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Propagation of Flames in Dust Clouds 283

4.2.3.4
Miscellaneous DusVGas Mixtures

Characteristicsof laminar flames of graphite in 02/N2mixtures richer in 0, than air have
been determined by Cassel (1964), Chamberlain and Gray (1967), Bryant (1971), and
Ballal(l983). Cassel(l964) and Ballal(l983) also give data for magnesium dust flames.
For a given particle size, the burning velocities of magnesium dust clouds in air are some-
what higher than for aluminum dust clouds. Ballal(l983) further investigatedthe influ-
ence of a higher oxygen concentration than in air and the addition of hydrogen and
methane to the gas phase (hybrid mixtures).

4.2.4
THEORIES OF ONE-DIMENSIONAL LAMINAR FLAME
PROPAGATION IN DUST CLOUDS

See also Section 9.2.4.2 in Chapter 9.

4.2.4.1
Theory by Cassel, Das Cupta, and Curuswamy
To obtain an approximate equation for laminar burning in dust clouds, Cassel, Das
Gupta, and Guruswamy (1949) modified the Mallard-le Chatelier (1883) theory for pre-
mixed gases by incorporating a term for thermal radiation effects due to the particles in
a dust cloud. Their equation was

(4.22)

Here, S, is the burning velocity and ,uis the heat conductivity; Tu,Tbtand Tjare the tem-
peratures of the unburned and burned masses and of ignition; ois the emissivity of the
particle surfaces and a is a correction factor, larger than 1, that accounts for the radia-
tion of glowing combustion products (solids and gas); F is a geometrical view factor; b
is the thickness of the burning zone; cp is the specific heat of the gas, p its density,
whereas cdis the specific heat of the dust, pd its density and w its concentration;and r is
the average particle radius.
Cassel et al. pointed out that the factor b,which is assumed to have the same value in both
the conductionand the radiation terms, dependson r, w, and F. By introducingthe burning
time of a single particle, T, and equation (4.18), the factor b can be replaced by zS,p,/p,.
Equation (4.22) then takes the form

(4.23)

where K is the thermal diffusivity and equals p/(cpp+ cdw).