Page 321 - Dust Explosions in the Process Industries

290 Dust Explosions in the Process Industries

The left-hand side of equation (4.41) is the net heat input to particle no. (n + I),
whereas the three terms on the right-hand side are the convective heat flow to particle
no. (n + 1) from the surrounding gas, the radiative heat flows to this particle from the
flame front and the hot gas sphere around the burned particle no. n, and the radiativeheat
loss from particle no. (n + 1).
Nomura and Tanaka analyzed the various parameters in equation (4.41) in detail and
concluded that the radiative heat loss from particle no. (n + 1) was only about 10% of
the radiative heat input to this particle from particle and gas element no. n. A simplified
equation (4.41), deleting the last term on the right-hand side, was then integrated from
t = 0 to t = z, the total burning time of a particle, to identify the unknown time Ati when
particle n reached its ignition temperature Tig.Tigwas assumed to be known from exper-
iments or other theory. The calculations started with n = 1 and were repeated for n = 2,
3, ... ,up to n =500.The time Atnfor ignitionof particle no. (n+ 1)decreaseswith increas-
ing I if the burning time zis considerably larger than AI. This is because more particles
burn simultaneously and produce a greater heat flow to the next unburned particle than
if only one particle burns. In the examples shown by Nomura and Tanaka, At, reached
a constant value At- for IZ > 100.
Nomura and Tanaka introduced the following expression for the burning time of a
particle:
T=K,D; (4.42)

The burning constant KO was assumed to be on the order of 1000 s/cm2for solid parti-
cles in general and about 2000 s/cm2for coal particles specifically.
By using the corresponding zfrom equation (4.42), Atmwas calculated, and the lam-
inar burning velocity is then given by the simple relationship
Su = L/Atm (4.43)

Calculated S, values for coal dust in air at a dust concentration of 600 g/m3are 0.70 m/s
for 20 pm diameter particles and 0.36 m/s for 40 pm diameter particles.
By requiring an experimental“ignitiontemperature”of a particle,the Nomura-Tanaka
theory suffers from the same basic weakness as the classicalMallard-leChatelier (1883)
theory for gases: The “ignition temperature” is not a true physical property of the parti-
cle but depends on the actual circumstances under which the particle is ignited.

4.2.4.5
Specific Theories for Coal Dust in Air

Smoot and Horton (1977) have a comprehensivereview of the theoretical work on lam-
inar coal dust/air flames up to the time of their paper, starting with the pioneering con-
tributions on carbodair flames by Nusselt (1924) and concludingwith the unified theory
for coal/air by Krazinski,Buckius, and Krier (1977).The last theory did not considerthe
devolatilizationprocess and assumed that the particles had the same velocity as the sur-
rounding gas. However, both thermal radiation and conduction were accounted for, as
well as char oxidation.The treatment of thermal radiation also included scattering effects.
However, the theory is limited to low-volatile coals and was not confirmed by experi-
ments. The predicted influence of particle size on the burning velocity was small.