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On the formation of bubbles in gas-particulate fluidized beds

Published online by Cambridge University Press:  19 April 2006

Jerome B. Fanucci ,
Nathan Ness  and
Ruey-Hor Yen
Jerome B. Fanucci
Affiliation:
Department of Aerospace Engineering, West Virginia University, Morgantown, West Virginia 26506
Nathan Ness
Affiliation:
Department of Aerospace Engineering, West Virginia University, Morgantown, West Virginia 26506
Ruey-Hor Yen
Affiliation:
Department of Aerospace Engineering, West Virginia University, Morgantown, West Virginia 26506
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Abstract

The method of characteristics is applied to the nonlinear equations describing two-phase flow in a fluidized bed. The method shows how a small disturbance changes with time and distance and can, eventually, produce a flow discontinuity similar to a shock wave in gases. The parameters entering the analysis are the amplitude of the initial disturbance, the wavelength of the original disturbance, the particulate pressure function, the particulate size, the uniform fluidization voidage, the uniform fluidization velocity, the fluid viscosity, the particulate density, and the fluid density. A parametric study shows that the following factors delay shock formation: a decrease in particulate size, an increase in bed density, an increase in fluid viscosity, and a decrease in particulate density. Experimental data on bubble formation in gas-particulate fluidized beds show that these same factors delay bubble formation. It is concluded, therefore, that the shock front and the bubble front are one and the same thing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 2 , 25 September 1979 , pp. 353 - 367
Copyright
© 1979 Cambridge University Press

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References

Anderson, T. B. & Jackson, R. 1967 A fluid mechanical description of fluidized beds. Ind. Eng. Chem. Fundamentals, 6, 527–539.Google Scholar
Bradshaw, P., Ferriss, D. H. & Atwele, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28, 596.Google Scholar
Calderbank, P. H., Pereira, J. & Burgess, J. M. 1976 The physical and mass transfer properties of bubbles in fluidized beds of electrically conducting particles. The physical and mass transfer properties of bubbles in fluidized beds of electrically conducting particles, vol. 1 (ed. D. L. Keairns), p. 158. Washington: Hemisphere Publishing Corporation.
Davies, R. M. & Taylor, G. I. 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. Roy. Soc. A. 200, 375–390.Google Scholar
El-Kaissy, M. M. & Homsy, G. M. 1976 Instability waves and the origin of bubbles in fluidized beds. Int. J. Multiphase Flow 2, 379–395.Google Scholar
Fanucci, J. B., Ness, N. & Yen, R.-H. 1978 On the formation of bubbles in gas-particulate fluidized beds. Department of Aerospace Engineering, West Virginia University, Morgan-town, West Virginia, TR-62.
Garg, S. K. & Pritchett, J. W. 1975 Dynamics of gas-fluidized beds. J. Appl. Phys. 46, 4493–4500.Google Scholar
Jackson, R. 1963 Part I The mechanics of fluidised beds. Part I: The stability of the state of uniform fluidisation. Trans. Instn Chem. Engrs. 41, 13–21.Google Scholar
Jackson, R. 1963 Part II. The mechanics of fluidised beds. Part I: The motion of fully developed bubbles. Trans. Instn Chem. Engrs. 41, 22–28.Google Scholar
Liepman, H. W. & Roshko, A. 1957 Elements of Gasdynamics, p. 76. Wiley.
Murray, J. D. 1965 On the mathematics of fluidization. Part 1. Fundamental equations and wave propagation. J. Fluid Mech. 21, 465–493.Google Scholar
Ness, N. & Fanucci, J. B. 1977 Fluidized bed flow equations. Department of Aerospace Engineering, West Virginia University, Morgantown, West Virginia, TR-56.
Pigford, R. L. & Baron, T. 1965 Hydrodynamic stability of a fluidized bed. Ind. Eng. Chem. Fundamentals, 4, 81–87.Google Scholar
Rowe, P. N. 1971 Experimental properties of bubbles. In Fluidization (eds. J. F. Davidson & D. Harrison) p. 186. Academic Press.
Ruckenstein, E. & Tzeculescu-Filipescu, M. 1967 On the hydrodynamics of the fluidized bed. Proc. Inter. Symp. Fluidization, p. 180. Netherlands Univ. Press-Amsterdam.
Verloop, J. & Heertjes, P. M. 1970 Shock waves as a criterion for the transition from homogeneous to heterogeneous fluidization. Chem. Engng Sci. 25, 825–832.Google Scholar
Verloop, J. & Heertjes, P. M. 1974 On the origin of bubbles in gas-fluidized beds. Chem. Engng. Sci. 29, 1101–1107.Google Scholar
Verloop, J., Heertjes, P. M. & Lerk, L. A. 1974 The velocity and stability of large porosity fluctuations in homogeneous fluidized systems. Chem. Engng Sci. 29, 1109–1114.Google Scholar
Wallis, G. B. 1962 A simplified one-dimensional representation of two-component vertical flow and its application to batch sedimentation. Symp. Interact. Fluids and Particles, pp. 9–16.
Wallis, G. B. 1969 One-dimensional two-phase flow, p. 139. McGraw-Hill.