Abstract

Numerical analysis and experimental results are presented to define a method for quantitatively measuring the temperature distribution of a spherical diffusion flame using rainbow schlieren deflectometry in microgravity. The method employed illustrates the necessary steps for the preliminary design of a rainbow schlieren system. The largest deflection for the normal gravity flame considered in this paper is 7.4×104 rad, which can be accurately measured with 2 m focal-length collimating and decollimating optics. The experimental uncertainty of deflection is less than 5×105 rad.

© 2006 Optical Society of America

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References

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  1. P. S. Greenburg, D. W. Griffin, K. J. Weiland, and W. Yanis, "Selected diagnostics for microgravity combustion science," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 275-280.
  2. P. S. Greenberg, M. P. Wernet, W. Yanis, D. L. Urban, and P. B. Sunderland, "Development of PIV for microgravity diffusion flames," in Proceedings of the Seventh Microgravity Combustion Workshop, NASA CP-2003-212376 (NASA, 2003), pp. 377-380.
  3. J. C. Ku and P. S. Greenberg, "Temperature and radiative heat flux measurements in microgravity diffusion flames," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 211-216.
  4. M. Long, K. Walsh, and M. Smooke, "Computational and experimental study of laminar diffusion flames in a microgravity environment," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 123-128.
  5. D. J. Kane and J. A. Silver, "Real time quantitative 3-D imaging of diffusion flame species," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 281-286.
  6. J. A. Silver, "Quantitative measurement of oxygen in microgravity combustion," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 293-298.
  7. J. A. Silver, W. R. Wood, S.-J. Chen, W. J. A. Dahm, and N. Piltch, "Quantitative species measurements in microgravity combustion flames," in Sixth International Microgravity Combustion Workshop, NASA/CP-2001-210826 (NASA, 2001), pp. 61-64.
  8. J. A. Silver, D. J. Kane, and P. S. Greenberg, "Quantitative species measurements in microgravity flames with near-IR diode lasers," Appl. Opt. 34, 2787-2801 (1995).
    [CrossRef] [PubMed]
  9. B. A. VanDerWege, C. J. O'Brien, and S. Hochgreb, "Application of shear plate interferometry to jet diffusion flame temperature measurements," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 141-146.
  10. J. Lim, Y. Sivathanu, and D. A. Feikema, "Fan beam emission tomography for estimating scalar properties in laminar flames," NASA/TM-2003-212302 (NASA, 2003).
  11. P. S. Greenberg, R. B. Klimek, and D. R. Buchele, "Quantitative rainbow schlieren deflectometry," Appl. Opt. 34, 3810-3822 (1995).
    [CrossRef] [PubMed]
  12. H. Schardin, "Schlieren methods and their applications," NASA Rep. TT-F-12731 (NASA, 1970).
  13. W. Merzkirch, Flow Visualization (Academic, 1974), pp. 71-102.
  14. G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).
  15. D. R. Buchele and D. W. Griffin, "Compact color schlieren optical system," Appl. Opt. 32, 4218-4222 (1993).
    [CrossRef] [PubMed]
  16. W. L. Howes, "Rainbow schlieren and its applications," Appl. Opt. 23, 2449-2460 (1984).
    [CrossRef] [PubMed]
  17. S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
    [CrossRef]
  18. F. J. Weinberg, Optics of Flames (Butterworth, 1963), pp. 23-37.
  19. R. C. Weast and M. J. Astle, eds., CRC Handbook of Chemistry and Physics, 62nd ed. (CRC Press, 1982).
  20. R. Rubinstein and P. S. Greenberg, "Rapid inversion of angular deflection data for certain axisymmetric refractive-index distributions," Appl. Opt. 33, 1141-1144 (1994).
    [CrossRef] [PubMed]
  21. K. N. Al-Ammar, "Scalar measurements and analysis of hydrogen gas-jet diffusion flames in normal and microgravity," Ph.D. dissertation (University of Oklahoma, 1998).
  22. K. Al-Ammar, A. K. Agrawal, S. R. Golhalli, and D. W. Griffin, "Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet," Exp. Fluids 25, 89-95 (1998).
    [CrossRef]
  23. R. J. Santoro, H. G. Semerjian, and R. A. Dobbins, "Soot particle measurements in diffusion flames," Combust. Flame 51, 203-218 (1983).
    [CrossRef]
  24. L. Kean, "Coefficients for axisymmetric schlieren evaluations," ASD Tech. Note 61-56, Unclassified U.S. Air Force Publication (Aeronautical Systems Division, Wright-Patterson Air Force Base, 1961).

2001 (1)

S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
[CrossRef]

1998 (1)

K. Al-Ammar, A. K. Agrawal, S. R. Golhalli, and D. W. Griffin, "Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet," Exp. Fluids 25, 89-95 (1998).
[CrossRef]

1995 (2)

1994 (1)

1993 (1)

1984 (1)

1983 (1)

R. J. Santoro, H. G. Semerjian, and R. A. Dobbins, "Soot particle measurements in diffusion flames," Combust. Flame 51, 203-218 (1983).
[CrossRef]

Agrawal, A. K.

K. Al-Ammar, A. K. Agrawal, S. R. Golhalli, and D. W. Griffin, "Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet," Exp. Fluids 25, 89-95 (1998).
[CrossRef]

Al-Ammar, K.

K. Al-Ammar, A. K. Agrawal, S. R. Golhalli, and D. W. Griffin, "Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet," Exp. Fluids 25, 89-95 (1998).
[CrossRef]

Al-Ammar, K. N.

K. N. Al-Ammar, "Scalar measurements and analysis of hydrogen gas-jet diffusion flames in normal and microgravity," Ph.D. dissertation (University of Oklahoma, 1998).

Astle, M. J.

R. C. Weast and M. J. Astle, eds., CRC Handbook of Chemistry and Physics, 62nd ed. (CRC Press, 1982).

Buchele, D. R.

Chen, S.-J.

J. A. Silver, W. R. Wood, S.-J. Chen, W. J. A. Dahm, and N. Piltch, "Quantitative species measurements in microgravity combustion flames," in Sixth International Microgravity Combustion Workshop, NASA/CP-2001-210826 (NASA, 2001), pp. 61-64.

Dahm, W. J. A.

J. A. Silver, W. R. Wood, S.-J. Chen, W. J. A. Dahm, and N. Piltch, "Quantitative species measurements in microgravity combustion flames," in Sixth International Microgravity Combustion Workshop, NASA/CP-2001-210826 (NASA, 2001), pp. 61-64.

Dobbins, R. A.

R. J. Santoro, H. G. Semerjian, and R. A. Dobbins, "Soot particle measurements in diffusion flames," Combust. Flame 51, 203-218 (1983).
[CrossRef]

Feikema, D. A.

J. Lim, Y. Sivathanu, and D. A. Feikema, "Fan beam emission tomography for estimating scalar properties in laminar flames," NASA/TM-2003-212302 (NASA, 2003).

Golhalli, S. R.

K. Al-Ammar, A. K. Agrawal, S. R. Golhalli, and D. W. Griffin, "Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet," Exp. Fluids 25, 89-95 (1998).
[CrossRef]

Greenberg, P. S.

P. S. Greenberg, R. B. Klimek, and D. R. Buchele, "Quantitative rainbow schlieren deflectometry," Appl. Opt. 34, 3810-3822 (1995).
[CrossRef] [PubMed]

J. A. Silver, D. J. Kane, and P. S. Greenberg, "Quantitative species measurements in microgravity flames with near-IR diode lasers," Appl. Opt. 34, 2787-2801 (1995).
[CrossRef] [PubMed]

R. Rubinstein and P. S. Greenberg, "Rapid inversion of angular deflection data for certain axisymmetric refractive-index distributions," Appl. Opt. 33, 1141-1144 (1994).
[CrossRef] [PubMed]

J. C. Ku and P. S. Greenberg, "Temperature and radiative heat flux measurements in microgravity diffusion flames," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 211-216.

P. S. Greenberg, M. P. Wernet, W. Yanis, D. L. Urban, and P. B. Sunderland, "Development of PIV for microgravity diffusion flames," in Proceedings of the Seventh Microgravity Combustion Workshop, NASA CP-2003-212376 (NASA, 2003), pp. 377-380.

Greenburg, P. S.

P. S. Greenburg, D. W. Griffin, K. J. Weiland, and W. Yanis, "Selected diagnostics for microgravity combustion science," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 275-280.

Griffin, D. W.

K. Al-Ammar, A. K. Agrawal, S. R. Golhalli, and D. W. Griffin, "Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet," Exp. Fluids 25, 89-95 (1998).
[CrossRef]

D. R. Buchele and D. W. Griffin, "Compact color schlieren optical system," Appl. Opt. 32, 4218-4222 (1993).
[CrossRef] [PubMed]

P. S. Greenburg, D. W. Griffin, K. J. Weiland, and W. Yanis, "Selected diagnostics for microgravity combustion science," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 275-280.

He, L.

S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
[CrossRef]

Hochgreb, S.

B. A. VanDerWege, C. J. O'Brien, and S. Hochgreb, "Application of shear plate interferometry to jet diffusion flame temperature measurements," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 141-146.

Howes, W. L.

Kane, D. J.

J. A. Silver, D. J. Kane, and P. S. Greenberg, "Quantitative species measurements in microgravity flames with near-IR diode lasers," Appl. Opt. 34, 2787-2801 (1995).
[CrossRef] [PubMed]

D. J. Kane and J. A. Silver, "Real time quantitative 3-D imaging of diffusion flame species," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 281-286.

Kean, L.

L. Kean, "Coefficients for axisymmetric schlieren evaluations," ASD Tech. Note 61-56, Unclassified U.S. Air Force Publication (Aeronautical Systems Division, Wright-Patterson Air Force Base, 1961).

Klimek, R. B.

Ku, J. C.

J. C. Ku and P. S. Greenberg, "Temperature and radiative heat flux measurements in microgravity diffusion flames," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 211-216.

Law, C. K.

S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
[CrossRef]

Lim, J.

J. Lim, Y. Sivathanu, and D. A. Feikema, "Fan beam emission tomography for estimating scalar properties in laminar flames," NASA/TM-2003-212302 (NASA, 2003).

Long, M.

M. Long, K. Walsh, and M. Smooke, "Computational and experimental study of laminar diffusion flames in a microgravity environment," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 123-128.

Merzkirch, W.

W. Merzkirch, Flow Visualization (Academic, 1974), pp. 71-102.

O'Brien, C. J.

B. A. VanDerWege, C. J. O'Brien, and S. Hochgreb, "Application of shear plate interferometry to jet diffusion flame temperature measurements," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 141-146.

Piltch, N.

J. A. Silver, W. R. Wood, S.-J. Chen, W. J. A. Dahm, and N. Piltch, "Quantitative species measurements in microgravity combustion flames," in Sixth International Microgravity Combustion Workshop, NASA/CP-2001-210826 (NASA, 2001), pp. 61-64.

Rubinstein, R.

Santoro, R. J.

R. J. Santoro, H. G. Semerjian, and R. A. Dobbins, "Soot particle measurements in diffusion flames," Combust. Flame 51, 203-218 (1983).
[CrossRef]

Schardin, H.

H. Schardin, "Schlieren methods and their applications," NASA Rep. TT-F-12731 (NASA, 1970).

Semerjian, H. G.

R. J. Santoro, H. G. Semerjian, and R. A. Dobbins, "Soot particle measurements in diffusion flames," Combust. Flame 51, 203-218 (1983).
[CrossRef]

Settles, G. S.

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

Silver, J. A.

J. A. Silver, D. J. Kane, and P. S. Greenberg, "Quantitative species measurements in microgravity flames with near-IR diode lasers," Appl. Opt. 34, 2787-2801 (1995).
[CrossRef] [PubMed]

J. A. Silver, "Quantitative measurement of oxygen in microgravity combustion," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 293-298.

J. A. Silver, W. R. Wood, S.-J. Chen, W. J. A. Dahm, and N. Piltch, "Quantitative species measurements in microgravity combustion flames," in Sixth International Microgravity Combustion Workshop, NASA/CP-2001-210826 (NASA, 2001), pp. 61-64.

D. J. Kane and J. A. Silver, "Real time quantitative 3-D imaging of diffusion flame species," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 281-286.

Sivathanu, Y.

J. Lim, Y. Sivathanu, and D. A. Feikema, "Fan beam emission tomography for estimating scalar properties in laminar flames," NASA/TM-2003-212302 (NASA, 2003).

Smooke, M.

M. Long, K. Walsh, and M. Smooke, "Computational and experimental study of laminar diffusion flames in a microgravity environment," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 123-128.

Sunderland, P. B.

P. S. Greenberg, M. P. Wernet, W. Yanis, D. L. Urban, and P. B. Sunderland, "Development of PIV for microgravity diffusion flames," in Proceedings of the Seventh Microgravity Combustion Workshop, NASA CP-2003-212376 (NASA, 2003), pp. 377-380.

Sung, C. J.

S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
[CrossRef]

Tse, S. D.

S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
[CrossRef]

Urban, D. L.

P. S. Greenberg, M. P. Wernet, W. Yanis, D. L. Urban, and P. B. Sunderland, "Development of PIV for microgravity diffusion flames," in Proceedings of the Seventh Microgravity Combustion Workshop, NASA CP-2003-212376 (NASA, 2003), pp. 377-380.

VanDerWege, B. A.

B. A. VanDerWege, C. J. O'Brien, and S. Hochgreb, "Application of shear plate interferometry to jet diffusion flame temperature measurements," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 141-146.

Walsh, K.

M. Long, K. Walsh, and M. Smooke, "Computational and experimental study of laminar diffusion flames in a microgravity environment," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 123-128.

Weast, R. C.

R. C. Weast and M. J. Astle, eds., CRC Handbook of Chemistry and Physics, 62nd ed. (CRC Press, 1982).

Weiland, K. J.

P. S. Greenburg, D. W. Griffin, K. J. Weiland, and W. Yanis, "Selected diagnostics for microgravity combustion science," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 275-280.

Weinberg, F. J.

F. J. Weinberg, Optics of Flames (Butterworth, 1963), pp. 23-37.

Wernet, M. P.

P. S. Greenberg, M. P. Wernet, W. Yanis, D. L. Urban, and P. B. Sunderland, "Development of PIV for microgravity diffusion flames," in Proceedings of the Seventh Microgravity Combustion Workshop, NASA CP-2003-212376 (NASA, 2003), pp. 377-380.

Wood, W. R.

J. A. Silver, W. R. Wood, S.-J. Chen, W. J. A. Dahm, and N. Piltch, "Quantitative species measurements in microgravity combustion flames," in Sixth International Microgravity Combustion Workshop, NASA/CP-2001-210826 (NASA, 2001), pp. 61-64.

Yanis, W.

P. S. Greenberg, M. P. Wernet, W. Yanis, D. L. Urban, and P. B. Sunderland, "Development of PIV for microgravity diffusion flames," in Proceedings of the Seventh Microgravity Combustion Workshop, NASA CP-2003-212376 (NASA, 2003), pp. 377-380.

P. S. Greenburg, D. W. Griffin, K. J. Weiland, and W. Yanis, "Selected diagnostics for microgravity combustion science," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 275-280.

Zhu, D. L.

S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
[CrossRef]

Appl. Opt. (5)

Combust. Flame (2)

S. D. Tse, D. L. Zhu, L. He, C. J. Sung, and C. K. Law, "Microgravity burner-generated spherical diffusion flames: experiment and computation," Combust. Flame 125, 1265-1278 (2001).
[CrossRef]

R. J. Santoro, H. G. Semerjian, and R. A. Dobbins, "Soot particle measurements in diffusion flames," Combust. Flame 51, 203-218 (1983).
[CrossRef]

Exp. Fluids (1)

K. Al-Ammar, A. K. Agrawal, S. R. Golhalli, and D. W. Griffin, "Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet," Exp. Fluids 25, 89-95 (1998).
[CrossRef]

Other (16)

L. Kean, "Coefficients for axisymmetric schlieren evaluations," ASD Tech. Note 61-56, Unclassified U.S. Air Force Publication (Aeronautical Systems Division, Wright-Patterson Air Force Base, 1961).

B. A. VanDerWege, C. J. O'Brien, and S. Hochgreb, "Application of shear plate interferometry to jet diffusion flame temperature measurements," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 141-146.

J. Lim, Y. Sivathanu, and D. A. Feikema, "Fan beam emission tomography for estimating scalar properties in laminar flames," NASA/TM-2003-212302 (NASA, 2003).

F. J. Weinberg, Optics of Flames (Butterworth, 1963), pp. 23-37.

R. C. Weast and M. J. Astle, eds., CRC Handbook of Chemistry and Physics, 62nd ed. (CRC Press, 1982).

K. N. Al-Ammar, "Scalar measurements and analysis of hydrogen gas-jet diffusion flames in normal and microgravity," Ph.D. dissertation (University of Oklahoma, 1998).

P. S. Greenburg, D. W. Griffin, K. J. Weiland, and W. Yanis, "Selected diagnostics for microgravity combustion science," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 275-280.

P. S. Greenberg, M. P. Wernet, W. Yanis, D. L. Urban, and P. B. Sunderland, "Development of PIV for microgravity diffusion flames," in Proceedings of the Seventh Microgravity Combustion Workshop, NASA CP-2003-212376 (NASA, 2003), pp. 377-380.

J. C. Ku and P. S. Greenberg, "Temperature and radiative heat flux measurements in microgravity diffusion flames," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 211-216.

M. Long, K. Walsh, and M. Smooke, "Computational and experimental study of laminar diffusion flames in a microgravity environment," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 123-128.

D. J. Kane and J. A. Silver, "Real time quantitative 3-D imaging of diffusion flame species," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 281-286.

J. A. Silver, "Quantitative measurement of oxygen in microgravity combustion," in Proceedings of the Fourth Microgravity Combustion Workshop, NASA CP-10194 (NASA, 1997), pp. 293-298.

J. A. Silver, W. R. Wood, S.-J. Chen, W. J. A. Dahm, and N. Piltch, "Quantitative species measurements in microgravity combustion flames," in Sixth International Microgravity Combustion Workshop, NASA/CP-2001-210826 (NASA, 2001), pp. 61-64.

H. Schardin, "Schlieren methods and their applications," NASA Rep. TT-F-12731 (NASA, 1970).

W. Merzkirch, Flow Visualization (Academic, 1974), pp. 71-102.

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

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Figures (14)

Fig. 1
Fig. 1

Schematic drawing of a simple lens-type schlieren system.

Fig. 2
Fig. 2

Schematic representation of the spherical burner-generated gaseous diffusion flame experiment.

Fig. 3
Fig. 3

Computed temperature profile with a time-dependent Chemkin model for a spherical diffusion flame burning in air at 1.2 atm and 300 K; fuel type: 20% H2∕25% CH4∕55% N2 with a mass flow rate of 24 mg∕s; time from ignition is 5.4 s.

Fig. 4
Fig. 4

Fuel and oxidizer species mole fractions for an adiabatic calculation with fuel of 20% H2∕25% CH4∕55% N2 in air at 1.2 atm and a fuel mass flow rate of 24 mg∕s at 5.4 s after ignition.

Fig. 5
Fig. 5

(Color online) H2O, CO2, and CO species mole fractions for an adiabatic calculation with fuel of 20% H2∕25% CH4∕55% N2 in air at 1.2 atm and a fuel mass flow rate of 24 mg∕s at 5.4 s after ignition.

Fig. 6
Fig. 6

(Color online) Index of refraction n(r) profile of the flame with complete species (thick curve) and air (thin curve) as calculated with the Chemkin-computed species and temperature profiles, 20% H2∕25% CH4∕55% N2 in air at 1.2 atm and a fuel mass flow rate of 24 mg∕s at a time from ignition of 5.4 s.

Fig. 7
Fig. 7

(Color online) Angular defection of light rays through the flame shown in Figs. 3–6 as computed using Eq. (4).

Fig. 8
Fig. 8

Linear deflection at the filter plane for the flame shown in Figs. 3–6 as computed using Eq. (5) for a 3 m focal-length decollimating optic.

Fig. 9
Fig. 9

(Color online) Comparison of the numerically generated index of refraction field based on the Chemkin model with the Abel-transformed deflections from Fig. 6 [Eq. (6)] for the flame shown in Figs. 3–6.

Fig. 10
Fig. 10

(Color online) Comparison of the flame temperature profile with the Chemkin model (Fig. 3) and Abel-transformed angular deflection (Fig. 6).

Fig. 11
Fig. 11

Visible flame image of the 1 g coflow flame used for schlieren demonstration experiment for 20% H2∕25% CH4∕55% N2, fuel flow rate of 9.3 ml∕s, and airflow rate of 583 ml∕s.

Fig. 12
Fig. 12

Color schlieren image of flame shown in Fig. 11 with a symmetric color filter.

Fig. 13
Fig. 13

Measured angular deflections of light rays passing taken directly from Fig. 12 at 9 mm above the burner base.

Fig. 14
Fig. 14

Temperature comparison between Abel-transformed schlieren data (squares) and the radiation-corrected thermocouple measurements (triangles) of the flame shown in Fig. 11 at 9 mm above the burner.

Tables (1)

Tables Icon

Table 1 Index of Refraction at 273.15 K and 1 atm for Various Gases of Interest a , b

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

θ exit tan  θ exit = L n l .
[ n ( T ) 1 ] mix = i = 1 N X i [ n i ( T ) 1 ] i .
( n 1 ) hot = ( n 0 1 ) cold T 0 T ,
ε ( y ) = 2 y y d ( n 1 ) d r d r ( r 2 y 2 ) 1 / 2 .
d f ( y ) = F L ε ( y ) .
δ ( r ) = 1 π r ε ( y ) d y ( y 2 r 2 ) 1 / 2 ,

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