5. Concentration profiles in a laminar flame by bidirectional PLIF

The integral on the left side of Eq. (15) is defined as the relative integral absorption area Int.

ð∞ �∞

Meanwhile, it is noted that if the first-term integral of Eq. (21) is multiplied on the left side of

ð∞ �∞

σtotϕð Þν

σtotϕð Þ ν<sup>0</sup>

Eq. (23) is the relationship between the absorption cross section and the molecular absorption

where σ<sup>0</sup> is the effective peak absorption cross section; the numerical value of σtot can be calculated by Eq. (18). Eq. (24) is thought to be the experimental expression for measuring the effective peak absorption cross section of the molecule. Eq. (24) indicates that the effective peak absorption cross section of the molecule is related to the molecular absorption line shape and

As Versluis et al. have not clearly pointed out that the effective peak absorption cross section associates with the peak value ϕð Þ ν<sup>0</sup> of absorption line-shape, there is a difference between the effective peak absorption cross section and the actual value, if using the measurement equation given by Versluis et al. The difference is not obvious for the absorption band (0,0) of OH radical. However, this discrepancy will manifest significantly for the weak absorption band of (1,0). Therefore, the measurement equation of effective peak absorption cross section given by Versluis et al. is not applicable to the condition of weak absorption. To solve this problem, we revised the experimental equation. The corrected effective peak absorption cross section measurement equation is shown in Eq. (24). To confirm the validity of the modified measurement equation, the effective peak absorption cross section of the band (0,0) and band (1,0) within the Q1(8) line for the OH radical is measured, respectively. The experimental results show that the OH effective peak absorption cross section of the Q1(8) line for band (0,0) turns out to be about 5.5 times higher than that of band (1,0), while the theoretical calculation given by the LIFBASE simulation is about 6 times. The experimental result has been proven to be in good agreement with the

ϕð Þ ν

σð Þ ν dν ¼ σtot

σð Þ¼ ν

σ<sup>0</sup> ¼ σð Þ¼ ν<sup>0</sup>

gð Þ ν dν ¼ 1 (21)

Int <sup>d</sup><sup>ν</sup> (22)

Int (23)

Int (24)

Normalizing above integral, one will obtain

line profile measured experimentally.

the relative integral absorption area.

simulation results.

In particular, if ν ¼ ν0, then

Eq. (17), one will get

98 Laser Technology and its Applications

That is

ð∞ �∞

ð∞ �∞ ϕð Þ ν Int <sup>d</sup><sup>ν</sup> <sup>¼</sup>
