Abstract

Mapping of temperature of a premixed hydrogen–oxygen flame by moire deflectometry is demonstrated. The technique is based on deflection mapping of rays from a collimated light beam due to gradients of the refractive index across the flame. For an axially symmetric flame the radial distribution of the refractive index was derived by Abel transformation. The temperature profile of the flame was calculated for a known gas composition assuming ideal gas behavior.

© 1981 Optical Society of America

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References

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  1. D. P. Aeschliman, J. C. Cummings, R. A. Hill, J. Quant. Spectrosc. Radiat. Transfer 21, 293 (1979); J. H. Bechtel, Appl. Opt. 18, 2100 (1979).
    [Crossref] [PubMed]
  2. M. M. El-Wakil, in Combustion Measurements: Modern Technique Instrumentation, Proceedings, Project Squid Workshop Combustion Measurement Jet Propulsion Systems, 1975, R. J. Goulard, Ed. (Hemisphere Publishing, Washington, D.C., 1976), p. 225.
  3. S. Sugiyama, M. Nakamura, A. Sato, J. Kimura, Kagaku Kogaku 32, 1021 (1968).
    [Crossref]
  4. O. Kafri, Opt. Lett. 5, 555 (1980).
    [Crossref] [PubMed]
  5. O. Kafri, A. Livnat, Opt. Lett. 4, 314 (1979).
    [Crossref] [PubMed]
  6. D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).
  7. J. D. Algeo, M. B. Denton, Appl. Spectrosc. 35, 35 (1981); K. Bockasten, J. Opt. Soc. Am. 51, 943 (1961).
    [Crossref]
  8. A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970); J. Ebbeni, Nouv. Rev. Opt. Appl. 1, 333 (1970).
    [Crossref]
  9. J. C. Owens, Appl. Opt. 6, 51 (1967).
    [Crossref] [PubMed]

1981 (1)

1980 (1)

1979 (2)

O. Kafri, A. Livnat, Opt. Lett. 4, 314 (1979).
[Crossref] [PubMed]

D. P. Aeschliman, J. C. Cummings, R. A. Hill, J. Quant. Spectrosc. Radiat. Transfer 21, 293 (1979); J. H. Bechtel, Appl. Opt. 18, 2100 (1979).
[Crossref] [PubMed]

1968 (1)

S. Sugiyama, M. Nakamura, A. Sato, J. Kimura, Kagaku Kogaku 32, 1021 (1968).
[Crossref]

1967 (1)

Aeschliman, D. P.

D. P. Aeschliman, J. C. Cummings, R. A. Hill, J. Quant. Spectrosc. Radiat. Transfer 21, 293 (1979); J. H. Bechtel, Appl. Opt. 18, 2100 (1979).
[Crossref] [PubMed]

Algeo, J. D.

Cummings, J. C.

D. P. Aeschliman, J. C. Cummings, R. A. Hill, J. Quant. Spectrosc. Radiat. Transfer 21, 293 (1979); J. H. Bechtel, Appl. Opt. 18, 2100 (1979).
[Crossref] [PubMed]

Denton, M. B.

Durelli, A. J.

A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970); J. Ebbeni, Nouv. Rev. Opt. Appl. 1, 333 (1970).
[Crossref]

El-Wakil, M. M.

M. M. El-Wakil, in Combustion Measurements: Modern Technique Instrumentation, Proceedings, Project Squid Workshop Combustion Measurement Jet Propulsion Systems, 1975, R. J. Goulard, Ed. (Hemisphere Publishing, Washington, D.C., 1976), p. 225.

Hill, R. A.

D. P. Aeschliman, J. C. Cummings, R. A. Hill, J. Quant. Spectrosc. Radiat. Transfer 21, 293 (1979); J. H. Bechtel, Appl. Opt. 18, 2100 (1979).
[Crossref] [PubMed]

Kafri, O.

Kimura, J.

S. Sugiyama, M. Nakamura, A. Sato, J. Kimura, Kagaku Kogaku 32, 1021 (1968).
[Crossref]

Livnat, A.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).

Nakamura, M.

S. Sugiyama, M. Nakamura, A. Sato, J. Kimura, Kagaku Kogaku 32, 1021 (1968).
[Crossref]

Owens, J. C.

Parks, V. J.

A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970); J. Ebbeni, Nouv. Rev. Opt. Appl. 1, 333 (1970).
[Crossref]

Sato, A.

S. Sugiyama, M. Nakamura, A. Sato, J. Kimura, Kagaku Kogaku 32, 1021 (1968).
[Crossref]

Sugiyama, S.

S. Sugiyama, M. Nakamura, A. Sato, J. Kimura, Kagaku Kogaku 32, 1021 (1968).
[Crossref]

Appl. Opt. (1)

Appl. Spectrosc. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

D. P. Aeschliman, J. C. Cummings, R. A. Hill, J. Quant. Spectrosc. Radiat. Transfer 21, 293 (1979); J. H. Bechtel, Appl. Opt. 18, 2100 (1979).
[Crossref] [PubMed]

Kagaku Kogaku (1)

S. Sugiyama, M. Nakamura, A. Sato, J. Kimura, Kagaku Kogaku 32, 1021 (1968).
[Crossref]

Opt. Lett. (2)

Other (3)

D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).

M. M. El-Wakil, in Combustion Measurements: Modern Technique Instrumentation, Proceedings, Project Squid Workshop Combustion Measurement Jet Propulsion Systems, 1975, R. J. Goulard, Ed. (Hemisphere Publishing, Washington, D.C., 1976), p. 225.

A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970); J. Ebbeni, Nouv. Rev. Opt. Appl. 1, 333 (1970).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Geometry of the experiment. The z axis coincides with the symmetry axis of the flame: C.B., collimated light beam; rf, radius of the flame region; x0,y0, coordinates of the entrance point of a representative ray; xf,yf, coordinates of the exit point; ϕ, the deflection angle, G1,G2, gratings; d, the shift of the shadow of G1 on G2 in the y direction with respect to the nondeflected ray.

Fig. 2
Fig. 2

(a) Arbitrary ϕ vs y. (b) ψ vs y (smooth curve) and the corresponding coarse grained intensity of the moire pattern (broken curve). See text for the assignments of k and j.

Fig. 3
Fig. 3

Schematic representation of the experiment: C.B., collimated beam; F, flame; G1,G2, gratings; S, mat screen, T.V.C., vidicon camera; M, video monitor, TVLS, TV line selector; OSC, oscilloscope.

Fig. 4
Fig. 4

Typical deflectogram of a hydrogen–oxygen premixed flame. The horizontal line is the cursor of the TV line selector.

Fig. 5
Fig. 5

Intensity profile of a particular line: (a) f(y,z) vs y [the upper and lower envelopes refer to fmax(y,z) and fmin(y,z), respectively]; (b) I(y,z) vs y.

Fig. 6
Fig. 6

Typical radial profile of the temperature. The circle denotes the temperature measured with a thermocouple.

Equations (12)

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ϕ ( y , z ) = 1 n f x o ( y , z ) x f ( y , z ) n ( x , y , z ) y d x ,
ϕ ( y , z ) = 2 y n f y y f n ( r , z ) r · d r ( r 2 - y 2 ) 1 / 2 .
n ( r , z ) - n f = - n f π r r f ϕ ( y , z ) d y ( y 2 - r 2 ) 1 / 2 .
r 1 r f ( y 2 - r 2 ) - 1 / 2 d y
Ψ ( y , z ) = 2 π Δ cos ( θ / 2 ) p Φ ( y , z ) .
Ψ ( y , z ) = j π I ( y , z ) + 2 k π ;             j = ± 1 , k = 0 , ± 1 , ± 2 ,
n - 1 = i = 1 m k i N i ,
T = P ( n - 1 ) R i = 1 m k i N i i = 1 m N i ,
T ( r ) T f = n f - 1 n ( r ) - 1 · k ( r ) k f .
k ( r ) = j k j N j ( r ) j N j ( r ) ;             k f = l k l f N l f l N l f ,
T ( r ) T f = n f - 1 n ( r ) - 1 k a v k f .
I ( y , z ) = f ( y , z ) - f min ( y , z ) f max ( y , z ) - f min ( y , z ) ,

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