Page 493 - Dust Explosions in the Process Industries

460 Dust Explosions in the Process Industries

in such cases, the flow out of the vent is subsonic. However, in the case of quite strong
process units, such as certain types of mills, the pressure ratio PJP0 during the first
part of the venting process may exceed the critical value, and the sonic flow theory
applies.
The following sections include only venting theories that were developed specifically
for dust explosions.However, as long as the dust cloud is regarded as a combustiblecon-
tinuum, there is little difference between the theoretical treatment of a dust and a gas
explosion, apart from the dust dispersion and initial turbulenceproblem. Therefore, ref-
erence should be made at this point to some central publications on gas explosion vent-
ing, including Yao (1974);Anthony (1977/1978);Bradley and Mitcheson (1978a, 1978b);
McCann, Thomas, and Edwards (1985); Epstein, Swift, and Fauske (1986); and Swift
and Epstein (1987).

6.5.2
THEORY BY MAISEY

An early attempt to develop a partial theory of dust explosion venting was made by
Maisey (1965a). As a starting point, he used a simple theory for laminar gas explosion
development in a closed spherical vessel, with ignition at the center. The radial laminar
flame front speed was, as a first approximation,assumed to be a constantfor a given fuel.
For dusts, it was estimated from Hartmann bomb test data (see Chapter 7). A central
assumption was that the maximum pressure in a closed-bombtest is proportional to the
laminar radial flame speed. However, Maisey fully appreciated that, in the Hartmann
bomb test, as in any closed-bombdust explosiontest, the dust cloud is turbulent and that
turbulence increasesthe flame speed. He suggested that Hartmann bomb test data be con-
verted to equivalent turbulent flame speeds, correspondingto the turbulence level in the
test. However,because this turbulence level is probably higher than in dust clouds in most
industrial plants, Maisey recommended a reduction of this equivalent Hartmann bomb
flame speed, according to the actual industrial situation.
The second main part of the venting problem, the flow of gas and dust out of the vent
opening, was not treated theoretically by Maisey, who instead used various experimen-
tal results to derive semi-empiricalcorrelationsbetween maximum vented explosion pres-
sure and vent area for various enclosure volumes and closed-bomb flame speeds.

6.5.3
THEORY BY HEINRICHAND KOWALL

Heinrich and Kowall(1971), followingthe philosophy outlinedin Section 6.5.1 and con-
sidering subsonic flow, arrived at the following expression for the pressure equilibrium
at the maximum pressure Pred: