At combustion temperature, radiation is an important if not dominating mode of heat transfer. In a combustion process, radiatively participating species include soot and gaseous species such as CO2 and H2O. Heat is emitted, absorbed, and scattered in waves of various wavelengths. Assuming the scattering effect in the combustion flow is negligible, the radiative heat transfer becomes the balance of emissive and absorption powers. For each wavelength, local net radiation heat power is obtained by integrating the absorption of the incoming radiation from all other locations and subtracting the emitted power. A radiative transport equation is obtained by integrating the net radiation heat power over all wavelengths, Eq. (8):
qr(x, y, z) = к’1е’Ь1(Т’)е /K"dl"dv
in which l is wavelength, к is volume absorptivity, l is optical length, v is a control volume, and e^T) is the blackbody radiation function. The spectral volumetric absorptivities of these media must be determined from gas and soot radiation models.
The H2O species has five strong radiation bands, centered at wavelengths of 1.38, 1.87, 2.7, 6.3, and
20 цш, and the CO2 species has six bands, at 2.0, 2.7, 4.3, 9.4, 10.4, and 15 цш. A wideband model was introduced to calculate total band absorptance of these species. For each band, species concentrations, pressure, and temperature are used to determine a set of semiempirical parameters: the integrated band intensity, the bandwidth parameter, and the line width parameter. A semiempirical correlation is then used to calculate the total band absorptance from these parameters.
If the scattering is negligible, the Rayleigh-limit expression of the soot volume absorptance ks1 can be used:
ksl : 9)
[n2(1 + k2 )+2]2 + 4n4k2
Soot volume absorptance is proportional to the soot volume fraction fv and inversely proportional to the wavelength. The optical refraction indices, n and k, are weak functions of wavelength that can be derived from classical electromagnetic theory.