The nondimensionalization of equations describing fluidization with application to the correlation of jet penetration height

Abstract

A nondimensionalization of the basic continuum equations of fluidization and the boundary conditions for these equations provides dimensionless hydrodynamic and geometric parameters which characterize the state of fluidization. For an incompressible gas and monosize, rigid spherical particles in a nonreactive, isothermal environment with no interparticle forces, it is shown that there are four dimensionless hydrodynamic parameters, involving seven physical variables: ϱ s vd 2/μ x, Stokes number; ϱ/ϱ s , ratio of gas to solid density; v 2/gx, Froude number; and ϱ vd/μ, Reynolds number. The seven physical variables are ϱ(ϱ s ), gas (solid) density, v, jet velocity, d, particle diameter, x, bed dimension, g, gravity and μ, gas viscosity. The nature and number of the dimensionless geometric parameters depend upon the geometry of the fluidized bed. These dimensionless parameters are applied to correlating data on jet penetration height, in fluidized beds. For the data on single jets, a correlation of jet penetration height, l, can be represented by: ▪ where d 0 is the injector diameter. For the data on jets in multiple jet configurations, it is represented by: ▪ These correlations are developed from 260 data points for single jets and 122 data points for multiple jets. There is not a Reynolds number, ϱ vd/μ, in either of these correlations; for the range of experimental environments in the data, this parameter had little influence on the correlations.