Drag coefficient and relative velocity in bubbly, droplet or particulate flows

AICHE Journal - Tập 25 Số 5 - Trang 843-855 - 1979
Mamoru Ishii1, N. Zuber2
1Reactor Analysis and Safety Division Argonne National Laboratory Argonne, Illinois 60439
2Reactor Safety Division U. S. Nuclear Regulatory Commission Washington, D. C.

Tóm tắt

AbstractDrag coefficient and relative motion correlations for dispersed two‐phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model. The results are compared with a number of experimental data, and satisfactory agreements are obtained at wide ranges of the particle concentration and Reynolds number. Characteristics differences between fluid particle systems and solid particle systems at higher Reynolds numbers or at higher concentration regimes were successfully predicted by the model. Results showed that the drag law in various dispersed two‐phase flows could be put on a general and unified base by the present method.

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Tài liệu tham khảo

Basset A. B., 1888, A Treatise on Hydrodynamics

1961, A Treatise on Hydrodynamics

Boure J.andM. Réocruex “General Equations of Two‐phase Flows ” 4th All Union Heat and Mass Transfer Conference Minsk USSR (1972).

10.1002/aic.690100610

10.1063/1.1700493

Burgers J. M., 1941, Proc. Konikl. Akad. Wetenschap, 44, 1045

1942, Proc. Konikl. Akad. Wetenschap, 45, 9

10.1017/S0022112058000513

Collier J. G., 1972, Convective Boiling and Condensation, 24

Delhage J. M. Equations fondamentales des écoulements diphasiques Part 1 and 2 CEA‐R‐3429 France (1968).

10.1007/BF01503023

10.1016/0009-2509(67)80149-0

Gayler R., 1953, Liquid‐Liquid Extraction: Part IV, Trans. Inst. Chem. Eng., 31, 57

Govier G. W., 1972, Flow of Complex Mixtures in Pipe

10.1002/aic.690030230

10.1002/aic.690040214

10.1002/aic.690060222

Hawksley P. G. W., 1951, Some Aspects of Fluid Flow, 114

10.1002/aic.690010303

10.1002/aic.690210212

Ishii M. “One‐Dimensional Drift‐Flux Model and Constitutive Equations for Relative Motion between Phases in Various Two‐Phase Flow Regimes ” Argonne National Laboratory Report ANL‐77‐47 (1977).

Ishii M., 1975, Thermo‐Fluid Dynamic Theory of Two‐Phase Flow

10.1002/aic.690220210

Kutateladze S. S., 1972, Elements of the Hydrodynamics of Gas‐liquid Systems, J. Fluid Mech., 1, 29

Lackme C., 1973, Two Regimes of a Spray Column in Counter‐current Flow, AIChE Sym. Heat Transfer R. and D., 70, 59

Landel R. F. B. G. Moser andA. J.Bauman “Rheology of Concentrated Suspensions: Effects of a Surfactant ” 4th Int. Congress on Rheology Brown Univ. Proc. Part 2 p.663(1965).

10.1002/aic.690050312

10.1002/aic.690130311

10.1021/j150440a006

Novosad Z., 1954, Heat Transfer in Two‐phase Flow: Gas‐liquid, Chem. Listy, 48, 946

Peebles F. N., 1953, Studies on the Motion of Gas Bubbles in Liquid, Chem. Eng. Prog., 49, 88

Rannie W. D., 1962, Detonation and Two‐Phase Flow

Réocruex M. “Contribution á l'étude des désbits critiques en eculement disphasique eau vapeur ” Ph.D. Thesis Univ. of Grenoble France (1974).

Richardson J. F., 1953, Sedimentation and Fluidization: Part 1, Trans. Instn. Chem. Eng., 32, 35

10.1088/0508-3443/3/8/306

Serizawa A. “Fluid‐Dynamic Characteristics of Two‐phase Flow ” Ph.D. Thesis Kyoto University Japan (1974).

10.1002/cite.330261109

10.1021/ie50415a005

10.1098/rspa.1932.0169

Tchen C. M. “Mean Value and Correlation Problems Connected with the Motion of Small Particles Suspended in a Turbulent Fluid ” Ph.D. Thesis Delft Hague (1947).

Thomas D. G., 1963, Transport Characteristics of Suspensions VII, AIChE J., 9, 311

10.1016/0095-8522(65)90016-4

10.1016/0009-2509(56)80031-6

Vernier P., 1968, General Two‐Phase Flow Equations Applied to the Thermohydrodynamics of Boiling Nuclear Reactor, Energie Primaire, 4, 1

Wallis G. B., 1969, One‐Dimensional Two‐Phase Flow, 175

10.1016/0301-9322(74)90003-2

10.1002/aic.690050423

Wen C. Y., 1966, Mechanics of Fluidization, Chem. Eng. Prog. Sym. Series, Fluid Particle Technology, 62, 100

Werther J., 1974, Influence of the Bed Diameter on the Hydrodynamics of Gas Fluidized Beds, AIChE Sym. Series, 70, 53

10.1002/aic.690110106

Zenz F. A., 1960, Fluidization and Fluid Particle Systems

10.1016/0009-2509(64)85067-3

Zuber N. “Flow Excursions and Oscillations in Boiling Two‐Phase Flow Systems with Heat Addition ” Proceedings of Sym. of Two‐Phase Flow Dynamics 1 1071(1967).

Zuber N.andJ. Hench “Steady State and Transient Void Fraction of Bubbling Systems and Their Operating Limits ” General Electric Co. Report No. 62GL100 (1962).

10.1115/1.3689137

Zuber N. F. W. Staub G.Bijwaard andP. G.Kroeger “Steady State and Transient Void Fraction in Two‐Phase Flow Systems ” General Electric Co. Report GEAP‐5417 Vol. 1 (1967).