Description of Case

Practical applications of gas-liquid flow for two different components or for a single substance are encountered frequently in the petroleum, nuclear, and process industries. The two gas and liquid phases may exist in a flow of different components (e.g., air and water) and/or when there is phase change caused by evaporation and condensation of a single fluid. In the effort to gain a fundamental understanding of the complexities involved in two-phase flow, void fraction is one of the key pieces of the puzzle. In industrial applications in which there is two-phase flow, the task of sizing the equipment for gathering, pumping, transporting, and storing the two-phase mixture requires the formidable task of predicting the phase distribution in the system from the specific operating conditions. For example, in nuclear reactor technology, a boiling water reactor (BWR) uses light water as neutron moderator and coolant, and the void fraction is significant in estimating the reactivity of the reactor. The method for estimating the void fraction correctly and accurately becomes a requirement in the attempt to predict the phase distribution with reliable accuracy.

Statement of Problem

A plethora of void fraction correlations are available in the literature. This would not be a concern except for the fact that most of the correlations have some form of restrictions attached to them. For instance, one of the most common restrictions to the correlations—flow pattern dependency—is sometimes a purely subjective judgment of the investigator, especially for points on or near flow pattern boundaries. Another pitfall is that many void fraction correlations have been validated only with experimental data that are limited to specific conditions, such as pipe orientation, flow pattern, and gas-liquid combination. As a result, engineers are faced with the daunting task of choosing the appropriate correlation among the many correlations available. In a comprehensive literature search, Woldesemayat and Ghajar¹ conducted a very extensive comparison of 68 void fraction correlations available in the open literature against 2845 experimental data points obtained from various sources with different experimental facilities. The comparison showed that most of the correlations that have been developed are very restricted in terms of handling a wide variety of data sets. Thus, a general void fraction correlation for two-phase flow in pipes is needed.

Description of Solution

To predict void fraction in two-phase flow regardless of flow pattern, gas-liquid combination, and pipe inclination angle, a general void fraction correlation has been developed.¹ The correlation was based on the drift flux model and takes the following expression:

The two-phase distribution coefficient (C₀) and gas drift velocity (u_gm) in m/s are given as

where subscripts l and g refer to the liquid phase and gas phase and
C₀ = two-phase distribution coefficient
D = tube diameter, m
g = gravitational acceleration, m/s²
P_atm = atmosphere pressure, N/m²
P_sys = system pressure, N/m²
u_gm = gas drift velocity, m/s
V_sg = superficial gas velocity, m/s
V_sl = superficial liquid velocity, m/s
α = void fraction
ρ = density, kg/m³
σ = surface tension, N/m
θ = inclination angle, rad
The leading constant value of 2.9 in Equation (3) has a unit such that the drift flux velocity (u_gm) uses the units of meters per second, and Equation (3) should be used with parameters that conform to the International System of Units (SI).

Description of Results

The general two-phase void fraction correlation, Equation (1), was validated and compared with a total of 2845 experimental data points (900 data points for horizontal flow, 1542 data points for inclined flow, and 403 data points for vertical flow). The 2845 experimental data points were compiled from various sources with different experimental facilities (Table 1). The void fraction correlation, Equation (1), is a noticeable improvement over the other correlations analyzed by Woldesemayat and Ghajar.¹ Figure 1 shows the capability and robustness of the correlation to predict void fraction for various pipe sizes, inclinations, and two-phase fluid mixtures from various sources with different experimental facilities. The benefit of comparing experimental data from different facilities lies in the minimization of sample bias. Among all the 986 experimental data points, Equation (1) has predicted about 79% of the data points within ±10% and about 86% of the measured data within an error band of ±15%, as shown in Figure 1.

TABLE 1 Summary of Experimental Database Sources

Wider Applicability of Results

The general void fraction correlation, Equation (1), is widely applicable for estimating the void fraction for two-phase flow in pipes, which may include boiling and nonboiling flows. The correlation discussed here can be incorporated in analysis for estimating subcooled and saturated water flow boiling pressure drop in small-diameter helical coils.¹⁰ Helically coiled tubes often are found in heat transfer equipments that are widely used in the nuclear, chemical, cryogenic, food processing, and pharmaceutical industries. The general two-phase void fraction correlation has also shown its applicability in flow boiling of liquid nitrogen in a vertical minitube. In an experiment in flow boiling of liquid nitrogen in a vertical minitube, Fu and associates¹¹ showed that the general void fraction correlation, Equation (1), provided the best prediction in comparison with two other void fraction models. Also, in the development of analytical models, the general two-phase void fraction correlation can be incorporated in the modeling of adiabatic gas-liquid annular two-phase flow in both macroscale¹² and microscale¹² conditions. When compared with their results, Cioncolini and colleagues^12,13 noted that the general void fraction correlation, Equation (1), is among the most accurate general-purpose correlations currently available, with most of the data fitted within ±10% for macroscale¹² and ±20% for microscale.¹³

References
1. MA Woldesemayat, AJ Ghajar. Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes. International Journal of Multiphase Flow, vol. 33, no. 4, pp. 347–370, 2007.

2. BA Eaton. The Prediction of Flow Patterns, Liquid Holdup and Pressure Losses Occurring during Continuous Two-Phase Flow in Horizontal Pipelines. Ph.D. thesis, University of Texas, Austin, 1966.

3. HD Beggs. An Experimental Study of Two Phase Flow in Inclined Pipes. Ph.D. thesis, University of Tulsa, Oklahoma, 1972.

4. PL Spedding, VT Nguyen. Data on Holdup, Pressure Loss and Flow Patterns for Two-Phase Air-Water Flow in an Inclined Pipe. Eng. Report 122. University of Auckland, New Zealand, 1976.

5. H Mukherjee. An Experimental Study of Inclined Two-Phase Flow. Ph.D. thesis, University of Tulsa, Oklahoma, 1979.

6. K Minami, JP Brill. Liquid Holdup in Wet-Gas Pipelines. SPE Production Engineering, vol. 2, no. 1, pp. 36–44, 1987.

7. F Franca, RT Lahey Jr. The Use of Drift-Flux Techniques for the Analysis of Horizontal Two-Phase Flows. International Journal of Multiphase Flow, vol. 18, no. 6, pp. 787–801, 1992.

8. GH Abdul-Majeed. Liquid Holdup in Horizontal Two-Phase Gas-Liquid Flow. Journal of Petroleum Science and Engineering, vol. 15, pp. 271–280, 1996.

9. M Sujumnong. Heat Transfer, Pressure Drop and Void Fraction in Two-Phase, Two Component Flow in a Vertical Tube. Ph.D. thesis, University of Manitoba, Winnipeg, Canada, 1998.

10. A Cioncolini, L Santini, ME Ricotti. Subcooled and Saturated Water Flow Boiling Pressure Drop in Small Diameter Helical Coils at Low Pressure. Experimental Thermal and Fluid Science, vol. 32, no. 6, pp. 1301–1312, 2008.

11. X Fu, SL Qi, P Zhang, RZ Wang. Visualization of Flow Boiling of Liquid Nitrogen in a Vertical Mini-Tube. International Journal of Multiphase Flow, vol. 34, no. 4, pp. 333–351, 2008.

12. A Cioncolini, JR Thome, C Lombardi. Algebraic Turbulence Modeling in Adiabatic Gas-Liquid Annular Two-Phase Flow. International Journal of Multiphase Flow, vol. 35, no. 6, pp. 580–596, 2009.

13. A Cioncolini, JR Thome, L Consolini, CL Ong. Microscale Adiabatic Gas-Liquid Annular Two-Phase Flow: Analytical Model Description, Void Fraction, and Pressure Gradient Predictions. Heat Transfer Engineering, vol. 31, no. 4, pp. 310–320, 2010.

Be Sociable, Share!

•