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Research Papers: Multiphase Flows

A Hybrid Model to Predict the Onset of Gas Entrainment With Surface Tension Effects

[+] Author and Article Information
W. Saleh, R. C. Bowden, L. Kadem

Department of Mechanical and Industrial Engineering, Concordia University, Montreal, QC, H3G 2W1, Canada

I. G. Hassan1

Department of Mechanical and Industrial Engineering, Concordia University, Montreal, QC, H3G 2W1, CanadaIbrahimH@alcor.concordia.ca

1

Corresponding author.

J. Fluids Eng 131(1), 011305 (Dec 09, 2008) (10 pages) doi:10.1115/1.2969465 History: Received November 05, 2007; Revised May 30, 2008; Published December 09, 2008

The onset of gas entrainment in a single downward discharge, from a stratified gas-liquid region, was modeled. The discharge was modeled as a point-sink and Kelvin–Laplace’s equation was used to incorporate surface tension effects. Consequently, a criterion to characterize the dip radius of curvature, at the onset of gas entrainment, was required. The dip geometry was experimentally investigated and a correlation was developed relating the dip radius of curvature to the discharge Froude number. The correlation was used in conjunction with the theoretical model. It was found that the predicted critical height demonstrated good agreement with experimental data with the three-dimensional point-sink approach, while poor agreement using the two-dimensional finite-branch approach was found. The inclusion of surface tension improved the model’s capability to predict the critical height, particularly at discharge Froude numbers below 1.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A typical header-feeder bank geometry with stratified two-phase conditions

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Figure 2

Estimated dimensionless numbers of liquid flow in a feeder branch

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Figure 5

Sample image of dip formed prior to the onset of gas entrainment

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Figure 6

The dip shape at three discharge Froude numbers in branch C

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Figure 7

Geometry used in point-sink analysis

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Figure 8

Configuration for finite-branch analysis

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Figure 9

A balance of the flow across one of the imaginary branches

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Figure 10

Example of curve fitting the dip shape

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Figure 11

The dip radius of curvature as a function of the discharge Froude number

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Figure 12

Predicted values of the critical height with and without surface tension

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Figure 13

Predicted values of the critical height with and without surface tension with 2D finite-branch modeling

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