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Variational approach to the analysis of the effect of a distribution grid on the quality of fluidization

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Abstract

The article presents a theoretical analysis of the flow distribution in an apparatus with a fluidized bed on the assumption of minimum energy loss in the movement of the fluidizing agent through a distribution grid and the bed. The conditions of uniform fluidization were found.

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Abbreviations

S:

cross-sectional area of the apparatus or of the corresponding zone

w:

speed of the fluidizing agent

ɛ:

porosity of the bed

H:

height of the bed

ΔE:

energy loss of the fluidizing agent

ΔP:

hydraulic resistance

Δℰ, Z, s1, s2, ω1, ω0, and ψ:

dimensionless magnitudes determined by Eq. (3)

ξ:

resistance coefficient of the grid

ρ:

density of the fluidizing agent

ρs :

density of the particles of the solid phase

F:

clear cross section of the grid

g:

acceleration of gravity

K:

Coseni-Karman constant

ki :

inertial component of the coefficient of hydraulic resistance of the fixed granular bed

Re=wda/ν :

the Reynolds number for the particles

da :

particle diameter taking the shape factor into account

ν :

kinematic viscosity of the fluidizing agent

Ar=gd 3a (ρg−ρ)/ν 2ρ:

Archimedean number

δ :

relative dispersion of the concentration of the solid phase

u=(¯w−wo)/(w*−wo):

reduced speed of the fluidizing agent

w*:

swirling speed of the particles

Z*:

minimum permissible value of Z ensuring conditions of uniform fluidization

α and β:

dimensionless quantities determined by Eqs. (9)

A, B, and C:

dimensionless quantities determined by Eqs. (13)

W:

fluidization number

k:

coefficient in Zabrodsky's equation [2]

1):

zone 1

2):

zone 2

0):

at the speed of the onset of fluidization

fl):

fluidized bed

g):

grid

Literature cited

  1. N. I. Gel'perin, V. G. Ainshtein, and V. B. Kvasha, Fundamentals of the Technique of Fluidization [in Russian], Khimiya, Moscow (1967).

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  2. S. S. Zabrodsky, High-Temperature Installations with a Fluidized Bed [Russian translation], Énergiya, Moscow (1971).

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  3. Yu. A. Buevich and A. N. Deryabin, “Establishment of a nonuniform fluidization regime with uniform flow distribution of the fluiding agent,” Inzh.-Fiz. Zh.,36, No. 3, 416–425 (1979).

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  4. M. E. Aerov and O. M. Todes, Hydrodynamic and Thermal Foundations of the Operation of Apparatuses with Fixed and Fluidized Granular Bed [Russian translation], Khimiya, Leningrad (1968).

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  5. L. Neuzhil, B. Mairgofer, and G. K. Suris, “The effect of a grid on the nonuniformity of the fluidized bed,” Zh. Prikl. Khim.,49, No. 10, 2266–2273 (1976).

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Authors and Affiliations

  1. All-Union Research Institute of Organic Synthesis, Moscow

    L. S. Pozin

Authors
  1. L. S. Pozin
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Additional information

A bar above a quantity denotes its mean value, a tilde denotes uniform fluidization

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 681–686, October, 1980.

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Pozin, L.S. Variational approach to the analysis of the effect of a distribution grid on the quality of fluidization. Journal of Engineering Physics 39, 1108–1111 (1980). https://doi.org/10.1007/BF00822145

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  • DOI: https://doi.org/10.1007/BF00822145

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