Page 247 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 2 19

z,,called the velocity relaxation time of the motion, is a characteristic time constant for
the particle to reach its terminal velocity.
Rudinger differentiated among three cases of equation (3.19). In the first case, the flow
is stationary (i.e., b is O), and vJt) approaches vo asymptotically. If b has a finite, posi-
tive value, v,(t) approaches v(t)- bz, asymptotically. For a negative b, v,(t) catches up
with and starts to exceed v(t)at the time
t = z,In (I -vo/bzl,) (3.20)

after which it approaches v(t)- bz, asymptotically. The three different cases are illus-
trated in Figure 3.16.

Figure 3.1 6 Velocity v,,(t) of a particle introduced in a gas flow of velocity v, + b, at t = 0 (From
Rudinger, 7980).
In a turbulent dust cloud, b varies with time and space. The flow changes continuously
both in direction and magnitude, the particles move in all directions, and never attain the
same velocity as the gas element in which it is at any instant. The fact that real particles
not only are in translatory motion but also rotate adds to the complexity of the problem.
The irregular movement of particles causes the local dust concentration to vary irregu-
larly with time.
A number of experimental and theoretical studies have been published on various
aspects of the interaction of dust particles and gas in turbulent flows. Some of these are
discussed in Section 3.8.

3.5.4
SPEED OF SOUND IN A DUST CLOUD

The speed of sound plays an important role in all compressible flow phenomena, includ-
ing dust explosions. Rudinger (1980) distinguished between two extreme cases. In the
first case, the particles are considered in equilibrium with the gas at all times; that is, the
particles follow the gas movement exactly and have the same temperature as the gas.
Provided the volume fraction of the particles in the cloud is small, as it is in an explosi-
ble dust cloud, the equilibrium speed of sound, a,, is given by the expression

(3.21)