Page 316 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 285

reaction takes place in the gaseous phase, B is a complex function of boiling point, gas
temperature, surface temperature, heat of combustion, and the like.
By consideringthe theoreticalinfluence of these variables,Ballal(l983) arrived at the
following expressions for tq,t,, and t, in Equation (4.26):

t4 = [ag/6;+(9q/c,,,pf )(C:/C~)(~32)-i~~Tp?/AT,]-1 (4.27)

t, = c33Pf 0322 (truly evaporating particles) (4.28)
8C1(k/~p)gln(l+ B)

t, = c:PfD312 (carbon, coal) (4.29)
8f’”C,(k/~,)~4ln(l+ B)

t, = 6,/SL4 (4.30)

where the thickness of the reaction zone, S,, is defined as

(4.31)

The notation for equations (4.27)-(4.3 1) is as follows:

B is the mass transfer number (-);
C1is the ratio of mean particle diameters 020/D32(-);
C3is the ratio of mean particle diametersD30/D32(-);
Tpis the particle temperature (K);
Tp,.is the preheat zone temperature (K);
T, is the reaction zone temperature (K);
S, is the laminar burning velocity (ds);
q is the dust concentration (g/m3);
k is the thermal conductivity (J/msK);
q is the equivalence ratio (=1 for stoichiometric concentration);
6, is the thickness of reaction zone (m);
cpis the specific heat of gas at constant pressure (JkgK);
g is the subscript for gas;
pu is the density of unburned gas (kg/m3);
pf is the density of particle (kg/m3);
fis the swelling factor for particle (-);
E is the emissivity of fuel particles (-);
ois the Stefan-Boltzmannconstant (= 5.66 low8J/sm2K4);
a is the thermal diffusivity k/cpp(m2/s).

By substituting equations (4.27), (4.28), or (4.29) and (4.30) and (4.31) into equation
(4.26), a complex expression for the flame thickness 6, results. The equation is com-
posed of three main terms: a diffusion term, a chemical kinetics term, and a radiative