Page 362 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 33 7

FLAME PROPAGATION

Figure 4.38 Postulated microstructure of burning turbulent fluid. Theshaded areas represent burned
fluid, unshaded are unburned (From Spalding, 1982).
and I-’ as a measure of the corresponding specific interface surface area. He then assumed
a differential equation of the form
d(lP) =M+B+A (4.84)
dt

where M represents the influence of mechanicalprocesses such as stretching,breakage,
impact,and coalescence;B represents the influenceof the burning; andA represents influ-
ences of other processes, such as wrinkling, smoothing, and simple interdiffusion.
Spalding indicated tentative equations for M, B, and A, but emphasized that the identi-
fication of expressions and associated constants that correspond to physical reality over
wide ranges, “is a task for the future.”
It is nevertheless clear that the strong enhancing effect of turbulence on the combus-
tion rate of dust clouds and premixed gases is due primarily to the increase of the spe-
cific interface area between burned and unburned fluid by turbulence, inducedby mutual
entrainment of the two phases. The circumstancesunder which the interface itself is a
laminar flame or some thinner, elementary flame front remains to be clarified.
When discussing the specific influence of turbulence on particle combustion mecha-
nisms, Beer et al. (1984) distinguished between microscale effects and macroscale
effects. On the microscale,turbulencedirectly affects the heat and mass transfer and there-
fore the particle combustion rate. They discussed the detailed implications of this for coal
particle combustion, assuming that CO is the only primary product of heterogeneous coal
oxidation.On the macroscale, there is a competitionbetween the devolatilizationprocess
and turbulent mixing. Concerning modeling of turbulent combustion of dust clouds,
these authors stressed that three-dimensional microscopic models are too detailed to
allow ecimputer simulation without use of excessive computer capacity and computing
time. They therefore suggested alternative methods based on theories like the k-Emodel,
adopting the Lagrangian Escimo approach proposed by Spalding and coworkers (Ma,
Spalding, and Sun, 1983) or alternative methods developed to account for the primary
coherent large-scale turbulence structures (Ghoniem, Chorin, and Qppenheim, I981).
Lee (1987) suggested that the length scale that characterizes the reaction zone of a tur-
bulent dust flame is at least an order of magnitude greater than that of a premixed gas flame.