Page 418 - Dust Explosions in the Process Industries

hapter 5

nition of Dust Clouds and Dust Deposits:
Further Consideration of Some

Selected Aspects

5.1
WHAT IS IGNITION?

The word ignitionis meaningful only when applied to substances able to propagate a self-
sustained combustion or exothermal decomposition wave. Ignition may then be defined
as the process by which such propagation is initiated.
Ignition occws when the heat generation rate in some volume of the substance exceeds
the rate of heat dissipation from the volume and continues to do so as the temperature
rises further. Eventually a temperature is reached at which diffusion of reactants controls
the rate of heat generation, and a characteristic stable state of combustion or decompo-
sition is established.
The characteristic dimension of the volume within which ignitiodno ignition is decided
is on the order of the thickness of the front of a self-sustained flame through the mix-
ture. This is because self-sustained flame propagation can be regarded as a continuing
ignition wave exposing progressively new parts of the cloud to conditions where the heat
generation rate exceeds the rate of heat dissipation. A similar line of thought applies to
propagation of smoldering fires in powder deposits and layers, as discussed in Section
5.2.2.4.
In the ignition process, the concepts of stability and instability play key roles. Thorne
(1985) has an instructive, simplified outline of some basic features of the instability
theory of ignition, which is rendered in the following section. In most situations, diffu-
sion, molecular as well as convective, plays a decisive role in the ignition process.
Systems that can ignite may be characterized by a dimensionless number D,, the
Damkohler number, which is the ratio of the rate of heat production within the system
due to exothermic chemical reactions to the rate of heat loss from the system by con-
duction, convection, and radiation. Often D, is expressed as the ratio of two character-
istic time constants, one for the heat loss and one for the heat generation:

0, = z,/z, (5.1)
The influence of temperature on the rate of chemical reactions is normally described
by the exponential Arrhenius law:
k = fexp(-E/RT) (52)

where k is the rate constant,fis the preexponential or frequency factor, E is the activa-
tion energy. R is the gas constant, and Tis the absolute temperature.