doi:10.1016/S0301-9322(99)00041-5
Copyright © 1999 Elsevier Science Ltd. All rights reserved.
Shape of long bubbles in horizontal slug flow
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J. R. Fagundes Netto, J. Fabre
, 
and L. Peresson
Institut de Mécanique des Fluides de Toulouse, UMR CNRS-INP-UPS 5502, Allée du Professeur Camille Soula, 31400 Toulouse, France
Received 28 December 1998;
revised 14 April 1999.
Available online 14 October 1999.
Abstract
This paper presents a theoretical and experimental study of the shape of long isolated bubbles similar to those observed in horizontal slug flows. Bubbles of different volumes were studied, their lengths varying from 30 to 100 times the pipe diameter. Two different shapes were observed corresponding to plug and slug flow regimes. The transition between plug and slug flow was shown to depend on both Froude number and bubble length. A model based on the mass and momentum conservation equations of each phase is proposed. It is able to predict the transition between plug and slug flow regimes as well as the volume and the shape of long bubbles. It is shown that usual slug flow codes that aim to predict the void fraction tend to overestimate the gas fraction in the bubble region. The model may be easily implemented into slug tracking codes.
Author Keywords: Two-phase flow; Slug flow; Plug flow; Bubble shape; Flow pattern; Transition
Fig. 1. Gas–liquid horizontal slug flow.
Fig. 2. Lengths probability density functions (PDF), after Grenier (1997); jL=jG=1.0 m/s; D=53 mm; measured at 84 m from inlet: (a) long bubble, (b) liquid slug.
Fig. 4. Test loop scheme.
Fig. 5. Comparison between wire and ring sensor: (a) 0.7 m/s, (b) 1.5 m/s. ——— Wire; ——— Ring.
Fig. 6. Superposition of the signal from five wires: (a) 0.5 m/s, (b) 1.8 m/s.
Fig. 7. Bubble tail: (a) 0.6 m/s, (b) 1.0 m/s, (c) 1.5 m/s.
Fig. 8. Bubble nose: (a) 0.6 m/s, (b) 1.0 m/s, (c) 1.5 m/s.
Fig. 9. Influence of the bubble volume: (a) 0.6 m/s, (b) 1.2 m/s.
Fig. 11. Bubble shape: body solution for U=1.8 m/s and V=2.2 m/s.
Fig. 12. Hydraulic jump at the back of the bubble.
Fig. 13. Transition between the two intermittent regimes.
Fig. 14. Regime transition, D=95.3 mm, LS=32D.
Fig. 15. Model validation: low liquid flow rates: (a) 0.5 m/s, (b) 0.6 m/s, (c) 0.7 m/s, (d) 0.8 m/s. ——— Exp. data; ——— Model.
Fig. 16. Model validation: high liquid flow rates: (a) 1.0 m/s, (b) 1.2 m/s, (c) 1.5 m/s, (d) 1.8 m/s. ——— Exp. data; ——— Model.
Fig. 17. Level jump position: comparison between model and experimental data.
Fig. 18. Shape at low flow rates: FrU=+ 1.0; □ 1.5; • 2.0.
Fig. 19. Shape at high flow rates: FrU= • 3.0; □ 5.0; + 10.0.
Fig. 20. Ratio between the actual mean void fraction and the void fraction of a bubble of infinite length: FrU= • 3.0; □ 5.0; + 10.0.
Fig. 21. Length of bubbles where 
αG
=0.90αG∞
Fig. A1. Geometric relations.
Fig. A2. Evolution of the wetted perimeter with the liquid volume fraction ——— Exact value; ------ .
Fig. A3. Evolution of (dh/dαL) with the liquid volume fraction ——— Exact value; ------ dh/dαL=0.820.
Fig. A4. Evolution of Φ with the liquid volume fraction. ——— Exact value; ------ .
Table 1. Acquisition frequency
Corresponding author. Tel.: +33-5-6128-5853; fax: +33-5-6128-5899; email: fabre@imft.fr
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