Page 371 - Dust Explosions in the Process Industries

340 Dust Explosions in the Process Industries

intensity. The effect of turbulence and dust concentration on flame thickness was also
studied.
Bradley et al. (1988) measured turbulent burning velocities in clouds of well-dis-
persed maize starch in air, in a fan-stirred 22 liter explosion bomb. Turbulence was
varied by varying the fan speed. Isotropic turbulence in the central measurementregion
of the bomb was created by using four fans. Turbulent velocities and integral length
scales corresponding to different conditions of stirring were measured in the stirred
air, in the absence of dust, by laser-doppler velocimetry. It was found that the corre-
lation of the ratio of turbulent to laminar burning velocities with the ratio of effective
rms turbulent velocity to laminar burning velocity and the Karlovitz flame stretch
factor were similar to that obtained in stirred premixed gas explosions (methane/air).
Further comparative investigations of turbulent dust and gas explosions are discussed
in Section 4.4.5, and in Sections 9.2.4.5 and 9.2.4.7 in Chapter 9.

4.4.3.3
K,, and the “Cube Root Law”

The K,, concept was introduced by Bartknecht (1971,1978). He claimed (1978) that the
so-called cube root law
(d~/dt),, v’‘~= constant = K,, (4.85)

had been confirmed in experiments with numerous dusts in vessel volumes from 0.04 m3
and upward. The Ks, value (bar ds), being numerically identical with the (dpldt),,
(bar/s) in the 1 m3 standard IS0 test (InternationalStandards Organization, 1985), was
denoted “a specificdust constant,” which has led to some confusion. From what has been
said in Sections 4.2.5.1,4.4.3.1, and 4.4.3.2, the cube root law is valid only in geomet-
rically similar vessels, if the flame thickness is negligible compared to the vessel radius,
and if the burning velocity as a function of pressure and temperature is identical in all
volumes. Furthermore, the flame surface must be geometrically similar (for example,
spherical).In view of the relationships in Figures 4.40-4.43, it is clear that Ks, is bound
to be an arbitrary measure of dust explosion violence, because the state of turbulence to
which it refers is arbitrary. As pointed out by Eckhoff (1984/1985), this fact has some-
times been neglected when discussing K,, in relation to industrial practice and may
therefore need to be brought into focus again. Table 4.13 shows an arbitrary selection of
Kst values for corn starch dust clouds in air, determined in various apparatuses. The
values range from 5-10 bar m/s to over 200 bar m/s, corresponding to a factor of more
than 20. Some of the discrepancies can probably be attributed to differences in moisture
content and effectiveparticle size of the starch and to different data interpretation (peak
or mean values).However, differences in the turbulence of the dust clouds probably play
the main role.
When using Kst values to size vent areas and for other purposes according to various
codes, it is absolutely essential to use only data obtained from the standard test method
specifiedfor determining Kst.Normally, this is the method of the International Standards
Organization (1985)or a smaller-scalemethod calibrated against the IS0 method. In addi-
tion, it is necessary to appreciate the relative and arbitrary nature even of these Ks,values
(see Chapter 7).