Resistance of particle beds at Reynolds numbers up to Re ≈ 10 4

Abstract

In a paper previously published, a coherent representation of pressure drop in fixed beds and of fluidized bed expansion, both with spherical particles was presented. The theoretical treatment was based on an analysis of the Navier-Stokes equations. A semi-empirical formula, which combines an Euler number, a Reynolds number and a characteristic dimensional ratio r 0δ was quantitatively verified from the analysis of experimental results with Reynolds numbers not exceeding Re=200 in the case of fixed bed percolation. Recently, fixed bed percolation was investigated up to Reynolds numbers in excess of Re=10 4 with particle packings as dense as ε≈0.35 at pressures up to 25 bar. Unsatisfactory prediction of these new measurement results necessitated reexamination of the theoretical treament, resulting in an extension of the previously suggested approximation for pressure drop behaviour with packings of monodisperse spherical particles. Introduction of a pressure drop shape factor Φ D enabled the extension of the same concept to packings of non spherical polydisperse particles. The underlying idea is based on the simple consideration that it is always possible to find a packing of spherical particles with a smaller particle diameter which has the same dimensionless pressure drop behaviour as the real packing with irregularly shaped material. A practical way is shown to simply evaluate the pressure drop shape factor using a single pressure drop measurement point at any bed porosity and any gas velocity. A quantitative verification of the validity of the underlying concept has been obtained from the analysis of experimental results.