Page 322 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 29 1

In another paper, Smoot, Horton, and Williams (1977) presented their own, improved
theory for laminar coal/air flame propagation, assuming particle/gas dynamic equilib-
rium and constant pressure. The general transformation method for computerized cal-
culations of laminar burning velocities developed by Spalding, Stephenson, and Taylor
(1971)was adopted. The effects of gaseous diffusion,coal pyrolysis, char oxidation,and
gaseous reaction were considered; whereas the effects of gravity, viscous dissipation,
forced diffusion,thermal diffusion, and temperature gradients within particles were ne-
glected. The unsteady state equations were solved numerically using finite difference
techniques. The theory suggested that, in a laminar coal-dust flame, gas phase diffusion
and conduction,gas particle conduction,and coal pyrolysis are importantrate-determining
steps, while hydrocarbon and char oxidation may not be rate limiting. The importance
of gas phase diffusion processes in such flames was suggested.
The theory comprised six basic, one-dimensionaldifferential equations for

1. Conservation of gas species.
2. Conservation of particle species.
3. Particle mass consumption rate.
4. Gas phase thermal energy balance.
5. Particle thermal energy balance including radiation.
6. Particle number balance.
Computed laminar burning velocitiesfor coal dust in air,neglectingradiative effects, gen-
erally differed from experimental values by less than 25%.
Although not directly related to the theory of laminar flames, it should be mentioned
that Wolanski (1977) developed a comparatively simple, one-dimensional theoretical
model of coal dust combustion in a constant-pressure combustion chamber with recir-
culation of some of the exhaust gases.The model comprised five basic differentialequa-
tions for

1. Energy balance for the gas, including heat conduction and convection.
2. Energy balance for the solid residue, including conduction and radiation
3. Mass balance for the released volatiles.
4. Mass balance for the solid residue.
5. Mass balance for oxygen.
The set of equations is similar to that used by Smoot et al. (1977).
Wolanski calculated gas and particle temperature-versus-timeprofiles, with and with-
out recirculation and for various particle sizes and dust concentrations.For a coal of 35%
volatiles, primary and secondary air temperatures of 360 and 600 K and a wall temper-
ature of 650 K, the calculatedpeak temperatures were about 1500K for the gas and 3600 K
and 2300 K for 10 pm and 80 pm diameter particles, respectively.
The laminar burning of clouds of graphite dust in methane/air and coal dust in air was
investigated theoretically by Bradley et al. (1986). They calculated laminar burning
velocities from the profile of net heat release rate Q versus dimensionless gas tempera-
ture z,using Spalding’s(1957) analytical approach. Their equation was

e= fi (z>fz(z)h (4.44)
Here,.fi(z)is the ratio between the thermal gas conductivities at actual and unburned gas
temperatures,expressed as a function of gas temperature;f2( z)is the volumetric reaction