Flow Pattern and Pipe Orientation Independent Semi-Empirical Void Fraction Correlation for a Gas-Liquid Two Phase Flow Based on the Concept of Drift Flux Model

Abstract

A flow pattern and pipe orientation independent void fraction correlation is proposed in the present study. The correlation is based on the concept of drift flux model and proposes two separate expressions to model distribution parameter and drift velocity. The distribution parameter is expressed as a function of pipe orientation, phase superficial velocities and the void fraction in implicit form, while the drift velocity parameter is modeled as a function of fluid thermo physical properties, pipe orientation and void fraction. The drift velocity equation proposed by Zukoski [1] is extended for downward inclined pipe orientations. The performance of the proposed void fraction correlation is verified against void fraction data set of 5928 data points including the data for fifteen pipe diameters and eight different fluid combinations. The superiority of the proposed correlation is also illustrated by comparing it against the top performing correlations in horizontal, vertical upward and vertical downward pipe orientations and the predictions of the Woldesemayat and Ghajar [2] and Chexal et al. [3] correlations for incline pipe orientations.

Flow Patterns, Void Fraction and Pressure Drop in Gas-Liquid Two Phase Flow at Different Pipe Orientations

“…For the lowest range of void fraction in vertical upward flow, the correlation of [86] gives best performance and predicts 89 % of data points within ±30 % error bands. The correlation of [12] also gives comparable performance for the first three ranges of void fraction i.e., for a B 0.75. Similar to vertical upward flow, for the last range of void fraction in vertical upward flow [25,105] are among the top performers.…”

“…It is observed that the correlation of [105] gives consistent and superior performance in all three ranges of the void fraction. Although the accuracy of [12] correlation is not comparable with the other top performing correlations listed in Table 4.9, it is evident that this correlation gives comparable performance for the first two ranges of the void fraction. Overall it is found that for refrigerant two phases flow, even the top performing correlations have limited success in prediction of the void fraction for 0 \ a B 0.5 and 0.5 \ a B 0.75.…”

“…Thus, it is recommended for users to first verify the gas volumetric flow fraction range and then use the appropriate correlation for corresponding void fraction range. As shown in Table 4.5, for the first two ranges of void fraction in vertical downward pipe orientation, the correlation of [12] predicts the highest number of data points within ±30 and ±20 % error bands. For the next two ranges of void fraction i.e., 0.5 \ a B 0.75 and 0.75 \ a \ 1, the correlations of [25,105] give better accuracy than [12] correlation.…”

“…As shown in Table 4.5, for the first two ranges of void fraction in vertical downward pipe orientation, the correlation of [12] predicts the highest number of data points within ±30 and ±20 % error bands. For the next two ranges of void fraction i.e., 0.5 \ a B 0.75 and 0.75 \ a \ 1, the correlations of [25,105] give better accuracy than [12] correlation. As pointed out earlier, the correlation of [25] is based on a modeling method in biochemical kinetics and is neither a separated flow nor a drift flux model based correlation whereas [105] is a drift flux model based void fraction correlation.…”

“…Due to very limited data available in the literature, the entire range of void fraction is divided into three categories i.e., 0 \ a B 0.5, 0.5 \ a B 0.75 and 0.75 \ a \ 1. As listed in Table 4 Similar to downward inclined pipe orientations, the top performing correlations for the void fraction data in upward inclined pipe orientations are also categorized [12] correlation predicts the highest number of data points for the first three ranges of the void fraction up to a B 0.75. For the highest range of the void fraction i.e., 0.75 \ a \ 1, correlation of [105] is observed to give best performance and is followed by the performance of [91] correlation.…”