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D-2 Radiation from and through Luminous Flames and Gases
with Particles
Several factors complicate radiative transfer in a flame
region that is actively burning. The simultaneous production and loss of energy
produces a temperature variation within the flame, and thus variations of local
emission and properties. Intermediate combustion products from the complex
reaction chemistry can significantly alter the radiation characteristics from
those of the final products. If soot forms in burning hydrocarbons, it is a very
important radiating constituent. Soot emits a continuous spectrum in the visible
and infrared regions and can often double or triple the radiation emitted by
only the gaseous products. Soot also provides radiant absorption and emission in
the spectral regions between the gas absorption bands. A method for increasing
flame emission, if desired, is to promote slow initial mixing of the oxygen with
the fuel so that large amounts of soot form at the base of the flame. Ash
particles in the combustion gases can also contribute to absorption and emission
[Viskanta and Mengüc (1987), Sarofim and Hottel (1978), Boothroyd and Jones
(1986), Marakis et al. (2000)], and can significantly scatter radiation [Im and
Ahluwalia (1993)].
Calculating the effect of soot on flame radiation requires
knowledge of the soot concentration and its distribution in the flame; this is a
serious obstacle for predictive calculations. The soot concentration and
distribution depend on the type of fuel, the mixing of fuel and oxidant, and the
flame temperature. This is illustrated by the experimental results and
calculations in Santoro et al. (1987) and Coelho and Carvalho (1995). A
semi-empirical correlation is developed in De Champlain et al. (1997) for trying
to predict the amount of smoke in the exhaust of a gas-turbine engine. The
correlation is based on residence time of the fuel in the combustor, flow rates,
reaction rates, and other parameters. The correlation does not yet yield
generalized results, and further developments are continuing. Soot concentration
in a propane turbulent diffusion flame was predicted in Coelho and Carvalho
(1995) using several models that use basic flow and energy equations. The models
are found to need further improvement to obtain accurate predictions of soot
formation.
If the soot concentration and distribution can be estimated
from basic equations or from observations for similar flames, another
requirement for making radiative transfer calculations is that the soot
radiative properties can be specified. These properties are known only
approximately. If flames in both the laboratory and industry are included, the
soot particles produced in hydrocarbon flames generally range in diameter from
0.005 μm to more than 0.3 μm. Typical diameters measured in
Charalampopoulos and Felske (1987) were 0.02–0.7 μm. Soot can be in the
form of spherical particles, agglomerated masses, or long filaments. The
experimental determination of the physical form of the soot is difficult, as a
probe used to gather soot for photomicrographic analysis may cause agglomeration
of particles or otherwise alter the soot characteristics. The nucleation and
growth of the soot particles are not well understood. Some soot can be nucleated
in less than a millisecond after the fuel enters the flame, and the rate at
which soot continues to form does not seem to be influenced much by the
residence time of the fuel in the flame. An unknown precipitation mechanism
governs soot production. In typical gaseous diffusion flames, the volume of soot
per total volume of combustion products has been found experimentally to range
from 10−8 to 10−5 [Sarofim and Hottel (1978), Santoro et
al. (1983, 1987), Ku and Shim (1991), Lee et al. (1984), Ang et al. (1988), Sato
et al. (1969), and Kunugi and Jinno (1966)]. The aggregation of soot into long
clusters is examined in Köylü and Faeth (1994) and Farias et al. (1995b), where
structural details are given.
Along a path in a transparent carrier gas containing
suspended soot, it has been found experimentally that the attenuation of
radiation obeys Bouguer’s law,
From Mie theory the soot radiative properties depend on the
size parameter πD/λ (D is the particle diameter) and the optical
constants n and k of the particles, which depend on
the soot chemical composition. The n and k depend
somewhat on λ, as shown later, but do not depend strongly on temperature [Lee
and Tien (1981), Howarth et al. (1966), Dalzell and Sarofim (1969)]. At the
temperatures in combustion systems, radiation is mostly in the wavelength range
of 1 μm and larger; hence, for small soot particles πD/λ is
generally much less than 0.3. In this range, Mie theory implies that the
scattering cross section depends on (πD/λ)4 and that the
absorption cross section depends on πD/λ to the first power. Thus
scattering is small compared with absorption, and kλ
in (D-1) is the absorption coefficient of the soot rather than the extinction
coefficient. Then the spectral emittance of an isothermal volume composed of
soot suspended uniformly in a nonradiating carrier gas is
where Le is the mean beam length for the
volume. Radiation by the carrier gas will be included later. |
