Page 346 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 3 75

Jaeckel considered a constant volume explosion. In a typical real case, a dust explosion
is probably neither a pure constant pressure nor a pure constant volume process, since
pressure gradually builds up in the unburned cloud, althoughthe flame may not be fully
confined in volume.
As can be seen from equations (4.69) and (4.71), a substitution of e, by ep increases
C, and decreases C,. The loss L is difficult to estimate, and Jaeckel suggested, as a first
approximation, that the loss factor L be neglected. If this is done and e, is replaced by
ep2equations (4.69) and (4.71) can be written

(4.72)

(4.73)

e (eft-hand sides of equations (4.68) and (4.70), representing the heat production,
are denoted Hp, it is seen that for 0 < C < Cs,Hp is a linear function of C; and for C >
C,, it is constant and independent of dust concentration.
If the ignition temperature is considered independent of dust concentration and the loss
L is neglected, and the right-hand sides of equations (4.68) and (4.70), representingthe
heat consumption, are denoted He,He becomes a linear function of the dust concentra-
tion. According to Jaeckel’s simple model, the condition of self-sustainedflame propa-
gation is

Hp 2 He (4.74)

Zehr (1957) suggested that Jaeckel’s theory be modified by replacing the assumption of
an ignition temperature of finite value by the assumption that the dust flames of con-
centrations near the minimum explosible limit have a temperature of 1000 K above the
ambienttemperature. Zehr further assumed that the combustionis adiabatic and runs com-
pletely to products of the highest degree of oxidation and the dust particles are so small
that the dust cloud can be treated as a premixed gas. The resulting equationsfor the min-
imum explosible concentration in air are

1000M
C =- 1 (4.75)
107rn +2.966[Qm-CAI]

for constant pressure, and
1000 M
c1= (g/m3) (4.76)
107m +4.024[Qm-CAU]

for constant volume. Here M is the mole weight of the dust material and m is the number
of moles of O2required for complete oxidation of 1mole of dust; Q, is the molar heat
of combustion of the dust; ZAZ is the enthalpy increase of the combustionproducts; and
CAU is the energy increase of the combustion products.