Page 315 - Dust Explosions in the Process Industries

284 Dust Explosions in the Process Industries

Assuming that oxygen diffusiongoverns the burning of individualparticles, an upper
limit for the burning velocity is obtained if zis expressed in terms of the diffusion rate
of oxygen:
z = pdr2Rq3’2/(2MDpT:‘2) (4.24)

Here, D is the diffusioncoefficient at temperature Tu,R is the gas constant, T, is the aver-
age ambient gas temperature around a particle as it passes through the reaction zone, p
is the averagepartial pressure of oxygen,M is the oxygen equivalentof the fuel,expressed
in grams of fuel per mol. of oxygen. Equation (4.23)therefore takes the form

(4.25)

where k = pdp,Rq3’2/(2Mp,c‘2)
Cassel et al. illustratedthe implicationsof equation (4.25)by first estimatingthe burn-
ing time of a representative dust particle from equation (4.24).For instance, for a 25 pm
diameter aluminum particle, a time zof about 0.01 s is obtained. Assuming a value of
Su(pulpb)on the order of 2.5 m/s from experimentaldata for S,, the thickness of the burn-
ing zone in an aluminum dust flame is calculated to be on the order of 25 mm. This is.
25-100 times greater than typical values for flames of premixed gases. This compara-
tively great thickness of the burning zone is a characteristicfeature of laminar aluminum
dust flames, as confirmed by experiments (see Section 4.2.3.1).

4.2.4.2
Ballal’s Theory for Zero Gravity Conditions

Ballal (1983) postulated that the necessary and sufficient condition for the self-propa-
gation of a laminar flame through a dust cloud is

t = te +t, (4.26)
4
where t4is the quenching time; te is the evaporation,pyrolysis, or devolatilizationtime;
and t, is the chemical reaction time. The criterion simply says that a flame can propa-
gate steadily only if the quenching timejust equals the sum of the time required to gen-
erate an explosible gas mixture and the time required for completionof the chemical gas
phase reaction. Ballal claimed this approach to be universally applicable to dust clouds
of any combustible material, from metals to organic materials and even liquid sprays.
In pure carbon in 02/N,, he considered the reaction 2C + O2 +2CO as the “evapora-
tion” stage associated with te.
Evidence from flame propagation experiments under zero gravity conditions (Ballal,
1983) suggested that the laminar burning velocity of dust clouds in air is influenced by
particle size, dust concentration,volatile matter content (for coal), heat loss by radiation
from burning dust particles, and a mass transfer number B of the particles. B has the
dimensions of dust concentration and equals the stoichiometric dust concentration for
particles that react directly with oxygen in the solid state. If the main chemicaloxidation