Page 264 - Dust Explosions in the Process Industries

236 Dust Explosions in the Process Industries

by Gutterman and Ranz was stationaryin both time and y direction, and the average ver-
tical gas velocity vz was 0. Therefore,

(3.38)

Here, c is a function of z only, dcldz could be determined from experimental c(z)corre-
lations (Figure 3.27), vtem can be calculated, and therefore an “experimental”diffusion
coefficient, D,. could be found. This was compared with the theoretical turbulent dif-
fusion coefficient Dmrb (related to the turbulent eddy viscosity) for the gas and for par-
ticles so small that they follow the turbulent gas motion. Some results are shown in the
middle column of Table 3.4.

Table 3.4 Average ratios between experimentally determined diffusion coefficients for various par-
ticle types and theoretical turbulent diffusion coefficients for the gas

Particles DexplDturb DexplDbounce
Glass
3-40 pm 1.I -
2.50 g/cm3
Sand
30-1 65 pm 5.6 1.8
2.65 g/cm3
Tin
30-90 pm 4.3 -
7.3 glcm3

Because of the small size of the glass beads, Dexpwas very close to &b; that is, the
glass beads followed the gas motion fairly well, whereas the coarser sand particles and
the high-density tin particles had considerablyhigher diffusioncoefficients than the gas.
According to Gutterman and Ranz, the turbulent gas diffusion behavior of particles
can be expected if the Weiss-Longwellcriterion for diffusion of solid particles in an oscil-
latory gas velocity field

(3.39)

is close to unity. This is the case for smallparticle diametersx,for which w2<< 18p/pgx2,
w being the average rotational frequency (radians per second) of the gas eddies.
Guttermanand Ranz also compared their experimentaldiffusioncoefficientsbased on
measured dust concentrationgradients with coefficients derived theoreticallyby assum-
ing the governing diffusion mechanism was back-mixing of particles into the gas flow
by irregular statistical bouncing when the particles hit the bottom and roof of the wind
tunnel. The third column of Table 3.4 gives the result for angular sand particles. This
shows that, for coarse particles in a narrow boundary zone of a few cm from the wall of
the wind tunnel, the theory of back-mixing by bouncing against the wall findsbetter agree-
ment with experiments than the theory of turbulent gas diffusion.