Page 252 - Dust Explosions in the Process Industries

224 Dust Explosions in the Process Industries

3.6.2
AIRFLOW PARALLELTO THE SURFACE OF A POWDER
OR DUST DEPOSIT

Several investigations have also been carried out on the entrainment of particles from
powder beds by a gas flowing past the bed. Under steady conditions of turbulent gas flow
parallel with the surface of a powder bed of uniform roughness, the Prandtl-Karmanrela-
tion for rough boundaries applies (Bagnold, 1960):

(3.22)

Here v is the mean gas velocity parallel with the powder surface, measured at a distance
z from the surface,x is the characteristic surfaceroughness dimension (characteristicpar-
ticle size), zois the shear stress at the interface between gas flow and powder surface,
and p is the density of the gas. The term (~~/p)l/~= v+ called the drag velocity, has the
dimensions of a velocity. It characterizes a specific gas flow.
Bagnold (1960) suggested a two-stage mechanism for the reentrainment process. In
the first stage, the horizontal gas flow fluidizes a relatively thin layer of the powder sur-
face, whereby the interparticlebonds are broken. In the second stage, the detached par-
ticles are moved upward against gravity by eddies in the turbulent gas. This requires that
at least some of the eddies have upward vertical gas velocities exceedingthe gravitational
settling velocity of the particle in the gas. Bagnold reported experiments showing that,
in the case of deposits of particles of uniform size, the gas flow required to generate such
conditions is much higher than that needed to produce the initial fluidization of the
powder surface layer. His experimental values for v* for initial fluidization of the sur-
face of beds of monosized silica sand are shown in Figure 3.20. Bagnold suggested that
the measured increaseof v*as the particle diameterbecomes smallerin the range 80-40 pm
is not primarily caused by interparticleadhesion but by the way in which the viscous gas
interacts with the particle surface. (Interparticleforces, however, dominate when the par-
ticles become considerably smaller than 40 pm.)

0.6

0.5

0.4
c
E
0.3
>
0.2

0.1
0.0 Figure 3.20 Critical drag velocity v* for initial
fluidization of the surface of a bed of monosized
lo 40 loo *O0 400 6o08001000 l5Oo silica sand as a function of particle size of the
Particle diameter [pml sand (From Bagnold, 1960).