Abstract

We present quantitative rainbow schlieren deflectometry with tomography for measurements of temperature in three-dimensional gas flows. The schlieren apparatus with a continuously graded spectral filter of known transmissivity was used to create color schlieren images of the test media. These images at multiple viewing angles were used to infer beam deflection angles by the medium. The deflection data were used with a tomographic technique to reconstruct the refractive index and thus the temperature field. The temperature distributions obtained by the rainbow schlieren tomography agreed with those measured by a thermocouple probe. This research demonstrates that tomography can be used with full-field schlieren deflectometry to measure quantitatively temperature in asymmetric gas flows. The technique could be used to obtain related properties such as pressure, density, and gas composition.

© 1998 Optical Society of America

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References

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  1. R. M. Fristrom, Flame Structure and Processes (Oxford U. Press, New York, 1995).
  2. R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24, 1139–1150 (1981).
    [CrossRef]
  3. S. R. Ray, H. G. Semerjan, “Laser tomography for simultaneous concentration and temperature measurements in reacting flows,” in Combustion Diagnostics by Nonintrusive Methods, T. D. McCoy, J. A. Roux, eds. (American Institute of Aeronautics and Astronautics, New York, 1984), Vol. 92, pp. 490–501.
  4. D. W. Sweeney, “Interferometric measurement of three-dimensional temperature fields,” Ph.D. dissertation (University of Michigan, Ann Arbor, Michigan, 1972).
  5. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  6. R. Snyder, L. Hesselink, “Optical tomography for flow visualization of the density field around revolving helicopter rotor blade,” Appl. Opt. 23, 3650–3656 (1984).
    [CrossRef] [PubMed]
  7. R. Snyder, L. Hesselink, “Measurement of mixing fluids flows with optical tomography,” Opt. Lett. 13, 87–91 (1988).
    [CrossRef] [PubMed]
  8. J. Stricker, “Analysis of 3D phase objects by moire deflectometry,” Appl. Opt. 23, 3657–3659 (1984).
    [CrossRef] [PubMed]
  9. G. W. Faris, “Quantitative optical tomographic imaging of fluid flows and flames,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1986).
  10. G. W. Faris, R. L. Byer, “Three dimensional beam deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202–5212 (1988).
    [CrossRef] [PubMed]
  11. E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of temperature distribution of flames by moire deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
    [CrossRef] [PubMed]
  12. P. V. Farrell, D. L. Hofeldt, “Temperature measurement in gases using speckle photography,” Appl. Opt. 23, 1055–1059 (1984).
    [CrossRef] [PubMed]
  13. P. S. Greenberg, R. B. Klimek, D. R. Buchele, “Quantitative rainbow schlieren deflectometry,” Appl. Opt. 34, 3810–3822 (1995).
    [CrossRef] [PubMed]
  14. R. A. William, M. S. Beck, Process Tomography: Principles, Techniques and Applications (Butterworth, New York, 1995).
  15. A. J. Decker, “Tomographic methods in flow diagnostics,” in Optical Diagnostics for Flow Processes, L. Lading, G. Wigley, P. Buchhave, eds. (Plenum, New York, 1994), pp. 337–353.
  16. G. N. Ramachandran, A. V. Lakshminarayana, “Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolution instead of Fourier transform,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236–2240 (1971).
    [CrossRef] [PubMed]
  17. G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).
  18. R. J. Goldstein, T. H. Kuehn, “Optical systems for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics Measurements, R. J. Goldstein, ed. (Taylor & Francis, London, 1996), pp. 451–508.
  19. C. J. Chen, W. Rodi, Vertical Turbulent Buoyant Jets—A Review of Experimental Data (Pergamon, Oxford, 1980).
  20. D. Verhoeven, “Limited-data computed tomography algorithms for the physical sciences,” Appl. Opt. 32, 3736–3754 (1993).
    [CrossRef] [PubMed]
  21. K Al-Ammar, A. K. Agrawal, S. R. Gollahalli, D Griffin, “Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium,” Exp. Fluids (to be published).

1995

1993

1988

1984

1981

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24, 1139–1150 (1981).
[CrossRef]

E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of temperature distribution of flames by moire deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
[CrossRef] [PubMed]

1971

G. N. Ramachandran, A. V. Lakshminarayana, “Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolution instead of Fourier transform,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Agrawal, A. K.

K Al-Ammar, A. K. Agrawal, S. R. Gollahalli, D Griffin, “Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium,” Exp. Fluids (to be published).

Al-Ammar, K

K Al-Ammar, A. K. Agrawal, S. R. Gollahalli, D Griffin, “Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium,” Exp. Fluids (to be published).

Bar-Ziv, E.

Beck, M. S.

R. A. William, M. S. Beck, Process Tomography: Principles, Techniques and Applications (Butterworth, New York, 1995).

Buchele, D. R.

Byer, R. L.

Chen, C. J.

C. J. Chen, W. Rodi, Vertical Turbulent Buoyant Jets—A Review of Experimental Data (Pergamon, Oxford, 1980).

Decker, A. J.

A. J. Decker, “Tomographic methods in flow diagnostics,” in Optical Diagnostics for Flow Processes, L. Lading, G. Wigley, P. Buchhave, eds. (Plenum, New York, 1994), pp. 337–353.

Emmerman, P. J.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24, 1139–1150 (1981).
[CrossRef]

Faris, G. W.

G. W. Faris, R. L. Byer, “Three dimensional beam deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202–5212 (1988).
[CrossRef] [PubMed]

G. W. Faris, “Quantitative optical tomographic imaging of fluid flows and flames,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1986).

Farrell, P. V.

Fristrom, R. M.

R. M. Fristrom, Flame Structure and Processes (Oxford U. Press, New York, 1995).

Glatt, I.

Goldstein, R. J.

R. J. Goldstein, T. H. Kuehn, “Optical systems for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics Measurements, R. J. Goldstein, ed. (Taylor & Francis, London, 1996), pp. 451–508.

Gollahalli, S. R.

K Al-Ammar, A. K. Agrawal, S. R. Gollahalli, D Griffin, “Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium,” Exp. Fluids (to be published).

Goulard, R.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24, 1139–1150 (1981).
[CrossRef]

Greenberg, P. S.

Griffin, D

K Al-Ammar, A. K. Agrawal, S. R. Gollahalli, D Griffin, “Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium,” Exp. Fluids (to be published).

Herman, G. T.

G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).

Hesselink, L.

Hofeldt, D. L.

Kafri, O.

Keren, E.

Klimek, R. B.

Kuehn, T. H.

R. J. Goldstein, T. H. Kuehn, “Optical systems for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics Measurements, R. J. Goldstein, ed. (Taylor & Francis, London, 1996), pp. 451–508.

Lakshminarayana, A. V.

G. N. Ramachandran, A. V. Lakshminarayana, “Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolution instead of Fourier transform,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Ramachandran, G. N.

G. N. Ramachandran, A. V. Lakshminarayana, “Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolution instead of Fourier transform,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Ray, S. R.

S. R. Ray, H. G. Semerjan, “Laser tomography for simultaneous concentration and temperature measurements in reacting flows,” in Combustion Diagnostics by Nonintrusive Methods, T. D. McCoy, J. A. Roux, eds. (American Institute of Aeronautics and Astronautics, New York, 1984), Vol. 92, pp. 490–501.

Rodi, W.

C. J. Chen, W. Rodi, Vertical Turbulent Buoyant Jets—A Review of Experimental Data (Pergamon, Oxford, 1980).

Santoro, R. J.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24, 1139–1150 (1981).
[CrossRef]

Semerjan, H. G.

S. R. Ray, H. G. Semerjan, “Laser tomography for simultaneous concentration and temperature measurements in reacting flows,” in Combustion Diagnostics by Nonintrusive Methods, T. D. McCoy, J. A. Roux, eds. (American Institute of Aeronautics and Astronautics, New York, 1984), Vol. 92, pp. 490–501.

Semerjian, H. G.

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24, 1139–1150 (1981).
[CrossRef]

Snyder, R.

Stricker, J.

Sweeney, D. W.

D. W. Sweeney, “Interferometric measurement of three-dimensional temperature fields,” Ph.D. dissertation (University of Michigan, Ann Arbor, Michigan, 1972).

Verhoeven, D.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

William, R. A.

R. A. William, M. S. Beck, Process Tomography: Principles, Techniques and Applications (Butterworth, New York, 1995).

Appl. Opt.

Int. J. Heat Mass Transfer

R. J. Santoro, H. G. Semerjian, P. J. Emmerman, R. Goulard, “Optical tomography for flow field diagnostics,” Int. J. Heat Mass Transfer 24, 1139–1150 (1981).
[CrossRef]

Opt. Lett.

Proc. Natl. Acad. Sci. U.S.A.

G. N. Ramachandran, A. V. Lakshminarayana, “Three-dimensional reconstruction from radiographs and electron micrographs: applications of convolution instead of Fourier transform,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Other

G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).

R. J. Goldstein, T. H. Kuehn, “Optical systems for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics Measurements, R. J. Goldstein, ed. (Taylor & Francis, London, 1996), pp. 451–508.

C. J. Chen, W. Rodi, Vertical Turbulent Buoyant Jets—A Review of Experimental Data (Pergamon, Oxford, 1980).

K Al-Ammar, A. K. Agrawal, S. R. Gollahalli, D Griffin, “Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium,” Exp. Fluids (to be published).

S. R. Ray, H. G. Semerjan, “Laser tomography for simultaneous concentration and temperature measurements in reacting flows,” in Combustion Diagnostics by Nonintrusive Methods, T. D. McCoy, J. A. Roux, eds. (American Institute of Aeronautics and Astronautics, New York, 1984), Vol. 92, pp. 490–501.

D. W. Sweeney, “Interferometric measurement of three-dimensional temperature fields,” Ph.D. dissertation (University of Michigan, Ann Arbor, Michigan, 1972).

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

G. W. Faris, “Quantitative optical tomographic imaging of fluid flows and flames,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1986).

R. A. William, M. S. Beck, Process Tomography: Principles, Techniques and Applications (Butterworth, New York, 1995).

A. J. Decker, “Tomographic methods in flow diagnostics,” in Optical Diagnostics for Flow Processes, L. Lading, G. Wigley, P. Buchhave, eds. (Plenum, New York, 1994), pp. 337–353.

R. M. Fristrom, Flame Structure and Processes (Oxford U. Press, New York, 1995).

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Figures (9)

Fig. 1
Fig. 1

Schlieren apparatus with lenses.

Fig. 2
Fig. 2

Coordinate system.

Fig. 3
Fig. 3

Schematic of the jet apparatus.

Fig. 4
Fig. 4

Temperature distributions along x = 12 mm at z = 5 mm.

Fig. 5
Fig. 5

Temperature distributions along y = 0 mm at z = 5 mm.

Fig. 6
Fig. 6

Temperature distributions along x = 5 mm at z = 10 mm.

Fig. 7
Fig. 7

Temperature distributions along y = 0 mm at z = 10 mm.

Fig. 8
Fig. 8

Temperature contours on a vertical (xz) plane at y = 3 mm.

Fig. 9
Fig. 9

Temperature contours on a horizontal (xy) plane at z = 5 mm.

Equations (10)

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α y d y d x = tan   α y = 1 n 0     d n x ,   y ,   z d y d x ,
α z d z d x = tan   α z = 1 n 0     d n x ,   y ,   z d z d x .
α θ t d t d s = tan   α θ t = 1 n 0     d n t ,   s d t d s =   d η t ,   s d t d s ,
η x ,   y = 0 π α θ t * k t d θ ,
k r = - f max f max   K f r exp i 2 π f r r d f r = 1 π 2 r sin 2 π rf max ,
K f r = i / 2 π   - f max f r < 0 , = - i / 2 π     0 < f r < f max , = 0   | f r | f max .
η x ,   y = i = 1 I π I - 1 j = 1 J   α i π I - 1 ,   j Δ t × k y   cos   θ - x   sin   θ - j Δ t Δ t
n - 1 = ρ C ,
T = n 0 - 1 n - 1   T 0 ,
d θ t = f c α θ t ,

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