Page 403 - Dust Explosions in the Process Industries

372 Dust Explosions in the Process Industries

4.5.3.2
The ZND-Theory

The first significant steps toward explaining the details of how chemical reactions are
initiated by shock compression and how the resulting energy is transferred to the flow
of reaction products were taken independently by Zeldovich (1940), Neumann (1942),
and Doring (1943). As pointed out by Nettleton (1987), the resulting original ZND
model of gaseous detonations assumed that the leading shock wave generated a flow of
the density and temperature required to initiate exothermic chemical reactions not far
behind the shock (1-10 mm).
However, Lee (1987) pointed out that the one-dimensional ZND structure of the det-
onation front in homogeneous gaseous or liquid explosiveshas been found to be unsta-
ble theoretically and the ZND structurehas in fact never been observed experimentally
in self-sustainedgaseous detonations,which rather have a cellular structure.Lee proposed
that the intense turbulence generated in the shear layers at the cell boundaries causesrapid
mixing of unburned mixture and combustion products and therefore plays a main role
in causing ignition just behind the leading shock.
The need to account for the role of turbulencein detonationwave propagation was also
emphasized by Davis (1987). By doing this, it may also be possible to describe DDT
within a unified theory for turbulent flame propagation.

4.5.3.3
Dust Clouds
Wolanski et al. (1984) were concernedwith the detailed structureof dust cloud detonation
waves and developed a first-order model for the reaction zone, accounting for both two-
phase flow effects and wall losses. The flow in the reaction zone was assumed to be one-
dimensional and steady, the dust particles were assumed to be spherical and of the same
temperatureas the surrounding gas. A simplifieddust combustion rate model was adopted,
assuming a heterogeneousreaction. After tuning the constants of the model against exper-
imental pressure profile data from the detonationof wheat dusdair,the reaction zone pro-
files of particle and gas velocities, temperature, and density could be computed. The
calculated detonation velocities were in good agreement with experimentalvalues.
Kulikovskii (1987) discussed the existence of convergent cylindrical and spherical C-J
waves in dust clouds. The theoretical analysis revealed that the ratio between two
dimensionless parameters determines the influence of the particles on the detonation wave
structure. The first parameter is the ratio of solid particle volume to total dust cloud
volume; the second is the product of the mean curvature of the cylindrical or spherical
wave and the characteristicparticle dimension.If the first parameter is much smallerthan
the second, the particles have negligible influence. If, however, the first parameter is on
the same order or greater than the second, the particles begin to play an important role
by significantly altering the flow behind the C-J wave, and the range of its existence.
In another theoretical investigation,Ishii (1983) analyzed the influence of the size dis-
tribution of the dust particle on the flow structurebehind a shock front passing through
a dust cloud. Main conclusions were that the particle size distribution is important and
that the assumption of monosized particles, which is often adopted in theoretical work,
can lead to poor predictions if the size distribution is in reality comparatively wide.