Abstract

Rainbow schlieren deflectometry (RSD) provides a simple and nonintrusive way of determining the temperature field of axisymmetric flames. This technique is specially suited for the detection of large temperature gradients, such as those near the flame location. We explore the feasibility and accuracy of using RSD to obtain the flame location and thermal structure of premixed Bunsen flames for varying fuel types, equivalence ratios, and soot loadings. Uncertainty analysis is also carried out to provide various ways to reduce RSD experimental error. The RSD technique is demonstrated to give useful data even for moderately and heavily sooting flames.

© 2005 Optical Society of America

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References

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  1. C. J. Sun, C. J. Sung, L. He, C. K. Law, “Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters,” Combust. Flame 118, 108–128 (1999).
    [CrossRef]
  2. A. F. Ibarreta, C. J. Sung, T. Hirasawa, H. Wang, “Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow schlieren deflectometry,” Combust. Flame 140, 93–102 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  4. P. S. Greenberg, R. B. Klimek, D. R. Buchele, “Quantitative rainbow schlieren deflectometry,” Appl. Opt. 34, 3810–3822 (1995).
    [CrossRef] [PubMed]
  5. F. J. Weinberg, Optics of Flames (Butterworth, Washington, 1963), pp. 23–39.
  6. A. K. Agrawal, B. W. Albers, D. W. Griffin, “Abel inversion of deflectometric measurements in dynamic flows,” Appl. Opt. 38, 3394–3398 (1999).
    [CrossRef]
  7. X. Xiao, I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
    [CrossRef]
  8. X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
    [CrossRef]
  9. X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
    [CrossRef]
  10. K. N. Al-ammar, A. K. Agrawal, S. R. Gollahalli, “Quantitative measurements of laminar hydrogen gas-jet diffusion flames in a 2.2s drop tower,” Proc. Combust. Inst. 28, 1997–2004 (2000).
    [CrossRef]
  11. X. Xiao, I. K. Puri, A. K. Agrawal, “Temperature measurements in steady axisymmetric partially premixed flames by use of rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
    [CrossRef] [PubMed]
  12. R. Rubinstein, P. S. Greenberg, “Rapid inversion of angular deflection data for certain axisymmetric refractive index distributions,” Appl. Opt. 33, 1141–1144 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  15. A. E. Lutz, R. J. Kee, J. F. Grcar, F. M. Rupley, “oppdif: A Fortran program for computing opposed flow diffusion flames,” (Sandia National Laboratories, Liver-more, Calif., 1997).
  16. H. Wang, A. Laskin, “A comprehensive kinetic model of ethylene and acetylene oxidation at high temperatures,” (2000), http://ignis.usc.edu/c2_download.html .
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. Y. Ikeda, J. Kojima, H. Hashimoto, “Local chemiluminescence spectra measurements in high-pressure laminar methane/air premixed flame,” Proc. Combust. Inst. 29, 1495–1501 (2002).
    [CrossRef]
  25. L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
    [CrossRef]
  26. K. T. Walsh, J. Fielding, M. B. Long, “Effect of light collection geometry on reconstruction errors in Abel inversions,” Opt. Lett. 25, 457–459 (1999).
    [CrossRef]
  27. G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
    [CrossRef]

2005

A. F. Ibarreta, C. J. Sung, T. Hirasawa, H. Wang, “Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow schlieren deflectometry,” Combust. Flame 140, 93–102 (2005).
[CrossRef]

2002

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, I. K. Puri, A. K. Agrawal, “Temperature measurements in steady axisymmetric partially premixed flames by use of rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
[CrossRef] [PubMed]

Y. Ikeda, J. Kojima, H. Hashimoto, “Local chemiluminescence spectra measurements in high-pressure laminar methane/air premixed flame,” Proc. Combust. Inst. 29, 1495–1501 (2002).
[CrossRef]

G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
[CrossRef]

2001

2000

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

K. N. Al-ammar, A. K. Agrawal, S. R. Gollahalli, “Quantitative measurements of laminar hydrogen gas-jet diffusion flames in a 2.2s drop tower,” Proc. Combust. Inst. 28, 1997–2004 (2000).
[CrossRef]

1999

A. K. Agrawal, B. W. Albers, D. W. Griffin, “Abel inversion of deflectometric measurements in dynamic flows,” Appl. Opt. 38, 3394–3398 (1999).
[CrossRef]

C. J. Sun, C. J. Sung, L. He, C. K. Law, “Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters,” Combust. Flame 118, 108–128 (1999).
[CrossRef]

C. R. Shaddix, “Correcting thermocouple measurements for radiation loss: a critical review,” in Proceedings of 33rd National Heat Transfer Conference (n.p., 1999), paper HTD99-282.

L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
[CrossRef]

K. T. Walsh, J. Fielding, M. B. Long, “Effect of light collection geometry on reconstruction errors in Abel inversions,” Opt. Lett. 25, 457–459 (1999).
[CrossRef]

1998

1997

T. Echekki, “A quasi-one-dimensional premixed flame model with cross-stream diffusion,” Combust. Flame 110, 335–350 (1997).
[CrossRef]

1995

1994

1992

1984

1982

G. Dixon-Lewis, S. M. Islam, “Flame modeling and burning velocity measurement,” Proc. Combust. Inst. 19, 283–291 (1982).
[CrossRef]

1981

W. C. Gardiner, Y. Hidaka, T. Tanzawa, “Refractivity of combustion gases,” Combust. Flame 40, 213–219 (1981).
[CrossRef]

Aggarwal, S. K.

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

Agrawal, A. K.

Al-ammar, K. N.

K. N. Al-ammar, A. K. Agrawal, S. R. Gollahalli, “Quantitative measurements of laminar hydrogen gas-jet diffusion flames in a 2.2s drop tower,” Proc. Combust. Inst. 28, 1997–2004 (2000).
[CrossRef]

Albers, B. W.

Basile, G.

G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
[CrossRef]

Blevins, L. G.

L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
[CrossRef]

Buchele, D. R.

Butuk, N. K.

Choi, C. W.

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

D’Alessio, A.

G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
[CrossRef]

D’Anna, A.

G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
[CrossRef]

Dash, C. J.

Dixon-Lewis, G.

G. Dixon-Lewis, S. M. Islam, “Flame modeling and burning velocity measurement,” Proc. Combust. Inst. 19, 283–291 (1982).
[CrossRef]

Echekki, T.

T. Echekki, “A quasi-one-dimensional premixed flame model with cross-stream diffusion,” Combust. Flame 110, 335–350 (1997).
[CrossRef]

Fielding, J.

Gardiner, W. C.

W. C. Gardiner, Y. Hidaka, T. Tanzawa, “Refractivity of combustion gases,” Combust. Flame 40, 213–219 (1981).
[CrossRef]

Gollahalli, S. R.

K. N. Al-ammar, A. K. Agrawal, S. R. Gollahalli, “Quantitative measurements of laminar hydrogen gas-jet diffusion flames in a 2.2s drop tower,” Proc. Combust. Inst. 28, 1997–2004 (2000).
[CrossRef]

A. K. Agrawal, N. K. Butuk, S. R. Gollahalli, D. W. Griffin, “Three-dimensional rainbow schlieren tomography of a temperature field in gas flows,” Appl. Opt. 37, 479–485 (1998).
[CrossRef]

Gore, J. P.

L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
[CrossRef]

Grcar, J. F.

A. E. Lutz, R. J. Kee, J. F. Grcar, F. M. Rupley, “oppdif: A Fortran program for computing opposed flow diffusion flames,” (Sandia National Laboratories, Liver-more, Calif., 1997).

R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, “A Fortran programming tool for modeling steady laminar one-dimensional premixed flames” (Sandia National Laboratories, Livermore, Calif., 1993).

Greenberg, P. S.

Griffin, D. W.

Hashimoto, H.

Y. Ikeda, J. Kojima, H. Hashimoto, “Local chemiluminescence spectra measurements in high-pressure laminar methane/air premixed flame,” Proc. Combust. Inst. 29, 1495–1501 (2002).
[CrossRef]

He, L.

C. J. Sun, C. J. Sung, L. He, C. K. Law, “Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters,” Combust. Flame 118, 108–128 (1999).
[CrossRef]

Hidaka, Y.

W. C. Gardiner, Y. Hidaka, T. Tanzawa, “Refractivity of combustion gases,” Combust. Flame 40, 213–219 (1981).
[CrossRef]

Hirasawa, T.

A. F. Ibarreta, C. J. Sung, T. Hirasawa, H. Wang, “Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow schlieren deflectometry,” Combust. Flame 140, 93–102 (2005).
[CrossRef]

Howes, W. L.

Ibarreta, A. F.

A. F. Ibarreta, C. J. Sung, T. Hirasawa, H. Wang, “Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow schlieren deflectometry,” Combust. Flame 140, 93–102 (2005).
[CrossRef]

Ikeda, Y.

Y. Ikeda, J. Kojima, H. Hashimoto, “Local chemiluminescence spectra measurements in high-pressure laminar methane/air premixed flame,” Proc. Combust. Inst. 29, 1495–1501 (2002).
[CrossRef]

Islam, S. M.

G. Dixon-Lewis, S. M. Islam, “Flame modeling and burning velocity measurement,” Proc. Combust. Inst. 19, 283–291 (1982).
[CrossRef]

Kee, R. J.

A. E. Lutz, R. J. Kee, J. F. Grcar, F. M. Rupley, “oppdif: A Fortran program for computing opposed flow diffusion flames,” (Sandia National Laboratories, Liver-more, Calif., 1997).

R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, “A Fortran programming tool for modeling steady laminar one-dimensional premixed flames” (Sandia National Laboratories, Livermore, Calif., 1993).

Klimek, R. B.

Kojima, J.

Y. Ikeda, J. Kojima, H. Hashimoto, “Local chemiluminescence spectra measurements in high-pressure laminar methane/air premixed flame,” Proc. Combust. Inst. 29, 1495–1501 (2002).
[CrossRef]

Laurendeau, N. M.

L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
[CrossRef]

Law, C. K.

C. J. Sun, C. J. Sung, L. He, C. K. Law, “Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters,” Combust. Flame 118, 108–128 (1999).
[CrossRef]

Long, M. B.

Lutz, A. E.

A. E. Lutz, R. J. Kee, J. F. Grcar, F. M. Rupley, “oppdif: A Fortran program for computing opposed flow diffusion flames,” (Sandia National Laboratories, Liver-more, Calif., 1997).

Lyle, K. H.

L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
[CrossRef]

Merzkirch, W.

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, Orlando, Fla., 1987).

Miller, J. A.

R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, “A Fortran programming tool for modeling steady laminar one-dimensional premixed flames” (Sandia National Laboratories, Livermore, Calif., 1993).

Minutolo, P.

G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
[CrossRef]

Orlando, A.

G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
[CrossRef]

Puri, I. K.

X. Xiao, I. K. Puri, A. K. Agrawal, “Temperature measurements in steady axisymmetric partially premixed flames by use of rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
[CrossRef] [PubMed]

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
[CrossRef]

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

Qin, X.

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

Renfro, M. W.

L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
[CrossRef]

Rubinstein, R.

Rupley, F. M.

A. E. Lutz, R. J. Kee, J. F. Grcar, F. M. Rupley, “oppdif: A Fortran program for computing opposed flow diffusion flames,” (Sandia National Laboratories, Liver-more, Calif., 1997).

Shaddix, C. R.

C. R. Shaddix, “Correcting thermocouple measurements for radiation loss: a critical review,” in Proceedings of 33rd National Heat Transfer Conference (n.p., 1999), paper HTD99-282.

Smooke, M. D.

R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, “A Fortran programming tool for modeling steady laminar one-dimensional premixed flames” (Sandia National Laboratories, Livermore, Calif., 1993).

Sun, C. J.

C. J. Sun, C. J. Sung, L. He, C. K. Law, “Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters,” Combust. Flame 118, 108–128 (1999).
[CrossRef]

Sung, C. J.

A. F. Ibarreta, C. J. Sung, T. Hirasawa, H. Wang, “Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow schlieren deflectometry,” Combust. Flame 140, 93–102 (2005).
[CrossRef]

C. J. Sun, C. J. Sung, L. He, C. K. Law, “Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters,” Combust. Flame 118, 108–128 (1999).
[CrossRef]

Tanzawa, T.

W. C. Gardiner, Y. Hidaka, T. Tanzawa, “Refractivity of combustion gases,” Combust. Flame 40, 213–219 (1981).
[CrossRef]

Walsh, K. T.

Wang, H.

A. F. Ibarreta, C. J. Sung, T. Hirasawa, H. Wang, “Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow schlieren deflectometry,” Combust. Flame 140, 93–102 (2005).
[CrossRef]

Weinberg, F. J.

F. J. Weinberg, Optics of Flames (Butterworth, Washington, 1963), pp. 23–39.

Xiao, X.

X. Xiao, I. K. Puri, A. K. Agrawal, “Temperature measurements in steady axisymmetric partially premixed flames by use of rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
[CrossRef] [PubMed]

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
[CrossRef]

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

Appl. Opt.

Combust. Flame

X. Qin, X. Xiao, I. K. Puri, S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao, C. W. Choi, I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

C. J. Sun, C. J. Sung, L. He, C. K. Law, “Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters,” Combust. Flame 118, 108–128 (1999).
[CrossRef]

A. F. Ibarreta, C. J. Sung, T. Hirasawa, H. Wang, “Burning velocity measurements of microgravity spherical sooting premixed flames using rainbow schlieren deflectometry,” Combust. Flame 140, 93–102 (2005).
[CrossRef]

W. C. Gardiner, Y. Hidaka, T. Tanzawa, “Refractivity of combustion gases,” Combust. Flame 40, 213–219 (1981).
[CrossRef]

T. Echekki, “A quasi-one-dimensional premixed flame model with cross-stream diffusion,” Combust. Flame 110, 335–350 (1997).
[CrossRef]

L. G. Blevins, M. W. Renfro, K. H. Lyle, N. M. Laurendeau, J. P. Gore, “Experimental study of temperature and CH radical location in partially premixed CH4/air coflow flames,” Combust. Flame 118, 684–696 (1999).
[CrossRef]

Opt. Lett.

Proc. Combust. Inst.

G. Basile, A. Orlando, A. D’Alessio, A. D’Anna, P. Minutolo, “Coagulation and carbonization processes in slightly sooting premixed flames,” Proc. Combust. Inst. 29, 2391–2397 (2002).
[CrossRef]

Y. Ikeda, J. Kojima, H. Hashimoto, “Local chemiluminescence spectra measurements in high-pressure laminar methane/air premixed flame,” Proc. Combust. Inst. 29, 1495–1501 (2002).
[CrossRef]

G. Dixon-Lewis, S. M. Islam, “Flame modeling and burning velocity measurement,” Proc. Combust. Inst. 19, 283–291 (1982).
[CrossRef]

K. N. Al-ammar, A. K. Agrawal, S. R. Gollahalli, “Quantitative measurements of laminar hydrogen gas-jet diffusion flames in a 2.2s drop tower,” Proc. Combust. Inst. 28, 1997–2004 (2000).
[CrossRef]

Proceedings of 33rd National Heat Transfer Conference

C. R. Shaddix, “Correcting thermocouple measurements for radiation loss: a critical review,” in Proceedings of 33rd National Heat Transfer Conference (n.p., 1999), paper HTD99-282.

Other

R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, “A Fortran programming tool for modeling steady laminar one-dimensional premixed flames” (Sandia National Laboratories, Livermore, Calif., 1993).

C. T. Bowman, R. K. Hanson, D. F. Davidson, W. C. Gardiner, V. Lissianski, G. P. Smith, D. M. Golden, M. Frenklach, M. Goldenberg, http://www.me.berkeley.edu/gri_mech/ .

A. E. Lutz, R. J. Kee, J. F. Grcar, F. M. Rupley, “oppdif: A Fortran program for computing opposed flow diffusion flames,” (Sandia National Laboratories, Liver-more, Calif., 1997).

H. Wang, A. Laskin, “A comprehensive kinetic model of ethylene and acetylene oxidation at high temperatures,” (2000), http://ignis.usc.edu/c2_download.html .

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, Orlando, Fla., 1987).

F. J. Weinberg, Optics of Flames (Butterworth, Washington, 1963), pp. 23–39.

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Figures (14)

Fig. 1
Fig. 1

Correlation between index of refraction and temperature. The three curves correspond to pure air (dashed), ethylene and air at Φ = 2.5 with no reactions (dotted–dashed), and the oppdif calculations for an ethylene–air mixture of Φ = 2.5 impinging against air (solid).

Fig. 2
Fig. 2

Picture of the RSD optical setup. The labels describe the major components. The line indicates the optical path.

Fig. 3
Fig. 3

Comparison between the inverse of a direct luminosity image (left) and a raw RSD image (right) for a methane–air flame at Φ = 0.75.

Fig. 4
Fig. 4

Comparison of results for a methane–air (Φ = 0.75) flame. The left side shows the 2D temperature field obtained with a thermocouple; the shaded triangle indicates the region in which thermocouple measurements are not permitted owing to interference of the probe with the flame surface. The right side displays the temperature contours obtained with the RSD technique.

Fig. 5
Fig. 5

Comparison of radial temperature profiles at different heights above the burner for the methane–air flame (Φ = 0.75). The small x’s represent individual thermocouple measurements. The dashed curves are the RSD results obtained when the outer cold boundary (300 K) is chosen as the reference point. The solid curves represent the RSD results obtained by our anchoring the solution at the 1700-K contour.

Fig. 6
Fig. 6

Comparison of the methane–air (Φ = 0.75) flame structure obtained from the RSD results at varying heights (points) with that predicted with premix20 and the gri-mech 2.1121 detailed mechanism (dashed curve).

Fig. 7
Fig. 7

Error in determining the flame location with the RSD methodology versus that with the flame chemiluminescence. Symbols indicate individual measurements, and the solid curve represents the polynomial fit.

Fig. 8
Fig. 8

Comparison between the inverse of a direct luminosity image (left) and a raw RSD image (right) for an ethylene–air premixed flame at Φ = 2.55.

Fig. 9
Fig. 9

Comparison of results for the ethylene–air (Φ = 2.45) premixed flame. The left side shows the 2D temperature field obtained with a thermocouple; the shaded rectangle indicates the region in which soot deposition prohibits temperature measurements with the thermocouple. The right side displays the temperature contours obtained with the RSD technique.

Fig. 10
Fig. 10

Comparison of radial temperature profiles at different heights above the burner for the ethylene–air premixed flame (Φ = 2.45). The small x’s represent individual thermocouple measurements. The solid curves represents the RSD results obtained by our anchoring the solution at the 1500-K contour.

Fig. 11
Fig. 11

Comparison of the ethylene–air premixed flame (Φ = 2.45) structure obtained from the RSD results at varying heights (points) with that predicted with premix20 and the mechanism of Wang and Laskin16 (dashed curve).

Fig. 12
Fig. 12

Comparison of results for the ethylene–air (Φ = 2.55) premixed flame. The left side shows the 2D temperature field obtained with a thermocouple; the shaded area indicates the region in which soot deposition prohibits temperature measurements with the thermocouple. The right side displays the temperature contours obtained with the RSD technique.

Fig. 13
Fig. 13

Comparison of radial temperature profiles at different heights above the burner for the ethylene–air premixed flame (Φ = 2.55). The small x’s represent individual thermocouple measurements. The solid curves represents the RSD results obtained by our anchoring the solution at the 1500-K contour.

Fig. 14
Fig. 14

Comparison of the ethylene–air premixed flame (Φ = 2.55) structure obtained from the RSD results at varying heights (points) with that predicted with premix20 and the mechanism of Wang and Laskin16 (dashed curve).

Equations (13)

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α = 1 n d n d q d s ,
α ( R ) = 2 R n R d n ( r ) d r d r ( r 2 R 2 ) 1 / 2 ,
n ( R ) n 1 = 1 π R α ( r ) d r ( r 2 R 2 ) 1 / 2 .
T = 1 n 1 ( P ) Y i k i Y i / W i ,
T = n o 1 n 1 T o ,
| Δ T | = T 2 δ o T o | Δ δ | .
η = n n 1 = 1 n ( n n ) n n = δ δ .
η η ref δ δ ref ,
δ = ( n 1 ) η η ref + δ ref ,
| Δ δ | = | Δ ( η η ref ) | + | Δ δ ref | = | Δ η | + | Δ δ ref | ,
| Δ T | = T 2 δ o T o | Δ η | + ( T T ref ) 2 | Δ T ref | ,
| Δ [ n ( R ) n ] | = | Δ α | π R d r ( r 2 R 2 ) 1 / 2 .
| Δ [ n ( R ) ] | = n | Δ α | π cosh 1 ( R max R ) ,

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