Abstract
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.
Issue Section:
Multiphase Flows
1.
Zuber
, N.
, 1980, “Problems in Modeling of Small Break LOCA
,” Nuclear Regulatory Commission, Report No. NUREG-0724.2.
Reimann
, J.
, and Khan
, M.
, 1984, “Flow Through a Small Break at the Bottom of a Large Pipe With Stratified Flow
,” Nucl. Sci. Eng.
0029-5639, 88
, pp. 297
–310
.3.
Smoglie
, C.
, and Reimann
, J.
, 1986, “Two-Phase Flow Through Small Branches in a Horizontal Pipe With Stratified Flow
,” Int. J. Multiphase Flow
0301-9322, 12
, pp. 609
–625
.4.
Yonomoto
, T.
, and Tasaka
, K.
, 1991, “Liquid and Gas Entrainment to a Small Break Hole From a Stratified Two-Phase Region
,” Int. J. Multiphase Flow
0301-9322, 17
, pp. 745
–765
.5.
Parrott
, S. D.
, Soliman
, H. M.
, Sims
, G. E.
, and Krishnan
, V. S.
, 1991, “Experiments on the Onset of Gas Pull-Through During Dual Discharge From a Reservoir
,” Int. J. Multiphase Flow
0301-9322, 17
, pp. 119
–129
.6.
Hassan
, I. G.
, Soliman
, H. M.
, Sims
, G. E.
, and Kowalski
, J. E.
, 1996, “Experimental Investigation of the Two-Phase Discharge From a Stratified Region Through Two Side Branches Oriented Vertically
,” Exp. Therm. Fluid Sci.
0894-1777, 13
, pp. 117
—128
.7.
Hassan
, I. G.
, Soliman
, H. M.
, Sims
, G. E.
, and Kowalski
, J. E.
, 1996, “Discharge From a Smooth Stratified Two-Phase Region Through Two Horizontal Side Branches Located in the Same Vertical Plane
,” Int. J. Multiphase Flow
0301-9322, 22
, pp. 1123
–1142
.8.
Maier
, M. R.
, Soliman
, H. M.
, and Sims
, G. E.
, 2001, “Onsets of Entrainment During Dual Discharge from a Stratified Two-Phase Region Through Horizontal Branches With Centerlines Falling in an Inclined Plane: Part 2—Experiments on Gas and Liquid Entrainment
,” Int. J. Multiphase Flow
0301-9322, 27
, pp. 1029
–1049
.9.
Ahmad
, T.
, and Hassan
, I.
, 2006, “Experimental Investigation on the Onset of Gas Entrainment From a Stratified Two-Phase Region Through Multiple Branches Mounted on a Curved Surface
,” ASME J. Fluids Eng.
0098-2202, 128
, pp. 726
–733
.10.
Soliman
, H. M.
, and Sims
, G. E.
, 1991, “Theoretical Analysis of the Onset of Liquid Entrainment for Slots of Finite Width
,” Int. J. Heat Fluid Flow
0142-727X, 12
, pp. 360
–354
.11.
Soliman
, H. M.
, and Sims
, G. E.
, 1992, “Theoretical Analysis of the Onset of Liquid Entrainment for Orifices of Finite Diameter
,” Int. J. Multiphase Flow
0301-9322, 18
, pp. 229
–235
.12.
Armstrong
, K. F.
, Parrott
, S. D.
, Sims
, G. E.
, Soliman
, H. M.
, and Krishnan
, V. S.
, 1992, “Theoretical and Experimental Study of the Onset of Liquid Entrainment During Dual Discharge From Large Reservoirs
,” Int. J. Multiphase Flow
0301-9322, 18
, pp. 217
–227
.13.
Hassan
, I. G.
, Soliman
, H. M.
, Sims
, G. E.
, and Kowalski
, J. E.
, 1999, “The Onset of Liquid Entrainment During Discharge From Two Branches on an Inclined Wall
,” Can. J. Chem. Eng.
0008-4034, 77
, pp. 433
–438
.14.
Maier
, M. R.
, Soliman
, H. M.
, and Sims
, G. E.
, 2001, “Onsets of Entrainment During Dual Discharge From a Stratified Two-Phase Region Through Horizontal Branches With Centerlines Falling in an Inclined Plane: Part 1—Analysis of Liquid Entrainment
,” Int. J. Multiphase Flow
0301-9322, 27
, pp. 1011
–1028
.15.
Ahmed
, M.
, Hassan
, I.
, and Esmail
, N.
, 2003, “Modeling the Onset of Gas Entrainment Through a Finite-Side Branch
,” ASME J. Fluids Eng.
0098-2202, 125
, pp. 902
–909
.16.
Taylor
, G. I.
, 1950, “The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to the Planes
,” Proc. R. Soc. London, Ser. A
1364-5021, 201
, pp. 192
–196
.17.
Andaleeb
, A. F.
, Hassan
, I.
, Saleh
, W.
, and Ahmad
, T.
, 2006, “Modeling the Onset of Gas Entrainment From a Stratified Two-Phase Region Through Branches on a Curved Surface
,” ASME J. Fluids Eng.
0098-2202, 128
, pp. 717
–725
.18.
Craya
, A.
, 1949, “Theoretical Research on the Flow of Nonhomogeneous Fluids
,” Houille Blanche
0018-6368, 4
, pp. 44
–55
.19.
Banerjee
, S.
, and Nieman
, Re.
, 1982, “Fundamental Studies on Heavy Water Reactor Thermal Hydraulics
,” Heat Transfer in Nuclear Reactor Safety
, Hemisphere
, Washington, DC
, 49
–86
.20.
White
, F. M.
, 1991, Viscous Fluid Flow
, McGraw-Hill
, New York
.21.
Smith
, M. G.
, 1967, Introduction to the Theory of Partial Differential Equations
, Van Nostrand
, London
.22.
Zwillinger
, D.
, 1996, Standard Mathematical Tables and Formulae
, 30th ed., CRC
, Boca Raton, FL
.23.
Kline
, S. J.
, and McClintock
, F. A.
, 1953, “Describing Uncertainties in Single-Sample Experiments
,” Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501, 75
, pp. 3
–8
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.
