Encyclopaedia Index

7. Radiative properties of the Medium

In general the radiative properties of the medium vary with the local composition and wave-length.

The products of combustion, such as CO2 and H2O, are strong selective adsorbers and emitters; but they do not scatter radiation significantly.

Particulates on the other hand, such as pulverised coal, ash and soot, scatter strongly.

The absorptivities of N2, O2 and H2 are so small that these gases are almost completely transparent to radiation.

However, a detailed modelling of the radiative properties is not warranted for the differential radiation models considered here.

Rather these models require specification of the mean absorption coefficient, a, and the mean scattering coefficient, s, which may be interpreted as 'gray' values that are representative of the entire spectrum.

It should be noted that the absorption coefficient a is not to be confused with the conventional coefficient which appears in the RTE.

The specification of these coefficients has been discussed in some detail by Gosman and Lockwood [1973a, 1973b], although many workers simply use constant values or values dependent only on the local composition.

For example, Hoffmann and Markatos [1988] used a=0.1 m^-1 and s=0.01 m^-1 for hydrocarbon combustion, whereas Khalil et al [1975] used a=0.2*mfu+0.1*mpr where mfu and mpr are the mass fractions of fuel and product species, respectively.

Another approach is to use the "mixed gray and clear" gas formulation of Hottel and Sarofim [1967] to determine the total gas emissivity e,gas.

The value of the absorption coefficient a is then obtained from the "pseudo-gray" approximation:

e,gas = 1 - exp (-a*L) (5.9)

where L is a characteristic path length for a cell.

In general this method implies that a varies from cell to cell as a function of L, temperature and composition. However, the method may be used to estimate a representative constant value of a.

Further details can be found in the following references: Abbas et al [1984], Gosman and Lockwood [1973b], Kjaldman [1993], Siegel and Howell [1992], Taylor and Foster [1974] and Viskanta and Menguc [1987].