Page 265 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 237

Hwang, Singerand Hartz (1974) performed theoretical studies of the dispersion of dust
in a turbulent gas flow in a duct, following the initial entrainment of the dust deposits
from the duct wall. In particular, they studied the entrainment of deposited dust by the
nonstationary turbulent air blast ahead of a self-sustained dust explosion sweeping
through a long duct. The objective was to predict the dust concentration in the gas flow
as a function of time and location in the duct.
The dust flux leaving the duct walls was treated as originating from single or multiple
stationaryor moving sources.Formulas and samplecomputationsfor various types of dust
somces in circular and rectangular channels were derived based on experimental dust
entrainment rates. The theoretical results appeared to agree with the physical characteris-
tics of explosion-drivendust dispersion in a 0.6 m diameter and 50 m long explosiontunnel.
In the theoretical analysis, the process of turbulent mixing was treated as a diffusion
process, using diffusion-type equations that had been successfully applied to the dis-
persion of dusts in pipes, open channels, and semi-infinite systems. The generalized
form of the diffusion equation used was

ac -
-+v .grad c = div (k grad c) (3.40)
at
where c is the dust concentration,kis the diffusioncoefficient (assumed to be 25-100 cm2/s),
and ir is the velocity with which the dust particles were convected, in addition to being
diffused, V differs from the gas velocity because of the inertia of the dust particles in the
flow. It was assumed that the effect of gravity could be neglected during the initial period
of the dispersion process and that equation (3.40), employing an appropriate value of k,
determined the gross behavior of the dust cloud.
Figure 3.28 shows an example of the computational results obtained. Dust concen-
trations that would be in the middle of the explosible range for combustible dusts have
developed at 2.5 m downstream of the dust source. However, at 3.5 m downstream, the
concentrations are below the typical minimum explosible limit range.
Hinze (1975) discussed the Tchen theory of diffusion of discrete solid particles in a
fluid of homogeneous turbulence. This theory makes the following assumptions:
1 e The turbulence of the fluid is homogeneous and steady.
2. The domain of turbulence is infinite in extent.
3. The particle is spherical and so small that its motion relative to the ambient fluid fol-
lows Stokes’law of resistance.
4. The particle is small compared with the smallest structure present in the turbulence.
5. The particle is embedded in the same fluid element during the motion.
4. Any external force acting on the particle originates from a potential field, such as the
field of gravity.

All assumptions, except number 5, may in reality actually be satisfied. However, the
mechanism of a real turbulence is such that it is hardly possible for assumption 5 to be
satisfied. If the element of fluid containing a small discrete particle could be considered
nondefonnable, it might satisfy this assumption, provided its size was larger than the
amplitude of the motion of the discrete particle relative to the fluid (no overshooting).
However, in turbulent motion, the fluid elements are distorted and stretched into long,
thin ribbons and it seems; unreasonable that the fluid element should continue to con-
tain the same discrete particles during this stretching process.