Page 323 - Dust Explosions in the Process Industries

292 Dust Explosions in the Process Industries

rate, expressed as a function of gas temperature; and h is the heat of reaction. This equa-
tion implies the calculation of the eigenvalue using the centroid of area expression given
by Spalding (1957).
Bradley et al. (1986) assumed that the fuel was essentially premixed gas generated by
rapid devolatilization of the coal particles and subsequent rapid mixing of the volatiles
with the air.Furthermore, they assumed that the methane was the essential component of
the volatiles and the presence of the char particles in the gas phase did not change the gas
compositionor chemicalkinetics.The radiativeloss from the char particles as they moved
through the flame was computed. For a chemical heat release rate q per unit surface area
of a smooth spherical particle, the total energy equation for a particle was taken as

(4.45)

Here, a is the convective heat transfer coefficient; Tpand Tgare the particle and gas tem-
peratures; E is the particle emissivity,assumed equal to unity throughout; ois the Stefan-
Boltzmann constant;v,pp,and h are the particle radius, density, and enthalpy; and tis the
time. The equation neglects radiative absorption from the walls, gas, and other particles.
The net heat-release-rate-versus-gas-temperatureprofile was calculatedusing the com-
prehensive chemical kinetic model for methane/air combustion developed by Dixon-
Lewis and Islam (1982), correcting for the rate of net energy supply from the particles
due to their heating by oxidation of the char or graphite.The correction, which was gen-
erally found to be small compared with the heat release rate from the gas combustion,
is given by

H =4m2an(Tp-T,) (4.46)

where n is the number density of particles in the cloud, and the other notations as for
equation (4.45).
Figure 4.22 shows a comparison of burning velocities predicted theoretically by
Bradley et al. and experimental data from Smoot et al. In general, Bradley et al. found
that their theory agreed well with experiments as long as devolatilization and gas phase
mixing were sufficientlyfast and the char did not create a significantheat sink. This was
found to be satisfied if the particle diameter was <lo pm and the volatile content >25%.
The basic approach suggestedby Hertzberg et al. (1982,1987)is similar to that of Ballal
(1983). It was assumed that three sequential processes are involved in the propagation
of flame through a dust/air mixture:
1. Heating and devolatilizationof dust particles.
2. Mixing of the volatiles with air.
3. Gas phase combustion of the premixed volatiles.

The characteristictime constants for the three consecutiveprocesses are z,,,z,, and
zpm.It was realized that the process of particle heating and devolatilizationis a complex
combination of conductive,convective, and radiativeheat exchangebetween the burned
products and the unburned reactants. However, the problem was simplifiedby handling
those processes implicitly in the laminar burning velocity, S,, which characterizes the
overall rate of flame propagation.A laminar flame propagating at S, has an overall reaction