Abstract

A full vibrational–rotational level rate equation model has been used to investigate the applicability of laser-induced fluorescence techniques to number density measurements of hydroxide in a combustion environment. The variation of the population in both the laser-pumped rotational and vibrational levels was investigated for a range of pressures, temperatures, laser intensities, and collisional exchange rates when excitation is to the upper electronic state v′ = 1 vibrational level.

© 1984 Optical Society of America

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References

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  1. D. H. Campbell, Appl. Opt. 23, 689 (1984).
    [CrossRef] [PubMed]
  2. J. W. Daily, Appl. Opt. 15, 955 (1976).
    [CrossRef] [PubMed]
  3. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, N.J., 1971).
  4. G. P. Smith, D. R. Crosley, Appl. Opt. 22, 1428 (1983).
    [CrossRef] [PubMed]
  5. R. P. Lucht, Ph.D. Thesis, Purdue University (1981).

1984

1983

1976

Campbell, D. H.

Crosley, D. R.

Daily, J. W.

Gear, C. W.

C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, N.J., 1971).

Lucht, R. P.

R. P. Lucht, Ph.D. Thesis, Purdue University (1981).

Smith, G. P.

Appl. Opt.

Other

R. P. Lucht, Ph.D. Thesis, Purdue University (1981).

C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, N.J., 1971).

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Figures (12)

Fig. 1
Fig. 1

Effect on normalized rotational level number density of variation in laser intensity and pressure at constant saturation parameter S = 50, T = 2000 K.

Fig. 2
Fig. 2

Effect on normalized rotational level number density of variation in laser intensity for high values of laser radiation density; P = 1 atm, T = 2000 K.

Fig. 3
Fig. 3

Saturation curves for P = 1 atm, T = 2000 K: (a) 0–0 excitation, (b) 1–0 excitation.

Fig. 4
Fig. 4

Effect on normalized rotational level number density of variation in quenching rate for P = 1 atm, ρν = 10−8 ergs/cm3 Hz, T = 2000 K.

Fig. 5
Fig. 5

Effect on normalized rotational level number density of variation in rotational relaxation rate for P = 1 atm, ρν = 10−8 ergs/cm3 Hz, T = 2000 K.

Fig. 6
Fig. 6

Effect on normalized vibrational level number density of variation in laser intensity for P = 0.1 atm, T = 2000 K.

Fig. 7
Fig. 7

Effect on normalized vibrational level number density of variation in laser intensity for P = 1 atm, T = 2000 K.

Fig. 8
Fig. 8

Effect on normalized vibrational level number density of variation in laser intensity for P = 10 atm, T = 2000 K.

Fig. 9
Fig. 9

Effect on normalized vibrational level number density of variation in laser intensity for P = 100 atm, T = 2000 K.

Fig. 10
Fig. 10

Effect on normalized vibrational level number density of variation in vibrational relaxation rate for P = 1 atm, ρν = 10−10 ergs/cm3 Hz, T = 2000 K.

Fig. 11
Fig. 11

Effect on normalized vibrational level number density of variation in quenching rates for P = 1 atm, ρν = 10−8 ergs/cm3 Hz, T = 2000 K.

Fig. 12
Fig. 12

Effect on normalized vibrational level number density of variation of rotational relaxation rate for P = 1 atm, ρν = 10−8 ergs/cm3 Hz, T = 2000 K.

Tables (10)

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Table I Effects of Pressure and Laser Intensity on Rotational Level Population*

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Table II Effect of Vibrational Relaxation Rates on Rotational Level Population*

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Table III Effects of Quenching Rates on Rotational Level Population*

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Table IV Effects of Rotational Relaxation Rates on Rotational Level Population*

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Table V Effects of Temperature on Rotational Level Population*

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Table VI Effects of Pressure and Laser Intensity on Vibrational Level Population*

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Table VII Effects of Vibrational Relaxation Rates on Vibrational Level Population*

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Table VIII Effects of Quenching Rates on Vibrational Level Population*

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Table IX Effects of Rotational Relaxation Rates on Vibrational Level Population*

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Table X Effects of Temperature on Vibrational Level Population*

Equations (9)

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d N 2 d t = N 1 B 12 ρ ν - [ Q 21 + A 21 + B 21 ρ ν ] N 2 ,
N 1 0 = N 1 + N 2 .
N 2 = N 1 0 B 12 ρ ν Q 21 + A 21 + ( B 12 + B 21 ) ρ ν ,
S = ( B 12 + B 21 ) ρ ν Q 21
N p P = C 1 ,
N two ρ ν = C 2 ,
ρ ν P = C 3 .
N p N two = C ,
k ( N ) k ( 0 ) = 1 - 0.0343 N ,

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