Abstract

The scattering and extinction behavior of multicomponent particles formed in flame systems is significant in a number of research areas and practical applications, such as the production of superconducting and other ceramic materials by means of the aerosol route as well as pollutant suppression through the use of metal additives. The objective of this study is to assess the role of iron pentacarbonyl vapor addition on the light scattering and extinction behavior of flame soot. Calculations were carried out by using the scattering models for homogeneous and coated spheres and comparisons were made between the particle diameters and volume fractions. In addition, scattering, absorption, and dynamic light-scattering measurements at the wavelength of 488 nm in a premixed propane–oxygen flame with a fuel-equivalence ratio of ϕ = 2.4 unseeded and seeded with iron pentacarbonyl vapor 0.32% by weight iron to fuel were performed. The refractive index and number densities of the soot particles in the unseeded flame were determined as functions of position above the burner by combining the scattering and absorption measurements with the particle size-distribution parameters determined from photocorrelation. In the seeded flames the soot particles were found to contain iron oxide throughout the flame. Thus the data were analyzed by using both the scattering–absorption model for coated spheres and the Maxwell-Garnett relation for the effective refractive index. Differences up to 131% in particle-volume fractions were found from the data analysis by using the constant and variable effective index of the mixture (soot plus iron oxide). The results of the coated-sphere analysis are discussed and the effects of particle agglomeration on the inference of particle-volume fractions are assessed. It is concluded that the effects of particle optical inhomogeneity in the analysis of scattering and absorption data from multicomponent particles cannot be neglected.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News, (6August1984), pp. 23–28.
  2. T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 89–99 (1991).
    [CrossRef]
  3. T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering,” Prog. Energy Combust. Sci. 18, 13–45 (1992).
    [CrossRef]
  4. K. E. Ritrievi, J. P. Longwell, A. F. Sarofim, “The effects of ferrocene addition on soot particle inception and growth in premixed ethylene flames,” Combust. Flame 70, 17–31 (1987).
    [CrossRef]
  5. D. W. Hahn, “The role of iron additives in soot suppression in flames,” Ph.D. dissertation (Louisiana State University, Baton Rouge, La., 1992).
  6. D. W. Hahn, T. T. Charalampopoulos, “The role of iron additives in sooting premixed in flames,” presented at the Twenty Fourth International Symposium on Combustion, Sidney, Australia, 5–10 July 1992.
  7. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  8. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  9. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  10. A. L. Faymat, “Radiative properties of optically anisotropic spheres and their climatic implications,” J. Opt. Soc. Am. 72, 1307–1310 (1982).
    [CrossRef]
  11. J. J. Jagoda, G. Prado, J. Lahaye, “An experimental investigation into soot formation and distribution in polymer diffusion flames,” Combust. Flame 37, 261–274 (1980).
    [CrossRef]
  12. T. T. Charalampopoulos, H. Chang, “In-situ optical properties of soot particles in the wavelength range from 340 nm to 600 nm,” Combust. Sci. Technol. 59, 4–6, 401–421 (1988).
    [CrossRef]
  13. A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
    [CrossRef]
  14. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385 (1904).
    [CrossRef]
  15. D. A. G. Bruggerman, “Berechnung verschiedener physi-Kalischer Konstanten von heterogen Substanzen. I. Dielektrizitätskonstanten and Leitfähigkeiten der MischKorper aus isotropen Substanzen,” Ann. Phys. 24, 636 (1935).
    [CrossRef]
  16. J. D. Felske, T. T. Charalampopoulos, H. S. Hura, “Determination of the refractive indices of soot particles from the reflectivities of compressed soot pellets,” Combust. Sci. Technol. 37, 263–284 (1984).
    [CrossRef]
  17. G. A. Niklason, C. G. Granqvist, O. Hunderi, “Effective medium models for the optical properties of inhomogeneous materials,” Appl. Opt. 20, 26–30 (1981).
    [CrossRef]
  18. R. W. Fenn, H. Oser, “Scattering properties of concentric soot water spheres for visible and infrared light,” Appl. Opt. 22, 1504–1508 (1965).
    [CrossRef]
  19. J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).
  20. T. W. Taylor, S. M. Scrivner, C. M. Sorensen, J. F. Merklin, “Determination of the relative number distribution of particle sizes using photon correlation spectroscopy,” Appl. Opt. 22, 3713–3717 (1985).
    [CrossRef]
  21. D. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
    [CrossRef]
  22. T. T. Charalampopoulos, “An automated laser light scattering system and a method for the in-situ measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
    [CrossRef]
  23. T. T. Charalampopoulos, H. Chang, B. Stagg, “The effects of temperature and composition on the complex refractive index of flame soot,” Fuel 68, 1173–1179 (1989).
    [CrossRef]
  24. H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
    [CrossRef]

1992

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering,” Prog. Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

1991

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 89–99 (1991).
[CrossRef]

1990

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

1989

T. T. Charalampopoulos, H. Chang, B. Stagg, “The effects of temperature and composition on the complex refractive index of flame soot,” Fuel 68, 1173–1179 (1989).
[CrossRef]

1988

T. T. Charalampopoulos, H. Chang, “In-situ optical properties of soot particles in the wavelength range from 340 nm to 600 nm,” Combust. Sci. Technol. 59, 4–6, 401–421 (1988).
[CrossRef]

1987

K. E. Ritrievi, J. P. Longwell, A. F. Sarofim, “The effects of ferrocene addition on soot particle inception and growth in premixed ethylene flames,” Combust. Flame 70, 17–31 (1987).
[CrossRef]

T. T. Charalampopoulos, “An automated laser light scattering system and a method for the in-situ measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
[CrossRef]

1985

T. W. Taylor, S. M. Scrivner, C. M. Sorensen, J. F. Merklin, “Determination of the relative number distribution of particle sizes using photon correlation spectroscopy,” Appl. Opt. 22, 3713–3717 (1985).
[CrossRef]

1984

J. D. Felske, T. T. Charalampopoulos, H. S. Hura, “Determination of the refractive indices of soot particles from the reflectivities of compressed soot pellets,” Combust. Sci. Technol. 37, 263–284 (1984).
[CrossRef]

G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News, (6August1984), pp. 23–28.

1982

1981

1980

J. J. Jagoda, G. Prado, J. Lahaye, “An experimental investigation into soot formation and distribution in polymer diffusion flames,” Combust. Flame 37, 261–274 (1980).
[CrossRef]

1972

D. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
[CrossRef]

1965

R. W. Fenn, H. Oser, “Scattering properties of concentric soot water spheres for visible and infrared light,” Appl. Opt. 22, 1504–1508 (1965).
[CrossRef]

1951

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

1935

D. A. G. Bruggerman, “Berechnung verschiedener physi-Kalischer Konstanten von heterogen Substanzen. I. Dielektrizitätskonstanten and Leitfähigkeiten der MischKorper aus isotropen Substanzen,” Ann. Phys. 24, 636 (1935).
[CrossRef]

1904

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385 (1904).
[CrossRef]

Aden, A. L.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bruggerman, D. A. G.

D. A. G. Bruggerman, “Berechnung verschiedener physi-Kalischer Konstanten von heterogen Substanzen. I. Dielektrizitätskonstanten and Leitfähigkeiten der MischKorper aus isotropen Substanzen,” Ann. Phys. 24, 636 (1935).
[CrossRef]

Chang, H.

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 89–99 (1991).
[CrossRef]

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

T. T. Charalampopoulos, H. Chang, B. Stagg, “The effects of temperature and composition on the complex refractive index of flame soot,” Fuel 68, 1173–1179 (1989).
[CrossRef]

T. T. Charalampopoulos, H. Chang, “In-situ optical properties of soot particles in the wavelength range from 340 nm to 600 nm,” Combust. Sci. Technol. 59, 4–6, 401–421 (1988).
[CrossRef]

Charalampopoulos, T. T.

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering,” Prog. Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 89–99 (1991).
[CrossRef]

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

T. T. Charalampopoulos, H. Chang, B. Stagg, “The effects of temperature and composition on the complex refractive index of flame soot,” Fuel 68, 1173–1179 (1989).
[CrossRef]

T. T. Charalampopoulos, H. Chang, “In-situ optical properties of soot particles in the wavelength range from 340 nm to 600 nm,” Combust. Sci. Technol. 59, 4–6, 401–421 (1988).
[CrossRef]

T. T. Charalampopoulos, “An automated laser light scattering system and a method for the in-situ measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
[CrossRef]

J. D. Felske, T. T. Charalampopoulos, H. S. Hura, “Determination of the refractive indices of soot particles from the reflectivities of compressed soot pellets,” Combust. Sci. Technol. 37, 263–284 (1984).
[CrossRef]

D. W. Hahn, T. T. Charalampopoulos, “The role of iron additives in sooting premixed in flames,” presented at the Twenty Fourth International Symposium on Combustion, Sidney, Australia, 5–10 July 1992.

Colavita, E.

J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).

Faymat, A. L.

Felske, J. D.

J. D. Felske, T. T. Charalampopoulos, H. S. Hura, “Determination of the refractive indices of soot particles from the reflectivities of compressed soot pellets,” Combust. Sci. Technol. 37, 263–284 (1984).
[CrossRef]

Fenn, R. W.

R. W. Fenn, H. Oser, “Scattering properties of concentric soot water spheres for visible and infrared light,” Appl. Opt. 22, 1504–1508 (1965).
[CrossRef]

Granqvist, C. G.

Hahn, D. W.

D. W. Hahn, “The role of iron additives in soot suppression in flames,” Ph.D. dissertation (Louisiana State University, Baton Rouge, La., 1992).

D. W. Hahn, T. T. Charalampopoulos, “The role of iron additives in sooting premixed in flames,” presented at the Twenty Fourth International Symposium on Combustion, Sidney, Australia, 5–10 July 1992.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hunderi, O.

Hura, H. S.

J. D. Felske, T. T. Charalampopoulos, H. S. Hura, “Determination of the refractive indices of soot particles from the reflectivities of compressed soot pellets,” Combust. Sci. Technol. 37, 263–284 (1984).
[CrossRef]

Jagoda, J. J.

J. J. Jagoda, G. Prado, J. Lahaye, “An experimental investigation into soot formation and distribution in polymer diffusion flames,” Combust. Flame 37, 261–274 (1980).
[CrossRef]

Kerker, M.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

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

Koppel, D.

D. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
[CrossRef]

Lahaye, J.

J. J. Jagoda, G. Prado, J. Lahaye, “An experimental investigation into soot formation and distribution in polymer diffusion flames,” Combust. Flame 37, 261–274 (1980).
[CrossRef]

Longwell, J. P.

K. E. Ritrievi, J. P. Longwell, A. F. Sarofim, “The effects of ferrocene addition on soot particle inception and growth in premixed ethylene flames,” Combust. Flame 70, 17–31 (1987).
[CrossRef]

Lynch, D. W.

J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385 (1904).
[CrossRef]

Merklin, J. F.

T. W. Taylor, S. M. Scrivner, C. M. Sorensen, J. F. Merklin, “Determination of the relative number distribution of particle sizes using photon correlation spectroscopy,” Appl. Opt. 22, 3713–3717 (1985).
[CrossRef]

Niklason, G. A.

Oser, H.

R. W. Fenn, H. Oser, “Scattering properties of concentric soot water spheres for visible and infrared light,” Appl. Opt. 22, 1504–1508 (1965).
[CrossRef]

Prado, G.

J. J. Jagoda, G. Prado, J. Lahaye, “An experimental investigation into soot formation and distribution in polymer diffusion flames,” Combust. Flame 37, 261–274 (1980).
[CrossRef]

Ritrievi, K. E.

K. E. Ritrievi, J. P. Longwell, A. F. Sarofim, “The effects of ferrocene addition on soot particle inception and growth in premixed ethylene flames,” Combust. Flame 70, 17–31 (1987).
[CrossRef]

Rosei, R.

J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).

Sarofim, A. F.

K. E. Ritrievi, J. P. Longwell, A. F. Sarofim, “The effects of ferrocene addition on soot particle inception and growth in premixed ethylene flames,” Combust. Flame 70, 17–31 (1987).
[CrossRef]

Scrivner, S. M.

T. W. Taylor, S. M. Scrivner, C. M. Sorensen, J. F. Merklin, “Determination of the relative number distribution of particle sizes using photon correlation spectroscopy,” Appl. Opt. 22, 3713–3717 (1985).
[CrossRef]

Sorensen, C. M.

T. W. Taylor, S. M. Scrivner, C. M. Sorensen, J. F. Merklin, “Determination of the relative number distribution of particle sizes using photon correlation spectroscopy,” Appl. Opt. 22, 3713–3717 (1985).
[CrossRef]

Stagg, B.

T. T. Charalampopoulos, H. Chang, B. Stagg, “The effects of temperature and composition on the complex refractive index of flame soot,” Fuel 68, 1173–1179 (1989).
[CrossRef]

Taylor, T. W.

T. W. Taylor, S. M. Scrivner, C. M. Sorensen, J. F. Merklin, “Determination of the relative number distribution of particle sizes using photon correlation spectroscopy,” Appl. Opt. 22, 3713–3717 (1985).
[CrossRef]

Ulrich, G. D.

G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News, (6August1984), pp. 23–28.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Weaver, J. H.

J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).

Ann. Phys.

D. A. G. Bruggerman, “Berechnung verschiedener physi-Kalischer Konstanten von heterogen Substanzen. I. Dielektrizitätskonstanten and Leitfähigkeiten der MischKorper aus isotropen Substanzen,” Ann. Phys. 24, 636 (1935).
[CrossRef]

Appl. Opt.

G. A. Niklason, C. G. Granqvist, O. Hunderi, “Effective medium models for the optical properties of inhomogeneous materials,” Appl. Opt. 20, 26–30 (1981).
[CrossRef]

R. W. Fenn, H. Oser, “Scattering properties of concentric soot water spheres for visible and infrared light,” Appl. Opt. 22, 1504–1508 (1965).
[CrossRef]

T. W. Taylor, S. M. Scrivner, C. M. Sorensen, J. F. Merklin, “Determination of the relative number distribution of particle sizes using photon correlation spectroscopy,” Appl. Opt. 22, 3713–3717 (1985).
[CrossRef]

Chem. Eng. News

G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News, (6August1984), pp. 23–28.

Combust. Flame

T. T. Charalampopoulos, H. Chang, “Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth,” Combust. Flame 87, 89–99 (1991).
[CrossRef]

K. E. Ritrievi, J. P. Longwell, A. F. Sarofim, “The effects of ferrocene addition on soot particle inception and growth in premixed ethylene flames,” Combust. Flame 70, 17–31 (1987).
[CrossRef]

J. J. Jagoda, G. Prado, J. Lahaye, “An experimental investigation into soot formation and distribution in polymer diffusion flames,” Combust. Flame 37, 261–274 (1980).
[CrossRef]

Combust. Sci. Technol.

T. T. Charalampopoulos, H. Chang, “In-situ optical properties of soot particles in the wavelength range from 340 nm to 600 nm,” Combust. Sci. Technol. 59, 4–6, 401–421 (1988).
[CrossRef]

J. D. Felske, T. T. Charalampopoulos, H. S. Hura, “Determination of the refractive indices of soot particles from the reflectivities of compressed soot pellets,” Combust. Sci. Technol. 37, 263–284 (1984).
[CrossRef]

Fuel

T. T. Charalampopoulos, H. Chang, B. Stagg, “The effects of temperature and composition on the complex refractive index of flame soot,” Fuel 68, 1173–1179 (1989).
[CrossRef]

J. Appl. Phys.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

J. Chem. Phys.

D. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
[CrossRef]

J. Opt. Soc. Am.

Philos. Trans. R. Soc. London A

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385 (1904).
[CrossRef]

Proc. R. Soc. London Ser. A

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

Prog. Energy Combust. Sci.

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering,” Prog. Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

Rev. Sci. Instrum.

T. T. Charalampopoulos, “An automated laser light scattering system and a method for the in-situ measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
[CrossRef]

Other

J. H. Weaver, E. Colavita, D. W. Lynch, R. Rosei, CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).

D. W. Hahn, “The role of iron additives in soot suppression in flames,” Ph.D. dissertation (Louisiana State University, Baton Rouge, La., 1992).

D. W. Hahn, T. T. Charalampopoulos, “The role of iron additives in sooting premixed in flames,” presented at the Twenty Fourth International Symposium on Combustion, Sidney, Australia, 5–10 July 1992.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Light-scattering and extinction experiment: I0, incident light intensity; V-pol, vertical component of polarization; H-pol, horizontal componont of polarization.

Fig. 2
Fig. 2

Variation of the soot volume fractions with respect to the real and imaginary parts of the refractive index.

Fig. 3
Fig. 3

Calculated percent differences between the diameters of the homogeneous and inhomogeneous particles inferred from the Mie analysis as functions of the ratio (dc/ds) and the size parameter (πds/λ) based on the shell diameter at the wavelength λ = 488 nm.

Fig. 4
Fig. 4

Calculated percent differences between the volume fractions of the homogeneous and inhomogeneous particles inferred from the Mie analysis as functions of the ratio (dc/ds) and the size parameter (πds/λ) based on the shell diameter at the wavelength λ = 488 nm.

Fig. 5
Fig. 5

Schematic of the vaporization and feeding system for the addition of the iron pentcarbonyl vapor to the premixed flame.

Fig. 6
Fig. 6

Volume fractions of particles as functions of position above the burner surface in the unseeded and seeded flame using the constant refractive index m ¯ = 1.57–0.56i and the variable effective index in the seeded flame.

Fig. 7
Fig. 7

Volume fractions of particles as functions of position above the burner surface in the unseeded and seeded flame using the constant refractive index m ¯ = 1.7–0.7i and the variable effective index in the seeded flame.

Tables (4)

Tables Icon

Table 1 Measured Scattering (KVV) and Extinction Coefficients (Kext) as Functions of Position Above the Burner Surface in a Premixed Propane–Oxygen Flame with a Fuel-Equivalence Ratio of ϕ = 2.4a

Tables Icon

Table 2 Photon Correlation Results for the Unseeded and Seeded Flame as a Function of Position Above the Burner Surface

Tables Icon

Table 3 Number Densities and Refractive Indices of Particles In the Unseeded and Seeded Flames Using the Homogeneous Analysis, the Coated-Sphere Model, and the Effective Refractive-index Model

Tables Icon

Table 4 Percent Differences in Volume Fractions in the Seeded Flames Inferred from the Variable Effective Refractive Indexa and Volume Fractions in the Unseeded and Seeded Flames Using Various Constant Indices

Equations (29)

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

S p p = I p p Δ Ω Δ V K p p η opt τ λ ,
K p p = N C ¯ p p ,
C ¯ p p = r = 0 C p p P ( r ) d r .
C p p = λ 2 4 π 2 i p p ,
i v v = | ν = 1 ( 2 ν + 1 ) ν ( ν + 1 ) ( a ν π ν + b ν τ ν ) | 2 ,
i H H = | ν = 1 ( 2 ν + 1 ) ν ( ν + 1 ) ( a ν τ ν + b ν π ν ) | 2 .
P ( r ) = exp ( - 1 2 ln 2 σ ) 2 π r 0 ln σ exp [ - ln 2 ( r / r 0 ) 2 ln 2 σ ] .
τ λ = I ( L 0 ) / I 0 = exp ( - K ext L 0 ) ,
K ext = N C ¯ ext .
C ¯ ext = r = 0 C ext P ( r ) d r ,
C ext = λ 2 2 π ν = 1 ( 2 ν + 1 ) Re ( a ν + b ν ) ,
K V V ( 90 ° ) , part λ = K V V ( 90 ° ) , gas S V V ( 90 ° ) , part λ S V V ( 90 ° ) , gas λ τ g τ λ .
Q ext = C ext π r 2 ,
K V V K ext = λ 2 i V V 4 π 3 r 2 Q ext ,
K V V K ext = λ 2 4 π 3 0 i V V P ( r ) d r 0 Q ext r 2 P ( r ) d r .
a ¯ ν = [ D ¯ ν / m ¯ 2 + ( ν / y ) ] ψ ν ( y ) - ψ ν - 1 ( y ) [ D ¯ ν / m ¯ 2 + ( ν / y ) ] ξ ν ( y ) - ξ ν - 1 ( y ) ,
b ¯ ν = [ m ¯ 2 / G ¯ ν + ( ν / y ) ] ψ ν ( y ) - ψ ν - 1 ( y ) [ m ¯ 2 / G ¯ ν + ( ν / y ) ] ξ ν ( y ) - ξ ν - 1 ( y ) ,
D ¯ ν = D ν ( m ¯ 2 y ) - A ν X ( m ¯ 2 y ) / ψ ν ( m ¯ 2 y ) 1 - A ν X ν ( m ¯ 2 y ) / ψ ν ( m ¯ 2 y ) , G ¯ ν = D ν ( m ¯ 2 y ) - B ν X ν ( m ¯ 2 y ) / ψ ν ( m ¯ 2 y ) 1 - B ν X ν ( m ¯ 2 y ) / ψ ν ( m ¯ 2 y ) ,
A ν = ψ ν ( m ¯ 2 x ) m ¯ r D ν ( m ¯ 1 x ) - D ν ( m ¯ 2 x ) m ¯ r D ν ( m ¯ 1 x ) X ν ( m ¯ 2 x ) - X ν ( m ¯ 2 x ) , B ν = ψ ν ( m ¯ 2 x ) m ¯ r D ν ( m ¯ 2 x ) - D ν ( m ¯ 1 x ) m ¯ r X ν ( m ¯ 2 x ) - D ν ( m ¯ 1 x ) X ν ( m ¯ 2 x ) .
m e = m ¯ 2 [ m ¯ 1 2 + 2 m ¯ 2 2 + 2 ( m ¯ 1 2 - m ¯ 2 2 ) m ¯ 1 2 + 2 m ¯ 2 2 - ( m ¯ 1 2 - m ¯ 2 2 ) ] 1 / 2 .
D T = K B T 6 π μ r C s .
Γ = D T q 2 ,
q = 4 π λ sin ( θ ) .
C ( t ) = B { 1 + b 0 [ 0 G ( Γ ) exp ( - Γ t ) d Γ ] 2 } ,
Γ ¯ = r = 0 r 6 Γ P ( r ) d r r = 0 r 6 P ( r ) d r ,
Q = r = 0 r 6 ( Γ - Γ ¯ ) 2 P ( r ) d r Γ ¯ 2 r = 0 r 6 P ( r ) d r .
ln [ C ( m Δ t ) - B ] = ln α - 2 Γ ¯ ( m Δ t ) + Q Γ ¯ 2 ( m Δ t ) 2 ,
Γ ¯ M = 0 i V V Γ P ( r ) d r 0 i V V P ( r ) d r ,
Q ¯ M = 0 i V V ( Γ - Γ ¯ ) 2 P ( r ) d r Γ ¯ 2 0 i V V P ( r ) d r ,

Metrics