Abstract

Interferometry has been used for many years as a semi-quantitative image-based diagnostic for combustion research. In this paper, we use image-plane, double-pulse holographic interferograms of axisymmetric flames to infer their radial temperature distribution. An Abel inversion is performed on the fringe data to account for line-of-sight integration through the flame. The sensitivity of nonresonant refractive diagnostics decreases inversely with temperature, and the accuracy of the technique is discussed in this context. A small, nonpremixed capillary flame is investigated, and the temperatures inferred from interferometry are compared with those obtained with N2 coherent anti-Stokes Raman spectroscopy thermometry. Additionally, the thermal field of a burning monodisperse methanol droplet stream is investigated interferometrically. Because of their small size, both of these flames challenge the performance limit of temperature interferometery.

© 2003 Optical Society of America

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References

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  1. N. Abel, “Auflosung einer mechanischen Aufgabe,” J. Für Die Reine und Angewandte Mathematik 1, 153–157 (1826).
    [CrossRef]
  2. R. Hall, P. Bonczyk, “Sooting flame thermometry using emission/absorption tomography,” Appl. Opt. 29, 4590–4598 (1990).
    [CrossRef] [PubMed]
  3. H. Uchiyama, M. Nakajima, S. Yuta, “Measurement of flame temperature distribution by IR emission computed tomography,” Appl. Opt. 24, 4111–4115 (1985).
    [CrossRef] [PubMed]
  4. C. Dasch, “One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods,” Appl. Opt. 31, 1146–1152 (1992).
    [CrossRef] [PubMed]
  5. P. Hariharan, Optical Holography, 2nd ed., Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1996).
  6. C. Vest, Holographic Interferometry (Wiley, New York, 1979).
  7. B. Strayer, J. Posner, D. Dunn-Rankin, “CARS temperature measurements of a nonpremixed flame under electric field control,” presented at the Combustion Institute Fall Meeting, Western States Section, 13–14 March 2000, paper WSS/CI 00S-17.
  8. B. Strayer, J. Posner, D. Dunn-Rankin, F. Weinberg, “Simulating microgravity in small diffusion flames by using electric fields to counterbalance natural convection,” Proc. R. Soc. London Ser. A 458, 1151–1166 (2002).
    [CrossRef]
  9. F. Carleton, F. Weinberg, “Simulation of microgravity by the application of electric field to flame,” presented at the Joint meeting of the Portuguese, British, Spanish, and Swedish Sections of The Combustion Institute, 1–4 April 1996, Funchal, Portugal.
  10. J. Lawton, F. Weinberg, Electrical Aspects of Combustion (Clarendon, Oxford, 1969).
  11. F. Carleton, F. Weinberg, “Electric field-induced flame convection in the absence of gravity,” Nature 330, 635–636 (1987).
    [CrossRef]
  12. B. Strayer, J. Posner, D. Dunn-Rankin, “Temperature field measurements of a nonpremixed flame under electric field control,” presented at the The Combustion Institute Fall Meeting, Western States Section, 25 October 1999, paper WSS/CI 99F-16.
  13. C. Connon, R. Dimalanta, C. Choi, D. Dunn-Rankin, “LIF measurements of fuel vapor in an acetone droplet stream,” Combust. Sci. Technol. 129, 197–216 (1997).
    [CrossRef]
  14. J. Virepinte, Y. Biscos, G. Lavergne, P. Magre, “A rectilinear droplet stream in combustion: droplet and gas phase properties,” Combust. Sci. Technol. 150, 143–159 (2000).
    [CrossRef]
  15. F. Weinberg, Optics of Flames (Butterworth, Washington, D.C., 1963).
  16. X. Xiao, C. Choi, I. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
    [CrossRef]
  17. I. Markhvida, L. Chvyaleva, P. Sumin, “Abel inversion: optical pre-processing,” in Photonic Processing Technology and Applications, A. Pirich, R. Boncek, eds.Proc. SPIE3075, 176–180 (1997).
    [CrossRef]
  18. A. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Energy and Engineering Science Series (Abacus, Kent, 1988).
  19. J. Garman, D. Dunn-Rankin, “Spatial averaging effects in CARS thermometry of a nonpremixed flame,” Combust. Flame 115, 481–486 (1998).
    [CrossRef]
  20. J. Millerd, N. Brock, M. Brown, J. Segall, P. DeBarber, “Near infrared real-time resonant holography of combusting sprays,” presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit8–12 January 1996, Reno, Nev., paper AIAA 96-0533.
  21. J. Zhu, D. Dunn-Rankin, “Using CARS to probe the temperature field of a combusting droplet stream,” Appl. Opt. 30, 2672–2674 (1991).
    [CrossRef] [PubMed]

2002 (1)

B. Strayer, J. Posner, D. Dunn-Rankin, F. Weinberg, “Simulating microgravity in small diffusion flames by using electric fields to counterbalance natural convection,” Proc. R. Soc. London Ser. A 458, 1151–1166 (2002).
[CrossRef]

2000 (2)

J. Virepinte, Y. Biscos, G. Lavergne, P. Magre, “A rectilinear droplet stream in combustion: droplet and gas phase properties,” Combust. Sci. Technol. 150, 143–159 (2000).
[CrossRef]

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

1998 (1)

J. Garman, D. Dunn-Rankin, “Spatial averaging effects in CARS thermometry of a nonpremixed flame,” Combust. Flame 115, 481–486 (1998).
[CrossRef]

1997 (1)

C. Connon, R. Dimalanta, C. Choi, D. Dunn-Rankin, “LIF measurements of fuel vapor in an acetone droplet stream,” Combust. Sci. Technol. 129, 197–216 (1997).
[CrossRef]

1992 (1)

1991 (1)

1990 (1)

1987 (1)

F. Carleton, F. Weinberg, “Electric field-induced flame convection in the absence of gravity,” Nature 330, 635–636 (1987).
[CrossRef]

1985 (1)

1826 (1)

N. Abel, “Auflosung einer mechanischen Aufgabe,” J. Für Die Reine und Angewandte Mathematik 1, 153–157 (1826).
[CrossRef]

Abel, N.

N. Abel, “Auflosung einer mechanischen Aufgabe,” J. Für Die Reine und Angewandte Mathematik 1, 153–157 (1826).
[CrossRef]

Biscos, Y.

J. Virepinte, Y. Biscos, G. Lavergne, P. Magre, “A rectilinear droplet stream in combustion: droplet and gas phase properties,” Combust. Sci. Technol. 150, 143–159 (2000).
[CrossRef]

Bonczyk, P.

Brock, N.

J. Millerd, N. Brock, M. Brown, J. Segall, P. DeBarber, “Near infrared real-time resonant holography of combusting sprays,” presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit8–12 January 1996, Reno, Nev., paper AIAA 96-0533.

Brown, M.

J. Millerd, N. Brock, M. Brown, J. Segall, P. DeBarber, “Near infrared real-time resonant holography of combusting sprays,” presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit8–12 January 1996, Reno, Nev., paper AIAA 96-0533.

Carleton, F.

F. Carleton, F. Weinberg, “Electric field-induced flame convection in the absence of gravity,” Nature 330, 635–636 (1987).
[CrossRef]

F. Carleton, F. Weinberg, “Simulation of microgravity by the application of electric field to flame,” presented at the Joint meeting of the Portuguese, British, Spanish, and Swedish Sections of The Combustion Institute, 1–4 April 1996, Funchal, Portugal.

Choi, C.

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

C. Connon, R. Dimalanta, C. Choi, D. Dunn-Rankin, “LIF measurements of fuel vapor in an acetone droplet stream,” Combust. Sci. Technol. 129, 197–216 (1997).
[CrossRef]

Chvyaleva, L.

I. Markhvida, L. Chvyaleva, P. Sumin, “Abel inversion: optical pre-processing,” in Photonic Processing Technology and Applications, A. Pirich, R. Boncek, eds.Proc. SPIE3075, 176–180 (1997).
[CrossRef]

Connon, C.

C. Connon, R. Dimalanta, C. Choi, D. Dunn-Rankin, “LIF measurements of fuel vapor in an acetone droplet stream,” Combust. Sci. Technol. 129, 197–216 (1997).
[CrossRef]

Dasch, C.

DeBarber, P.

J. Millerd, N. Brock, M. Brown, J. Segall, P. DeBarber, “Near infrared real-time resonant holography of combusting sprays,” presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit8–12 January 1996, Reno, Nev., paper AIAA 96-0533.

Dimalanta, R.

C. Connon, R. Dimalanta, C. Choi, D. Dunn-Rankin, “LIF measurements of fuel vapor in an acetone droplet stream,” Combust. Sci. Technol. 129, 197–216 (1997).
[CrossRef]

Dunn-Rankin, D.

B. Strayer, J. Posner, D. Dunn-Rankin, F. Weinberg, “Simulating microgravity in small diffusion flames by using electric fields to counterbalance natural convection,” Proc. R. Soc. London Ser. A 458, 1151–1166 (2002).
[CrossRef]

J. Garman, D. Dunn-Rankin, “Spatial averaging effects in CARS thermometry of a nonpremixed flame,” Combust. Flame 115, 481–486 (1998).
[CrossRef]

C. Connon, R. Dimalanta, C. Choi, D. Dunn-Rankin, “LIF measurements of fuel vapor in an acetone droplet stream,” Combust. Sci. Technol. 129, 197–216 (1997).
[CrossRef]

J. Zhu, D. Dunn-Rankin, “Using CARS to probe the temperature field of a combusting droplet stream,” Appl. Opt. 30, 2672–2674 (1991).
[CrossRef] [PubMed]

B. Strayer, J. Posner, D. Dunn-Rankin, “Temperature field measurements of a nonpremixed flame under electric field control,” presented at the The Combustion Institute Fall Meeting, Western States Section, 25 October 1999, paper WSS/CI 99F-16.

B. Strayer, J. Posner, D. Dunn-Rankin, “CARS temperature measurements of a nonpremixed flame under electric field control,” presented at the Combustion Institute Fall Meeting, Western States Section, 13–14 March 2000, paper WSS/CI 00S-17.

Eckbreth, A.

A. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Energy and Engineering Science Series (Abacus, Kent, 1988).

Garman, J.

J. Garman, D. Dunn-Rankin, “Spatial averaging effects in CARS thermometry of a nonpremixed flame,” Combust. Flame 115, 481–486 (1998).
[CrossRef]

Hall, R.

Hariharan, P.

P. Hariharan, Optical Holography, 2nd ed., Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1996).

Lavergne, G.

J. Virepinte, Y. Biscos, G. Lavergne, P. Magre, “A rectilinear droplet stream in combustion: droplet and gas phase properties,” Combust. Sci. Technol. 150, 143–159 (2000).
[CrossRef]

Lawton, J.

J. Lawton, F. Weinberg, Electrical Aspects of Combustion (Clarendon, Oxford, 1969).

Magre, P.

J. Virepinte, Y. Biscos, G. Lavergne, P. Magre, “A rectilinear droplet stream in combustion: droplet and gas phase properties,” Combust. Sci. Technol. 150, 143–159 (2000).
[CrossRef]

Markhvida, I.

I. Markhvida, L. Chvyaleva, P. Sumin, “Abel inversion: optical pre-processing,” in Photonic Processing Technology and Applications, A. Pirich, R. Boncek, eds.Proc. SPIE3075, 176–180 (1997).
[CrossRef]

Millerd, J.

J. Millerd, N. Brock, M. Brown, J. Segall, P. DeBarber, “Near infrared real-time resonant holography of combusting sprays,” presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit8–12 January 1996, Reno, Nev., paper AIAA 96-0533.

Nakajima, M.

Posner, J.

B. Strayer, J. Posner, D. Dunn-Rankin, F. Weinberg, “Simulating microgravity in small diffusion flames by using electric fields to counterbalance natural convection,” Proc. R. Soc. London Ser. A 458, 1151–1166 (2002).
[CrossRef]

B. Strayer, J. Posner, D. Dunn-Rankin, “CARS temperature measurements of a nonpremixed flame under electric field control,” presented at the Combustion Institute Fall Meeting, Western States Section, 13–14 March 2000, paper WSS/CI 00S-17.

B. Strayer, J. Posner, D. Dunn-Rankin, “Temperature field measurements of a nonpremixed flame under electric field control,” presented at the The Combustion Institute Fall Meeting, Western States Section, 25 October 1999, paper WSS/CI 99F-16.

Puri, I.

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

Segall, J.

J. Millerd, N. Brock, M. Brown, J. Segall, P. DeBarber, “Near infrared real-time resonant holography of combusting sprays,” presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit8–12 January 1996, Reno, Nev., paper AIAA 96-0533.

Strayer, B.

B. Strayer, J. Posner, D. Dunn-Rankin, F. Weinberg, “Simulating microgravity in small diffusion flames by using electric fields to counterbalance natural convection,” Proc. R. Soc. London Ser. A 458, 1151–1166 (2002).
[CrossRef]

B. Strayer, J. Posner, D. Dunn-Rankin, “CARS temperature measurements of a nonpremixed flame under electric field control,” presented at the Combustion Institute Fall Meeting, Western States Section, 13–14 March 2000, paper WSS/CI 00S-17.

B. Strayer, J. Posner, D. Dunn-Rankin, “Temperature field measurements of a nonpremixed flame under electric field control,” presented at the The Combustion Institute Fall Meeting, Western States Section, 25 October 1999, paper WSS/CI 99F-16.

Sumin, P.

I. Markhvida, L. Chvyaleva, P. Sumin, “Abel inversion: optical pre-processing,” in Photonic Processing Technology and Applications, A. Pirich, R. Boncek, eds.Proc. SPIE3075, 176–180 (1997).
[CrossRef]

Uchiyama, H.

Vest, C.

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

Virepinte, J.

J. Virepinte, Y. Biscos, G. Lavergne, P. Magre, “A rectilinear droplet stream in combustion: droplet and gas phase properties,” Combust. Sci. Technol. 150, 143–159 (2000).
[CrossRef]

Weinberg, F.

B. Strayer, J. Posner, D. Dunn-Rankin, F. Weinberg, “Simulating microgravity in small diffusion flames by using electric fields to counterbalance natural convection,” Proc. R. Soc. London Ser. A 458, 1151–1166 (2002).
[CrossRef]

F. Carleton, F. Weinberg, “Electric field-induced flame convection in the absence of gravity,” Nature 330, 635–636 (1987).
[CrossRef]

J. Lawton, F. Weinberg, Electrical Aspects of Combustion (Clarendon, Oxford, 1969).

F. Carleton, F. Weinberg, “Simulation of microgravity by the application of electric field to flame,” presented at the Joint meeting of the Portuguese, British, Spanish, and Swedish Sections of The Combustion Institute, 1–4 April 1996, Funchal, Portugal.

F. Weinberg, Optics of Flames (Butterworth, Washington, D.C., 1963).

Xiao, X.

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

Yuta, S.

Zhu, J.

Appl. Opt. (4)

Combust. Flame (2)

J. Garman, D. Dunn-Rankin, “Spatial averaging effects in CARS thermometry of a nonpremixed flame,” Combust. Flame 115, 481–486 (1998).
[CrossRef]

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

Combust. Sci. Technol. (2)

C. Connon, R. Dimalanta, C. Choi, D. Dunn-Rankin, “LIF measurements of fuel vapor in an acetone droplet stream,” Combust. Sci. Technol. 129, 197–216 (1997).
[CrossRef]

J. Virepinte, Y. Biscos, G. Lavergne, P. Magre, “A rectilinear droplet stream in combustion: droplet and gas phase properties,” Combust. Sci. Technol. 150, 143–159 (2000).
[CrossRef]

J. Für Die Reine und Angewandte Mathematik (1)

N. Abel, “Auflosung einer mechanischen Aufgabe,” J. Für Die Reine und Angewandte Mathematik 1, 153–157 (1826).
[CrossRef]

Nature (1)

F. Carleton, F. Weinberg, “Electric field-induced flame convection in the absence of gravity,” Nature 330, 635–636 (1987).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

B. Strayer, J. Posner, D. Dunn-Rankin, F. Weinberg, “Simulating microgravity in small diffusion flames by using electric fields to counterbalance natural convection,” Proc. R. Soc. London Ser. A 458, 1151–1166 (2002).
[CrossRef]

Other (10)

F. Carleton, F. Weinberg, “Simulation of microgravity by the application of electric field to flame,” presented at the Joint meeting of the Portuguese, British, Spanish, and Swedish Sections of The Combustion Institute, 1–4 April 1996, Funchal, Portugal.

J. Lawton, F. Weinberg, Electrical Aspects of Combustion (Clarendon, Oxford, 1969).

B. Strayer, J. Posner, D. Dunn-Rankin, “Temperature field measurements of a nonpremixed flame under electric field control,” presented at the The Combustion Institute Fall Meeting, Western States Section, 25 October 1999, paper WSS/CI 99F-16.

P. Hariharan, Optical Holography, 2nd ed., Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1996).

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

B. Strayer, J. Posner, D. Dunn-Rankin, “CARS temperature measurements of a nonpremixed flame under electric field control,” presented at the Combustion Institute Fall Meeting, Western States Section, 13–14 March 2000, paper WSS/CI 00S-17.

J. Millerd, N. Brock, M. Brown, J. Segall, P. DeBarber, “Near infrared real-time resonant holography of combusting sprays,” presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit8–12 January 1996, Reno, Nev., paper AIAA 96-0533.

F. Weinberg, Optics of Flames (Butterworth, Washington, D.C., 1963).

I. Markhvida, L. Chvyaleva, P. Sumin, “Abel inversion: optical pre-processing,” in Photonic Processing Technology and Applications, A. Pirich, R. Boncek, eds.Proc. SPIE3075, 176–180 (1997).
[CrossRef]

A. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Energy and Engineering Science Series (Abacus, Kent, 1988).

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Figures (11)

Fig. 1
Fig. 1

Abel transform of an arbitrary function. (a) original and reconstructed distributions, (b) line-of-sight integral.

Fig. 2
Fig. 2

Experimental setup for electric-field-controlled capillary flame.

Fig. 3
Fig. 3

Images of electric-field-controlled capillary flame under increasing voltage. The arrow at the top of the figure marks the approximate point of balance between the electric field forces and the buoyancy.

Fig. 4
Fig. 4

Experimental setup for burning monodisperse droplet stream. DG, droplet generator; IC, ignition coil; SL, strobe lamp; FG, frequency generator; FD, frequency divider; PS, strobe power supply; DR, droplet reservoir; PT, pressure tank.

Fig. 5
Fig. 5

Image of combusting monodisperse methanol droplet stream ignited by a resistive coil.

Fig. 6
Fig. 6

Double exposure holographic interferometric image of capillary flame. (a) natural flame, no field; (b) balanced flame, 2222 V.

Fig. 7
Fig. 7

Plots of capillary flame Abel inversion as a function of the radial location from the vertical centerline of the flame (a) fringe shift (wavelengths, λ = 488 nm), (b) total phase through δn of hot gas (wavelengths), (c) index of refraction (n - 1) (o denotes δn of air at 300 K), and (d) temperature (K).

Fig. 8
Fig. 8

Temperature comparison of N2 CARS (symbols) and Abel inversions of double-pulse holographic interferograms (lines) of a capillary flame.

Fig. 9
Fig. 9

Color temperature interferogram of burning methanol droplet stream. The optical aberrations caused by the droplets is barely visible through the fringe pattern. The large dark object is the shadow of a heat sink attached to the ignition coil. The horizontal line is the location of the fringe counting.

Fig. 10
Fig. 10

Comparison of CARS thermometry and an uncorrected Abel inverted interferogram of a burning droplet stream. Symbols, CARS; curve, interferogram.

Fig. 11
Fig. 11

Simulated interferogram of a burning droplet stream.

Equations (9)

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px=2 xFrrr2-x21/2dr,
Fr=1πrpxx2-r21/2dx,
ϕ=0L nzdz,
Δϕ=ϕ-ϕ0=0Lnz-n0zdz.
n=1+δn,
δn=δn0T0T.
dδn=-δn0T0T2dT,
ϕx=2λxRnrrr2-x21/2dr,
nr=λ rRϕxx2-r21/2dx,

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