Page 325 - Dust Explosions in the Process Industries

294 Dust Explosions in the Process Industries

Hertzberg et al. (1987) suggested that, for such rapidly propagating dust flames, only the
surface regions of the dust particles can contribute volatiles to the flame. The flame
“rides the crest” of a near-stoichiometric concentration of volatiles regardless of the
dust concentration.This was considered the reason why Hertzberg et al. were unable to
detect a sharp upper explosible concentration limit for dusts.
Although excess volatiles may continue to be emitted in the burned gases at high dust
concentrations,they are emitted too late to dilute the flame front with excess fuel vapor.
Krazinski, Buckius, and Krier (1978) developed a theory for flame propagation in mix-
tures of monosized particles of low volatile coal dust and air, neglecting the role of the
volatiles but accountingfor radiative heat transfer from the burning to the unburned par-
ticles. For a stoichiometric mixture of air and 30 pm particles, an adiabatic burning
velocity of 0.72 m/s was predicted. The flame thickness was on the order of several m,
and this may in part explain why clouds of pure carbon in air are unable to propagate a
flame in laboratory-scale apparatus.
Greenberg and Goldman (1989) developed a simplified theory for coal dustlair com-
bustion for investigating the characteristicsof a counterflow pulverized coal combustor.
The model should be applicable even to laminar flames. It is related to the microscopic
behavior of the coal particles only, whereas the velocity, temperature, and composition
of the gas has to be obtainedindependentlyfrom experimentsor other theories. The model
includes drag between particle and gas, particle devolatilizationand combustion, and heat
transfer to and from the particles due to convection, radiation, and chemical reactions.

4.2.5
THEORIES OF LAMINAR FLAME PROPAGATION IN CLOSED VESSELS

See also Section 9.2.4.5 in Chapter 9.

4.2.5.1
Theories by Nagy, Conn, and Verakis

Sections 4.2.3 and 4.2.4 show that both experimentand theory confirms that the concept
of laminar burning is applicable to combustible dust clouds as well as to combustible
premixed gases. Therefore, the characteristic features of laminar dust explosions in
closed vessels should be similarto those of laminar gas explosions in closed vessels. The
explosion development in a closed spherical vessel was studied theoretically by Nagy,
Conn, and Verakis (1969). This treatment is also included in the book by Nagy and
Verakis (1983). The following simplifying assumptionswere made:

1. The equation of state for ideal gases is applicable.
2. Point ignition is at the sphere center by a negligible energy supply.
3. Viscosity and heat capacities are constant.
4. Burning velocity is low compared to the velocity of sound; that is, the pressure is spa-
tially uniform throughout the vessel at any instant.
5. The thicknessof the propagatingreaction zone is negligiblecompared to the vesselradius.
The overall flame speed 5’’ with reference to the vessel was considered as the sum of
three additive velocities: the laminar burning velocity S,, the gas expansion or contraction