Spectroscopic Temperature Profile Measurements in Inhomogeneous Hot Gases

Burton Krakow

doi:10.1364/AO.5.000201

Applied Optics
Vol. 5,
Issue 2,
pp. 201-209
(1966)
•https://doi.org/10.1364/AO.5.000201

Spectroscopic Temperature Profile Measurements in Inhomogeneous Hot Gases

Burton Krakow

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Burton Krakow, "Spectroscopic Temperature Profile Measurements in Inhomogeneous Hot Gases," Appl. Opt. 5, 201-209 (1966)

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Abstract

Temperature distributions in inhomogeneous hot gases were determined from line-of-sight infrared spectral measurements. Radiance and transmittance of combustion products of flat flames were measured at each of several CO₂-band frequencies near 4.3 μ. Measurements of isothermal-samples showed how the CO₂ transmittance varied with temperature. Radiance measurements were made on samples with known nonisothermal temperature profiles. Radiance equations were so formulated that they could be solved for the temperature profile of the nonisothermal sample by an iterative procedure, using the transmittance and radiance data described above. Temperature profiles obtained by this procedure were in good agreement with the predetermined thermal structures of the specimens.

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Temperature (°K)	Mole fraction of H₂O
1460	0.09
1780	0.04
2160	0.02
2480	0.002
2760	0.001

Measurement	Position	Wavelength (μ)	Radiance (W cm⁻² sr⁻¹μ⁻¹)	Weighted average temperature (°K)
A	1	4.179	0.71	1500
B	1	4.555	0.90	1550
C	1	4.865	0.89	2620
D	2	4.179	1.07	1790
E	2	4.555	2.60	2640
F	2	4.865	0.92	2670

Calculation number	Measurements used	Initial approximation		γ	λ* (μ)	Result		Cycles

		T₁(°K)	T₂(°K)			T₁(°K)	T₂(°K)
1a	A, C	1900	2400	10⁻³	4.550	1520	2680	4
1b	A, C	1520	2680	10⁻⁴	4.550	1510	2730	2
1c	A, C	1510	2730	0	4.550	1510	2740	1
2a	B, C	1900	2400	10⁻³	4.700	1470	2690	5
2b	B, C	1470	2690	10⁻⁴	4.700	1460	2730	2
2c	B, C	1460	2730	0	4.700	1460	2740	1
3a	D, F	1900	2400	10⁻³	4.550	1490	2670	4
3b	D, F	1490	2670	10⁻⁴	4.550	1520	2720	4
3c	D, F	1520	2720	0	4.550	1510	2730	2
4a	D, E	1900	2400	10⁻³	4.550	1550	2750	6
4b	D, E	1550	2750	10⁻⁴	4.550	1540	2760	2
4c	D, E	1540	2760	0	4.550	1540	2760	1
5a	A, B, C	1900	2400	10⁻³	4.550	1490	2670	5
5b	A, B, C	1490	2670	10⁻⁴	4.550	1490	2720	2
5c	A, B, C	1490	2720	0	4.550	1490	2730	1
6a	D, E, F	1900	2400	10⁻³	4.550	1550	2750	5
6b	D, E, F	1550	2750	10⁻⁴	4.550	1530	2760	2
6c	D, E, F	1530	2760	0	4.550	1530	2760	1
7	B, E	1900	2400	0	4.555	1460	2780	5

Calculation number	Measurements used	Initial approximation		γ	λ* (μ)	Results		Cycles

		T₁(°K)	T₂(°K)			T₁(°K)	T₂(°K)
8	A, C	1510	2730	0	4.550	1460	2740	4
9	D, F	1490	2730	0	4.550	1490	2730	1
10	D, E	1540	2760	0	4.550	1500	2770	1
11	A, B, C	1490	2730	0	4.550	1460	2740	2
12	D, E, F	1500	2760	0	4.550	1500	2760	1

Measurement	Position	Wavelength (μ)	Radiance (W cm⁻² sr⁻¹μ⁻¹)	Weighted average temperature (°K)
G	1	4.555	0.87	1520
H	1	4.696	1.46	2070
I	1	4.865	1.06	2410

Calculation number	Measurements used	Initial approximation			γ	λ* (μ)	Result			Cycles

		T₁(°K)	T₂(°K)	T₃(°K)			T₁(°K)	T₂(°K)	T₃(°K)
13a	G, H, I	1520	2070	2410	10⁻³	4.700	1460	2210	2630	8
13b	G, H, I	1460	2210	2630	10⁻⁴	4.700	1460	2170	2750	4
13c	G, H, I	1460	2170	2750	0	4.700	1460	2180	2760	2

Abstract

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Tables (11)

Equations (24)

Applied Optics