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Research Papers: Multiphase Flows

Modeling the Onset of Gas Entrainment in a Single Downward Discharge From a Stratified Gas-Liquid Region With Liquid Crossflow

[+] Author and Article Information
R. C. Bowden

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(3), 031304 (Feb 05, 2009) (8 pages) doi:10.1115/1.3059586 History: Received August 01, 2007; Revised November 19, 2008; Published February 05, 2009

The critical height at the onset of gas entrainment, in a single downward oriented discharge from a stratified gas-liquid region with liquid crossflow, was modeled. The assumptions made in the development of the model reduced the problem to that of a potential flow. The discharge was modeled as a point-sink while the crossflow was said to be uniform at the main pipe inlet. The potential function was determined from a superposition of known solutions for a point-sink and uniform flow. The resulting system of three equations demonstrated that the flow field was dominated by the discharge and crossflow Froude numbers. The system was solved numerically and provided a relationship between the geometry, flow conditions, dip location, and critical height. The model predicted that the critical height increased with the discharge Froude number and decreased with the crossflow Froude number. With no imposed crossflow, the model prediction demonstrated agreement with transient and quasisteady experimental data to within ±30%. Existing experimental correlations showed inconsistent crossflow effects on the critical height and disagreed with the model predictions at high discharge Froude numbers.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry and coordinate system

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Figure 2

Effect of FrU on the critical height H/d

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Figure 3

Variation in dip height, h/d

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Figure 7

Example of critical values causing flow reversal (d/W=0.05)

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Figure 8

Comparison of the special case model (FrU=0) with theoretical work of (1) Andaleeb (17), and experimental works of (2) Bowden and Hassan (14), (3) Ahmad and Hassan (13), (4) Hassan (12), (5) Abdalla and Berenyi (5), and (6) Lubin and Springer (4)

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Figure 9

Effect of crossflow with comparison to experimentally obtained correlations by (1) Smoglie and Reimann (19), (2) Schrock (21), (3) Kowalski and Krishnan (23), (4) Maciaszek and Micaelli (20), and (5) Yonomoto and Tasaka (22)

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Figure 4

Variation in HOGE/h

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Figure 5

Variation in dip offset distance, b/d

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Figure 6

Variation in the offset distance, b, with the dip height, h

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Figure 10

Comparison of point-sink model with experimentally derived correlation compensating for crossflow effects (20) using ratio of exit to discharge momentum fluxes in Eq. 5

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Figure 11

Comparison with correlation compensating for crossflow effects (22) using ratio of exit to inlet mass flow rates in Eq. 10

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