Dust explosions in spherical vessels: The role of flame thickness
in the validity of the 'cube-root law'
Journal of Loss Prevention in the Process Industries, 9 (1):
33--44 (1996)DOI: http://dx.doi.org/10.1016/0950-4230(95)00054-2
Abstract
A well known limitation of the 'cube-root law' is that it becomes
invalid when the flame thickness is significant with respect to the
vessel radius. In the literature, flame thicknesses in dust-air mixtures
ranging from 15 to 80 cm have been reported, which exceed the radii
of the 20 litre sphere and the 1 m$^3$ vessel. Therefore, we have
developed a model (the three-zone model) for the pressure evolution
of confined dust explosions in spherical vessels which takes the
flame thickness into account. The pressure-time curves that are generated
with this model show a good resemblance with those measured in practice.
It is shown by numerical simulations that the maximum rate of pressure
rise can be normalized with respect to the vessel volume as well
as to the flame thickness and that the 'cube-root law' becomes inaccurate
for relative flame thicknesses exceeding 1\%. Furthermore, the actual
burning velocity and the flame thickness during real dust explosions
can be obtained by fitting the model to the experimental pressure-time
curve.