Prediction Of Interfacial Area Concentration Research Articles

Experimental research and model development on interfacial drag in rectangle channel bubbly and slug flow

As one of the most important constitutive models, interfacial drag determines the phase distribution directly and impose significant influences on pressure drop and heat transfer. Due to the limited study on interfacial drag for rectangle channel, experimental research and model development were performed in this paper. The air-water flow experiments in rectangular channels were carried out to obtain local parameters such as void fraction, interfacial area concentration and bubble chord length. These parameters were all characterized with core peak distribution except for the situations of void fraction at lower gas velocity and interfacial area concentration at higher gas velocity. The development of interfacial drag model in bubbly and slug flow was proposed based on the experimental data. The drag coefficient and interfacial area concentration in bubbly and slug flow were modified for distorted bubble, Taylor bubble and liquid slug respectively. Further validation was performed with system analysis codes. Better prediction of interfacial area concentration and void fraction, as well as numerical stability were obtained, proving the validity of interfacial drag model developed for rectangle channel bubbly and slug flow.

Modeling sensitivity in prediction of interfacial area concentration in boiling flow

A comprehensive review and validation of three approaches to predict interfacial area concentration in subcooled boiling flow are presented. The three methods are geometry-based semi-empirical correlations, empirical correlations, and the interfacial area transport equation (IATE). Extensive boiling experiment databases with the measurement of local interfacial area concentration and other local two-phase parameters are employed in the validation. The benchmark shows that the most suitable semi-empirical or empirical correlations chosen to predict the interfacial area concentration are different in the low void fraction region and high void fraction region. The closure model sensitivity in the IATE evaluation is analyzed for the bubble layer thickness models, point of net vapor generation (PNVG) determination approaches, and the presence of large cap and slug bubbles. The analysis of the bubble layer thickness model in IATE reveals that the model is necessary for subcooled boiling systems and the flat bubble layer thickness model is more appropriate than the triangle bubble layer thickness model. The result suggests a necessity of measuring the Point of Net Vapor Generation (PNVG) information in experiments for IATE calculation and the necessity of improvement to the PNVG models. The benchmark shows that the one-group IATE has exceptional performance in low group-2 void fraction region; while in high void fraction flows, the multi-group approach is needed to account for the different characteristics between small and large bubbles.

Evaluation of typical interfacial area transport models for bubbly flow

Interfacial area concentration is one of the most important parameters in two-phase flow. This parameter also reflects the interfacial area of mass, momentum and energy transfer in two-fluid model. The prediction of interfacial area concentration is essential to close the interfacial transfer terms in the two-fluid model. For the modeling of the one-dimensional interfacial area transport equation for adiabatic bubbly flow, existing typical sink and source terms have been reviewed and evaluated by the experimental data of vertical pipes and rod bundles. The interactive mechanisms of bubbles and turbulent eddies have also been analyzed, including bubbles breakup and bubbles coalescence. The evaluation results show the interfacial area transport model of Hibiki and Ishii (Liu and Hibiki) can provide the most accurate prediction of interfacial area concentration for pipes with the relative error of 8.22% for bubbly flow. Their model has also been evaluated by the experiment data of rod bundle with the relative error of 21.89% for bubbly flow.

Prediction of interfacial area concentration in a small diameter round pipe

Accurate prediction of interfacial area concentration (IAC) is of great importance in the two-fluid model. As a promising IAC prediction method, the interfacial area transport equation (IATE) was developed to dynamically predict the IAC and to eliminate the shortcomings of the flow regime-based IAC correlations, which is currently used in most thermal–hydraulic system codes. To extend the applicability of the IATE from bubbly flow to slug and churn-turbulent flow, the two-group IATE was developed by representing the IAC of sphere/distorted bubbles and cap/slug bubbles separately. Several studies have been performed in the past focusing on the constitutive modeling and experimental benchmark. However, few data are collected in small size pipes (DH⩽2Dc), hence the applicability of the current two-group IATE models on small size pipes has not been well evaluated. In this study, a comprehensive database including bubbly, slug, churn-turbulent flow is established in a round pipe with a diameter of 25.4 mm (DH ≈ 2Dc), and the applicability of two-group IATE models for round pipe has been checked against the data. The measured IAC can be predicted by the two-group IATE with the constitutive models developed for moderate size pipe with errors less than 25% except at the bubbly to slug transition flow conditions. At the transition flow, drastic intergroup void fraction and IAC transport are observed along the flow direction. The model cannot predict this intergroup transfer and overestimates the IAC. Recent improvements on the original models focusing on the one-group to two-group transition flow in a moderate size pipe are also evaluated and the results are still not satisfying. The reasons for this discrepancy are analyzed in detail and improvements including re-deriving the coalescence terms using more accurate log-normal bubble size distribution and experimental coefficients optimizing have been performed. Using the newly derived models with optimized coefficients, the two-group IATE can predict the IAC axial development for all flow conditions with an error less than 25%. The averaged prediction error for the bubbly to slug transition flow conditions decreases from 47.19% to 8.03%.

Validation and model sensitivity of the interfacial area transport equation in condensing flows

The interfacial area transport equation (IATE) in condensing flows is thoroughly reviewed and validated with available experimental data. The IATE provides a dynamic prediction of flow structure consistent with the two-fluid model and has been studied extensively for adiabatic two-phase flows. However, the IATE still requires attention in flows with phase change. The modeling of the condensation interfacial area term and volume sink term is reviewed along with the void fraction prediction since the IATE is closely related to the void fraction development. The emphasis in this work is to expand the validation of the IATE in condensing flows to higher pressure and higher flow rate conditions as well as evaluating the modeling sensitivity in both the decoupled IATE and the IATE coupled with the void transport equation. Two datasets have been used for validation, both consisting of condensing two-phase flow data in the unheated section of a vertical annulus with conditions spanning a range of pressure, inlet subcooling and mass flux. The analysis shows that the current form of the condensation modeling results in an over-prediction of both condensation mass transfer and interfacial area concentration loss across all conditions. From the decoupled IATE simulation, it is established that the boundary diameter must be used in the Nusselt number correlation in the condensation model to get good predictions of the interfacial area concentration. Moreover, the convection term in the IATE is found to contribute to interfacial area concentration at high mass flux conditions. The coupled IATE simulation model results in better agreement in the predictions of the void fraction and the interfacial area concentration under nearly all conditions with the proposed modifications to the condensation model. Sensitivity studies show the impact of Nusselt number correlation and gas velocity on the prediction of interfacial area concentration. Overall, a coupled simulation is recommended for benchmarking the IATE in phase change flows.

Gas-liquid bubbly flow structure in a vertical large-diameter square duct

An experimental study was performed on the local structure of atmospheric upward-moving air–water two-phase flow in a vertical large-diameter square duct with a cross-section of 100 mm × 100 mm and a height of 3 m by using a four-sensor probe at the axial position of z/DH = 29.2. The flow regime was simultaneously observed by a high speed camera at z/DH = 12.5. The four-sensor probe method classifying spherical and non-spherical bubbles was applied as a key measurement way to obtain local parameters such as 3-D bubble velocity vector, bubble diameter and interfacial area concentration, which are necessary for people to know the internal flow structures as well as local void fraction change. The local measurements were performed at 66 points within an octant symmetric triangular area of the cross-section, which agreed well with area-averaged void fractions from differential pressure gauges and the superficial gas velocity from air flow meters. Both the local void fraction and interfacial area concentration indicated radial core-peak and wall-peak distributions at low and high liquid flow rates respectively. Main flow component of the bubble velocity vector showed a power-law distribution shape with its center peak increasing with the liquid flow rate. The 2 components of the bubble velocity vector in the cross-section revealed that there exists a rotating secondary flow in the octant symmetric triangular area and the magnitude of the rotating secondary flow increases with the liquid flow rate. Some of constitutive correlations of drift-flux model for rectangular flow channels and large-diameter circular flow channels and interfacial area concentration correlations for small-diameter and large-diameter circular flow channels are selected and reviewed to study their predictabilities against the present experimental data. The comparison study shows that the drift-flux correlations by Hibiki and Ishii (2003) reasonably predict void fraction and the interfacial-area-concentration correlations by Hibiki and Ishii (2002) and Shen and Hibiki (2015) can be recommended for the prediction of interfacial area concentration in the bubbly flows in large-diameter square ducts.

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.

Evaluation of interfacial area transport equation in vertical bubbly two-phase flow in large diameter pipes

The introduction of interfacial area transport equation (IATE) has greatly improved the overall performance of two-fluid model due to the fact that the IATE can predict the interfacial area concentration (IAC) more accurately. However, models in the source and sink terms of IATE that are developed for predicting bubble coalescence and breakup are mainly based on small diameter pipe flows. Since the two-phase flow in a large diameter pipe is characterized by its multi-dimensional nature, the IATE should be confirmed before being applied to large pipe flows. From this point of view, local measurements in air–water bubbly flow systems in a large pipe with 101.6mm diameter were performed by using four-sensor optical probes. The radial profiles of the void fraction, IAC, bubble Sauter mean diameter and interfacial velocity were obtained at two axial locations of z/D=2 and 29. The simplified one-dimensional, steady-state, adiabatic one-group IATE with eight sets of bubble coalescence and breakup models was evaluated against the present experimental data and that from the literatures. The evaluation results showed that the Sun et al. (2004a) model is the best one for large diameter pipes. This model can well reflect the interfacial transfer mechanisms and can provide a reasonable prediction in general. Besides, the models of Smith et al. (2012a) and Ishii and Kim (2001) are also recommended due to their relative good performance in the prediction of IAC. Further work should be undertaken to develop a new bubble coalescence and breakup model with extra consideration of the multi-dimensional flow behavior in large pipes, if necessary.