Page 395 - Dust Explosions in the Process Industries

364 Dust Explosions in the Process Industries

of the present experimentaland theoretical knowledge of the complexphysics and chem-
istry involved and that must be accountedfor in a comprehensivedust explosion model.
In his model of gas explosions, Hjertager (1982, 1984, 1986) used the induction time
for ignition, as determined in shock tube ignition experiments, as a global measure of
the chemical kinetics for the conibustionreaction.As reviewed by Eckhoff (1987), sim-
ilar experiments have been conducted with dust clouds and induction times for various
types of dust are available. A more recent example is the induction time determination
for aluminum and magnesium dust clouds in oxygen of 0.1 to 1.O bar(abs) initial pres-
sure by Boiko, Lotov, and Papyrin (1989).

4.4.8.2
Simplified Model by Ogle, Beddow, and Chen for Aluminum Dust/Air

Ogle, Beddow, and Chen (1988) developed their model for numerical simulation of tur-
bulent spherical aluminudair explosions in a closed bomb, assuming spatially uniform
pressure at any instant. Due to lack of computational power, Ogle et al. were unable to
use the k-E model or an equivalent model for describing the turbulence. Instead, they
adopted the empirical Abdel-Gayed eddy diffusivity correlation for confined turbulent
combustion of premixed gases to obtain first-orderapproximate values of the turbulent
diffusivities of heat and mass:

elv = 11Re:56 (4.87)
Here, e is the eddy diffusivity and v is the kinematic viscosity of the gas; Ren is the tur-
bulent Reynolds number, defined as Ren = v’ilh, where v’is the turbulence intensity, or
characteristic fluctuating velocity component, and il is the characteristic microscale of
the turbulence. When comparing theoretical predictions with dust explosion experi-
ments in a spherical bomb of diameter 0.34 m, Ogle et al. fixed the turbulence intensity
at 0.1 ds and the large-scale eddy size at 0.1 m in all the computations.
The model was formulated for aluminum dustlair explosions, and corresponding
experiments were conducted in the 0.34 m diameter sphericalbomb with a range of alu-
minum powders of differentparticle sizes and shapes. In the model, the influence of par-
ticle size and dust concentration was accounted for by assuming that the rate of oxidation
of the aluminum particles in the cloud was proportional to the surface area of the parti-
cles per unit volume of dust cloud. On the assumption that Al(1iquid) +A10 +AlzOis
the rate-controllingreaction in the combustion of aluminum,Ogle et al. reformulatedthe
expression for the combustionrate in terms of consumptionof molecular species, adopt-
ing the standardArrhenius form of the reaction rate coefficient.

4.4.8.3
Model by Kjaldman for PeaVAir
Kjaldman (1987) used the k-E turbulence model for homogeneous gas flow in his finite
volume simulation of dust explosions in closed and vented vessels. Referring to explo-
sion experiments in the 20 liter Siwek-sphere (Siwek, 1977) and the turbulence meas-
urements of Kauffman et al. (1984a) in a 0.95 m3spherical vessel, the values of k and E
and
at the moment of ignition in the 20 liter sphere were taken as k = (m/~)~E =