Page 360 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 329

explosions. Later, as is discussed in Section 4.4.8, it was also adopted for simulating
turbulent dust explosions.
While the k-E theory has wide popularity, it should be pointed out that it is only one
of several theoretical approaches. Launder and Spalding (1972) gave a classical review
of the mathematicalmodeling of turbulence, including stress transport models, which is
still relevant.
When the structure of turbulent dust clouds is to be described, further problems have
to be addressed. Some of these were discussed in Chapter 3. Beer et al. (1984) pointed
out that there are two aspects of the turbulence/particleinteraction problem. The first is
the influence of turbulence on the particles, the second is the influence of particles on
the turbulence. With regard to the influence of turbulence on the particles in a burning
dust cloud, two effects are important, mechanical interactions associated with particle
diffusion, deposition, coagulation, and acceleration and convective interactions associ-
ated with heat and mass transfer between gas and particles, which influence the particle
combustion rate. Beer et al. (1984) discussed available theory for the various regimes
of Reynolds numbers (see Chapter 3) for the particle motion in the fluid. They empha-
sized that turbulence is a rotational phenomenon, and therefore the motion of the parti-
cles also includes a rotationalcomponent. Consequently,one can define a relaxation time
for the particle rotation zpras well as one for the translatoryparticle motion, zp.Both relax-
ation times are proportional to the square off the particle diameter and, hence, decrease
markedly as the particles get smaller.
When zp >> T,,, where z, is the characteristic Lagrangian time of the turbulent
motion, the particle is not convected by the turbulent fluctuations and its motion is
fully determined by the mean flow. However, when zp<< z,, the particle adjusts to
the instantaneous gas velocity. If the particle follows the turbulent fluctuations, its
turbulent diffusivity is equal to the gas diffusivity. If the particle does not follow the
turbulence, its diffusivity is practically equal to 0. An interesting but most compli-
cated case occurs when the characteristic relaxation times and turbulence times are
on the same order. In this case, the particle only partially follows the fluid and its
motion depends partially on Lagrangian interaction with the fluid and partially on
Eulerian interaction over the distance it travels outside the originally surrounding
fluid.
The effects of particles on the turbulence structure are complex. The simplest effect
is the introductionof additionalviscouslike dissipationof turbulent energy caused by the
slip between the two phases. This effect is substantial in the range of explosibledust con-
centrations. Even small changes in dissipation can have a strong influence on the tur-
bulence level. This is because turbulence energy is the result of competition between two
large, almost equal sources of production and dissipation.
Beer et al. (1984) state that the change in turbulence intensity and structure caused
by the increased dissipation affects the mean flow parameters and, in turn, the turbu-
lence production terms, so that the outcome of the chain of changes is difficult to pre-
dict, even when the most advanced techniques are used. The difficulties are enhanced
by a liack of reliable experimental data. For example, some experiments demonstrate
dramatic effects of even minute admixtures of particles on turbulent jet behavior.
Others demonstrate smaller effects even for high dust concentrations (see Section 3.8
in Chapter 3).