Begell House Inc.
Multiphase Science and Technology
MST
0276-1459
8
1-4
1994
Preface
xii-xxii
10.1615/MultScienTechn.v8.i1-4.10
FUNDAMENTALS OF TWO-PHASE FLOW MODELING
1-67
10.1615/MultScienTechn.v8.i1-4.20
Donald A.
Drew
Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY USA
Graham B.
Wallis
Thayer School of Engineering, Dartmouth College, USA
The balance equations (mass, momentum and energy) for each phase in a two-phase flow are derived using ensemble averaging techniques. In order to close the constitutive equations, the results from two different computations were studied, namely a general potential flow around a rigid solid matrix and an irritational flow of an inviscid fluid around a single sphere. The systematic inclusion of all terms arising in the averaged momentum equations yields an appropriate working model for dispersed bubbly flow.
PHASE DISTRIBUTION PHENOMENA AND WALL EFFECTS IN BUBBLY TWO-PHASE FLOWS
69-123
10.1615/MultScienTechn.v8.i1-4.30
Michel
Lance
Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA), Ecole Centrale de Lyon, Ecully, France
M. Lopez
de Bertodano
Center for Multiphase Flows, Rensselaer Polytechnic Institute, Troy, New York, 12180-3590, USA
This paper summarizes the state-of-the-art in the understanding and modelling of phase distribution in bubbly flows, which is of fundamental importance for many industrial applications. The available experimental results are first discussed. The capability of the two-fluid model to predict two-phase bubbly flows in different geometries is examined. In particular, results obtained independently at Rensselaer Polytechnic Institute and Ecole Centrale de Lyon, using different numerical codes but similar closure laws are presented. The closure hypotheses adopted are based on analytical and experimental information on the dynamics of a single bubble, and on the assumption of linear superposition of shear-induced and bubble-induced turbulence. The test cases chosen here include the flow of a bubbly mixture in a vertical pipe, in a triangular duct, over a flat plate and through a sudden expansion. It is found that most of the experimental data can be reproduced with reasonable accuracy using a multidimensional two-fluid model. However, in spite of the success of such models, some important physical mechanisms are still not well understood, and are discussed in the last section.
DISPERSED FLOW - I
125-194
10.1615/MultScienTechn.v8.i1-4.40
Akimi
Serizawa
Department of Nuclear Engineering, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan
Isao
Kataoka
Institute of Atomic Energy, Kyoto University, Japan
This contribution discusses dispersed (eg. bubbly) flows, starting with a discussion of the approaches to solution of the basic conservation equations (Eulerian and Lagrangian) and the closure problem for void fraction. The interactions between the dispersed phase and turbulent eddies are then discussed and the influence of these interactions on break up and coalescence of the dispersed phase and ways in which the turbulence is modified by the interactions are reviewed. Finally, the associated experimental techniques are reviewed.
DISPERSED FLOW - II
195-206
10.1615/MultScienTechn.v8.i1-4.50
Leen
van Winjngaarden
J. M. Burgerscentre for Fluid Mechanics, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands
This paper discusses various aspects of bubbly flow including bubble interactions, averaged equations, pair distribution function, mean rise velocity and void waves. It is noted that, in the average laboratory experiment with bubbly flow, no appreciable coalescence takes place and bouncing of bubbles is the rule. It is concluded that the primary cause for transition to slug flow is that of the formation of void waves.
ANALYSIS OF MULTIPHASE FLOWS
207-255
10.1615/MultScienTechn.v8.i1-4.60
J. E.
Flaherty
Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York 12180-3590, USA
Some results and techniques are presented for analysing the two-fluid model for two-phase flow. This model is based on the equations of balance of mass and momentum for each phase. Such models can become ill posed as an initial value problem due to complex characteristics which seem to arise from the coupling between the two momentum equations. Whilst it is true that a viscous system has real characteristics, in the limit of vanishing viscosity, the complex characteristics of the inviscid system give rise to small-scale instabilities which are artefacts of the model, and not physically real. It has been shown that the problem of complex characteristics can be overcome by numerical viscosity, though this does not seem to provide inadequate replacement for the missing physics. These problems are discussed in the context of various forms of numerical modelling.
STEADY TWO-PHASE CHOKED FLOW IN CHANNELS OF VARIABLE CROSS SECTIONAL AREA
257-353
10.1615/MultScienTechn.v8.i1-4.70
Herve
Lemonnier
DTN/SE2T/LIEX/ CEA/Grenoble, 38054 Grenoble Cedex 9, France
Zbigniew
Bilicki
Institute of Fluid-Flow Machinery, Polish Academy of Sciences, ul. Gen. J. Fiszera 14, PL-80-952 Gdansk and Technical University of Koszalin, Poland
This contribution begins with a description of some experiments on choked flow in channels and then goes on to discuss a general mathematical model and its interpretation in terms of topological structure in phase space. Two models for choke flow are then presented in detail, namely the homogenous equilibrium model (and the associated gas dynamics) and the dispersed flow model. Though the modelling of critical flow has not yet reached the state where all problems and questions raised can be addressed, it is concluded that, by analysing each situation, a sufficiently high level of understanding will be reached to allow simple engineering problems to be solved confidently (for instance the problem of sizing of emergency or relief venting systems).
GAS-LIQUID SLUG FLOW:
355-469
10.1615/MultScienTechn.v8.i1-4.80
A. E.
Dukler
University of Houston, Chemical Engineering Department, Houston, Texas, 77204, USA
J.
Fabre
Insitut National Polytechnique de Toulouse, Institut de Mechanique des Fluides (UA CNRS 005), Av. C. Soula 31400, Toulouse, France
This contribution begins with a discussion of the occurrence and characteristics of slug flow. Slug flow results in high liquid velocities and hence high pressure gradients and large fluctuations in pressure gradient. However, it does provide a means of transporting large amounts of liquid. The most prevalent model of slug flow is the cell model in which a unit cell encompassing the slug and its associated stratified region is set up. To close this model, various relationships are required (slug velocity, void fraction in the slug, slug frequency etc.) and available relationships of this type are discussed. The mixing zone at the slug front is a particularly important one and is discussed in detail. Evaluation of the statistical characteristics of slug flow can be extremely useful in dealing with design problems (for example the maximum length of a slug which influences the separation equipment) and such distributions are discussed. Finally, the two-equation model for gas-liquid slug flow is presented.
CHURN FLOW
471-521
10.1615/MultScienTechn.v8.i1-4.90
S.
Jayanti
Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, London, England
Neima
Brauner
School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Ramat Aviv 6139001, Israel
The present study presents and overview of the reported work on gas-liquid churn flow, and attempts to elucidate the important physical phenomena and mechanisms associated with it. The following features of this flow pattern have been addressed: mechanisms and models for the slug-to-churn flow transition; transition from churn to annular flow; prevalence of churn flow at high liquid flow rates; churn flow in inclined tubes; and prediction of pressure drop and holdup characteristics. It is concluded that although churn flow has a complex and chaotic nature, some basic mechanisms of the flow can be identified which provide the framework for a relatively ordered view (and lines of study) of the flow pattern.
Procedures have been outlined to calculate when the flow regime would occur, and what the pressure drop and the holdup would then be. However, these design recommendations have been developed using air-water data, and their extension to other fluid systems and geometries should be investigated.
PHENOMENOLOGICAL UNDERSTANDING
523-593
10.1615/MultScienTechn.v8.i1-4.100
Thomas J.
Hanratty
Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign Urbana, Illinois 61801, USA
Mark J.
McCready
University of Notre Dame, Notre Dame, IN USA
This review discusses stratified and annular flows, with an emphasis on interfacial structure and droplet dynamics.
REVIEW OF THE PROBLEM OF MODELLING DISPERSED TWO-PHASE FLOWS
595-643
10.1615/MultScienTechn.v8.i1-4.110
Julian C. R.
Hunt
Laboratory for Aero & Hydrodynamics, Delft University of Technology Leeghwaterstraat 21, 2628 CA Delft, Netherlands
R. J .
Perkins
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW, UK
J. C. H.
Fung
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW, UK
This review of recent literature and new concepts begins with a consideration of the force of a small rigid particle, and the relevant dimensionless parameters which are defined in terms of properties of the flow field, the particle and the fluid. Force expressions are developed for the limiting cases of inviscid flow and viscous flow, and we discuss how these should be combined for low Reynolds number and high Reynolds number flows (since different interactions occur in the two extremes). The final expressions agree with experimental data and recent numerical calculations.
We then consider the motion of a particle or bubble, beginning with rising bubbles in still fluid, followed by particles in simple non-uniform flows. The importance of difference forms of lift force is discussed.
We review previous studies of the motion of small particles in turbulence. Recent computer simulations are presented to show how the lift and acceleration forces affect bubbles in non-uniform turbulent pipe flows inclined at different angles to the origin. A simple 1-D model of turbulence is developed to explain why most previous models gave incorrect results for the diffusivity of particles as a result of neglecting the spatial structure of turbulence. This model provides the basis for order-of-magnitude calculations of the diffusivity of particles in turbulence and the spectra of their velocities. These hypotheses are tested by computing the trajectories of particles in velocity fields that simulate turbulence (Kinematic Simulation).
In the last section we review how low concentrations of particles interact between each other and affect the average flow field. The latter effect is larger than the former, so that, to a good approximation, direct interactions between particles can be neglected. By a fundamental examination of how a mean flow can be generated by the drag of many small particles, it is shown that a steady flow can only be generated by a steady stream of particles if the particles interact.
PHASE SEPARATION AT T JUNCTIONS
645-713
10.1615/MultScienTechn.v8.i1-4.120
E.
Hervieu
Comissariat a l’Energie Atomique, Laboratoire d’Etude Fondamentales, Service de Thermohydraulique pour les Applications Industrielles, Centre d'etudes Nucleaire de Grenoble, 38041, Grenoble Cedex, France
Barry J.
Azzopardi
Department of Chemical, Environmental and Mining Engineering, The University of Nottingham, University Park, Nottingham NG7 2RD, England
Because of the wide variety of phenomena associated with the split of two-phase flow at junction, the problem has been approached from two extreme ends. High quality annular or stratified flow and low quality, stratified or bubbly flow are considered separately. Data, phenomena and models are considered for each case.
SOME NON-INTRUSIVE METHODS FOR DIAGNOSIS IN TWO-PHASE FLOWS
715-782
10.1615/MultScienTechn.v8.i1-4.130
J.
Leblond
ESPCI, Laboratoire de Physique et Mechanique des Milieux Heterogenes, URA C.N.R.S. 857, 10 rue Vauquelin, 75231 Paris cedex 05, France
D.
Stepowski
UMR 6614—Coria, CNRS et Universite de Rouen, Site universitaire du Madrillet, Avenue de l’universite, BP 12, 76 801 Saint Etienne du Rouvray Cedex, France
This paper presents some non-intrusive techniques which cannot be considered as common tools for the characterization of two-phase flows, but have been successfully used in other application fields. Some methods based on microwave techniques, positron emission tomography and Nuclear Magnetic Resonance seem promising for dense media characterization, others based on incoherent interaction between laser radiation and molecules in vapour or condensed phases may apply to two-phase flows where radiations are reasonably well transmitted, i.e. turbidity is lower than unity.