Page 253 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 225

Even if the gas flow passing over the powder bed is turbulent, there is a thin laminar
boundary layer of thickness on the order of pl(pvx),where p is the viscosity of the gas
and p is its density. If the particles are on the same order or smaller than the thickness
of the laminar layer, they cannot be caught by the turbulent eddies and entrained in the
gas flow. Furthermore,reducing the particle size also reduces the effect of the disturbance
of one particle in the surface layer by the impact of others.
According to Gutterman and Ranz (1959), the thickness 6of the laminar boundary layer
of gas in contact with a smooth powder surface is given by

6- (7,P) 1'2 -11.4 (3.23)
2)
where 7, is the shear stress at the interfacebetween the flowing gas and the powder sur-
face, "L) is the kinematic viscosity of the gas, and p is the gas density. The total bound-
ary layer is then the sum of the laminar sublayer and the buffer layer, as illustrated in
Figure 3.17. The simple approximate expression (an alternative to the Prandtl-Karman
equation (3.22)) for the gas velocity gradient in the laminar layer near the powder sur-
face, adopted by Gutterman and Ranz (1959), is

(3.24)

For the experimentalconditionsemployed by Gutterman and Ranz, 6was at least 250 pm.
Therefore, in the case of a smooth dust surface,most particle sizes associated with dust
explosions would be submerged in the boundary layer and subjectedto velocities accord-
ing to equation (3.24).
To estimate the aerodynamic force acting on a particle of diameterx in the powder layer
surface, Gutterman and Ranz assumed sphericalparticles, no interparticleforces except
gravity, the effective velocity of the laminar flow acting on the particle is given by equa-
tion (3.24) for z = x/2, the aerodynamic drag force on the particle is the same as if the
particle had been suspended in an infinite gas volume, and the aerodynamic drag is
resisted by the particles having to roll over neighboring particles against gravity.
Gutterman and Ranz then arrived at the following set of equations for the critical
shear stress at the particle bed surface for initiation of particle movement

C$e2 = 0.65 1012x3pp$ (3.25)

z0 = 5.9* 10-l' Relx2 [N/m2] (3.26)

where C, is the viscous drag coefficientas discussed in Section 3.5.2,Re is the Reynolds
number,x is the particle diameter,ppis the particle density, q is the internal friction factor
of the bulk powder (0 < q < l),and q was measured in a shear box similar to the Jenike
shear cell (Section 3.4.2). The powder was charged gently into the shear box by means
of a funnel, after which the box was rapped sharply three times to obtain a standard degree
of consolidation of the powder. The shear force required for causing powder samplespre-
pared in this way to fail was measured as a function of the vertical force acting on the
sample (similar to the determination of failure loci as discussed in Section 3.4.2). The
plot of shear stress at failure versus vertical force usually gave an approximately straight