Abstract

Changes in infrared emission and absorption spectra of hot gases brought about by controlled variations of gas temperature profile were measured. Spectral emission-absorption temperatures were determined from the spectral data as a function of wavelength, using the Kirchhoff and Planck laws. These temperatures proved independent of wavelength for an isothermal profile, despite a large variation of absorptance with wavelength. For nonisothermal profiles, the emission-absorption temperature varied with wavelength in a characteristic manner for each profile. These results established more firmly the validity of the infrared emission-absorption technique of gas temperature measurement, and confirmed a previous hypothesis that the wavelength dependence of spectrally determined temperature, observed for most flames, is a temperature profile effect. The spectral emittance equation for a gas was formulated in terms of observable quantities for isothermal and nonisothermal cases, taking the spectrometer slit function into account.

© 1965 Optical Society of America

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References

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  1. S. Silverman, J. Opt. Soc. Am. 39, 275 (1949).
    [CrossRef] [PubMed]
  2. G. A. Hornbeck, L. O. Olsen, WADC Tech. Rept. 57–516 (Wright-Patterson Air Force Base, Ohio, 1958).
  3. R. H. Tourin, Combust. Flame 2, 353 (1958).
    [CrossRef]
  4. L. D. Kaplan, J. Opt. Soc. Am. 49, 504 (1959).
    [CrossRef]
  5. F. P. Bundy, H. M. Strong, J. Appl. Phys. 25, 1531 (1954).
    [CrossRef]
  6. F. J. Weinberg, Optics of Flames (Butterworth, Washington, D.C., 1963).
  7. W. J. Pearce, in High Temperatures, H. Fischer, L. C. Mansur, eds. (Wiley, New York, 1958), p. 123.
  8. M. P. Freeman, S. Katz, J. Opt. Soc. Am. 50, 826 (1960).
    [CrossRef]
  9. M. P. Freeman, S. Katz, J. Opt. Soc. Am. 53, 1172 (1963).
    [CrossRef]
  10. R. H. Tourin, Temperature, Its Measurement and Control in Science and Industry, Vol. III, C. M. Herzfeld, ed. (Reinhold, New York, 1962), pt. 2, chap. 43.
  11. H. J. Babrov, R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 15 (1963).
    [CrossRef]
  12. W. E. Kaskan, Sixth Symposium (International) on Combustion (Reinhold, New York, 1957), p. 134.
    [CrossRef]

1963 (2)

M. P. Freeman, S. Katz, J. Opt. Soc. Am. 53, 1172 (1963).
[CrossRef]

H. J. Babrov, R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 15 (1963).
[CrossRef]

1960 (1)

1959 (1)

L. D. Kaplan, J. Opt. Soc. Am. 49, 504 (1959).
[CrossRef]

1958 (1)

R. H. Tourin, Combust. Flame 2, 353 (1958).
[CrossRef]

1954 (1)

F. P. Bundy, H. M. Strong, J. Appl. Phys. 25, 1531 (1954).
[CrossRef]

1949 (1)

Babrov, H. J.

H. J. Babrov, R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 15 (1963).
[CrossRef]

Bundy, F. P.

F. P. Bundy, H. M. Strong, J. Appl. Phys. 25, 1531 (1954).
[CrossRef]

Freeman, M. P.

Hornbeck, G. A.

G. A. Hornbeck, L. O. Olsen, WADC Tech. Rept. 57–516 (Wright-Patterson Air Force Base, Ohio, 1958).

Kaplan, L. D.

L. D. Kaplan, J. Opt. Soc. Am. 49, 504 (1959).
[CrossRef]

Kaskan, W. E.

W. E. Kaskan, Sixth Symposium (International) on Combustion (Reinhold, New York, 1957), p. 134.
[CrossRef]

Katz, S.

Olsen, L. O.

G. A. Hornbeck, L. O. Olsen, WADC Tech. Rept. 57–516 (Wright-Patterson Air Force Base, Ohio, 1958).

Pearce, W. J.

W. J. Pearce, in High Temperatures, H. Fischer, L. C. Mansur, eds. (Wiley, New York, 1958), p. 123.

Silverman, S.

Strong, H. M.

F. P. Bundy, H. M. Strong, J. Appl. Phys. 25, 1531 (1954).
[CrossRef]

Tourin, R. H.

H. J. Babrov, R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 15 (1963).
[CrossRef]

R. H. Tourin, Combust. Flame 2, 353 (1958).
[CrossRef]

R. H. Tourin, Temperature, Its Measurement and Control in Science and Industry, Vol. III, C. M. Herzfeld, ed. (Reinhold, New York, 1962), pt. 2, chap. 43.

Weinberg, F. J.

F. J. Weinberg, Optics of Flames (Butterworth, Washington, D.C., 1963).

Combust. Flame (1)

R. H. Tourin, Combust. Flame 2, 353 (1958).
[CrossRef]

J. Appl. Phys. (1)

F. P. Bundy, H. M. Strong, J. Appl. Phys. 25, 1531 (1954).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Quant. Spectry. Radiative Transfer (1)

H. J. Babrov, R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 15 (1963).
[CrossRef]

Other (5)

W. E. Kaskan, Sixth Symposium (International) on Combustion (Reinhold, New York, 1957), p. 134.
[CrossRef]

G. A. Hornbeck, L. O. Olsen, WADC Tech. Rept. 57–516 (Wright-Patterson Air Force Base, Ohio, 1958).

R. H. Tourin, Temperature, Its Measurement and Control in Science and Industry, Vol. III, C. M. Herzfeld, ed. (Reinhold, New York, 1962), pt. 2, chap. 43.

F. J. Weinberg, Optics of Flames (Butterworth, Washington, D.C., 1963).

W. J. Pearce, in High Temperatures, H. Fischer, L. C. Mansur, eds. (Wiley, New York, 1958), p. 123.

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Figures (8)

Fig. 1
Fig. 1

Schematic cross section of concentric porous plug burner.

Fig. 2
Fig. 2

Temperatures of pure gas samples heated in a closed vessel in a furnace under equilibrium conditions. Two separate experiments were performed, one with pure H2O and one with pure CO2. Temperatures were measured by the infrared spectroradiometric method described in the text. The temperature measurements are independent of wavelength, indicating thermal equilibrium.

Fig. 3
Fig. 3

Boundary determination and temperature distribution along the optical axis for the isothermal case.

Fig. 4
Fig. 4

Gas flame temperatures, measured by the infrared spectroradiometric method.

Fig. 5
Fig. 5

Thermocouple temperature distribution along the optical axis for a C3H8-air flame with a 350°K gradient introduced at three positions.

Fig. 6
Fig. 6

Tile effect of a 350°K gradient at three positions oil the spectral emittance of a C3H8-air flame.

Fig. 7
Fig. 7

Spectroradiometric temperatures and spectral absorptance vs wavelength for a propane-air flame with a 350°K cold-spot introduced at three positions.

Fig. 8
Fig. 8

The effect of a 350°K discontinuity at three positions on the Kirchhoff law ratio of a propane-air flame at 4.4 μ, 4.5 μ, and 4.6 μ.

Equations (9)

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d H ( λ j , x ) = k ( λ j , x ) [ H ( λ j , x ) - W b ( λ j , T x ) ] d x ,
H ( λ j , x ) exp [ - k ( λ j , x ) d x ] = - W b ( λ j , T x ) exp [ - k ( λ j , x ) d x ] k ( λ j , x ) d x + C ,
H ( λ j , 0 ) = ( exp [ L 0 k ( λ j , x ) d x ] ) L 0 - W b ( λ j , T x ) × exp [ - L x k ( λ j , x ) d x ] k ( λ j , x ) d x .
H ( λ j , 0 ) = exp [ - k ( λ j ) L ] L 0 - W b ( λ j , T ) × exp [ - k ( λ j ) ( x - L ) ] k ( λ j ) d x = W b ( λ j , T ) [ 1 - exp { - k ( λ j ) L } ] = W b ( λ j , T ) [ 1 - τ ( λ j ) ] ,
H ( λ j ) = exp [ i = 0 n k i ( λ j ) { l ( i - 1 ) - l i } ] × i = 1 n l ( i ) l ( i - 1 ) - W b ( λ j , T i ) exp [ i + 1 n - k h ( λ j ) { l ( h - 1 ) - l h } ] × exp [ - k i ( λ j ) { x - l i } ] k i ( λ j ) d x = i = 1 n W b ( λ j , T i ) × [ 1 - τ i ( λ j ) ] h = 0 i - 1 τ h ( λ j ) ,
H m ( λ j ) = Δ λ H ( λ ) g ( λ j , λ ) d λ = i = 1 n W b ( λ j , T i ) Δ λ [ 1 - τ i ( λ ) ] h = 0 i - 1 τ h ( λ ) g ( λ j , λ ) d λ = i = 1 n W b m ( λ j , T i ) [ τ ¯ ( i - 1 ) ( λ j ) - τ ¯ i ( λ ) ] ,
τ ¯ i ( λ j ) = Δ λ h = 0 i τ h ( λ ) g ( λ j , λ ) d λ Δ λ g ( λ j , λ ) d λ .
W b m ( λ j , T i ) = W b ( λ j , T i ) Δ λ g ( λ j , λ ) d λ .
H m ( λ j ) = W b m ( λ j , T ) [ 1 - τ ¯ ( λ j ) ] .

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