Abstract

Through numerical calculations we have investigated the possibility of developing soot diagnostics based on laser heating of the soot particles. Two strategies, one using the laser-modulated incandescence of the particles, and the other using direct detection of the evaporated C2 molecules, were examined. Both strategies can yield size distribution and volume fraction information provided the laser wavelength is near the graphite absorption band at 260 nm; otherwise, only volume fractions can be obtained.

© 1984 Optical Society of America

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References

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  1. A. C. Eckbreth, “Effects of Laser-Modulated Particulate Incandescence on Raman Scattering Diagnostics,” J. Appl. Phys. 48, 4473 (1977).
    [CrossRef]
  2. D. A. Greenhalgh, “RECLAS: Resonant-Enhanced CARS from C2 Produced by Laser Ablation of Soot Particles,” Appl. Opt. 22, 1128 (1983).
    [CrossRef] [PubMed]
  3. C. Dasch, General Motors Research Center; private communication.
  4. R. W. Weeks, W. W. Duley, “Aerosol Particulate Sizes from Light Emission during Excitation by TEA (Transversely Excited Atmospheric Pressure) Carbon Dioxide Laser Pulses,” J. Appl. Phys. 45, 4661 (1974).
    [CrossRef]
  5. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  6. A. C. Eckbreth, in Experimental Diagnostics in Gas Phase Combustion Systems, B. T. Zinn, Ed. (AIAA, New York, 1977), pp. 517–547.
  7. A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, EPA Report R79-954403-13 (1979).
  8. A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, “Combustion Diagnostics by Laser Raman and Fluorescence Techniques,” Prog. Energy Combust. Sci. 5, 253 (1979).
    [CrossRef]
  9. B. J. McCoy, C. Y. Cha, “Transport Phenomena in the Rarefied Gas Transport Regime,” Chem. Eng. Sci. 29, 381 (1974).
    [CrossRef]
  10. D. C. Lencioni, H. Kleiman, MIT LTP-27 (1974), unpublished.
  11. A. J. Cantor, A Mie Scattering Computer Program, UTRC 77–28 (1977), unpublished.
  12. W. H. Dalzell, A. F. Sarofim, “Optical Constants of Soot and their Application to Heat Flux Calculations,” Trans. ASME, J. Heat Transfer 91, 100 (1969).
    [CrossRef]
  13. V. R. Stull, G. N. Plass, “Emissivity of Dispersed Carbon Particles,” J. Opt. Soc. Am. 50, 121 (1960).
    [CrossRef]
  14. S. Chippet, W. A. Gray, “The Size and Optical Properties of Soot Particles,” Combust. Flame 31, 149 (1978).
    [CrossRef]
  15. J. J. Janzen, “The Refractive Index of Colloidal Carbon,” J. Colloid Interface Sci. 69, 436 (1979).
    [CrossRef]
  16. S. C. Lee, C. L. Tien, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1159–1166.
  17. E. A. Taft, H. R. Philipp, “Optical Properties of Graphite,” Phys. Rev. A 138, 197 (1965).
  18. A. Voet, “The Absorption Spectrum of Carbon Black Dispersions,” Rubber Age 82, 657 (1958).
  19. J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical Properties of Graphite in the Region 1100–3000 Å,” Phys. Rev. A 137, 639 (1965).
  20. J. Lahaye, G. Prado, in Chemistry and Physics of Carbon, Vol. 14, P. L. Walker, P. A. Thrower, Eds. (Marcel Dekker, New York, 1978), Chap. 3.
  21. R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 431.
  22. J. Berkowitz, W. A. Chupka, “Mass Spectrometric Study of Vapor Ejected from Graphite and Other Solids by Focussed Laser Beams,” J. Chem. Phys. 40, 2735 (1964).
    [CrossRef]
  23. D. W. Marquardt, IBM SHARE Library, SDA 3094 (1966).
  24. H. Bockhorn, F. Felting, V. Meyer, R. Beck, G. Wannemacher, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1137–47.
  25. B. S. Haynes, H. G. Wagner, “Soot Formation,” Prog. Energy Combust. Sci. 7, 229 (1981).
    [CrossRef]

1983 (1)

1981 (1)

B. S. Haynes, H. G. Wagner, “Soot Formation,” Prog. Energy Combust. Sci. 7, 229 (1981).
[CrossRef]

1979 (2)

J. J. Janzen, “The Refractive Index of Colloidal Carbon,” J. Colloid Interface Sci. 69, 436 (1979).
[CrossRef]

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, “Combustion Diagnostics by Laser Raman and Fluorescence Techniques,” Prog. Energy Combust. Sci. 5, 253 (1979).
[CrossRef]

1978 (1)

S. Chippet, W. A. Gray, “The Size and Optical Properties of Soot Particles,” Combust. Flame 31, 149 (1978).
[CrossRef]

1977 (1)

A. C. Eckbreth, “Effects of Laser-Modulated Particulate Incandescence on Raman Scattering Diagnostics,” J. Appl. Phys. 48, 4473 (1977).
[CrossRef]

1974 (2)

R. W. Weeks, W. W. Duley, “Aerosol Particulate Sizes from Light Emission during Excitation by TEA (Transversely Excited Atmospheric Pressure) Carbon Dioxide Laser Pulses,” J. Appl. Phys. 45, 4661 (1974).
[CrossRef]

B. J. McCoy, C. Y. Cha, “Transport Phenomena in the Rarefied Gas Transport Regime,” Chem. Eng. Sci. 29, 381 (1974).
[CrossRef]

1969 (1)

W. H. Dalzell, A. F. Sarofim, “Optical Constants of Soot and their Application to Heat Flux Calculations,” Trans. ASME, J. Heat Transfer 91, 100 (1969).
[CrossRef]

1966 (1)

D. W. Marquardt, IBM SHARE Library, SDA 3094 (1966).

1965 (2)

E. A. Taft, H. R. Philipp, “Optical Properties of Graphite,” Phys. Rev. A 138, 197 (1965).

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical Properties of Graphite in the Region 1100–3000 Å,” Phys. Rev. A 137, 639 (1965).

1964 (1)

J. Berkowitz, W. A. Chupka, “Mass Spectrometric Study of Vapor Ejected from Graphite and Other Solids by Focussed Laser Beams,” J. Chem. Phys. 40, 2735 (1964).
[CrossRef]

1960 (1)

1958 (1)

A. Voet, “The Absorption Spectrum of Carbon Black Dispersions,” Rubber Age 82, 657 (1958).

Beck, R.

H. Bockhorn, F. Felting, V. Meyer, R. Beck, G. Wannemacher, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1137–47.

Berkowitz, J.

J. Berkowitz, W. A. Chupka, “Mass Spectrometric Study of Vapor Ejected from Graphite and Other Solids by Focussed Laser Beams,” J. Chem. Phys. 40, 2735 (1964).
[CrossRef]

Bird, R. B.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 431.

Birkhoff, R. D.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical Properties of Graphite in the Region 1100–3000 Å,” Phys. Rev. A 137, 639 (1965).

Bockhorn, H.

H. Bockhorn, F. Felting, V. Meyer, R. Beck, G. Wannemacher, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1137–47.

Bonczyk, P. A.

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, “Combustion Diagnostics by Laser Raman and Fluorescence Techniques,” Prog. Energy Combust. Sci. 5, 253 (1979).
[CrossRef]

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, EPA Report R79-954403-13 (1979).

Cantor, A. J.

A. J. Cantor, A Mie Scattering Computer Program, UTRC 77–28 (1977), unpublished.

Carter, J. G.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical Properties of Graphite in the Region 1100–3000 Å,” Phys. Rev. A 137, 639 (1965).

Cha, C. Y.

B. J. McCoy, C. Y. Cha, “Transport Phenomena in the Rarefied Gas Transport Regime,” Chem. Eng. Sci. 29, 381 (1974).
[CrossRef]

Chippet, S.

S. Chippet, W. A. Gray, “The Size and Optical Properties of Soot Particles,” Combust. Flame 31, 149 (1978).
[CrossRef]

Chupka, W. A.

J. Berkowitz, W. A. Chupka, “Mass Spectrometric Study of Vapor Ejected from Graphite and Other Solids by Focussed Laser Beams,” J. Chem. Phys. 40, 2735 (1964).
[CrossRef]

Dalzell, W. H.

W. H. Dalzell, A. F. Sarofim, “Optical Constants of Soot and their Application to Heat Flux Calculations,” Trans. ASME, J. Heat Transfer 91, 100 (1969).
[CrossRef]

Dasch, C.

C. Dasch, General Motors Research Center; private communication.

Duley, W. W.

R. W. Weeks, W. W. Duley, “Aerosol Particulate Sizes from Light Emission during Excitation by TEA (Transversely Excited Atmospheric Pressure) Carbon Dioxide Laser Pulses,” J. Appl. Phys. 45, 4661 (1974).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, “Combustion Diagnostics by Laser Raman and Fluorescence Techniques,” Prog. Energy Combust. Sci. 5, 253 (1979).
[CrossRef]

A. C. Eckbreth, “Effects of Laser-Modulated Particulate Incandescence on Raman Scattering Diagnostics,” J. Appl. Phys. 48, 4473 (1977).
[CrossRef]

A. C. Eckbreth, in Experimental Diagnostics in Gas Phase Combustion Systems, B. T. Zinn, Ed. (AIAA, New York, 1977), pp. 517–547.

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, EPA Report R79-954403-13 (1979).

Felting, F.

H. Bockhorn, F. Felting, V. Meyer, R. Beck, G. Wannemacher, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1137–47.

Gray, W. A.

S. Chippet, W. A. Gray, “The Size and Optical Properties of Soot Particles,” Combust. Flame 31, 149 (1978).
[CrossRef]

Greenhalgh, D. A.

Hamm, R. N.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical Properties of Graphite in the Region 1100–3000 Å,” Phys. Rev. A 137, 639 (1965).

Haynes, B. S.

B. S. Haynes, H. G. Wagner, “Soot Formation,” Prog. Energy Combust. Sci. 7, 229 (1981).
[CrossRef]

Huebner, R. H.

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical Properties of Graphite in the Region 1100–3000 Å,” Phys. Rev. A 137, 639 (1965).

Janzen, J. J.

J. J. Janzen, “The Refractive Index of Colloidal Carbon,” J. Colloid Interface Sci. 69, 436 (1979).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kleiman, H.

D. C. Lencioni, H. Kleiman, MIT LTP-27 (1974), unpublished.

Lahaye, J.

J. Lahaye, G. Prado, in Chemistry and Physics of Carbon, Vol. 14, P. L. Walker, P. A. Thrower, Eds. (Marcel Dekker, New York, 1978), Chap. 3.

Lee, S. C.

S. C. Lee, C. L. Tien, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1159–1166.

Lencioni, D. C.

D. C. Lencioni, H. Kleiman, MIT LTP-27 (1974), unpublished.

Lightfoot, E. N.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 431.

Marquardt, D. W.

D. W. Marquardt, IBM SHARE Library, SDA 3094 (1966).

McCoy, B. J.

B. J. McCoy, C. Y. Cha, “Transport Phenomena in the Rarefied Gas Transport Regime,” Chem. Eng. Sci. 29, 381 (1974).
[CrossRef]

Meyer, V.

H. Bockhorn, F. Felting, V. Meyer, R. Beck, G. Wannemacher, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1137–47.

Philipp, H. R.

E. A. Taft, H. R. Philipp, “Optical Properties of Graphite,” Phys. Rev. A 138, 197 (1965).

Plass, G. N.

Prado, G.

J. Lahaye, G. Prado, in Chemistry and Physics of Carbon, Vol. 14, P. L. Walker, P. A. Thrower, Eds. (Marcel Dekker, New York, 1978), Chap. 3.

Sarofim, A. F.

W. H. Dalzell, A. F. Sarofim, “Optical Constants of Soot and their Application to Heat Flux Calculations,” Trans. ASME, J. Heat Transfer 91, 100 (1969).
[CrossRef]

Stewart, W. E.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 431.

Stull, V. R.

Taft, E. A.

E. A. Taft, H. R. Philipp, “Optical Properties of Graphite,” Phys. Rev. A 138, 197 (1965).

Tien, C. L.

S. C. Lee, C. L. Tien, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1159–1166.

Verdieck, J. F.

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, “Combustion Diagnostics by Laser Raman and Fluorescence Techniques,” Prog. Energy Combust. Sci. 5, 253 (1979).
[CrossRef]

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, EPA Report R79-954403-13 (1979).

Voet, A.

A. Voet, “The Absorption Spectrum of Carbon Black Dispersions,” Rubber Age 82, 657 (1958).

Wagner, H. G.

B. S. Haynes, H. G. Wagner, “Soot Formation,” Prog. Energy Combust. Sci. 7, 229 (1981).
[CrossRef]

Wannemacher, G.

H. Bockhorn, F. Felting, V. Meyer, R. Beck, G. Wannemacher, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1137–47.

Weeks, R. W.

R. W. Weeks, W. W. Duley, “Aerosol Particulate Sizes from Light Emission during Excitation by TEA (Transversely Excited Atmospheric Pressure) Carbon Dioxide Laser Pulses,” J. Appl. Phys. 45, 4661 (1974).
[CrossRef]

Appl. Opt. (1)

Chem. Eng. Sci. (1)

B. J. McCoy, C. Y. Cha, “Transport Phenomena in the Rarefied Gas Transport Regime,” Chem. Eng. Sci. 29, 381 (1974).
[CrossRef]

Combust. Flame (1)

S. Chippet, W. A. Gray, “The Size and Optical Properties of Soot Particles,” Combust. Flame 31, 149 (1978).
[CrossRef]

IBM SHARE Library, SDA 3094 (1)

D. W. Marquardt, IBM SHARE Library, SDA 3094 (1966).

J. Appl. Phys. (2)

A. C. Eckbreth, “Effects of Laser-Modulated Particulate Incandescence on Raman Scattering Diagnostics,” J. Appl. Phys. 48, 4473 (1977).
[CrossRef]

R. W. Weeks, W. W. Duley, “Aerosol Particulate Sizes from Light Emission during Excitation by TEA (Transversely Excited Atmospheric Pressure) Carbon Dioxide Laser Pulses,” J. Appl. Phys. 45, 4661 (1974).
[CrossRef]

J. Chem. Phys. (1)

J. Berkowitz, W. A. Chupka, “Mass Spectrometric Study of Vapor Ejected from Graphite and Other Solids by Focussed Laser Beams,” J. Chem. Phys. 40, 2735 (1964).
[CrossRef]

J. Colloid Interface Sci. (1)

J. J. Janzen, “The Refractive Index of Colloidal Carbon,” J. Colloid Interface Sci. 69, 436 (1979).
[CrossRef]

J. Heat Transfer (1)

W. H. Dalzell, A. F. Sarofim, “Optical Constants of Soot and their Application to Heat Flux Calculations,” Trans. ASME, J. Heat Transfer 91, 100 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. A (2)

E. A. Taft, H. R. Philipp, “Optical Properties of Graphite,” Phys. Rev. A 138, 197 (1965).

J. G. Carter, R. H. Huebner, R. N. Hamm, R. D. Birkhoff, “Optical Properties of Graphite in the Region 1100–3000 Å,” Phys. Rev. A 137, 639 (1965).

Prog. Energy Combust. Sci. (2)

B. S. Haynes, H. G. Wagner, “Soot Formation,” Prog. Energy Combust. Sci. 7, 229 (1981).
[CrossRef]

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, “Combustion Diagnostics by Laser Raman and Fluorescence Techniques,” Prog. Energy Combust. Sci. 5, 253 (1979).
[CrossRef]

Rubber Age (1)

A. Voet, “The Absorption Spectrum of Carbon Black Dispersions,” Rubber Age 82, 657 (1958).

Other (10)

S. C. Lee, C. L. Tien, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1159–1166.

D. C. Lencioni, H. Kleiman, MIT LTP-27 (1974), unpublished.

A. J. Cantor, A Mie Scattering Computer Program, UTRC 77–28 (1977), unpublished.

C. Dasch, General Motors Research Center; private communication.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

A. C. Eckbreth, in Experimental Diagnostics in Gas Phase Combustion Systems, B. T. Zinn, Ed. (AIAA, New York, 1977), pp. 517–547.

A. C. Eckbreth, P. A. Bonczyk, J. F. Verdieck, EPA Report R79-954403-13 (1979).

J. Lahaye, G. Prado, in Chemistry and Physics of Carbon, Vol. 14, P. L. Walker, P. A. Thrower, Eds. (Marcel Dekker, New York, 1978), Chap. 3.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 431.

H. Bockhorn, F. Felting, V. Meyer, R. Beck, G. Wannemacher, in Proceedings, Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), pp. 1137–47.

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Figures (9)

Fig. 1
Fig. 1

Absorption efficiencies as a function of particle radius, λex = 220, 270, and 532 nm.

Fig. 2
Fig. 2

Time evolution of particle properties - · -, a; - - -, laser intensity; …, response function; and —, temperature. a0 = 0.02 μm, T0 = 2000 K, q = 1.0 × 108 W/cm2.

Fig. 3
Fig. 3

Relative response functions: q = 1 × 106 W/cm2, λex = 220 nm, λem = 300 nm. Maximum of response function = RM = 0.61 × 10−4. - · -, t = 10 nsec; – · · – · ·, t = 15 nsec; —, t = 20 nsec.

Fig. 4
Fig. 4

Same as Fig. 3, q = 3 × 106 W/cm2, RM = 0.65 × 10−3.

Fig. 5
Fig. 5

Same as Fig. 3, q = 1 × 107 W/cm2, RM = 0.56 × 10−2.

Fig. 6
Fig. 6

Relative response functions: q = 1 × 106 W/cm2, λex = 270 nm, λem = 300 nm, RM = 0.38 × 10−5.

Fig. 7
Fig. 7

Same as Fig. 6, q = 3 × 106 W/cm2, RM = 0.54 × 10−3.

Fig. 8
Fig. 8

Same as Fig. 6, q = 1 × 107 W/cm2, RM = 0.69 × 10−2.

Fig. 9
Fig. 9

Relative response functions: q = 3 × 106 W/cm2, λex = 532 nm, λem = 600 nm, RM = 0.46 × 10−2.

Equations (20)

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

C ext = C scat + C abs ,
K ext = K scat + K abs ,
K abs ( a ) π a 2 q - K a a ( T - T 0 ) ( 4 π a 2 ) ( 1 + G K n ) + Δ H v W d M W d M d t - σ s b ( T 4 - T 0 4 ) × ( 4 π a 2 ) - 4 3 π a 3 ρ s C s d T d t = 0.
- ρ s d a d t = ρ v U v .
p ( T ) = p * exp Δ H ( T - T * ) R T T * ,
K abs ( a ) q - 8 K a ( T - T 0 ) G λ - Δ H v W ρ v U v - 4 σ S B ( T 4 - T 0 4 ) - 4 3 ρ s C s a d T d t = 0.
K abs = { β ( m ) a > δ , a / δ a < δ , 1 / δ = 2 ( 2 π ) k λ [ 12 n β - 1 ( m ) 4 n 2 k 2 - ( n 2 - k 2 - 2 ) 2 ] .
I em = 2 π c 2 h λ em 5 [ exp ( h c / λ em k t ) - 1 ] - 1 Δ λ ( ɛ 4 π a 2 ) .
R ( a , t , q , λ ex , λ em , Δ λ ) = 2 π 2 c 2 h λ em 5 a 2 ( t ) K abs ( a , λ em ) × { [ exp ( h c / λ em K T ) - 1 ] - 1 - [ exp ( h c / λ em k T 0 ) - 1 ] - 1 } .
J ( t , q , λ ex , λ em , Δ λ ) = 0 N p ( a ) R ( a , t , q , λ ex , λ em , Δ λ ) d a ,
p ( a ) = [ ( 2 π ) 1 / 2 a m σ 0 exp ( σ 0 2 / 2 ) ] - 1 × exp [ - ( log a - log a m ) 2 / 2 σ 0 2 ] .
R ( a , t , q , λ ex ) = d M d t = ρ v U v ( 4 π a 2 ) f ,
K abs ( a ) q + Δ H W ( 4 ρ s d a d t ) 0.
a q / δ - 1.22 × 10 + 8 T - 1 / 2 exp [ 23.9 ( 1 - 3915 T ) ] 0
1 T 1 3915 [ 1 - 1 23.9 log ( a q / δ ) ] ,
J = C 1 0 N P ( a ) a x d a ,
x = 3 + 0.154 λ em - 1 .
K abs ( a ) q π a 2 + Δ H v W d M d t 0 ,
J = 0 n ( a ) K abs ( a ) π a 2 q W Δ H v d a .
J π q W δ Δ H ν 0 n ( a ) a 3 d a .

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