Page 263 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 235

300

200

- +io0
rn E
2-l
Y
C
0
c 50
rn
+
L
c
ai
30
u
+
In
3
-a 20
d
2
0
2
10

5

0 0.01 0.02 0.03 0.04
Vertical distance from wind tunnet floor [ml

Figure 3.27 Dust concentration gradients in horizontal turbulent airflow in a wind tunnel (From
Cutterman and Ranz, 1959).

According to Guttermanand Ranz (1959), the general differentialequation for the dis-
tribution of dust concentrationin a dust cloud moving in a two-dimensionalflow can be
written as

ac ac ac ac= Deff(d”c a2c)
-+v -+vz-+vt, ay2 +a22 (3.37)
at yay az aZ

Here, c is dust concentration, t is time, vyis the average gas velocity in the horizontal
flow direction y, v, is the average gas velocity in the vertical direction z, vt, is the ter-
minal particle settling velocity in the gravitational field, and DeEis the effective diffu-
sion coefficient for the particles. De, is a function of both y and z. The system studied