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,

 

                                              (D-1)

 

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

 

                                                 (D-2)

 

where Le is the mean beam length for the volume. Radiation by the carrier gas will be included later.