Void fraction prediction in annular two-phase flow
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 Kεh 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.
References (62)
- et al.
Two-phase (gas–liquid) flow phenomena – I: Pressure drop and hold-up for two-phase flow in vertical tubes
Chem. Eng. Sci.
(1960) - et al.
Steam–water void fraction for vertical upflow in a 73.9 mm pipe
Int. J. Multiphase Flow
(1986) The physical closure laws in the CATHARE code
Nucl. Eng. Des.
(1990)- et al.
The effect of channel diameter on adiabatic two-phase flow characteristics in microchannels
Int. J. Multiphase Flow
(2004) - et al.
Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow
Int. J. Heat Fluid Flow
(2011) - et al.
Entrained liquid fraction prediction in adiabatic and evaporating annular two-phase flow
Nucl. Eng. Des.
(2012) - et al.
Algebraic turbulence modeling in adiabatic gas–liquid annular two-phase flow
Int. J. Multiphase Flow
(2009) - et al.
Unified macro-to-microscale method to predict two-phase frictional pressure drops of annular flows
Int. J. Multiphase Flow
(2009) - et al.
A study of the performance of void fraction correlations used in the context of drift-flux two-phase flow models
Nucl. Eng. Des.
(2002) - et al.
Sampling probe studies of the gas core in annular two-phase flow-II: Studies of the effect of phase flow rates on phase and velocity distribution
Chem. Eng. Sci.
(1964)
Data on the upwards annular flow of air–water mixtures
Chem. Eng. Sci.
The motion and frequency of large disturbance waves in annular two-phase flow of air–water mixtures
Chem. Eng. Sci.
The interrelation between void fraction fluctuations and flow patterns in two-phase flow
Int. J. Multiphase Flow
The effect of pipe diameter on the structure of gas/liquid flow in vertical pipes
Int. J. Multiphase Flow
Investigation of two-phase flow pattern, void fraction and pressure drop in a microchannel
Int. J. Multiphase Flow
Pressure drop for steam and water flow in heated tubes
Nucl. Eng. Des.
Experimental study on void fraction in a simulated BWR fuel assembly
Nucl. Eng. Des.
Calculation of void volume fraction in the subcooled and quality boiling regions
Int. J. Heat Mass Transfer
Two-phase flow in microchannels
Exp. Therm. Fluid Sci.
Quantitative CT-reconstruction of void fraction distributions in two-phase flow by neutron radiography
Nucl. Instrum. Methods Phys. Res. A
Prediction of pressure drop during forced circulation boiling of water
Int. J. Heat Mass Transfer
Gas–liquid two-phase flow in microchannels. Part II: Void fraction and pressure drop
Int. J. Multiphase Flow
Comparison of void fraction correlations for different flow patterns in horizontal and upward inclined pipes
Int. J. Multiphase Flow
Flow development in vertical annular flow
Chem. Eng. Sci.
Investigation of the resistance during the movement of steam–water mixtures in heated boiler pipes at high pressure
Izv. Ves. Teplotekh. Inst.
Parameter Estimation and Inverse Problems
A systematic correlation for two-phase pressure drop
Chem. Eng. Progr. Sym. Ser.
Cited by (103)
Influence of a restriction on flow patterns, void fraction, and pressure drop in gas–liquid pipe flow
2024, Experimental Thermal and Fluid ScienceAn experimental study on pressure drop of air-oil flow in horizontal pipes using two synthetic oils
2024, International Journal of Mechanical SciencesAn experimental data-driven charge model for round-tube-plate-fin heat exchangers using low-GWP refrigerants
2024, International Journal of RefrigerationStudy on structure optimization and distribution characteristics of centrifugal refrigerant distributor for air conditioner
2023, International Journal of RefrigerationAn improved void fraction prediction model for gas-liquid two-phase flows in pipeline-riser systems
2023, Chemical Engineering ScienceFlow boiling pressure drop of R-1270 in 1.0 mm tube
2023, Applied Thermal Engineering
- 1
Tel.: +41 21 693 5984; fax: +41 21 693 5960.