Abstract

A sooting flame temperature measurement technique has been demonstrated based on emission–absorption tomography. The approach applies the algorithms of Fourier transform tomography to deconvolve local soot absorption coefficient and Planck function (temperature) from sets of parallel line-of-sight measurements. The technique has the advantage that it is experimentally simple and does not require involved data reduction. For small particles, there is also no sensitivity of the inferred temperature to possibly uncertain medium parameters. Its main limitation seems to be that it will not work well for vanishingly small absorption, but this could be overcome in practice by seeding and then performing all work at the wavelength of a seed resonance. While in principle limited to optically thin flames, accurate corrections for moderate optical thickness can often be made. A self-consistent comparison of measured global radiation from a sooting ethylene flame with a radiative transfer calculation based on measured temperature and soot absorption parameters has been performed.

© 1990 Optical Society of America

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References

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  1. R. W. Porter, “Numerical Solution for Local Emission Coefficients in Axisymmetric Self-Absorbed Sources,” SIAM Soc. Ind. Appl. Math. Rev. 6, 228–242 (1964).
  2. G. Kuhn, R. S. Tankin, “Spectroscopic Measurements to Determine Temperature and Carbon Particle Size inan Absorbing Propane Diffusion Flame,” J. Quant. Spectrosc. Radiat. Transfer 8, 1281–1292 (1968).
    [CrossRef]
  3. H. G. Semerjian, S. R. Ray, R. J. Santoro, “Laser Tomography for Diagnostics in Reacting Flows,” AIAA Paper 82-0584 (1982).
  4. P. J. Emmerman, R. Goulard, R. J. Santoro, H. G. Semerjian, “Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet,” J. Energy 4, 70–77 (1980).
    [CrossRef]
  5. H. Uchiyama, M. Nakajima, S. Yuta, “Measurement of Flame Temperature Distribution by IR Emission Computed Tomography,” Appl. Opt. 24, 4111–4116 (1985).
    [CrossRef] [PubMed]
  6. P. R. Solomon et al., “FT-IR Emission/Transmission Spectroscopy for In Situ Combustion Diagnostics,” in Proceedings, Twenty-First International Symposium on Combustion (Combustion Institute, Pittsburgh, 1986), pp. 1763–1771.
  7. G. N. Ramachandran, A. V. Lakshminarayanan, “Three-Dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions Instead of Fourier Transforms,” Proc. Nat. Acad. Sci. USA, 68, 2236–2240 (1971).
    [CrossRef] [PubMed]
  8. L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).
  9. L. R. Boedeker, G. M. Dobbs, “Temperature and Soot Correlations in Sooting, Laminar Diffusion Flames,” UTRC Report 85-51 (1985).
  10. R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot Particle Measurements in Diffusion Flames,” Combust. Flame, 51, 203–218 (1983).
    [CrossRef]
  11. R. J. Santoro, H. G. Semerjian, “Soot Formation in Diffusion Flames: Flow Rate, Fuel Species, and Temperature Effects,” Proceedings, Twentieth International Symposium on Combustion (Combustion Institute, Pittsburgh, 1984), pp. 997–1006.
  12. M. V. Berry, I. C. Percival, “Optics of Fractal Clusters Such as Smoke,” Opt. Acta 33, 577–591 (1986).
    [CrossRef]
  13. R. D. Mountain, G. W. Mulholland, “Light Scattering from Simulated Smoke Aggregates,” Langmuir 4, 1321–1326 (1988).
    [CrossRef]
  14. G. H. Markstein, “Relationship Between Smoke Point and Radiant Emission From Buoyant Turbulent and Laminar Diffusion Flames,” in Proceedings, Twentieth International Symposium on Combustion (Combustion Institute, Pittsburgh, 1984), pp. 1055–1061.
  15. F. G. Roper, “Soot Escape from Diffusion Flames: a Comparison of Recent Work in this Field,” Combust. Sci. Technol. 40, 323–329 (1984).
    [CrossRef]

1988

R. D. Mountain, G. W. Mulholland, “Light Scattering from Simulated Smoke Aggregates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

1986

M. V. Berry, I. C. Percival, “Optics of Fractal Clusters Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

1985

1984

F. G. Roper, “Soot Escape from Diffusion Flames: a Comparison of Recent Work in this Field,” Combust. Sci. Technol. 40, 323–329 (1984).
[CrossRef]

1983

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot Particle Measurements in Diffusion Flames,” Combust. Flame, 51, 203–218 (1983).
[CrossRef]

1980

P. J. Emmerman, R. Goulard, R. J. Santoro, H. G. Semerjian, “Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet,” J. Energy 4, 70–77 (1980).
[CrossRef]

1974

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

1971

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-Dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions Instead of Fourier Transforms,” Proc. Nat. Acad. Sci. USA, 68, 2236–2240 (1971).
[CrossRef] [PubMed]

1968

G. Kuhn, R. S. Tankin, “Spectroscopic Measurements to Determine Temperature and Carbon Particle Size inan Absorbing Propane Diffusion Flame,” J. Quant. Spectrosc. Radiat. Transfer 8, 1281–1292 (1968).
[CrossRef]

1964

R. W. Porter, “Numerical Solution for Local Emission Coefficients in Axisymmetric Self-Absorbed Sources,” SIAM Soc. Ind. Appl. Math. Rev. 6, 228–242 (1964).

Berry, M. V.

M. V. Berry, I. C. Percival, “Optics of Fractal Clusters Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Boedeker, L. R.

L. R. Boedeker, G. M. Dobbs, “Temperature and Soot Correlations in Sooting, Laminar Diffusion Flames,” UTRC Report 85-51 (1985).

Dobbins, R. A.

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot Particle Measurements in Diffusion Flames,” Combust. Flame, 51, 203–218 (1983).
[CrossRef]

Dobbs, G. M.

L. R. Boedeker, G. M. Dobbs, “Temperature and Soot Correlations in Sooting, Laminar Diffusion Flames,” UTRC Report 85-51 (1985).

Emmerman, P. J.

P. J. Emmerman, R. Goulard, R. J. Santoro, H. G. Semerjian, “Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet,” J. Energy 4, 70–77 (1980).
[CrossRef]

Goulard, R.

P. J. Emmerman, R. Goulard, R. J. Santoro, H. G. Semerjian, “Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet,” J. Energy 4, 70–77 (1980).
[CrossRef]

Kuhn, G.

G. Kuhn, R. S. Tankin, “Spectroscopic Measurements to Determine Temperature and Carbon Particle Size inan Absorbing Propane Diffusion Flame,” J. Quant. Spectrosc. Radiat. Transfer 8, 1281–1292 (1968).
[CrossRef]

Lakshminarayanan, A. V.

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-Dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions Instead of Fourier Transforms,” Proc. Nat. Acad. Sci. USA, 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Logan, B. F.

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

Markstein, G. H.

G. H. Markstein, “Relationship Between Smoke Point and Radiant Emission From Buoyant Turbulent and Laminar Diffusion Flames,” in Proceedings, Twentieth International Symposium on Combustion (Combustion Institute, Pittsburgh, 1984), pp. 1055–1061.

Mountain, R. D.

R. D. Mountain, G. W. Mulholland, “Light Scattering from Simulated Smoke Aggregates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

Mulholland, G. W.

R. D. Mountain, G. W. Mulholland, “Light Scattering from Simulated Smoke Aggregates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

Nakajima, M.

Percival, I. C.

M. V. Berry, I. C. Percival, “Optics of Fractal Clusters Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Porter, R. W.

R. W. Porter, “Numerical Solution for Local Emission Coefficients in Axisymmetric Self-Absorbed Sources,” SIAM Soc. Ind. Appl. Math. Rev. 6, 228–242 (1964).

Ramachandran, G. N.

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-Dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions Instead of Fourier Transforms,” Proc. Nat. Acad. Sci. USA, 68, 2236–2240 (1971).
[CrossRef] [PubMed]

Ray, S. R.

H. G. Semerjian, S. R. Ray, R. J. Santoro, “Laser Tomography for Diagnostics in Reacting Flows,” AIAA Paper 82-0584 (1982).

Roper, F. G.

F. G. Roper, “Soot Escape from Diffusion Flames: a Comparison of Recent Work in this Field,” Combust. Sci. Technol. 40, 323–329 (1984).
[CrossRef]

Santoro, R. J.

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot Particle Measurements in Diffusion Flames,” Combust. Flame, 51, 203–218 (1983).
[CrossRef]

P. J. Emmerman, R. Goulard, R. J. Santoro, H. G. Semerjian, “Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet,” J. Energy 4, 70–77 (1980).
[CrossRef]

H. G. Semerjian, S. R. Ray, R. J. Santoro, “Laser Tomography for Diagnostics in Reacting Flows,” AIAA Paper 82-0584 (1982).

R. J. Santoro, H. G. Semerjian, “Soot Formation in Diffusion Flames: Flow Rate, Fuel Species, and Temperature Effects,” Proceedings, Twentieth International Symposium on Combustion (Combustion Institute, Pittsburgh, 1984), pp. 997–1006.

Semerjian, H. G.

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot Particle Measurements in Diffusion Flames,” Combust. Flame, 51, 203–218 (1983).
[CrossRef]

P. J. Emmerman, R. Goulard, R. J. Santoro, H. G. Semerjian, “Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet,” J. Energy 4, 70–77 (1980).
[CrossRef]

H. G. Semerjian, S. R. Ray, R. J. Santoro, “Laser Tomography for Diagnostics in Reacting Flows,” AIAA Paper 82-0584 (1982).

R. J. Santoro, H. G. Semerjian, “Soot Formation in Diffusion Flames: Flow Rate, Fuel Species, and Temperature Effects,” Proceedings, Twentieth International Symposium on Combustion (Combustion Institute, Pittsburgh, 1984), pp. 997–1006.

Shepp, L. A.

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

Solomon, P. R.

P. R. Solomon et al., “FT-IR Emission/Transmission Spectroscopy for In Situ Combustion Diagnostics,” in Proceedings, Twenty-First International Symposium on Combustion (Combustion Institute, Pittsburgh, 1986), pp. 1763–1771.

Tankin, R. S.

G. Kuhn, R. S. Tankin, “Spectroscopic Measurements to Determine Temperature and Carbon Particle Size inan Absorbing Propane Diffusion Flame,” J. Quant. Spectrosc. Radiat. Transfer 8, 1281–1292 (1968).
[CrossRef]

Uchiyama, H.

Yuta, S.

Appl. Opt.

Combust. Flame

R. J. Santoro, H. G. Semerjian, R. A. Dobbins, “Soot Particle Measurements in Diffusion Flames,” Combust. Flame, 51, 203–218 (1983).
[CrossRef]

Combust. Sci. Technol.

F. G. Roper, “Soot Escape from Diffusion Flames: a Comparison of Recent Work in this Field,” Combust. Sci. Technol. 40, 323–329 (1984).
[CrossRef]

IEEE Trans. Nucl. Sci.

L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

J. Energy

P. J. Emmerman, R. Goulard, R. J. Santoro, H. G. Semerjian, “Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet,” J. Energy 4, 70–77 (1980).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

G. Kuhn, R. S. Tankin, “Spectroscopic Measurements to Determine Temperature and Carbon Particle Size inan Absorbing Propane Diffusion Flame,” J. Quant. Spectrosc. Radiat. Transfer 8, 1281–1292 (1968).
[CrossRef]

Langmuir

R. D. Mountain, G. W. Mulholland, “Light Scattering from Simulated Smoke Aggregates,” Langmuir 4, 1321–1326 (1988).
[CrossRef]

Opt. Acta

M. V. Berry, I. C. Percival, “Optics of Fractal Clusters Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[CrossRef]

Proc. Nat. Acad. Sci. USA

G. N. Ramachandran, A. V. Lakshminarayanan, “Three-Dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions Instead of Fourier Transforms,” Proc. Nat. Acad. Sci. USA, 68, 2236–2240 (1971).
[CrossRef] [PubMed]

SIAM Soc. Ind. Appl. Math. Rev.

R. W. Porter, “Numerical Solution for Local Emission Coefficients in Axisymmetric Self-Absorbed Sources,” SIAM Soc. Ind. Appl. Math. Rev. 6, 228–242 (1964).

Other

H. G. Semerjian, S. R. Ray, R. J. Santoro, “Laser Tomography for Diagnostics in Reacting Flows,” AIAA Paper 82-0584 (1982).

L. R. Boedeker, G. M. Dobbs, “Temperature and Soot Correlations in Sooting, Laminar Diffusion Flames,” UTRC Report 85-51 (1985).

P. R. Solomon et al., “FT-IR Emission/Transmission Spectroscopy for In Situ Combustion Diagnostics,” in Proceedings, Twenty-First International Symposium on Combustion (Combustion Institute, Pittsburgh, 1986), pp. 1763–1771.

R. J. Santoro, H. G. Semerjian, “Soot Formation in Diffusion Flames: Flow Rate, Fuel Species, and Temperature Effects,” Proceedings, Twentieth International Symposium on Combustion (Combustion Institute, Pittsburgh, 1984), pp. 997–1006.

G. H. Markstein, “Relationship Between Smoke Point and Radiant Emission From Buoyant Turbulent and Laminar Diffusion Flames,” in Proceedings, Twentieth International Symposium on Combustion (Combustion Institute, Pittsburgh, 1984), pp. 1055–1061.

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Figures (11)

Fig. 1
Fig. 1

Generation of projections from parallel path measurements at various angles of incidence. (After Refs. 3, 4).

Fig. 2
Fig. 2

Schematic of experimental apparatus.

Fig. 3
Fig. 3

Line-of-sight projections in ethylene flame 4 cm above burner surface.

Fig. 4
Fig. 4

Reconstructed soot absorption coefficient–volume fraction profile at height of 4 cm. The approximate volume fraction can be obtained by dividing the absorption coefficients shown (in cm−1) by 4.9 × 104.

Fig. 5
Fig. 5

(a) Reconstructed soot temperature at 4-cm height in ethylene flame. (b) Comparison of tomographic soot and CARS temperatures.9

Fig. 6
Fig. 6

Evolution of soot volume fraction–absorption coefficient with height in ethylene flame.

Fig. 7
Fig. 7

(a) Reconstructed local emission rate profile at height of 1.5 cm in ethylene flame. (b) Reconstructed soot temperature at 1.5 cm.

Fig. 8
Fig. 8

Comparison of CARS9 and emission–absorption temperatures at 1.5-cm height in ethylene flame.

Fig. 9
Fig. 9

Reconstructed soot temperature at 5.5-cm height in ethylene flame.

Fig. 10
Fig. 10

Evolution of soot volume fraction–absorption coefficient with height in iso-octane–air diffusion flame.

Fig. 11
Fig. 11

Deconvolved soot temperature profiles in iso-octane–air diffusion flame.

Equations (6)

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I λ = α λ ( a ) ( x , y ) B λ [ T ( x , y ) ] exp [ - x , y α λ ( e ) ( x , y ) d s ] d s + I λ ( 0 ) exp [ - - α λ ( e ) ( x , y ) d s ] ,
B λ ( T ) = 2 h c 2 λ 5 [ exp ( h c λ k T ) - 1 ] .
F ( x , y ) = a 2 N j = 1 N k = 1 M P ( r k , θ j ) ϕ ( x cos θ j + y sin θ j - r k ) ,
ϕ ( r k ) = - 4 π a 2 ( 4 k 2 - 1 ) k = 0 , ± 1 , ± 2 , ( Shepp - Logan filter ) ϕ ¯ ( r k ) = 0.4 ϕ ( r k ) + 0.3 ϕ ( r k + 1 ) + 0.3 ϕ ( r k - 1 ) . ( Modified Shepp - Logan filter )
α λ = C f v λ ,
radiated power = d λ 4 π d Ω d V α λ B λ ( T ) = C d V f v T 5 ,

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