Page 249 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 22 7

3.5.5
PROPAGATION OF LARGE-AMPLITUDE PRESSURE WAVES
IN DUST CLOUDS

Rudinger (198O), also discussed the propagation of shock waves and large-amplitude
waves of arbitrary form in dust clouds. Shock waves are of primary importance in the
propagation of dust cloud detonations but are also generated in fast, high-turbulencedust
cloud deflagrations.Because the volume fraction of the particles in an explosibledust cloud
at atmospheric pressure is very small, it can be neglected in the theoretical treatment.
The speed of a shock wave is at least on the order of the speed of sound. This means
that, even for a particle of only 0.1 pm diameter,the velocity and thermal relaxation times
z, and z, are about lo3times longer than the period during which a shock passes the par-
ticle. Therefore, the dynamic and thermal conditions of particles are the same immedi-
ately after the shock front has passed as just before it passes, and particle movement can
be omitted from the equations describing conservation of mass momentum and energy
of the gas across the shock front itself.
However, immediately after a shock has passed, the dust cloud is in a state of non-
equilibrium and the particles start to move in relation to the gas. The distancebehind the
shock required to reach velocity equilibrium between particles and gas is on the order
of 0.5 in (0.3 m for 10pm glass spheresin air at a particle mass fraction q= 0.17 accord-
ing to Rudinger, 1980). Temperature equilibrium is established at a similar distance
behind the shock. However, these estimates are somewhatuncertain because they depend
on a number of assumptions.
The theoretical analysisor arbitrarynonsteady, large-amplitudepressure waves through
dust clouds is even more complicated than the shock wave analysis. As pointed out by
Rudinger (1980), it is necessary to solve a complete set of partial differentialequations,
using the method of characteristics.An analysis of this kind was undertaken by Rudinger
and Chang (1964).

3.6
DISLODGEMENT OF DUST PARTICLES FROMA DUST OR
POWDER DEPOSIT BY INTERACTIONWITH AN AIRFLOW

3.6.1
AIRFLOW PARALLELTO A MONOLAYER OF PARTICLES
ON A PLANE, SMOOTH SURFACE
A simple configuration for investigating particle dislodgement is a monolayer of parti-
cles adhering to a plane of smooth surface. This well-defined geometry enables system-
atic comparisonbetween the drag force exerted on the particle by the gas and the adhesion
force between the particle and the substrate. Corn and Stein (1965) carried out particle
monolayer dislodgementstudies in a small laboratory-scalewind tunnel of cross section
only 1 mm x 25 mm. In such systems, the gas velocity profile is well defined and hence
also the gas velocitypast the particles, and the drag forces acting on them can be estimated