Momentum transfer through packed beds of various particles in the turbulent flow regime

Abstract

The flow of air through packed beds of solid and hollow particles of a wide range of geometries was studied, with particular reference to the effect of the particle shape on the pressure drop in the turbulent range. A method of analysis based on the concept of stagnant void fraction and the principle of drag additivity has been developed. Equations for estimating the stagnant voidages for various particle shapes arranged in a random pattern in a packed bed were derived. A new type of friction factor based on this approach was correlated satisfactorily with a shape factor. The momentum transfer data were also correlated with the sphericity of the particles. SCOPEPacked beds play a far greater role in many aspects of chemical and metallurgical processing than commonly realized. Simple in design, low in capital cost, and of rugged construction, they find application in a wide variety of operations such as absorption, drying, dust collection, separation, combustion, filtration, catalysis, and solid-fluid contacting in general. Their major operating cost is directly related to the pressure drop they create in the fluid-handling system. It is therefore surprising to note that the latter can be predicted with so little reliability when the particles in the bed depart somewhat from the spherical shape.The objective of this work was to investigate and correlate the effect of particle shape on the behavior of fluid flow through beds of solid and hollow shapes arranged in isotropic randomness in the turbulent range. To this end, a wider range of particle shapes has been investigated than has been hitherto reported in the literature and particular attention has been paid to the behavior of mixtures of particles of different ihapes and sizes.Numerous investigations were carried out in the past on momentum transfer through packed beds. Scheidegger (1961) critically reviewed the earlier models which have been proposed to account for the flow behavior through packed beds and porous media. Of these, the most widely used is the channel model, which envisages the packed bed as consisting of an assembly of tortuous conduits.Typical of this school is the correlation developed by Ergun (1952).At a very early stage, Burke and Plummer (1928) had proposed a discrete particle model which regards the system as consisting of an assembly of particles submerged in the flowing fluid, each possessing its own individual boundary layer. This approach was later expanded somewhat by Ranz (1952). Both models provide reasonably good pressure drop predictions for spheres or nearspherical shapes but are inadequate for particles of low sphericity.The next advance in the field was provided by Kusik and Happel (1962) who proposed yet another model, based on the consideration that the particle wake effectively decreases the area available for flow, thus creating stagnant regions in the fluid, of void fraction € b e Galloway and Sage (1970) reported the values of Eb for different particle shapes from available transport data on single particles and on pack...

Flow maldistribution in packed beds: A comparison of measurements with predictions

“…It follows that the use of this equation, or the use of relation-ships derived from it, becomes questionable when applied to distances that are comparable to the size of the particles that make up the packing. Another important limitation of the Ergun equation, as cited by Gauvin and Katta (1973), is the fact that it is not appropriate for systems containing partides of low sphericity.…”

Effect of material type and particle size distribution on pressure drop in packed beds of large particles: Extending the Ergun equation

“…Therefore, for a sphere / = 1, and for non-spherical particles 0 < / < 1. Many experimental and modeling studies have been conducted to find a correlation between bed voidage and particle properties [15,[18][19][20][21][22][23]. These studies have shown that voidage of a packed bed depends not only on particle sphericity but also on several other factors including particle size and PSD, surface roughness, method of packing, and Nomenclature A, B constants in Eq.…”

Contact angle and film jumps

“…Each cell contains a particle surrounded by a fluid envelope, ie , the entire influence due to each particle is confined to the cell of fluid with which it is associated. See for an evaluation of this class of models [114,117] and also the recently proposed model of Neale and Nader [43,334], which predicts JD and k for random sphere packings solely as a function of e and d.…”