Abstract

An extended model of the original Gladstone–Dale (G-D) equation is proposed for optical computerized tomography (OCT) diagnosis of flame flow fields. For the purpose of verifying the newly established model, propane combustion is used as a practical example for experiment, and moiré deflection tomography is introduced with the probe wavelength 808nm. The results indicate that the temperature based on the extended model is more accurate than that based on the original G-D equation. In a word, the extended model can be suitable for all kinds of flame flow fields whatever the components, temperature, and ionization are.

© 2009 Optical Society of America

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References

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  1. H. M. Herts, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131-136 (1985).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258-1269 (2006).
    [Crossref]
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    [Crossref] [PubMed]
  7. C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125-2127 (1994).
    [Crossref] [PubMed]
  8. H. Kleine, H. Gronig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170-189 (2006).
    [Crossref]
  9. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Chap. 2, p. 92.
  10. D. E. Jensen and B. E. L. Travers, “Flame plasma diagnostic techniques,” in International Symposium on Plasma Chemistry (IUPAC, 1973).
  11. G. W. Faris and H. Bergstrom, “Two-wavelength beam deflection technique for electron density measurements in laser-produced plasmas,” Appl. Opt. 30, 2212-2218(1991).
    [Crossref] [PubMed]
  12. Y. Chen, Y. Song, A. He, and Z. Li, “Temperature and density distribution measurement of flame by use of moiré deflection tomography,” Acta Opt. Sin. 28, 2330-2234 (2008) (in Chinese).
  13. S. Yang and X.-H. Chen, “Numerical simulation of plasma density field of rocket plume,” Sci. Technol. China 8, 965-970 (2008) (in Chinese).
  14. X.-W. Ni, J. Lu, and A.-Z. He, “Interferometric diagnosis of laser-produced plasma on an aluminum target,” Microw. Opt. Technol. Lett. 14, 271-274 (1997).
    [Crossref]
  15. C. W. Allen, Astrophysical Quantities (University of London Athlone Press, 1963) Chap. 5, p. 92.
  16. H. Xue, H. Li, J. Li, and J. Liu, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40, 49-53 (2004) (in Chinese).
    [Crossref]
  17. Y.-M. Jin and Y.-S. Fan, Physical Basis of Low-Temperature Plasma (Tsinghua University, 1983), Chap. 4, pp. 58-61(in Chinese).
  18. F. J. Weinberg, Optics of Flames (Butterworths, 1963), Chap. 2, p. 23.
  19. http://www.uvi.edu/Physics/SCI3xxWeb/Energy/ChemicalEnergy.html.
  20. G. W. Faris and R. L. Byer, “Three-dimensional beam-deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202-5212 (1988).
    [Crossref] [PubMed]
  21. Y. Song, B. Zhang, and A. He, “Filtered back-projection algorithm of deflection tomography and error analysis,” Acta Opt. Sin. 26, 1657-1665 (2006) (in Chinese).
  22. S. M. Tieng, L. W. Zen, and T. Fujiwara, “Holographic temperature measurement on axisymmetric propane-air, fuel-lean flame,” Meas. Sci. Technol. 3, 1179-1187 (1992).
    [Crossref]
  23. http://www.engineeringtoolbox.com/flame-temperatures-gases-d_422.html.
  24. R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161 (1959).
    [Crossref]

2008 (2)

Y. Chen, Y. Song, A. He, and Z. Li, “Temperature and density distribution measurement of flame by use of moiré deflection tomography,” Acta Opt. Sin. 28, 2330-2234 (2008) (in Chinese).

S. Yang and X.-H. Chen, “Numerical simulation of plasma density field of rocket plume,” Sci. Technol. China 8, 965-970 (2008) (in Chinese).

2006 (3)

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258-1269 (2006).
[Crossref]

H. Kleine, H. Gronig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170-189 (2006).
[Crossref]

Y. Song, B. Zhang, and A. He, “Filtered back-projection algorithm of deflection tomography and error analysis,” Acta Opt. Sin. 26, 1657-1665 (2006) (in Chinese).

2004 (1)

H. Xue, H. Li, J. Li, and J. Liu, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40, 49-53 (2004) (in Chinese).
[Crossref]

2003 (1)

2002 (1)

1997 (1)

X.-W. Ni, J. Lu, and A.-Z. He, “Interferometric diagnosis of laser-produced plasma on an aluminum target,” Microw. Opt. Technol. Lett. 14, 271-274 (1997).
[Crossref]

1994 (1)

1992 (1)

S. M. Tieng, L. W. Zen, and T. Fujiwara, “Holographic temperature measurement on axisymmetric propane-air, fuel-lean flame,” Meas. Sci. Technol. 3, 1179-1187 (1992).
[Crossref]

1991 (1)

1988 (1)

1987 (1)

1985 (1)

H. M. Herts, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131-136 (1985).
[Crossref]

1981 (1)

1959 (1)

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161 (1959).
[Crossref]

Agrawal, A. K.

Allen, C. W.

C. W. Allen, Astrophysical Quantities (University of London Athlone Press, 1963) Chap. 5, p. 92.

Alpher, R. A.

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161 (1959).
[Crossref]

Bar-Ziv, E.

Bergstrom, H.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Chap. 2, p. 92.

Byer, R. L.

Chen, X.-H.

S. Yang and X.-H. Chen, “Numerical simulation of plasma density field of rocket plume,” Sci. Technol. China 8, 965-970 (2008) (in Chinese).

Chen, Y.

Y. Chen, Y. Song, A. He, and Z. Li, “Temperature and density distribution measurement of flame by use of moiré deflection tomography,” Acta Opt. Sin. 28, 2330-2234 (2008) (in Chinese).

Dunn-Rankin, D.

Fan, Y.-S.

Y.-M. Jin and Y.-S. Fan, Physical Basis of Low-Temperature Plasma (Tsinghua University, 1983), Chap. 4, pp. 58-61(in Chinese).

Faris, G. W.

Feng, H.-Q.

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258-1269 (2006).
[Crossref]

Fujiwara, T.

S. M. Tieng, L. W. Zen, and T. Fujiwara, “Holographic temperature measurement on axisymmetric propane-air, fuel-lean flame,” Meas. Sci. Technol. 3, 1179-1187 (1992).
[Crossref]

Glatt, I.

Gronig, H.

H. Kleine, H. Gronig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170-189 (2006).
[Crossref]

He, A.

Y. Chen, Y. Song, A. He, and Z. Li, “Temperature and density distribution measurement of flame by use of moiré deflection tomography,” Acta Opt. Sin. 28, 2330-2234 (2008) (in Chinese).

Y. Song, B. Zhang, and A. He, “Filtered back-projection algorithm of deflection tomography and error analysis,” Acta Opt. Sin. 26, 1657-1665 (2006) (in Chinese).

He, A.-Z.

X.-W. Ni, J. Lu, and A.-Z. He, “Interferometric diagnosis of laser-produced plasma on an aluminum target,” Microw. Opt. Technol. Lett. 14, 271-274 (1997).
[Crossref]

Herts, H. M.

H. M. Herts, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131-136 (1985).
[Crossref]

Jensen, D. E.

D. E. Jensen and B. E. L. Travers, “Flame plasma diagnostic techniques,” in International Symposium on Plasma Chemistry (IUPAC, 1973).

Jin, Y.-M.

Y.-M. Jin and Y.-S. Fan, Physical Basis of Low-Temperature Plasma (Tsinghua University, 1983), Chap. 4, pp. 58-61(in Chinese).

Kafri, O.

Keren, E.

Kleine, H.

H. Kleine, H. Gronig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170-189 (2006).
[Crossref]

Li, H.

H. Xue, H. Li, J. Li, and J. Liu, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40, 49-53 (2004) (in Chinese).
[Crossref]

Li, J.

H. Xue, H. Li, J. Li, and J. Liu, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40, 49-53 (2004) (in Chinese).
[Crossref]

Li, Z.

Y. Chen, Y. Song, A. He, and Z. Li, “Temperature and density distribution measurement of flame by use of moiré deflection tomography,” Acta Opt. Sin. 28, 2330-2234 (2008) (in Chinese).

Liu, D.-X.

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258-1269 (2006).
[Crossref]

Liu, J.

H. Xue, H. Li, J. Li, and J. Liu, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40, 49-53 (2004) (in Chinese).
[Crossref]

Lu, J.

X.-W. Ni, J. Lu, and A.-Z. He, “Interferometric diagnosis of laser-produced plasma on an aluminum target,” Microw. Opt. Technol. Lett. 14, 271-274 (1997).
[Crossref]

Ni, X.-W.

X.-W. Ni, J. Lu, and A.-Z. He, “Interferometric diagnosis of laser-produced plasma on an aluminum target,” Microw. Opt. Technol. Lett. 14, 271-274 (1997).
[Crossref]

Nirala, A. K.

Posner, J. D.

Puri, I. K.

Shakher, C.

Song, Y.

Y. Chen, Y. Song, A. He, and Z. Li, “Temperature and density distribution measurement of flame by use of moiré deflection tomography,” Acta Opt. Sin. 28, 2330-2234 (2008) (in Chinese).

Y. Song, B. Zhang, and A. He, “Filtered back-projection algorithm of deflection tomography and error analysis,” Acta Opt. Sin. 26, 1657-1665 (2006) (in Chinese).

Takayama, K.

H. Kleine, H. Gronig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170-189 (2006).
[Crossref]

Tieng, S. M.

S. M. Tieng, L. W. Zen, and T. Fujiwara, “Holographic temperature measurement on axisymmetric propane-air, fuel-lean flame,” Meas. Sci. Technol. 3, 1179-1187 (1992).
[Crossref]

Travers, B. E. L.

D. E. Jensen and B. E. L. Travers, “Flame plasma diagnostic techniques,” in International Symposium on Plasma Chemistry (IUPAC, 1973).

Weinberg, F. J.

F. J. Weinberg, Optics of Flames (Butterworths, 1963), Chap. 2, p. 23.

White, D. R.

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161 (1959).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Chap. 2, p. 92.

Xiao, X.

Xue, H.

H. Xue, H. Li, J. Li, and J. Liu, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40, 49-53 (2004) (in Chinese).
[Crossref]

Yang, S.

S. Yang and X.-H. Chen, “Numerical simulation of plasma density field of rocket plume,” Sci. Technol. China 8, 965-970 (2008) (in Chinese).

Zen, L. W.

S. M. Tieng, L. W. Zen, and T. Fujiwara, “Holographic temperature measurement on axisymmetric propane-air, fuel-lean flame,” Meas. Sci. Technol. 3, 1179-1187 (1992).
[Crossref]

Zhang, B.

Y. Song, B. Zhang, and A. He, “Filtered back-projection algorithm of deflection tomography and error analysis,” Acta Opt. Sin. 26, 1657-1665 (2006) (in Chinese).

Acta Opt. Sin. (2)

Y. Chen, Y. Song, A. He, and Z. Li, “Temperature and density distribution measurement of flame by use of moiré deflection tomography,” Acta Opt. Sin. 28, 2330-2234 (2008) (in Chinese).

Y. Song, B. Zhang, and A. He, “Filtered back-projection algorithm of deflection tomography and error analysis,” Acta Opt. Sin. 26, 1657-1665 (2006) (in Chinese).

Appl. Opt. (6)

Chin. J. Mech. Eng. (1)

H. Xue, H. Li, J. Li, and J. Liu, “Theoretical calculation of refraction index for arc plasma,” Chin. J. Mech. Eng. 40, 49-53 (2004) (in Chinese).
[Crossref]

Meas. Sci. Technol. (1)

S. M. Tieng, L. W. Zen, and T. Fujiwara, “Holographic temperature measurement on axisymmetric propane-air, fuel-lean flame,” Meas. Sci. Technol. 3, 1179-1187 (1992).
[Crossref]

Microw. Opt. Technol. Lett. (1)

X.-W. Ni, J. Lu, and A.-Z. He, “Interferometric diagnosis of laser-produced plasma on an aluminum target,” Microw. Opt. Technol. Lett. 14, 271-274 (1997).
[Crossref]

Opt. Commun. (1)

H. M. Herts, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131-136 (1985).
[Crossref]

Opt. Lasers Eng. (2)

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258-1269 (2006).
[Crossref]

H. Kleine, H. Gronig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170-189 (2006).
[Crossref]

Opt. Lett. (1)

Phys. Fluids (1)

R. A. Alpher and D. R. White, “Optical refractivity of high-temperature gases. I. Effects resulting from dissociation of diatomic gases,” Phys. Fluids 2, 153-161 (1959).
[Crossref]

Sci. Technol. China (1)

S. Yang and X.-H. Chen, “Numerical simulation of plasma density field of rocket plume,” Sci. Technol. China 8, 965-970 (2008) (in Chinese).

Other (7)

C. W. Allen, Astrophysical Quantities (University of London Athlone Press, 1963) Chap. 5, p. 92.

Y.-M. Jin and Y.-S. Fan, Physical Basis of Low-Temperature Plasma (Tsinghua University, 1983), Chap. 4, pp. 58-61(in Chinese).

F. J. Weinberg, Optics of Flames (Butterworths, 1963), Chap. 2, p. 23.

http://www.uvi.edu/Physics/SCI3xxWeb/Energy/ChemicalEnergy.html.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Chap. 2, p. 92.

D. E. Jensen and B. E. L. Travers, “Flame plasma diagnostic techniques,” in International Symposium on Plasma Chemistry (IUPAC, 1973).

http://www.engineeringtoolbox.com/flame-temperatures-gases-d_422.html.

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Figures (4)

Fig. 1
Fig. 1

Schematic of moiré deflection tomography.

Fig. 2
Fig. 2

Measured flame flow field.

Fig. 3
Fig. 3

(a) Moiré fringes, (b) deflection angles, (c) refractive index distribution.

Fig. 4
Fig. 4

Temperature distributions: (a) original G-D equation, (b) extended model.

Equations (25)

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n m 1 = 1 L ( A + B λ 2 ) N m ,
A = γ H 2 O A H 2 O + γ CO 2 A CO 2 ,
B = γ H 2 O B H 2 O + γ CO 2 B CO 2 ,
n e 1 1 2 N e e 2 λ 2 π m e c 2 = 4.46 × 10 14 λ 2 N e ( λ : cm , N e : cm 3 ) ,
n 1 = 1 L ( A + B λ 2 ) N m 4.46 × 10 14 λ 2 N e .
n 808 1 = 1.3641 × 10 23 N m 2.9118 × 10 22 N e .
N 1 ( CO 2 ) N e N m ( CO 2 ) = 2 Z 1 ( CO 2 ) Z 0 ( CO 2 ) ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 1 ( CO 2 ) κ T ) ,
N 1 ( H 2 O ) N e N m ( H 2 O ) = 2 Z 1 ( H 2 O ) Z 0 ( H 2 O ) ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 1 ( H 2 O ) κ T ) ,
2 Z 1 ( CO 2 ) Z 0 ( CO 2 ) ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 1 ( CO 2 ) κ T ) = C T 3 / 2 exp ( E 1 ( CO 2 ) κ T ) = K 1 ( CO 2 ) ,
2 Z 1 ( H 2 O ) Z 0 ( H 2 O ) ( 2 π κ T m e h 2 ) 3 / 2 exp ( E 1 ( H 2 O ) κ T ) = C T 3 / 2 exp ( E 1 ( H 2 O ) κ T ) = K 1 ( H 2 O ) ,
C = 2 ( 2 π κ m e h 2 ) 3 / 2 4 . 85 × 10 15 K 3 / 2
K 1 = γ CO 2 K 1 ( CO 2 ) + γ H 2 O K 1 ( H 2 O ) = 3 7 K 1 ( CO 2 ) + 4 7 K 1 ( H 2 O ) = 3 7 C T 3 / 2 e E 1 ( CO 2 ) κ T + 4 7 C T 3 / 2 e E 1 ( H 2 O ) κ T = C T 3 / 2 ( 3 7 e E 1 ( CO 2 ) κ T + 4 7 e E 1 ( H 2 O ) κ T ) .
K 1 C T 3 / 2 [ 3 7 ( 1 1 T + 1 2 T 2 1 6 T 3 ) E 1 ( CO 2 ) / κ + 4 7 ( 1 1 T + 1 2 T 2 1 6 T 3 ) E 1 ( H 2 O ) / κ ] .
N 1 N e / N m = K 1 ,
N 1 = N e ,
P = N t κ T = ( N 1 + N m + N e ) κT ,
N e 2 / N m = K 1 ,
P = ( N m + 2 N e ) κ T ,
N e = K 1 + K 1 2 + P K 1 κ T ,
N m = P κ T 2 ( K 1 + K 1 2 + P K 1 κ T ) .
n 1 = 1 L ( A + B λ 2 ) × ( 2 K 1 + P κ T 2 K 1 2 + P K 1 κ T ) 4.46 × 10 14 λ 2 × ( K 1 + K 1 2 + P K 1 κ T ) = 1 L ( A + B λ 2 ) · P κ T [ 2 L ( A + B λ 2 ) + 4.46 × 10 14 λ 2 ] ( K 1 2 + P K 1 κ T K 1 ) .
K 1 2 + P K 1 κ T K 1 = K 1 ( 1 + P K 1 κ T 1 ) K 1 ( P K 1 κ T 1 ) K 1 P K 1 κ T = P K 1 κ T .
n 1 1 L ( A + B λ 2 ) · P κ · 1 T [ 2 L ( A + B λ 2 ) + 4.46 × 10 14 λ 2 ] · P κ · K 1 T = 1 L ( A + B λ 2 ) · P κ · 1 T [ 2 L ( A + B λ 2 ) + 4.46 × 10 14 λ 2 ] · P C κ · { T 1 2 [ 3 7 ( 1 1 T + 1 2 T 2 1 6 T 3 ) E 1 ( CO 2 ) κ + 4 7 ( 1 1 T + 1 2 T 2 1 6 T 3 ) E 1 ( H 2 O ) κ ] } 1 2 .
n 1 = 0.1028 T + 0 . 0019 { T 1 / 2 [ 3 7 ( 1 1 T + 1 2 T 2 1 6 T 3 ) 1 . 59 × 10 5 + 4 7 ( 1 1 T + 1 2 T 2 1 6 T 3 ) 1 . 46 × 10 5 ] } 1 / 2 .
n 1 = ρ K = PMK / RT ,

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