Combustion Phenomena of High Temperature Air Combustion - High Temperature Air Combustion: From Energy Conservation to Pollution Reduction - page 105

TABLE 2.4
Typical Wavelengths
of Absorption Bands

CO 2 µ m H 2 O µ m

15.0 Rotational

10.4 6.3

9.4 2.7

4.3 1.87

2.7 1.38

2.0

Accordingly, the monochromatic absorption coefficient of nongray gas k ν 1/m can
be calculated as a summation of the absorption coefficient k ν i 1/m of every absorption
band as follows:

n

∑ 1

k = k (2.24)

ν ν

i

i =

where n is the total number of the absorption bands. Because the monochromatic
absorption coefficient of nongray gas is a function of wave number and temperature
and pressure of the gas as is clear from Equation 2.20 or 2.23, it is necessary to
understand the difference from the case where the coefficient is regarded constant
as the mean absorption coefficient in gray approximation.
In an actual numerical analysis, nongray gas can be treated in the same manner
as gray gas by dividing the entire range of radiation wave numbers into many bands
of monochromatic radiation wave numbers, and the behavior of the radiation energy
particles can be calculated regarding the wave number bands involved in the radiation
and those not involved in it. When it is necessary to apply the nongray conditions
to solid surfaces, behavior of the radiation energy particles can be calculated in the
same manner as gray bodies by dividing, similarly, the entire radiation wave number
range into many bands of monochromatic radiation wave numbers.
It would, of course, be necessary to take suitable measures such as use of a common
division of the radiation wave number range for both the nongray gas and the nongray
solid surfaces. The greater the number of bands the radiation wave number range is
divided into, the more accurately the nongray characteristics will be calculated.
Regarding the radiation characteristics of nongray gas and gray gas, whereas
the emissivity value of gray gas is 1 when its mean effective thickness is infinite,
that for nongray gas is less than 1 even when the mean effective thickness is infinite.
As a consequence of a supposition that the absorption coefficient of gray gas does
not change depending on its temperature, the coefficient is kept constant because
the change of the absorption effect by density fluctuation is compensated for by
temperature. But considering that the monochromatic absorption coefficient of non-
gray gas is strongly related with density, as is clear from Equation 2.20 or 2.24, it