THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Jordan Y. Hristov

SCALING OF PERMEABILITIES AND FRICTION FACTORS OF HOMOGENEOUSLY EXPANDING GAS-SOLIDS FLUIDIZED BEDS: GELDART’S A POWDERS AND MAGNETICALLY STABILIZED BEDS

ABSTRACT
The concept of a variable friction factor of fluid-driven de form able powder beds undergoing fluidization is discussed. The special problem discussed addresses the friction factor and bed permeability relationships of Geldart’s A powders and magnetically stabilized beds in axial fields. Governing equations and scaling relation ships are developed through three approaches (1) Minimization of the pressure drop with respect to the fluid velocity employing the Darcy-Forchheimer equation together with the Richardson-Zaki scaling law, (2) Minimization of the pres sure drop across an equivalent-channel replacing the actual packed beds by a straight pipe with bed-equivalent obstacle of a simple geometry, and (3) Entropy minimization method applied in cases of the Darcy-Forchheimer equation and the equivalent-channel model. Bed-to-surface heat transfer coefficients are commented in the context of the porosity/length scale relationships developed. Both the pressure drop curves developments and phase diagram de signs are illustrated by applications of the intersection of asymptotes technique to beds exhibiting certain degree of cohesion.
KEYWORDS
fluidization, magnetic field stabilized bed, friction factor, permeability, scaling, Richardson-Zaki law, Darcy-Forchheimer equation, entropy minimization method, bed-to surface heat transfer, intersection of asymptotes technique
PAPER SUBMITTED: 2004-12-02
PAPER REVISED: 2005-02-04
PAPER ACCEPTED: 2006-02-13
DOI REFERENCE: https://doi.org/10.2298/TSCI0601019H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2006, VOLUME 10, ISSUE Issue 1, PAGES [19 - 44]
REFERENCES
  1. Geldart, D. Types of Gas Fluidization, Powder Technology 7 (1973),pp. 285-292
  2. Hristov, J. Magnetic field assisted fluidization - A unified approach. Part 1. Fundamentals and relevant hydrodynamic of gas-fluidized beds, Reviews in Chemical Engineering, 18 (2002), 4-5, pp. 295-509.
  3. Hristov, J.Y., Expansion Scaling and Elastic moduli of gas-fluidized magnetizable beds, in: Current Issues on Heat and Mass Transfer in Porous Media, NATO ASI "Emerging Technologies and Techniques in Porous Media" (Eds.,D. Ingham, A. Bejan, E.Mamut and I. Pop), Kluwer, Dordrecht, 2004, pp. 477-489
  4. Hristov, J.Y, Friction Factors and Internal Flow Length Scales of Gas-Solid Magnetically Stabilized Beds in Axial Fields: Scaling and applications to bed-to-surface heat transfer, Thermal Science, (2005, in press)
  5. Hristov J., Magnetic field assisted fluidization - A unified approach. Part 2. Solids batch gas- fluidized beds: Versions and Rheology, Reviews in Chemical Engineering, 19 (2003), 1, pp.1 -132
  6. Beavers G.S., Wilson, T.A. and Masha B.A., Flow Through a Deformable Porous Material, J. Appl. Mech, 42 (1975), pp. 598 602.
  7. Beavers G.S., Sparrow, E.M., Compressible Gas Flow through a Porous Material, Int. J. Heat Mass Transfer, 14 (1971), pp. 1855-1899.
  8. Bejan, A., Advanced Engineering Thermodynamics,Wiley, New York,1989.
  9. A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, UK, 2000.
  10. Hristov, J.Y, Heat Transfer between Deformable Magnetic Beds and Immersed Surfaces: Cases of Gas-Fluidized Beds, Thermal Sciences 2004-Proceedings of ASME-ZSIS International Thermal Science Seminar ITSS II, Bled, A.Bergles, I. Golobic, Cr. Amon and A.Bejan, Eds., Slovenia, June13-16, 2004,pp-267-274.
  11. Cheng P, Hsu C.T. and Chowdhury A., Forced Convection in the Entraance Region of a packed Channel with Asymmetric heating, J. Heat Transfer, 110 (1988),pp.946-954
  12. F. A. L. Dullien, Porous Media - Fluid Transport and Pore Structure ,Academic, New York, 1979
  13. Carman, P. C., Fluid flow through granular beds. Trans. Instn Chem. Eng., 15 (1937),pp. 150-166.
  14. Denn M.M, Process Fluid Mechanics, 1st ed., Prentice-Hall, Englewood Cliffs, NJ.USA, 1980
  15. Naakteboren C, Krueger P.S. and Lage J.L., Limitations of Darcy's law of Inlet and exit pressure-drops, Proceedings of ICAPM 2004, Applications of Porous Media, (Eds.A.H. Reis and A.F. Miguel), Evora, Portugal, May 24-27, 2004., pp.1-7.
  16. Lage J.L., The Fundamental Theory of Flow through Permeable media from Darcy to Turbulence, in: Transport in Porous Media (Eds.D.B. Ingham and I.Pop), Pergamon, Oxford, pp. 1-30.
  17. Spiegelman, M. Flow in Deformable porous Media. I: Simple Analysis, J. Fluid. Mechanics,247(1983),pp.17-38.
  18. Kunii D, Levenspiel OFluidization Engineering, 2nd edn., Butterworth-Heinemann, Boston, (1991)
  19. Baerns M., Effect of interparticle adhesive forces on fluidization of fine particles, Ind. Eng. Chem. Fund. 5 (1966),pp. 508-516
  20. Brown R.L., Richards, D., Principle of Powder Mechanics, Pergamon Press, London, 1970
  21. Hristov J. Magnetic field assisted fluidization - A unified approach. Part 2. Solids batch gas-fluidized beds: Versions and Rheology. , Reviews in Chemical Engineering, 19, No. 1(2003),pp. 1-132
  22. Penchev I. and Hristov J., Behaviour of Fluidized Beds of Ferromagnetic Particles in an Axial Magnetic Field, Powder Technology, 61 (1990),pp. 103-118.
  23. Penchev, I.P. Hristov, J.Y., Fluidization of Ferromagnetic Particles in a Transverse Magnetic Field, Powder Technology, 62 (1990),pp. 1-11
PDF VERSION [DOWNLOAD]
Scaling of permeabilities and friction factors of homogeneously expanding gas-solids fluidized beds: Geldart’s A powders and magnetically stabilized beds

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence