Page 356 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 325

* The burning velocity, that is, the speed of flame relative to the unburned reactants, is
constant.
0 Friction can be neglected.
* The effect of having to disperse the dust can be neglected.
They realized that the three first assumptions are not in accordancewith reality in long
ducts, where extensive flame accelerationis observed,but they indicated that their the-
oretical analysis can be extended to accelerating flames by using numerical computer
models. It is nevertheless interesting to note that the simplified calculations predict the
kind of oscillation shown in Figure 4.36. The calculations, in fact, showed that, before
the flame reached the open end, the air velocity at the open end could become negative;
that is, the air would flow inward. Further reflections cause the flow to reverse again.
Artingstall and Corlett suggested that this theoretical result could help explain the pul-
sating flow observed in some actual dust explosionsin experimentalcoal mine galleries.
It is of interestto mention in this contextthat Samsonov (1984) studied the development
of a propagating gas flamein an impulsiveaccelerationfield generatedby a free-fallingexplo-
sion chamber being suddenly stopped by a rubber shock absorber. He observed the flame-
folding phenomena typical of those resulting from Taylor instabilities.These phenomena
were also similar to those resulting from passage of a weak shock wave through a flame.
Essenhigh and Woodhead (1958) used an apparatus similar to that used by Schlapfer
(19511,but of a large scale, to investigate flame propagationin clouds of cork dust in air
in a one-end-open vertical duct. The duct was 5 m long and of diameter either 760 or
5 10 mm. They studied both upward- and downward-propagatingflames and ignition at
the closed as well as the open end. With ignition at the open end and upward flame prog-
agation, constant flame velocities of 0.4-1 .O ds were measured. For upward propaga-
tion and the top end open, the maximum flame speeds were about 20 m/s. Some of this
difference was due to the expansion ratio burnedunburned material, but some was also
attributed to increased burning rate.
Photographs of the flames were similar to Figures 4.31 and 4.33. The total flame thick-
nesses were in the range 0.2-1.2 m. The minimum explosible concentrationof cork dust
in air was found to be 50 f10 g/m3independent of median particle size by mass in the
range 150-250 pm.
Phenomena of the kind just discussed are important to explain the moderate deviations
from ideal laminar conditions. However, the substantial deviationsgiving rise to the very
violent explosions that can occur in industry and coal mines are due to another mecha-
nism, combustion enhancement due to flow-generated turbulence. (See also Section
9.2.4.6 in Chapter 9.)

4.4
URBULENT FLAME PROPAGATION

4.4.1
TURBULENCE AND TURBULENCE MODELS

Before discussing the combustion of turbulent dust clouds, it is appropriateto include a
few in-troductoryparagraphs to briefly define and explain the concept of turbulence. A
classical source of information is the analysis by Hinze (1975). His basic theoretical