Systematic Study of the Pressure Drop in Confined Geometries with the Lattice Boltzmann Method

Article

Abstract

Predicting the pressure drop in the flow through a particle-filled reactor is of great importance in chemical engineering. When the particles are relatively large compared to the characteristic length of the reactor, the confining walls can have a great influence on the flow and thus on the pressure drop. Thus, the effect of geometry on the pressure drop in packed beds is subject of extensive research since decades. Many experimental findings and derived correlations exist which differ widely. In the present work, a computer-based approach is used to study this effect systematically and to contribute to a clarification of these discrepancies. In contrast to common correlations, the results clearly show, that the pressure drop is a nonmonotonic function of the reactor hydraulic diameter-to-sphere diameter ratio. Furthermore, three different reactor geometries, a pipe, a channel and two infinitely extended plates, are studied in order to investigate the universality of the correlations. The results show that for high ratios of hydraulic diameter of the reactor to sphere diameter the three geometries behave similar, whereas for small ratios the pressure drop is difficult to cast in simple correlations.

Keywords

LB method Pressure drop Wall effect Porous media 

List of Symbols

\(\epsilon \)

Porosity

\(\Delta P\)

Pressure drop

\(\varLambda \)

Dimensionless pressure drop

\(\mu \)

Dynamic viscosity

\(\rho \)

Fluid density

d

Sphere diameter

\(d_h\)

Hydraulic pore diameter

D

Hydraulic diameter of reactor

f

Friction factor

F

Force on spheres

H

Plate distance

K

Dimensionless drag

L

Length of reactor

Re

Reynolds number

u

Fluid velocity

\(u_0\)

Superficial velocity

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied MechanicsTU-ClausthalClausthal-ZellerfeldGermany

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