Page 329 - Dust Explosions in the Process Industries

298 Dust Explosions in the Process Industries

of the burned fraction. Bradley and Mitcheson further emphasized the importance of
knowing the dependence of S, on pressure and temperature, and they referred to a number
of suggested relationships, including equation (4.51) proposed by Nagy et al. (1969).
In the complete three-zone computer model of Bradley and Mitcheson (1976), equa-
tion (4.58) was superfluous,because most basic relationships were accounted for directly.
Flame propagation was considered as consumption of unburned combustible mixture in
small mass decrementsdm,. However, in reality, this mass does not bum instantaneously
but passes through a reaction zone of finite thickness, and this was accounted for. The
overall model, therefore, comprises three zones, the volumes of unburned, reacting, and
burned mixture, the sum of which equals the known vessel volume. The inclusion of a
finitereaction zone is of particular interest in the context of dust explosions,where reac-
tion zone thicknesses are generally much larger than in laminar premixed gases.
The flame was, in turn, considered to consist of two zones: a preheat zone, extending
from unburned mixture temperature T, to its ignition temperature Tig,.and a reaction zone,
in which the temperature increased from Tigto the ideal equilibnum temperature Tf
This picture is in agreementwith the classical model by Mallard and le Chatelier (1883).
Tigis not a fundamental constant for a given mixture but depends on the method of
determination.
The unburned gas was assumed isotropic, but each burned gas element arising from
each mass decrement dm, was treated independently to estimate its temperature after
isotropic compression.Any energy exchange between mixture elements by conduction,
convection, or radiation was neglected.
The comprehensivecomputermodel gave good agreement with experimentaldata for
pressure versus time in laminar closed-bomb explosions of methane/air mixtures.
However, no comparisons with dust explosions were made.

4.2.5.3
Theory by Nomura and Tanaka
Nomura and Tanaka (1980) extended their theory for plane laminar burning of dust
clouds at constantpressure (Nomura and Tanaka, 1978)to laminarburning in closed ves-
sels. By making certain assumptions, they derived the general equation

(4.59)

which is slightly different from equation (4.58) by having all three pressures raised to
the power of lly,where yis the average specific heat ratio for the burned and unburned
mixture.
As before (Nomura and Tanaka, 1978), it was assumed that the dust cloud consisted
of monosized particles arranged in a regular, static pattern. However, in this case, igni-
tion occurred at a point, as opposed to an infinite plane, and the flame propagation was
spherical, as opposed to the plane, one-dimensional propagation considered earlier.
Consequently, the particle centers were considered as located at concentric spherical
shells,rather than in the regular cubicalgrid structureapplicableto plane flames.In the spher-
ical geometry, the relationship between the average interparticle distance L, the particle