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TECHNICAL PAPERS

# Theoretical Analysis of the Onset of Gas Entrainment from a Stratified Two-Phase Region Through Two Side-Oriented Branches Mounted on a Vertical Wall

[+] Author and Article Information
Mahmoud A. Ahmed

Department of Mechanical Engineering, Assiut University, Assiut 71516, Egyptaminism@aun.edu.eg

J. Fluids Eng 128(1), 131-141 (Aug 14, 2005) (11 pages) doi:10.1115/1.2140804 History: Received May 31, 2004; Revised August 14, 2005

## Abstract

A theoretical analysis has been developed to predict the critical height and the location of the onset of gas entrainment during discharge from a stratified two-phase region through two oriented-side branches mounted on a vertical wall. In this analysis, a point sink model was first developed, followed by a more accurate three-dimensional finite branch model. The models are based on a new modified criterion for the onset of gas entrainment. The theoretically predicted critical height and the location of the onset of gas entrainment are found to be a function of the mass rate of each branch ($Fr1$ and $Fr2$), the distance between the centerlines of the two branches $(L∕d)$, and the inclination angle $(θ)$. The effects of these variables on the predicted critical height and the onset location were investigated. Furthermore, comparison between the theoretically predicted results and the available experimental data was carried out to verify the developed models. The comparison shows that the predicted results are very close to the measured data within a deviation percentage of 12% at $Fr1>10$. This small deviation percentage reflects a good agreement between the measured and predicted results.

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## Figures

Figure 8

Percent deviation from the predicted critical height by finite branch model using the experimental data of Maier (19) at L∕d=8.0 and θ=0 and 30deg

Figure 9

Percent deviation from the predicted critical height by finite branch model using the experimental data of Maier (19) and Parrott (14) at Fr2=56.6 and L∕d=1.5 and 2.0

Figure 10

Influence of L∕d on HOGE∕d and dual onset point for Fr2=60

Figure 11

Influence of Fr1 on HOGE∕d and dual onset point for L∕d=2.0

Figure 1

Geometry and coordinate system for finite-branch analysis

Figure 2

Comparisons between predicted and experimental results at different values of θ (0.0, 30, and 60deg) for L∕d=1.5

Figure 3

Comparisons between predicted and experimental results at different values of θ (0.0, 30, and 60deg) for L∕d=2.0

Figure 4

Comparisons between predicted and experimental results at different values of θ (0.0 and 30deg) for L∕d=8.0

Figure 5

Comparisons between predicted and experimental results at different values of L∕d (1.5 and 2) for Fr2=56.6

Figure 6

Percent deviation from the predicted critical height by finite branch model using the experimental data of Maier (19) at L∕d=1.5 and θ=0, 30, and 60deg

Figure 7

Percent deviation from the predicted critical height by finite branch model using the experimental data of Maier (19) at L∕d=2.0 and θ=0, 30, and 60deg

Figure 12

Prediction of the dual onset at different vales of L∕d (2 and 4)

## Errata

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