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TECHNICAL PAPERS

Numerical Study of Two-Phase Granular Flow for Process Equipment

[+] Author and Article Information
R. Djebbar, S. B. Beale, M. Sayed

National Research Council, Montreal Road, Ottawa, Ontario K1A 0R6, Canada

J. Pressure Vessel Technol 122(4), 462-468 (Feb 01, 2000) (7 pages) doi:10.1115/1.1310366 History: Received October 01, 1999; Revised February 01, 2000
Copyright © 2000 by ASME
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References

Härkönen, E. J., 1984, “A Mathematical Model for Two-Phase Flow. Acta Polytechnica Scandinavica,” Mech. Eng. Ser., No. 88.
Härkönen, E. J., 1987, “A Mathematical Model for Two-Phase Flow, in a Continuous Digester,” Tappi J., Dec., pp. 122–126.
Scheidegger, A. E., 1974, The Physics of Flow Through Porous Media, 3rd Ed. University of Toronto Press, Toronto, ON, Canada.
Michelsen,  F., and Foss,  B., 1996, “A Comprehensive Mechanistic Model of a Continuous Kamyr Digester,” Appl. Math. Model., 20, pp. 523–533.
Saltin, J. F., 1992, “A Predictive Dynamic Model for Continuous Digesters,” Proc TAPPI Pulping Conference, Boston, MA, pp. 261–267.
Brown, R. L., and Richards, J. C., 1970, Principles of Powder Mechanics, Pergamon, Oxford, UK.
Drucker,  D. C., and Prager,  W., 1952, “Soil Mechanics and Plastic Analysis of Limit Design,” Quarterly Appl. Math., 10, pp. 157–165.
Scott, R. F., 1963, Principles of Soil Mechanics, Addison-Wesley, Reading, PA.
Savage,  S. B., 1984, “The Mechanics of Granular Flow,” Adv. Appl. Mech., 24, pp. 289–366.
Savage,  S. B., 1998, “Analyses of Slow High-concentration flows of Granular Materials,” J. Fluid Mech., 377, pp. 1–26.
Patankar, S. V., 1980, Numerical Heat Transfer, Hemisphere, New York, NY.
Spalding, D. B., 1980, “Numerical Computation of Multiphase Fluid Flow and Heat Transfer,” Recent Advances in Numerical Methods in Fluids, ed., C. Taylor, Vol. 8, pp. 139–167.
Shamlou, P. A., 1988, Handling of Bulk Solids, Theory and Practice, Butterworth & Co., London, UK.

Figures

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Schematic of the reactor vessel used in the study
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Velocity vectors for frictional granular flow, D/H=2:12,ϕ=20  deg
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Fully developed velocity profiles for frictionless and frictional granular flow in a channel
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Effect of aspect ratio on pressure, P (Pa), for incompressible single-phase flow, ϕ=ϕw=30  deg
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Pressure, P (Pa), as a function of depth D/H=2:12. Various angles of internal friction, ϕ (deg).
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Velocity vectors, viscous/viscous compressible two-phase flow
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Solid pressure, P (Pa) contours—(a) viscous fluid formulation; (b) from Härkönen 1, with permission; (c) Mohr/Coulomb formulation
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Solid-phase pressure, P (Pa), for viscous and Mohr-Coulomb formulations
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Effect of angle of internal friction, ϕ (deg), on the solid pressure, P (Pa)

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