Collisional effects on laser-induced fluorescence measurements of hydroxide concentrations in a combustion environment. 2: Effects for v′ = 1 excitation

David H. Campbell

doi:10.1364/AO.23.001319

Collisional effects on laser-induced fluorescence measurements of hydroxide concentrations in a combustion environment. 2: Effects for v′ = 1 excitation

David H. Campbell

Applied Optics
Vol. 23,
Issue 9,
pp. 1319-1327
(1984)
•https://doi.org/10.1364/AO.23.001319

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David H. Campbell, "Collisional effects on laser-induced fluorescence measurements of hydroxide concentrations in a combustion environment. 2: Effects for v′ = 1 excitation," Appl. Opt. 23, 1319-1327 (1984)

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- Original Manuscript: January 31, 1984
- Published: May 1, 1984

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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.

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RUN	P (atm)	ρ_ν	N_p (cm⁻³)	$\frac{N_{p}}{N_{two}}$	t_p (nsec)	$\frac{N_{ss}}{N_{two}}$
(S=.005)
2	.1	10⁻¹¹	1.214×10¹⁰	.136	--	.136
3	1.0	10⁻¹⁰	1.214×10¹¹	.136	--	.136
4	10.0	10⁻⁹	1.213×10¹²	.136	--	.136
5	100.0	10⁻⁸	1.213×10¹³	.136	--	.136
(S=.5)
6	.1	10⁻⁹	1.110×10¹²	.187	33.0	.183
1	1.0	10⁻⁸	1.093×10¹³	.184	10.1	.170
7	10.0	10⁻⁷	1.016×10¹⁴	.171	--	.171
8	100.0	10⁻⁶	1.010×10¹⁵	.170	--	.170
(S=50)
9	.1	10⁻⁷	1.367×10¹³	.788	7.0	.488
10	1.0	10⁻⁶	1.149×10¹⁴	.662	2.5	.330
11	10.0	10⁻⁵	7.898×10¹⁴	.455	0.9	.330
12	100.0	10⁻⁴	5.736×10¹⁵	.330	--	.330
3	1.0	10⁻¹⁰	1.214×10¹¹	.136	--	.136
1	1.0	10⁻⁸	1.093×10¹³	.184	10.1	.170
13	1.0	4×10⁻⁸	3.371×10¹³	.284	9.2	.227
14	1.0	10⁻⁷	5.822×10¹³	.394	7.1	.272
10	1.0	10⁻⁶	1.149×10¹⁴	.662	2.5	.330
15	1.0	10⁻⁵	1.454×10¹⁴	.823	0.7	.339
16	1.0	10⁻⁴	1.613×10¹⁴	.911	0.16

RUN	ρ_ν	VT Rates	N_p (cm⁻³)	$\frac{N_{p}}{N_{two}}$	t_p (nsec)	$\frac{N_{ss}}{N_{two}}$
17	10⁻¹⁰	X.1	1.431×10¹¹	.160	--	.160
18	10⁻¹⁰	X1.0	1.213×10¹¹	.136	--	.136
19	10⁻¹⁰	X10.0	6.837×10¹⁰	.0766	--	.0766
20	10⁻¹⁰	lowerX.1	1.214×10¹¹	.136	--	.136
21	10⁻⁶	X.1	1.237×10¹⁴	.713	3.1	.593
10	10⁻⁶	X1.0	1.149×10¹⁴	.662	2.5	.330
22	10⁻⁶	X10.0	8.254×10¹³	.476	3.1	.468
1	10⁻⁸	Standard	1.093×10¹³	.184	10.1	.170
23	10⁻⁸	Flat over Rot. levels	1.082×10¹³	.182	10.1	.168
24	10⁻⁸	Linear N Dependence	1.115×10¹³	.187	10.3	.168

RUN	ρ_ν	Q	N_p (cm⁻³)	$\frac{N_{p}}{N_{two}}$	t_p (nsec)	$\frac{N_{ss}}{N_{two}}$
25	10⁻⁸	X.1	1.617×10¹³	.109	21.1	.105
1	10⁻⁸	X1.0	1.093×10¹³	.184	10.1	.170
26	10⁻⁸	X10.0	4.575×10¹²	.536	9.2	.496
27	10⁻⁶	X.1	1.291×10¹⁴	.731	3.0	.364
10	10⁻⁶	X1.0	1.149×10¹⁴	.662	2.5	.330
28	10⁻⁶	X10.0	6.605×10¹³	.447	2.4

RUN	ρ_ν	R–T	N_p (cm⁻³)	$\frac{N_{p}}{N_{two}}$	t_p (nsec)	$\frac{N_{ss}}{N_{two}}$
29	10⁻⁸	X.1	2.660×10¹³	.447	9.1	.407
1	10⁻⁸	X1.0	1.093×10¹³	.184	10.1	.170
30	10⁻⁸	X10.0	3.626×10¹²	.061	10.4	.056
31	10⁻⁶	X.1	1.219×10¹⁴	.703	0.82	.385
10	10⁻⁶	X1.0	1.149×10¹⁴	.662	2.5	.330
32	10⁻⁶	X10.0	7.688×10¹³	.443	3.0	.142

RUN	T (K)	N_p (cm⁻³)	$\frac{N_{p}}{N_{two}}$	t_p (nsec)	$\frac{N_{ss}}{N_{two}}$
33	1000	2.442×10¹³	.200	9.0	.179
1	2000	1.093×10¹³	.184	10.1	.170
34	3000	6.126×10¹²	.184	--	.184

RUN	P (atm)	ρ_ν	N_p (v′=1) (cm⁻³)	$\frac{{N_{p}}^{(v^{'} = 1)}}{N_{two}}$	t_p (nsec)	$\frac{N_{ss}}{N_{two}}$	$\frac{{N_{p}}^{(v^{'} = 0)}}{{N_{p}}^{(v^{'} = 1)}}$
(S=.005)
2	.1	10⁻¹¹	5.642×10¹⁰	0.634	--	0.634	.515
3	1.0	10⁻¹⁰	5.642×10¹¹	0.632	--	0.632	.515
4	10.0	10⁻⁹	5.638×10¹²	0.632	--	0.632	.515
5	100.0	10⁻⁸	5.638×10¹³	0.632	--	0.632	.515
(S=.5)
6	.1	10⁻⁹	5.135×10¹²	0.864	48.0	0.850	.512
1	1.0	10⁻⁸	5.069×10¹³	0.852	11.0	0.790	.513
7	10.0	10⁻⁷	4.723×10¹⁴	0.793	--	0.793	.516
8	100.0	10⁻⁶	4.697×10¹⁵	0.789	--	0.789	.515
(S=50)
9	.1	10⁻⁷	5.720×10¹³	3.30	20.2	2.31	.476
10	1.0	10⁻⁶	5.228×10¹⁴	3.01	3.5	1.54	.495
11	10.0	10⁻⁵	3.665×10¹⁵	2.11	1.0	1.54	.513
12	100.0	10⁻⁴	2.666×10¹⁶	1.54	--	1.54	.515
13	1.0	4×10⁻⁸	1.564×10¹⁴	1.32	9.2	1.06

RUN	ρ_ν	V–T	N_p (v′=1) (cm⁻³)	$\frac{{N_{p}}^{(v^{'} = 1)}}{N_{two}}$	t_p (nsec)	$\frac{{N_{ss}}^{(v^{'} = 1)}}{N_{two}}$	$\frac{{N_{p}}^{(v^{'} = 0)}}{{N_{p}}^{(v^{'} = 1)}}$
17	10⁻¹⁰	X.1	8.382×10¹¹	0.939	16.0	0.936	0.0545
18	10⁻¹⁰	X1.0	5.642×10¹¹	0.632	--	0.632	0.515
19	10⁻¹⁰	X10.0	2.004×10¹¹	0.225	--	0.225	3.35
20	10⁻¹⁰		5.642×10¹¹	0.632	15.0	0.630	0.515
21	10⁻⁶	X.1	7.058×10¹⁴	4.07	4.1	0.358	0.0523
10	10⁻⁶	X1.0	5.228×10¹⁴	3.01	2.1	1.540	0.495
22	10⁻⁶	X10.0	2.393×10¹⁴	1.379	6.0	1.372	3.340
1	10⁻⁸	Standard	5.069×10¹³	0.852	11.0	0.790	0.513
23	10⁻⁸	Flat over Rot. levels	5.059×10¹³	0.850	11.0	0.787	0.514
24	10⁻⁸	Linear N Dependence	5.410×10¹³	0.909	11.0	0.818	0.417

RUN	ρ_ν	Q	N_p (v′=1) (cm⁻³)	$\frac{{N_{p}}^{(v^{'} = 1)}}{N_{two}}$	t_p (nsec)	$\frac{{N_{ss}}^{(v^{'} = 1)}}{N_{two}}$	$\frac{{N_{p}}^{(v^{'} = 0)}}{{N_{p}}^{(v^{'} = 1)}}$
25	10⁻⁸	X.1	1.572×10¹⁴	1.064	36.5	1.042	3.326
1	10⁻⁸	X1.0	5.069×10¹³	0.852	11.0	0.790	0.513
26	10⁻⁸		7.767×10¹²	0.910	9.2	0.843	0.0552
27	10⁻⁶	X1.0	1.010×10¹⁵	5.72	6.2	3.60	2.667
10	10⁻⁶	X1.0	5.228×10¹⁴	3.01	2.1	1.54	0.495
28	10⁻⁶	X10.0	1.121×10¹⁴	0.759	2.4	0.320	0.0545

RUN	ρ_ν	R–T	N_p (v′=1) (cm⁻³)	$\frac{{N_{p}}^{(v^{'} = 1)}}{N_{two}}$	t_p (nsec)	$\frac{{N_{ss}}^{(v^{'} = 1)}}{N_{two}}$	$\frac{{N_{p}}^{(v^{'} = 0)}}{{N_{p}}^{(v^{'} = 1)}}$
29	10⁻⁸	X.1	3.982×10¹³	0.669	9.1	0.611	.513
1	10⁻⁸	X1.0	5.069×10¹³	0.852	11.0	0.790	.513
30	10⁻⁸	X10.0	5.342×10¹³	0.897	10.4	0.829	.513
31	10⁻⁶	X.1	1.605×10¹⁴	0.925	1.3	0.578	.460
10	10⁻⁶	X1.0	5.228×10¹⁴	3.01	2.1	1.536	.495
32	10⁻⁶	X10.0	1.120×10¹⁵	6.45	3.0	2.095	.480

RUN	T (K)	N_p (v′=1) (cm⁻³)	$\frac{{N_{p}}^{(v^{'} = 1)}}{N_{two}}$	t_p (nsec)	$\frac{{N_{ss}}^{(v^{'} = 1)}}{N_{two}}$	$\frac{{N_{p}}^{(v^{'} = 0)}}{{N_{p}}^{(v^{'} = 1)}}$
33	1000	9.328×10¹³	.765	9.0	.684	.371
1	2000	5.069×10¹³	.852	11.0	.790	.513
34	3000	3.187×10¹³	.960	--	.960	.623

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Equations (9)

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