Page 292 - Dust Explosions in the Process Industries

Propagation of flames in Dust Clouds 26 I

where

ifris the radiative heat flux received by the particle per unit time;
Hc is the convective heat flux received by the particle per unit time;
Hq is the heat of reaction per unit time;
Cpis the specific heat capacity of the particle;
Tpis the temperature of the particle;
p, is the density of the particle;
x is the diameter of the particle.
HTwas determined from the Stefan-Boltzmann law by assuming that the particle is in
radiative equilibrium with the furnace wall:

H,, = Ez(T; -Ti) (4.8)
where

E is the total emissivity of the coal;
zis the Stefan-Boltzmann constant;
Tf is the furnace wall temperature.
The convective heat flux H, was taken as

where Tgis the temperature of the gas around the particle and h, is the convective heat
transfer coefficientbetween the particle and the gas determined from the Nusselt number,
assuming laminar flow around a spherical particle.
The heat of reaction per unit time Hq was taken as
7c
Hq =AW-x2 (4.10)
4
where W is the rate of devolatilization per unit of particle surface area and A is a constant.
W,as a function of time, was calculated from the experimentally determined particle
temperature as a function of time, by inserting equations (4.8), (4.9), and (4.10) in (4.7)
and applying an iterative numerical method of solution. W was found to have a peak of
4 x IOp2kg/m2 s at about 17 ms and remain fairly constant at 3 x loF2- 2 x kg/m2 s
from 20-40 ms to about 55 ms, after which it dropped rapidly to 0.
In their study of ignition and combustion of single coal particles, Gieras et al. (1985,
1986) eliminated the influence of gravity by performing the experiment during 1.4 s of
free fall of the test chamber. In this way, gravity-driven convective heat transfer was
avoided and the exclusive roles of conductive and radiative heat transfer could be stud-
ied. The experiment was performed with one or more coal particles glued onto thin
quartz needles. The smallest particle size that could be used without the needle and glue
significantly influencing the particle ignition and combustion was about 300 pm.
Therefore, the most interesting particle sizes from a dust explosion point of view (diam-
eters 400 pm) could not be studied. The observed trends are nevertheless of interest.
In one series of experiments, pairs of equal-size particles separated by a fixed center-
to-center distance D were studied after a particle had been ignited by the flame from a
burning 1mm diameter drop of n-octane. For 700 pm diameter particles, the maximum