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Propagation of Flames in Dust Clouds 373

Lee (1987) anticipated some operational problems in applying the C-J theory to dust
clouds because of difficultiesin defining the relevant final states after compression and
chemical reaction. The assumption of complete chemical equilibrium may differ sig-
nificantly from actual detonation wave characteristics.
Wolanski (1988) also emphasized the complexity of the dust detonation wave, using
coal dust as an example.The measured ignition delays are on the order of 10times those
of premixed hydrocarbons. This indicates that release of volatiles from the particles is
the rate-controllingfactor. Volatiles mix with the oxidizer gas and ignite as soon as they
have been released. One cannot consider the induction period as consisting of two dis-
tinctly separable, consecutive steps, devolatilization and subsequent combustion of
volatiles. It would be expected that a similar argument applies to dusts of natural and
synthetic organic materials (see also Wolanski, 1987).
Fan Bao-Chun and Sichel(l988) developed a comprehensivemodel of the structure
of dust cloud detonations, comprisingboth the induction and the reaction zone, without
separatingthe two. The oxidation of the particles was treated as a heterogeneoussurface
reaction. Conductiveheat transfer within the particles, convectiveheat transfer between
the particles, and the gas and reaction heat release within the particles were included in
the model. However, because of lack of kinetic data, some constants in the model had
to be estimated by fitting theoretical predictions to experimental data. Transverse cellu-
lar structure was not accounted for by the model. According to Fan Bao-Chun and Sichel,
the existence of such structure in dust cloud detonations remains to be demonstrated.
Fan Zhang (1989) investigateddetonationpropagationin maize starch/oxygenclouds in
a horizontal tube of 140mm internal diameter and 17.4m length. The stoichiometriccon-
centration of maize starch in oxygen at 1 bar(abs) is 1110 g/m3.For an initial pressure of
1 bar(abs), stable detonation was observed over the dust concentrationrange from 300 to
9000 g/m3.The highest stable detonationvelocity of 1988m/s occurred at 2000 g/m3,and
the highest detonationpeak pressureof 66.9bar(abs) at 3000g/m3.The correspondingvalues
at 300 g/m3were 1766m/s and 35.8bar(abs),and at 9000 g/m3,1795ds and43.4 bar(abs).
Fan Zhang concluded, however, that the observed stable detonations could not generally
be regarded as classical C-J detonations. This is because of the comparatively long total
reactiontime, which makes the detonationpropagation dependent on the apparatus.Further
works on detonationsin dust clouds are reviewed in Section 9.2.4.9 in Chapter 9.

REFERENCES

Abdel-Gayed, R. G., D. Bradley, and M. Lawes. (1987) “Turbulent Burning Velocities: A General
Correlation in Terms of Straining Rates.” Pvoceedings of the Royal Society of London A414,
pp. 389413.
Abdel-Gayed, R. G., D. Bradley, and E K.-K. Lung. (1989) “Combustion Regimes and the Straining
of Turbulent Premixed Flames.” Combustion and Flame 76, pp. 213-218.
Aldis, D. E, R. S. Lee, and F. S. Lai. (1983, August) “Pressure Development in Explosions of
Cornstarch, Wheat Flour and Lycopodium Dust Clouds in a 20 Litre Spherical Chamber.” Pacific
Regional Meeting of Fine Particle Society, Honolulu.
Alekseev, A. G., and I. V. Sudakova. (1983) “Flame Propagation Rate in Air Suspensions of Metal
Powders.” Fizika Goreniya i Vzryva 19, no. 5, pp. 34-36. (English translation in Combustion,
Explosion, and Shock Waves (1984), pp. 564-566, published by Plenum Publishing Corporation,
New York.)