Page 288 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 257

by oxygen accordingto the consecutivescheme 2C +O2-+ 2CO and 2CO + 0, -+ 2C02
takes place close to the surface. Graaf carried out experiments that supported van der
Held’s theory.
However, conclusionsfrom experimentswith burning of comparatively large samples
of carbon may not necessarily apply to the burning of very small particles. Ubhayakar
and Williams (1976) studied the burning and extinction of single 50-200 pm diameter
carbon particles in quiescent mixtures of oxygen and nitrogen, ignited by a light flash
from a pulsed ruby laser. An initial objective of their study was to investigate whether a
gas phase burning mechanism or a surface burning mechanism, possibly accompanied
by pore diffusion, governs the combustion of submillimetercarbon particles. An addi-
tional objective was to obtain burning duration data for such small particles. The lowest
mass fsaction of oxygen used in the oxidizer gas was 0.5, which is considerably larger
than in air. They concluded that, in the temperature range 2000-3500 K, the kinetics of
the carbon oxidation could be represented by a surface reaction producing CO and
having an activation energy of 75 kJ/mole. As expected, the maximum temperature at
the particle surface increased with increasing oxygen fraction in the oxidizer gas, At
atmospheric pressure, it was about 3000 K in pure oxygen and about 2200 K at an
oxygen mass fraction of 0.6. Typical particle burning durations at atmosphericpressure
were 60 ms for 100pm diameter particles and 25 ms for 60 pm particles.For low oxygen
mass fractions, extinction occurred before the particles had burned away, and this
explairiedwhy burning times for a given particle size were shorter in atmospheres of lower
oxygen mass fractions than in pure oxygen.
In a purely theoretical investigation,Matalon (1982) considered the quasi-steady burn-
ing of a carbon particle that undergoes gasification at its surface by chemical reaction,
followedby a homogeneousreaction in the gas phase. The burning rate M was determined
as a function of the gas phase Damkbhler number D, (ratio of chemical and diffusioncon-
trolled reaction rates) for the whole range 0 < D, < 00. The monotonic M(D,) curve,
obtained for Comparatively hot or cool particles, described the gradual transition from
frozen flow to equilibrium.For moderateparticle temperatures,the transition was abrupt
and the M(D,) curve was either S-shaped or Z-shaped, depending on the relative impor-
tance of the two competitive surface reactions 2C + O2-+ 2C0 and C + C02-+ 2GO.
Specht and Jeschar (1987) also investigated the governing mechanisms for the com-
bustion of solid carbon particles of various diameters. The chemical reactions consid-
ered were the sameas discussed previously, but it was found that their relative importance
depends on particle size via its influence on the Damkohler number D,.
On the basis of idealized considerations, Fernandez-Pello (1982) derived theoretical
expressionsfor the instantaneouslocal mass burning rate and the overall regression rate
(rate of reduction of the particle radius) for the combustionof a sphericalcondensedfuel
(e.g.?carbon) particle in a forced convective oxidizing gas flow. The model is illustrated
schematicallyin Figure 4.3.
The equations derived are of the form
dwe a
-= ---(Re)’/’f,(B, 6, 0) (4.4)
dt re