Wärme - und Stoffübertragung

, Volume 21, Issue 5, pp 291–296 | Cite as

Analysis of flow channeling near the wall in packed beds

  • S. M. White
  • C. L. Tien
Article

Abstract

The phenomenon of flow channeling in packed beds is investigated in the present analysis. A closed-form solution is obtained from the volume-averaged second-order momentum equation with the no-slip condition at the wall, using an exponential porosity distribution typical of packed beds. The predicted velocity profile shows the most important features of flow channeling: the sharp peak in the velocity near the wall, and the approach to the Darcy velocity far from the wall. The predictions are consistent with previous numerical results and with velocity measurements made downstream of a packed bed. The compact expression for the velocity given here is shown to be convenient for analyzing other packed-bed characteristics, such as the effective permeability of a finite-sized bed.

Keywords

Permeability Porosity Velocity Profile Velocity Measurement Flow Channeling 

Nomenclature

D

physical length scale, particle diameter

Da

ϰ/L2, Darcy number

G

Green's function

s

e−t, width of the fluid film inz variable

T

dimensional fluid film thickness

t

T/D, dimensionless film thickness

U

dimensional velocity

UD

κ/μ)dP/dX, Darcy velocity used in scaling

u

U/U D , dimensionless velocity

w

approximate velocity profile

Y

dimensional distance from the solid boundary

y

Y/D, dimensionless physical distance

z

e−y, transformed variable

Greek letters

ɛ

porosity

κ

permeability

μ

fluid viscosity

ν

square root of modified inverse Darcy number

ξ

dummy integration variable

τ

wall shear

Subscripts

D

based on Darcy velocity

eff

effective value

s

superficial or area-averaged value

0

evaluated at the wall

evaluated far from a solid boundary

Analyse der Strömungskanalisierung in der Nähe der Wand eines Festbetts

Zusammenfassung

In der vorliegenden Analyse wird das Phänomen der Strömungskanalisierung im Festbett untersucht. Es gelang, eine geschlossene Lösung der volumetrisch gemittelten Impulsgleichung 2. Ordnung zu erzielen, wobei schlupflose Strömung an der Wand und eine exponentielle Porositätsverteilung, typisch für das Festbett, angenommen wurden. Das vorhergesagte Geschwindigkeitsprofil zeigt die wichtigsten Eigenschaften der Strömungskanalisierung: das scharf ausgebildete Maximum der Geschwindigkeit in Wandnähe und die Annäherung an die Darcy-Geschwindigkeit weit weg von der Wand. Die Vorhersagen sind konsistent mit früheren numerischen Ergebnissen und mit Geschwindigkeitsmessungen, die stromabwärts vom Festbett gemacht wurden. Die hier vorgestellten kompakten Formulierungen für die Geschwindigkeit erwiesen sich als bequeme Analysemethode für andere Charakteristiken eines Festbettes, wie z.B. die effektive Permeabilität eines endlichen Festbettes.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • S. M. White
    • 1
  • C. L. Tien
    • 1
  1. 1.Mechanical Engineering Dept.University of CaliforniaBerkeleyUSA

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