Void fraction prediction in annular two-phase flow

https://doi.org/10.1016/j.ijmultiphaseflow.2012.03.003Get rights and content

Abstract

A new method to predict the void fraction in annular two-phase flow in macroscale and microscale channels is presented. The underlying experimental database contains 2673 data points collected from 29 different literature studies for 8 different gas–liquid and vapor–liquid combinations (water–steam, R410a, water–air, water–argon, water–nitrogen, water plus alcohol–air, alcohol–air and kerosene–air), for tube diameters from 1.05 mm to 45.5 mm and for both circular and non-circular channels. The new prediction method is strongly simplified with respect to most existing correlations, as it depends only on vapor quality and the gas to liquid density ratio and reproduces the available data better than existing prediction methods. Importantly, this study shows that there appears to be no macro-to-microscale transition in annular flows, at least down to diameters of about 1.0 mm.

Highlights

► New method to predict the void fraction in annular two-phase flow. ► Method covers macroscale and microscale tubes, circular and non-circular channels. ► Method works for adiabatic and evaporating flows. ► Large underlying experimental database (2673 points). ► Method based on two flow parameters (vapor quality and density ratio) and three empirical constants.

Introduction

Annular two-phase flow is one of the most frequently observed flow patterns in gas–liquid and vapor–liquid two-phase flow systems, such as steam generators, air conditioning and refrigeration systems, chemical processing plants and nuclear reactors. In annular flow, a part of the liquid phase flows as a continuous film that streams along the channel wall, while the rest of the liquid phase is dispersed as entrained droplets in the gas or vapor phase that flows in the center of the channel. Due to its practical relevance, annular flow has been extensively studied in the last decades. Nonetheless, annular flow is still actively investigated as more accurate and reliable prediction methods are required for several cutting-edge applications, such as nuclear reactor fuel optimization and power uprate, nuclear systems transient and safety analyses and microevaporators design for the thermal management of computer chips, microelectronic components, laser diodes and high energy physics particle detectors.

One of the most important parameters used to characterize two-phase flows is the cross sectional void fraction ε (simply referred to as the void fraction in what follows) representing the fraction of the channel cross sectional area occupied by the gas or vapor phase. As such, the void fraction is a flow parameter bounded between 0, corresponding to single-phase liquid flow, and 1 corresponding to single-phase gas flow. The accurate prediction of the void fraction is required in virtually any two-phase flow calculation, since it is used as input for determining numerous other key flow parameters, including the two-phase flow density, the two-phase flow viscosity and the average velocities of the two phases. Besides, the void fraction plays a fundamental role in the modeling of two-phase flow pattern transitions, heat transfer and pressure drop. The knowledge of the void fraction is also crucial in many thermal–hydraulic simulations, such as coupled neutronics–thermal hydraulics calculations and two-phase natural circulation loop flow rates and heat transport rates predictions.

Due to its importance, numerous void fraction prediction methods have been proposed so far and several assessments of prediction methods have been published, including the recent contributions by Vijayan et al., 2000, Coddington and Macian, 2002, Woldesemayat and Ghajar, 2007 and Godbole et al. (2011). According to Vijayan et al. (2000), in particular, the available void fraction prediction methods can be classified into four groups. The first group is given by slip ratio models, which specify an empirical relationship for predicting the slip between the phases. The second group is given by h models that predict the void fraction by multiplying the homogeneous model void fraction εh with an empirically derived correction factor K. Then, the third group is given by drift-flux correlations, which are based on the Zuber and Findlay (1965) drift-flux model and specify two empirical relations to predict the distribution parameter and the drift velocity. Finally, the fourth group is the so called miscellaneous correlations, which are empirical relations that do not fit into any of the other groups. By far, the majority of the void fraction prediction methods proposed to date are based on the drift-flux model. As a matter of fact, the three most accurate correlations recommended in the recent review by Woldesemayat and Ghajar (2007) are drift-flux models.

The purpose of the present study is to present a new void fraction prediction method specifically designed for annular two-phase flow. This new prediction method covers both macroscale and microscale channels, adiabatic and evaporating flow conditions and is strongly simplified with respect to most existing correlations, as it depends only on vapor quality and the gas to liquid density ratio. As will be shown, the new prediction method reproduces the available data better than existing correlations and extrapolates to non-circular channels. This new method is part of a unified annular flow modeling suite that is currently being developed by the authors that also includes methods to predict the axial frictional and total pressure gradients, the annular liquid film thickness, the liquid film and gas core velocity profiles, the convective boiling heat transfer coefficient and the entrained liquid fraction (Cioncolini et al., 2009a, Cioncolini et al., 2009b, Cioncolini and Thome, 2011, Cioncolini and Thome, 2012). The present method replaces the correlation of Woldesemayat and Ghajar (2007) that has been used previously in this modeling suite.

In what follows, the experimental void fraction databank collected for use here is presented in Section 2. The new void fraction prediction method is described in Section 3, followed by results and discussion presented in Section 4.

Section snippets

Experimental database description

The main details regarding the experimental annular flow databank for circular tubes are summarized in Table 1, while a selection of histograms that further describes the collected data is shown in Fig. 1. The database includes 2633 measurements of the void fraction collected from 24 different literature studies that cover 8 different gas–liquid and vapor–liquid combinations (both single-component saturated fluids such as water–steam and refrigerant R410a and two-component fluids, such as

New prediction method

As already discussed, the drift-flux model framework has been quite successful in developing general purpose void fraction prediction methods, capable of handling two-phase flows regardless of the flow pattern. As noted by Beattie and Sugawara (1986) and Brennen (2005), however, the drift-flux approach is not particularly appropriate for modeling annular flows. Drift-flux models, in fact, are designed to handle distributed and unseparated two-phase flows where one phase is continuous, the other

Results and discussion

The comparison of the measured void fraction data from Table 1 with the predictions of Eqs. (15), (16) is presented in Fig. 4 (top). The statistical comparison between measured data from Table 1 and predictions is reported in Table 3, which includes also the results of a selection of other frequently used void fraction prediction methods, such as the homogeneous model and those of Lockhart and Martinelli, 1949, Baroczy, 1966, Zivi, 1964, Smith, 1969, Armand and Treschev, 1947, Woldesemayat and

Conclusions

A new prediction method for the void fraction in annular two-phase flow has been proposed. The underlying experimental database contains 2633 data points for circular tubes covering both macroscale and microscale flow conditions and 40 additional data points for non-circular channels. The new prediction method is strongly simplified with respect to most existing correlations, as it depends only on vapor quality and the gas to liquid density ratio, and covers vapor qualities from 0 to 1, density

Acknowledgements

G.P. Celata (ENEA), A. Ghajar (Oklahoma State University) and T. Shedd (University of Wisconsin) are gratefully acknowledged for providing their void fraction data. A. Cioncolini is supported by the Swiss National Science Foundation (SNSF) under Contract No. 200020-129624/1.

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