Page 397 - Dust Explosions in the Process Industries

366 Dust Explosions in the Process Industries

necessary to replace even the k-Emodel with better approximations in the range of low
Reynolds numbers, where it is known that k-Emodel may fall short in reproducing real-
ity. Furthermore, the assumption of isotropic turbulence, which is inherent in the k-E
model, may not be acceptable for real dust clouds. Dust explosions in industry are often
comparatively slow, particularly in the initial stages, and the turbulence levels corre-
spondingly low.
It should be mentioned that Kjaldman also used his model for some introductory com-
putations of the pressure development in vented explosions, but experimental data were
not available for comparison. Kjaldman (1989) also extended the application of his
numerical model, in a slightly modified form, to simulating pulverized peat dust com-
bustion in a 5 MW furnace for heat production. Good agreement between the experimental
and the computed furnace temperature distributions was obtained.

4.4.8.4
The Clark-Smoot Model for Accelerating Coal Dust Flames

Explosions in one-end-open ducts with ignition at the closed end, as illustrated in Figure
4.63, constitutes a case where the positive feedback from combustion via expansion, flow,
and turbulence and back to combustion is particularly strong. At the same time, this case
is of primary practical significance in mine gallery explosions. This was the motivation
for the development of a numerical model of accelerating coal dust flames in long ducts
undertaken by Clark and Smoot (1985).
Like Ogle et al. (1988), Clark and Smoot adopted a comparatively simple submodel
for the coupling between flow, turbulence, and combustion rate. They used an empiri-
cal correlation of the ratio between turbulent and laminar burning velocity and the tur-
bulent Reynolds number based on the gas explosion data of Andrews et al. (1975) and
data from Richmond and Liebman’s (1975) and Richmond et al.’s (1978) large-scale
gallery coal dust explosion experiments. The correlation was

S,/S, = CRe, (4.88)

where S, and SI are the turbulent and laminar burning velocities, C is an empirical con-
stant, and Renis the turbulent Reynolds number defined as for equation (4.87). With the
eddy viscosity ,ueequal to v’Z, where v’ is the turbulence intensity and I the macroscale
of the turbulence, and introducing further correlations and assumptions, Clark and Smoot
expressed Ren as

(4.89)
and

Rei = 24.3[(1+ 0.096f(Re)2) - (4.90)

Here 2) is the kinematic viscosity,fis the Fanning friction factor of the gallery wall, Re
the Reynolds number for the overall flow in the gallery, and pdand pgare the dust cloud
density and gas phase density, respectively.