertical annulus with 19.1 mm inner diameter and 38.1 mm outer diameter. The two-phase interfacial parameters including time-averaged local vapor fraction, interfacial area concentration, and bubble interfacial velocity are obtained using high-temperature miniature four-sensor electrical conductivity probes. In this study, the conductivity probe signal is processed using the newly-developed signal processing algorithm developed for small spherical bubbles by Shen and Nakamura (2014) , instead of the algorithm used in the previous subcooled boiling experimental studies Ozar (2009) and Kumar et al. (2019), [3] for large bubbles developed by Kataoka et al. (1986). The flow conditions cover a wide range of inlet subcooling temperature at 12.9–21.2 °C, heat flux at 57.9–197.3 kW/m2, and inlet flow rate at 0.265–0.536 m/s. The vapor fractions are cross-validated with impedance void meter measurements. The state-of-art two-group interfacial area transport equations (IATE) [6], (Ozar, 2009) and (Brooks and Hibiki, 2016) is evaluated with the experimental data. The result shows that the two-group IATE gives fairly good predictions on the transition phenomena. Besides, a defect was identified in the condensation model (Park et al., 2007) used in IATE, which is the bubble boundary diameter classifying the two condensation mechanisms: heat-transfer-controlled and inertia-controlled condensation. A rigorous approach to estimate this boundary diameter is established in this study.

Validation of the Interfacial Area Transport Equation Coupled with the Void Transport Equation for Prediction of Flashing Flows

The static correlations from RELAP5 and TRACE as well as the interfacial area transport equation (IATE) are benchmarked for flashing flow with selected cases from a recently published experimental data set. The RELAP5 correlation is able to predict the interfacial area concentration more accurately than the TRACE correlation. The one-group decoupled IATE, supplied with experimental void fraction, shows overprediction of interfacial area concentration, especially at low-pressure conditions. Additionally, the one-group IATE is solved simultaneously with the void transport equation where at low pressures, the accuracy of the predicted interfacial area concentration improves even with the void fraction being underpredicted. However, as the pressure increases, the improving accuracy of the predicted void fraction leads to an overprediction of the interfacial area concentration. The two-group IATE is also benchmarked, first using the interfacial mass generation model from RELAP5 and TRACE and then with a model derived through a mass-energy balance approach. The accuracy of the two-group IATE is observed to be sensitive to the choice of the heat transfer length scale and Nusselt number correlations.

Interfacial Structures in Bubbly-to-Slug Transition Flows in a Duct

As a critical closure equation to the two-fluid model and an important tool to characterize the two-phase-flow interfacial transport, the interfacial area transport equation (IATE) was formulated by taking various physical mechanisms causing interfacial area change into account. To fulfill the dynamic prediction advantage of IATE and further replace the flow regime–based constitutive relations, the IATE model should be validated by transition data to ensure model reliability and robustness. Air-water experiments are performed in bubbly-to-slug transition flows in a 200 × 10-mm narrow rectangular duct. Four-sensor conductivity probes are used to measure the local void fraction, interfacial area concentration (IAC), and bubble velocity at three axial locations. The void fraction distribution changes significantly with the flow developing. Flow conditions with a similar area-averaged void fraction but different superficial mixture velocities are compared, and it is found that the superficial mixture velocity significantly affects the IAC. In addition, the two-group IATE model for narrow rectangular channel is evaluated using the collected data. The average relative error for the total IAC prediction is 11.4%, but the group II IAC is overestimated for most flow conditions.

Beyond bubbly two-phase flow investigation using a CFD three-field two-fluid model

Modeling and simulation study of industrial scale beyond-bubbly flows, like cap-bubbly, cap-turbulent and churn-turbulent, using the two-fluid model, has been limited due to the wide range of interfacial length scales involved and lack of physics-based models for bubble hydrodynamics and interaction mechanisms for such flow conditions. One important feature of beyond bubbly flow is the existence of a wide range of bubble sizes and shapes and thus different transport characteristics. The accuracy of two-fluid model predictions is strongly dependent on the constitutive relations used for the two-fluid model. The objectives of this proposed work are the following: select a set of physics-based constitutive relations and implement these models into CFX; evaluate these models for a wide range of test conditions in cap-turbulent and churn-turbulent flows. The interfacial structure is dynamically evaluated using bubble interaction mechanisms (coalescence and break up) from the two-group Interfacial Area Transport Equation implemented as source and sink terms into ANSYS CFX. The assessments for the validity of the models were carried out in comparison to data collected at Purdue University for two-phase flow in a narrow, rectangular duct. Non-uniform inlet conditions were applied in order to evaluate phase diffusion models in CFX. A new turbulence-induced bubble collision diffusion model for the two-group bubbles system has been implemented in ANSYS CFX. The CFD results predict the measured data to within the expected error, correctly capturing the transverse redistribution of phases due to diffusion for both uniform and non-uniform inlet phase distributions. This illustrates the importance of bubble collision phenomena in correctly predicting phase distributions in a channel.

Evaluation of two-group interfacial area transport equation model for vertical small diameter pipes against high-resolution experimental data

Two-phase flow is ubiquitous in industrial, chemical and thermal plants alike. The current state-of-the-art system-code model for predicting fluid transport in two-phase flows is the two-fluid model. In the two-fluid transport model, the coupling of mass, momentum and energy transfer between phases is highly dependent on interfacial area transfer terms. Several research efforts in the past have been focused on the development of an interfacial area transport equation model (IATE) in order to eliminate the drawbacks of static regime flow maps currently used in best-estimate thermal-hydraulic system codes. The IATE attempts to model the dynamic evolution of the vapor/liquid interface by accounting for the different interaction mechanisms affecting gaseous phase transport.The further development and validation of IATE models has been hindered by the lack of adequate experimental data in regions beyond the bubbly flow regime. At the Helmoltz-Zentrum Dresden-Rossendorf (HZDR) experiments utilizing wire-mesh sensors have been performed over all flow regimes, establishing a database of high-resolution (in space and time) data. A 52.3mm diameter pipe with a 16 by 16 wire-mesh sensor operating at 2.5kHz is utilized in the air-water experimental database used in this work. There are a total of 37 tests (with varying superficial gas and liquid velocities, at approximately 0.25MPa). Analysis of IATE performance in the bubbly flow and slug flow regimes is presented.The performance of the Fu-Ishii two-group IATE model is evaluated. In all regions, the interfacial area concentration for small bubbles is predicted well. The model performs poorly in high void fraction regimes, in which large irregularly shaped bubbles are present. The interaction mechanisms that support and deter performance of the IATE model are highlighted. A sensitivity analysis indicates modification of the group-2 wake entrainment coefficient may extend the validity of the Fu-Ishii model. An optimization study is presented to further explore improving IATE performance. It is concluded that the availability of accurate data at high void fractions from the HZDR facility provides a path to improve IATE performance.

Experimental study on interfacial structure and interfacial area transport in downward two-phase flow

In view of the importance of two-group interfacial area transport equation and lack of corresponding accurate downward flow database that can reveal two-group interfacial area transport, a systematic database for adiabatic, air-water, vertical downward two-phase flow in a round pipe with inner diameter of 25.4mm was collected to gain an insight of interfacial structure and provide benchmarking data for two-group interfacial area transport model. Four-sensor conductivity probes were used to measure the local two phase flow parameters at high data sampling frequency to ensure the accuracy. Axial development of local flow parameter profiles including void fraction, interfacial area concentration, and Sauter mean diameter were presented. Drastic inter-group transfer of void fraction and interfacial area as well as the wall peaked interfacial area concentration profiles were observed and discussed.

Two-group modeling of interfacial area transport in large diameter channels

A comparison of the existing two-group interfacial area transport equation source and sink terms for large diameter channels with recently collected interfacial area concentration measurements (Schlegel et al., 2012, 2014. Int. J. Heat Fluid Flow 47, 42) has indicated that the model does not perform well in predicting interfacial area transport outside of the range of flow conditions used in the original benchmarking effort. In order to reduce the error in the prediction of interfacial area concentration by the interfacial area transport equation, several constitutive relations have been updated including the turbulence model and relative velocity correlation. The transport equation utilizing these updated models has been modified by updating the inter-group transfer and Group 2 coalescence and disintegration kernels using an expanded range of experimental conditions extending to pipe sizes of 0.304m [12in.], gas velocities of up to nearly 11m/s [36.1ft/s] and liquid velocities of up to 2m/s [6.56ft/s], as well as conditions with both bubbly flow and cap-bubbly flow injection (Schlegel et al., 2012, 2014). The modifications to the transport equation have resulted in a decrease in the RMS error for void fraction and interfacial area concentration from 17.32% to 12.3% and 21.26% to 19.6%. The combined RMS error, for both void fraction and interfacial area concentration, is below 15% for most of the experiments used in the comparison, a distinct improvement over the previous version of the model.

Experiments in Cap-Bubbly Two-Phase Flows for Two-Group IATE Development

In the two-group interfacial area transport equation (IATE) used to calculate the interfacial area concentration (ai), bubbles are categorized into two groups. Namely, group-I consists of spherical/distorted bubbles, and group-II consists of cap/slug/churn-turbulent bubbles. Robust models for the major bubble interaction mechanisms that cause the transition from purely one-group to two-group flows are essential to the dynamic closure of the two-fluid model with the two-group IATE. Therefore, the present study seeks to establish an experimental database in cap-bubbly flows that highlights this transition to support model development. A four-sensor conductivity probe is used to obtain measurements of local time-averaged two-phase flow parameters, including the void fraction and ai, in vertical-upward air-water two-phase flows in a 5.08-cm pipe. Four flow conditions are investigated at ⟨jf⟩ = 2 m/s with increasing ⟨jg⟩ to study the generation and growth of group-II bubbles. Characteristic features of the local void fraction and ai distributions are discussed. Additionally, axial development of area-averaged void fraction and ai that is indicative of exchange between the bubble groups is presented.

A correlation for interfacial area concentration in high void fraction flows in large diameter channels

Two phase flows exist as a part of many industrial processes, including chemical processes, nuclear reactor systems, and heat exchangers. In all of these applications the interfacial area concentration is an important parameter for evaluating the interactions between the phases, including drag forces, heat transfer or chemical reaction rates. Many models for interfacial area concentration exist for dispersed bubbly flows; however this type of flow only exists at relatively low void fractions. Very few correlations exist for the prediction of cap-turbulent, slug, or churn-turbulent flows. In this paper a new correlation for predicting the interfacial area concentration beyond bubbly flows in large diameter pipes is derived using a two-bubble-group method (spherical and distorted bubbles as Group-1 bubbles and cap and churn-turbulent bubbles as Group-2 bubbles) and the two-group interfacial area transport equation. The derivation assumes steady state and fully developed flow, and is based on interfacial area transport source and sink terms for large diameter pipes developed by Smith et al., 2012a. Int. J. Heat Fluid Flow 33, 156–167. The resulting equations can be used to predict the void fraction for each group of bubbles and the Sauter mean diameter for each group of bubbles in addition to the total interfacial area concentration. The model is then benchmarked based on the data collected by Schlegel et al., 2012. Exp. Therm. Fluid Sci. 41, 12–22; Schlegel et al., 2014. Int. J. Heat Fluid Flow 47, 42–56. It is found that the correlation predicts the data for Sauter mean diameter of Group 1 bubbles with RMS error of 23.3% and bias of +1.83%. For Group 2 bubbles the RMS error is 24.0% and the bias is +5.35%. This indicates that the correlation somewhat over-predicts the bubble sizes. In spite of this the prediction error remains reasonable compared to the accuracy of previous correlations, and given that the experimental uncertainty can be as high as 15% for some flow conditions. The RMS error and bias in the total interfacial area concentration are 22.6% and −4.29%, respectively. This is consistent with the over-prediction of the Sauter mean diameters, but again is reasonable considering the experimental uncertainty and the prediction error of previous correlations. The model is also able to predict the trends found in the experimental data with varied liquid and gas velocities, representing a large improvement over previous modeling efforts. An expanded database of accurate interfacial area concentration measurements at higher pressures would allow further improvement of the model benchmark and expansion of the range of applicability of the model.