Page 361 - Dust Explosions in the Process Industries

330 Dust Explosions in the Process Industries

4.4.2
TURBULENT DUST FLAMES: AN INTRODUCTORY OVERVIEW

The literature on turbulent dust flames and explosions is substantial. This is because it
has long been realized that turbulence plays a primary role in deciding the rate with which
a given dust cloud will burn, and this role is not easy to evaluate either experimentally
or theoretically. There are close similarities with turbulent combustion of premixed
gases, as shown by Bradley, Chen, and Swithenbank (1988), although the two-phase
nature of dust clouds adds to the complexity of the problem. Hayes, Napier, and
Roopchand (1983) mentioned two predominant groups of theories of turbulent burning
of a premixed fluid system of a fuel and an oxidizer:
1. The laminar flame continues to be the basic element of flame propagation.The essen-
tial role of turbulence is to increase the area of the flame surface that burns simulta-
neously.
2. Turbulence alters the nature of the basic element of flame propagation by increasing
rates of heat and mass transport down to the scale of the “elementary flame front,”
which is no longer identical with the laminar flame.
In their comprehensive survey Andrews, Bradley, and Lwakamba (1975) emphasized
the importance of the turbulent Reynolds number Ra = v’mv for the turbulent flame
propagation,where vfis the turbulenceintensity defined by equation (4.81), A is the Taylor
microscale: and v is the kinematic viscosity. They suggested that, for Rn > 100, a wrin-
kled laminar flame structure is unlikely and turbulent flame propagation is then associ-
ated with small dissipativeeddies.A supplementary formulationis that laminar flamelets
can exist in a turbulent flow only if the laminar flame thickness is smaller than the
Kolmogoroff microscale of the turbulence. Bray (1980) gave a comprehensive discus-
sion of the two physical conceptions and pointed out that the Kolmogoroff microscales
and laminar flame thicknesses are difficult to resolve experimentally in a turbulent flame.
Because of the experimental difficulties,the real nature of the fine structure of premixed
flames in intense turbulence is still largely unknown.
Abdel-Gayed, Bradley, and Lung (1989) proposed a modified Borghi diagram for
classifying various combustion regimes in turbulent premixed flames, using the origi-
nal Borghi parameters WS, and uf/ulas abscissa and ordinate. Here L is the integral length
scale, 6, is the thickness of the laminar flame, u’ is the root mean square turbulent veloc-
ity, and u1 is the laminar burning velocity. The diagram identifies regimes of flame prop-
agation and quenching, and the corresponding values of the Karlovitz stretch factor, the
turbulent Reynolds number, and the ratio of turbulent to laminar burning velocity.
Spalding (1982) discussed an overall model that contains elements of both of the
physical conceptions 1 and 2 of a turbulent flame defined previously, see Figure 4.38.
Eddies of hot, burned fluid and cold unburned fluid interact with the consequencesthat
both fluids become mutually entrained.
Entrainmentof burned fluid into unburned and vice versa is the rate-controllingfactor
as long as the chemistry is fast enough to consume the hot reactants as they appear. In
other words, the instantaneouscombustionrate per unit volume of mixture of burned and
unburned increases with the total instantaneous interface area between burned and
unburned per unit volume of the mixture. Spalding introduced the length I as a charac-
teristic mean dimension of the entrained “particles” of either burned or unburned fluid,