Combustion Phenomena of High Temperature Air Combustion - High Temperature Air Combustion: From Energy Conservation to Pollution Reduction - page 149

1. The radiation incoming from the wall is well approximated by a blackbody
emitter at the temperature T w so that: I v ( S = 0) ≅ I v 0 ( T w )
2. The variations in the blackbody function are small over the spectral
intervals.

3. The mechanisms of gas emission-absorption take place in M non-over-

lapping bands.

Equation 2.30 becomes:

M N − 1

[ ]

∑ ∑

( ) − () ( )

τ

() = () +

0 0

IL I L I T I TASS ,

ej ′ ,

(2.31)

soot ν k + 1 ν k nhj k + 1 Ns + 1

ej ′ , ej ′ , k + 1

j = 1 k = 0

4

σ
π

T C β T

15

3

I =

0

Ψ 1 +

0 N 0

soot 4

π C

2

(2.32)

N

' -

4

−

15 σ

π

T C α T CT

C

α

∑

k 3 0 k + 1 k 3 0 k k

+ Ψ 1 + Ψ 1 +

,
,

/
/

4

π C

* .

2 2

k = 1

where
v c

the frequency at the center of the band in cm -1

σ, C 2 the Stefan-Boltzmann constant and the second Planck constant,

respectively

A nh the non-homogeneous total band absorptance, A nh , is calculated using

the Chan and Tien scaling method

τ s k +1 the soot emissivity on the j th gas band over the path length L - S k +1 .

This term accounted for the effect of overlapping bands between the
gas mixture and the soot. The soot emissivity is calculated using the
soot spectral absorption coefficient, approximated by the relation:

v c ′ , j

Cf

ν ν

k

ν

=

0

(2.33)

s 4

10

where f v is the soot volumetric fraction in [m 3 /m 3 ], v is the wave length in cm -1 , and
C 0 is a constant
ψ 3 the pentagamma function
α k and β k the integrals of the soot volumetric fraction over the path length L -
S k and S k +1 - 0, respectively

I soot the total radiance from soot only