Page 324 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Ciouds 293

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THEORY EXPERIMENTAL
29% VM SEWELL Figure 4.22 Curves oftheoretical burning veioc-
37% VM PITTSBURGH ities for clouds in air of coal dusts of 29 and 37%
00 I I volatile matter and particle diameter IO pm; the
100 200 300 experimental points are from Srnoot et al. (I 977)
COAL CONCENTRATION [g/rn31 (From Bradley et al., 1986).

zone thickness of 6= a/&,where a is the effective diffusivity across the flame front.
The overallreaction time for speciespassing through the reaction zone is z=6/SLc;therefore,
su= (a/z)1/2 (4.47)

and, by definition,

r= zd, + z, + 7p;~z (4.48)
According to Hertzberg et al. (1982), the mixing process is normally comparatively
rapid and z, is shorter than both zdvand zpm.Furthermore,for small particles zdv << zpm,
and the process essentially is controlled by premixed gas combustion. For larger pa-
des, it was assumed that the fraction of a particle devolatilized at a time t after the par-
ticle has entered the reaction zone equals

p = I -(1 -2i,t/oO)3 (4.49)

where X is the constantrate with which the pyrolysis or devolatilizationwave progresses
into the spherical particle of initial diameter DO.It is further assumed that
io= kSucp(T,-T) (4.50)

where k is the rate constantfor the pyrolysis or devolatilizationprocess, c is the heat capac-
ity, p is the density of the unburned mixture, and Tband Tuare the gas temperatures of
the burned and unburned mixture.As the dust particles become coarser and the dust con-
centration higher, the heating and devolatilization processes begin to control the com-
bustion rate; that is, z,,> zpm.At conditions that give the highest burning velocities,
approaching 0.40 m/s, the overall time constant zis on the order of only 1 ms.