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.

© 1966 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. R. H. Tourin, B. Krakow, Appl. Opt. 4, 237 (1965).
    [CrossRef]
  3. D. L. Phillips, J. Assoc. Computing Machinery 9, 84 (1962).
    [CrossRef]
  4. S. Twomey, J. Assoc. Computing Machinery 8, 97 (1963).
    [CrossRef]
  5. G. N. Plass, Appl. Opt. 4, 69 (1965).
    [CrossRef]
  6. B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), p. 680.
  7. R. H. Tourin, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, ed. (Reinhold, New York, 1957), Vol. III, Part II, p. 459.

1965

1963

S. Twomey, J. Assoc. Computing Machinery 8, 97 (1963).
[CrossRef]

1962

D. L. Phillips, J. Assoc. Computing Machinery 9, 84 (1962).
[CrossRef]

1949

Krakow, B.

Lewis, B.

B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), p. 680.

Phillips, D. L.

D. L. Phillips, J. Assoc. Computing Machinery 9, 84 (1962).
[CrossRef]

Plass, G. N.

Silverman, S.

Tourin, R. H.

R. H. Tourin, B. Krakow, Appl. Opt. 4, 237 (1965).
[CrossRef]

R. H. Tourin, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, ed. (Reinhold, New York, 1957), Vol. III, Part II, p. 459.

Twomey, S.

S. Twomey, J. Assoc. Computing Machinery 8, 97 (1963).
[CrossRef]

von Elbe, G.

B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), p. 680.

Appl. Opt.

J. Assoc. Computing Machinery

D. L. Phillips, J. Assoc. Computing Machinery 9, 84 (1962).
[CrossRef]

S. Twomey, J. Assoc. Computing Machinery 8, 97 (1963).
[CrossRef]

J. Opt. Soc. Am.

Other

B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), p. 680.

R. H. Tourin, in Temperature, Its Measurement and Control in Science and Industry, C. M. Herzfeld, ed. (Reinhold, New York, 1957), Vol. III, Part II, p. 459.

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Figures (3)

Fig. 1
Fig. 1

Three-zone burner assembly. Each zone consists of a 5 cm × 5 cm main burner flanked by a pair of 1.3 cm × 5 cm guard burners. At each end of the assembly is a 1.3 cm × 5 cm sparger that has the same appearance as a guard burner.

Fig. 2
Fig. 2

Zonal transmittances.

Fig. 3
Fig. 3

Zonal transmittances.

Tables (11)

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Table I Water Vapor Contents of Samples

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Table II Two-Zone Specimen Parameters

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Table III Two-Zone Radiance Measurements

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Table IV Spectroscopically Measured Two-Zone Temperature Profile

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Table V Spectroscopically Measured Two-Zone Temperature Profile Using Measured Value of τ ¯ 2 = τ ¯ 1 at 4.179 μ

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Table VI Monotonic Three-Zone Specimen Parameters

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Table VII Monotonic Three-Zone Radiance Measurements

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Table VIII Spectroscopically Measured Three-Zone Monotonic Temperature Profile

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Table IX Nonmonotonic Three-Zone Specimen Parameters

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Table X Nonmonotonic Three-Zone Radiance Measurements

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Table XI Spectroscopically Measured Three-Zone Nonmonotonic Temperature Profile

Equations (24)

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N m ( λ j ) = H m ( λ j ) N b ( λ j , T b ) H b ( λ j , T b ) = i = 1 n N b ( λ j , T i ) [ τ ¯ ( i - 1 ) ( λ i ) - τ ¯ i ( λ j ) ] .
N m ( λ j ) = i = 1 n N b ( λ i , T i ) [ τ ¯ ( i + 1 ) ( λ j ) - τ ¯ i ( λ j ) ] ,
N b ( λ j , T i ) = ( λ * / λ j ) 3 N b ( λ * , T i ) - Δ N b ( λ j , T i ) .
j = 1 p ( λ * / λ j ) 3 [ τ ¯ ( k - 1 ) ( λ j ) - τ ¯ k ( λ j ) ] × { - N m ( λ j ) + i = 1 n [ ( λ * / λ j ) 3 N b ( λ * , T i ) - Δ N b ( λ j , T i ) ] [ τ ¯ ( i - 1 ) ( λ j ) - τ ¯ i ( λ j ) ] } + j = 1 p ( λ * / λ j ) 3 [ τ ¯ ( k + 1 ) ( λ j ) - τ ¯ k ( λ j ) ] × { - N m ( λ j ) + i = 1 n [ ( λ * / λ j ) 3 N b ( λ * , T i ) - Δ N b ( λ j , T i ) ] [ τ ¯ ( i + 1 ) ( λ j ) - τ ¯ i ( λ j ) ] } + γ { N b [ λ * , T ( k - 2 ) ] - 4 N b [ λ * , T ( k - 1 ) ] + 6 N b ( λ * , T k ) - 4 N b [ λ * , T ( k + 1 ) ] + N b [ λ * , T ( k + 2 ) ] } = 0 ,
k = 1 , 2 , 3 n , p + p n ,
N b ( λ * , T - 1 ) = - N b ( λ * , T i ) .
N b [ λ * , T ( n + 2 ) ] = - N b ( λ * , T n ) ,
N b ( λ * , T 0 ) = N b [ λ * , T ( n + 1 ) ] = 0.
[ ln τ ¯ i ( λ j ) ] 2 = h = 0 i [ ln τ ¯ ( λ j , T h ) ] 2 ,
N m ( λ j ) = N b ( λ j , T ) [ 1 - τ ¯ ( λ j ) ] .
N b ( λ j , T i ) = A ( λ j , T i ) - Δ N b ( λ j , T i ) = b ( λ j ) B ( T i ) + C ( λ j ) - Δ N b ( λ j , T i ) .
A ( λ j , T i ) = N b ( λ j , T * ) + ( δ N b ( λ j , T * ) δ T ) λ j ( T i - T * )
A ( λ j , T i ) = b ( λ j ) N b ( λ * , T i ) .
b ( λ j ) = ( λ * / λ j ) c i .
c i = λ * N b ( λ * , T i ) [ δ N b ( λ * , T i ) δ λ * ]
c i = c = λ * N b ( λ * , T * ) [ δ N b ( λ * , T * ) δ λ * ] .
N m ( λ j ) + j = i = 1 n N b ( λ j , T i ) [ τ ¯ ( i - 1 ) ( λ j ) - τ ¯ i ( λ j ) ] .
N m ( λ j ) + j = i = 1 n N b ( λ j , T i ) [ τ ¯ ( i + 1 ) ( λ j ) - τ ¯ i ( λ j ) ] .
a j i = b ( λ j ) [ τ ¯ ( i - 1 ) ( λ j ) - τ ¯ i ( λ j ) ]
a j i = b ( λ j ) [ τ ¯ ( i + 1 ) ( λ j ) - τ ¯ i ( λ j ) ] , f i = B ( T i ) , g j = N m ( λ j ) - i = 1 n [ τ ¯ ( i - 1 ) ( λ j ) - τ ¯ i ( λ j ) ] [ C ( λ j ) - Δ N b ( λ j ) ]
g j = N m ( λ j ) - i = 1 n [ τ ¯ ( i + 1 ) ( λ j ) - τ ¯ i ( λ j ) ] [ C ( λ j ) - Δ N b ( λ j ) ] .
j = 1 p b ( λ j ) [ τ ¯ ( k - 1 ) ( λ j ) - τ ¯ k ( λ j ) ] j + j = 1 p b ( λ j ) [ τ ¯ ( k + 1 ) ( λ j ) - τ ¯ k ( λ j ) ] j + γ { B [ T ( k - 2 ) ] - 4 B [ T ( k - 1 ) ] + 6 B ( T k ) - 4 B [ T ( k + 1 ) ] + B [ T ( k + 2 ) ] } = 0.
k = 1 , 2 , 3 , n , p + p n ,
B ( T - 1 ) = - B ( T 1 ) , B ( T n + 2 ) = - B ( T n ) , B ( T 0 )             = 0 , B ( T n + 1 ) = 0.

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