Page 450 - Dust Explosions in the Process Industries

Ignition of Dust Clouds and Dust Deposits 4 7 7

In their theoretical analysis, Kalkert and Schecker (1979) used the basic equation in
the Jost theory for ignition of premixed gases:

(5.38)

as the point of departure. Here, ilis the heat conductivity of the gas, Tis the tempera-
ture, Y is the radius, p is the gas density, c is the specific heat of the gas at constant pres-
sure, and t is the time.
By making several simplifying assumptions, they were able to derive the following
equation for Emin:

(5.31)

where K= A/(px c) is the “temperature conductivity” of air, d is the diameter of the dust
particles (monosized), psand c, are the density and specific heat of the particle material,
and Tfis the flame temperature (defined as 1300 K).
A central feature of equation (5.31) is that E,, - d3. Figure 1.30 in Chapter 1 shows
the close agreement between predictions by equation (5.31) and experimental values for
polyethylene dust. (Note: E,, and MIE are interchangeable notations for the minimum
electric spark ignition energy.)
Klemens and Wojcicki (1981) were specifically interested in modeling the electric spark
ignition of coal dust clouds in air. They were able to validate their model predictions
against unique experimental evidence of the development of the spark kernel and sub-
sequent establishment of self-sustained flame propagation through the dust cloud away
from the spark. An example is shown in Figure 5.22.
The overall physical picture of the ignition process on which the model of Klemens
and Wojcicki was based is as follows: During and following the spark discharge, the dust
particles and the air in the vicinity of the spark kernel are heated. As a consequence,
volatiles are evolved from the particles, mix with air,and the mixture ignites. As the tem-
perature increases further, the oxidation of the solid particle phase (coke) begins.
The temperature in the spark kernel and its close vicinity decreases with time due to
heat drain. However, if ignition occurs, a flame front appears at the same time, at a cer-
tain distance from the spark axis, and starts to propagate outward at the laminar flame
speed of the coal dust/air cloud in question.
The rate of energy delivery to the spark channel during spark discharge was taken into
account in the mathematical model. Typically,the duration of a 50 mJ spark is about 0.IO
rns. It was assumed that the energy density along the radius of the spark channel was linear
at any instant. Plane, cylindrical, and spherical models all were formulated.
Numerical simulations, using the model, were carried out, employing the establish-
ment of a flame front propagating at a defined speed, as the criterion of ignition. In other
words, whenever the spark energy exceeds the minimum ignition energy, the region over
which the temperature rises is not limited to the spark region but spreads into t
ture at the speed corresponding to the fundamental burning velocity of the dust cloud.