Abstract

A particle sizing counter suitable for in situ measurements in two-phase flows is presented in a two-part sequence. The technique employs near forwardscatter from the focus of a He–Ne laser beam, together with pulse-height analysis of the signals from individual particles. A novel and essential feature of the technique is a numerical inversion scheme to unfold the dependence of the scattered signals on particle trajectory through the measurement volume. This feature allows the capability of truly in situ measurements with a working space of 50 cm between optical elements. The inversion procedure is performed by an on-line computer or microprocessor unit and uses a prior calibration with monodisperse aerosols of known size. As presently configured, the instrument has a demonstrated capability of determining size distributions in the 1–30-μm diam range, at concentrations up to ~105 cm−3 in flows of temperatures up to 1600 K. The measured dependence of response on particle diameter agrees well with calculations from the Mie scattering theory. It is anticipated that the technique can be extended to cover particle diameters in the 0.5–50-μm range with concentrations up to 106 cm−3. Adaptation to measurements of absorbing and irregular particles can be achieved by a straightforward calibration technique. Part 1 describes the trade offs in the optical design and develops the numerical inversion scheme. Part 2 discusses experimental measurements at ambient conditions and combustion temperatures (1600 K). An assessment of the accuracy of the technique is also presented.

© 1979 Optical Society of America

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References

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  1. R. D. Cadle, Measurement of Airborne Particles (Wiley, New York, 1975).
  2. T. Allen, Particle Size Measurement (Halsted Press, New York, 1975).
  3. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  4. M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  5. C. McCreath, M. Roett, N. Chigier, J. Phys. E 5, 601 (1972).
    [CrossRef]
  6. R. Belz, N. Dougherty, “In-Line Holography of Reacting Liquid Sprays,” in Proceedings of the Engineering Applications of Holography, Los Angeles, California (1972).
  7. J. Hodkinson, “Optical Measurement of Aerosols,” in Aerosol Science, C. Davies, Ed. (Academic, New York, 1966).
  8. D. Holve, S. Self, “Optical Measurements of Mean Particle Size in the Exhaust of a Coal-Fired MHD Generator,” Fall Meeting of the Western States Section of the Combustion Institute, La Jolla, California (1976).
  9. R. Dobbins, L. Crocco, I. Glassman, AIAA J. 1, 1882 (1963).
    [CrossRef]
  10. A. L. Wertheimer, W. L. Wilcock, Appl. Opt. 15, 1616 (1976).
    [CrossRef] [PubMed]
  11. J. Swithenbank, J. Beer, D. Taylor, “Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” AIAA Fourteenth Aerospace Science Meeting, Washington, D.C. (1976).
  12. B. Liu, R. Berglund, J. Agarwal, Atmos. Environ. 8, 717 (1974).
    [CrossRef]
  13. D. D. Cooke, M. Kerker, Appl. Opt. 14, 734 (1975).
    [CrossRef] [PubMed]
  14. R. G. Knollenberg, Sampling Aerosol by In Situ Versus Standard Methods: Some Results from Recent Experiments and Developmental Work (Particle Measuring Systems, Inc., Boulder, Colorado 80301), 1978.
  15. W. M. Farmer, Appl. Opt. 11, 2603 (1972).
    [CrossRef] [PubMed]
  16. W. M. Farmer, Appl. Opt. 13, 610 (1974).
    [CrossRef] [PubMed]
  17. F. Durst, “Development and Application of Optical Anemometer,” Ph.D. Thesis, U. London (1972).
  18. R. J. Adrian, K. L. Orloff, Appl. Opt. 16, 677 (1977).
    [CrossRef] [PubMed]
  19. R. Adrian, W. Early, in Proceedings of the Minnesota Symposium on Laser Anemometry (U. Minnesota, Department of Conferences, Minneapolis, 1976), p. 426.
  20. E. Hirleman, S. Wittig, “In Situ Optical Measurement of Automobile Exhaust Gas Particulate Size Distributions: Regular Fuel and Methanol Mixtures,” Sixteenth International Symposium on Combustion, MIT (1976).
  21. J. Hodkinson, I. Greenleaves, J. Opt. Soc. Am. 53, 577 (1963).
    [CrossRef]
  22. A. Lieberman, R. Allen, “Theoretical and Experimental Light-Scattering Data for a Near Forward System,” presented at the American Association for Contamination Control, 19–22 May (1969).
  23. F. Oeseburg, J. Aerosol Sci. 3, 307 (1972).
    [CrossRef]
  24. J. V. Davé, “Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere,” IBM Palo Alto Scientific Center Report 320-3237, May1968.
  25. P. Ariessohn, Stanford University; private communication.
  26. R. Brooks, G. Chiro, Phys. Med. Biol. 21, 689 (1976).
    [CrossRef] [PubMed]
  27. C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

1977

1976

1975

1974

W. M. Farmer, Appl. Opt. 13, 610 (1974).
[CrossRef] [PubMed]

B. Liu, R. Berglund, J. Agarwal, Atmos. Environ. 8, 717 (1974).
[CrossRef]

1972

F. Oeseburg, J. Aerosol Sci. 3, 307 (1972).
[CrossRef]

C. McCreath, M. Roett, N. Chigier, J. Phys. E 5, 601 (1972).
[CrossRef]

W. M. Farmer, Appl. Opt. 11, 2603 (1972).
[CrossRef] [PubMed]

1963

R. Dobbins, L. Crocco, I. Glassman, AIAA J. 1, 1882 (1963).
[CrossRef]

J. Hodkinson, I. Greenleaves, J. Opt. Soc. Am. 53, 577 (1963).
[CrossRef]

Adrian, R.

R. Adrian, W. Early, in Proceedings of the Minnesota Symposium on Laser Anemometry (U. Minnesota, Department of Conferences, Minneapolis, 1976), p. 426.

Adrian, R. J.

Agarwal, J.

B. Liu, R. Berglund, J. Agarwal, Atmos. Environ. 8, 717 (1974).
[CrossRef]

Allen, R.

A. Lieberman, R. Allen, “Theoretical and Experimental Light-Scattering Data for a Near Forward System,” presented at the American Association for Contamination Control, 19–22 May (1969).

Allen, T.

T. Allen, Particle Size Measurement (Halsted Press, New York, 1975).

Ariessohn, P.

P. Ariessohn, Stanford University; private communication.

Beer, J.

J. Swithenbank, J. Beer, D. Taylor, “Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” AIAA Fourteenth Aerospace Science Meeting, Washington, D.C. (1976).

Belz, R.

R. Belz, N. Dougherty, “In-Line Holography of Reacting Liquid Sprays,” in Proceedings of the Engineering Applications of Holography, Los Angeles, California (1972).

Berglund, R.

B. Liu, R. Berglund, J. Agarwal, Atmos. Environ. 8, 717 (1974).
[CrossRef]

Brooks, R.

R. Brooks, G. Chiro, Phys. Med. Biol. 21, 689 (1976).
[CrossRef] [PubMed]

Cadle, R. D.

R. D. Cadle, Measurement of Airborne Particles (Wiley, New York, 1975).

Chigier, N.

C. McCreath, M. Roett, N. Chigier, J. Phys. E 5, 601 (1972).
[CrossRef]

Chiro, G.

R. Brooks, G. Chiro, Phys. Med. Biol. 21, 689 (1976).
[CrossRef] [PubMed]

Cooke, D. D.

Crocco, L.

R. Dobbins, L. Crocco, I. Glassman, AIAA J. 1, 1882 (1963).
[CrossRef]

Davé, J. V.

J. V. Davé, “Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere,” IBM Palo Alto Scientific Center Report 320-3237, May1968.

Dobbins, R.

R. Dobbins, L. Crocco, I. Glassman, AIAA J. 1, 1882 (1963).
[CrossRef]

Dougherty, N.

R. Belz, N. Dougherty, “In-Line Holography of Reacting Liquid Sprays,” in Proceedings of the Engineering Applications of Holography, Los Angeles, California (1972).

Durst, F.

F. Durst, “Development and Application of Optical Anemometer,” Ph.D. Thesis, U. London (1972).

Early, W.

R. Adrian, W. Early, in Proceedings of the Minnesota Symposium on Laser Anemometry (U. Minnesota, Department of Conferences, Minneapolis, 1976), p. 426.

Farmer, W. M.

Glassman, I.

R. Dobbins, L. Crocco, I. Glassman, AIAA J. 1, 1882 (1963).
[CrossRef]

Greenleaves, I.

Hanson, R.

C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Hirleman, E.

E. Hirleman, S. Wittig, “In Situ Optical Measurement of Automobile Exhaust Gas Particulate Size Distributions: Regular Fuel and Methanol Mixtures,” Sixteenth International Symposium on Combustion, MIT (1976).

Hodkinson, J.

J. Hodkinson, I. Greenleaves, J. Opt. Soc. Am. 53, 577 (1963).
[CrossRef]

J. Hodkinson, “Optical Measurement of Aerosols,” in Aerosol Science, C. Davies, Ed. (Academic, New York, 1966).

Holve, D.

D. Holve, S. Self, “Optical Measurements of Mean Particle Size in the Exhaust of a Coal-Fired MHD Generator,” Fall Meeting of the Western States Section of the Combustion Institute, La Jolla, California (1976).

Kerker, M.

D. D. Cooke, M. Kerker, Appl. Opt. 14, 734 (1975).
[CrossRef] [PubMed]

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

Knollenberg, R. G.

R. G. Knollenberg, Sampling Aerosol by In Situ Versus Standard Methods: Some Results from Recent Experiments and Developmental Work (Particle Measuring Systems, Inc., Boulder, Colorado 80301), 1978.

Lawson, C.

C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Lieberman, A.

A. Lieberman, R. Allen, “Theoretical and Experimental Light-Scattering Data for a Near Forward System,” presented at the American Association for Contamination Control, 19–22 May (1969).

Liu, B.

B. Liu, R. Berglund, J. Agarwal, Atmos. Environ. 8, 717 (1974).
[CrossRef]

McCreath, C.

C. McCreath, M. Roett, N. Chigier, J. Phys. E 5, 601 (1972).
[CrossRef]

Oeseburg, F.

F. Oeseburg, J. Aerosol Sci. 3, 307 (1972).
[CrossRef]

Orloff, K. L.

Roett, M.

C. McCreath, M. Roett, N. Chigier, J. Phys. E 5, 601 (1972).
[CrossRef]

Self, S.

D. Holve, S. Self, “Optical Measurements of Mean Particle Size in the Exhaust of a Coal-Fired MHD Generator,” Fall Meeting of the Western States Section of the Combustion Institute, La Jolla, California (1976).

Swithenbank, J.

J. Swithenbank, J. Beer, D. Taylor, “Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” AIAA Fourteenth Aerospace Science Meeting, Washington, D.C. (1976).

Taylor, D.

J. Swithenbank, J. Beer, D. Taylor, “Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” AIAA Fourteenth Aerospace Science Meeting, Washington, D.C. (1976).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wertheimer, A. L.

Wilcock, W. L.

Wittig, S.

E. Hirleman, S. Wittig, “In Situ Optical Measurement of Automobile Exhaust Gas Particulate Size Distributions: Regular Fuel and Methanol Mixtures,” Sixteenth International Symposium on Combustion, MIT (1976).

AIAA J.

R. Dobbins, L. Crocco, I. Glassman, AIAA J. 1, 1882 (1963).
[CrossRef]

Appl. Opt.

Atmos. Environ.

B. Liu, R. Berglund, J. Agarwal, Atmos. Environ. 8, 717 (1974).
[CrossRef]

J. Aerosol Sci.

F. Oeseburg, J. Aerosol Sci. 3, 307 (1972).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. E

C. McCreath, M. Roett, N. Chigier, J. Phys. E 5, 601 (1972).
[CrossRef]

Phys. Med. Biol.

R. Brooks, G. Chiro, Phys. Med. Biol. 21, 689 (1976).
[CrossRef] [PubMed]

Other

C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

R. Belz, N. Dougherty, “In-Line Holography of Reacting Liquid Sprays,” in Proceedings of the Engineering Applications of Holography, Los Angeles, California (1972).

J. Hodkinson, “Optical Measurement of Aerosols,” in Aerosol Science, C. Davies, Ed. (Academic, New York, 1966).

D. Holve, S. Self, “Optical Measurements of Mean Particle Size in the Exhaust of a Coal-Fired MHD Generator,” Fall Meeting of the Western States Section of the Combustion Institute, La Jolla, California (1976).

R. D. Cadle, Measurement of Airborne Particles (Wiley, New York, 1975).

T. Allen, Particle Size Measurement (Halsted Press, New York, 1975).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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

J. V. Davé, “Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere,” IBM Palo Alto Scientific Center Report 320-3237, May1968.

P. Ariessohn, Stanford University; private communication.

J. Swithenbank, J. Beer, D. Taylor, “Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” AIAA Fourteenth Aerospace Science Meeting, Washington, D.C. (1976).

R. G. Knollenberg, Sampling Aerosol by In Situ Versus Standard Methods: Some Results from Recent Experiments and Developmental Work (Particle Measuring Systems, Inc., Boulder, Colorado 80301), 1978.

F. Durst, “Development and Application of Optical Anemometer,” Ph.D. Thesis, U. London (1972).

R. Adrian, W. Early, in Proceedings of the Minnesota Symposium on Laser Anemometry (U. Minnesota, Department of Conferences, Minneapolis, 1976), p. 426.

E. Hirleman, S. Wittig, “In Situ Optical Measurement of Automobile Exhaust Gas Particulate Size Distributions: Regular Fuel and Methanol Mixtures,” Sixteenth International Symposium on Combustion, MIT (1976).

A. Lieberman, R. Allen, “Theoretical and Experimental Light-Scattering Data for a Near Forward System,” presented at the American Association for Contamination Control, 19–22 May (1969).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the optical system.

Fig. 2
Fig. 2

Response function for a Royco counter using white light illumination.

Fig. 3
Fig. 3

Scattered light collection geometry for the present optical system.

Fig. 4
Fig. 4

Variation of response function with θL for θc = 4°, n1 = 1.6, and n2 = 0.0.

Fig. 5
Fig. 5

Variation of response function with θc for θL = 20°, n1 = 1.6, and n2 = 0.0.

Fig. 6
Fig. 6

Variation of response function with complex refractive index n2 (absorption) for θc = 4°, θL = 20°, and n1 = 1.6.

Fig. 7
Fig. 7

Variation of response function with complex refractive index n2 (absorption) for θc = 1°, θL = 20°, and n1 = 1.6.

Fig. 8
Fig. 8

Schematic of a quadrant of the measurement volume function J(x,z,d).

Fig. 9
Fig. 9

Schematic of ΔSl corresponding to Jl of Fig. 8.

Tables (1)

Tables Icon

Table 1 Resonance Widths for Fig. 4(b)

Equations (69)

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I ( r , z ) = ( 2 P / π w 2 ) exp [ - 2 ( r / w ) 2 ] ,
w ( z ) = w 0 [ 1 + ( λ z / π w 0 2 ) 2 ] 1 / 2 .
w 0 = λ / π θ b .
z R = π w 0 2 / λ .
I diff = α 2 4 π [ 2 J 1 ( α sin θ ) α sin θ ] 2 ,
I int = 2 π 0 θ I diff sin θ d θ = 1 - J 0 2 ( α sin θ ) - J 1 2 ( α sin θ ) .
I = 1 k 2 r 2 F ( α , θ , n ) · I 0 ,
I | I e I r u v | ,
F | M 2 0 0 0 0 M 1 0 0 0 0 S 21 D 21 0 0 D 21 S 21 | .
I = 1 k 2 r 2 ( M 1 + M 2 2 ) I 0 .
P = I 0 λ 2 4 π 2 Ω ( M 1 + M 2 2 ) d Ω ,
= I 0 λ 2 4 π 2 F ( α , n ˜ , Ω ) ,
F ( α , n , Ω ) = Ω ( M 1 + M 2 2 ) d Ω
J ( x , z , α ) = I 0 ( x , y ) H ( x , z , α ) .
A = G · ( λ 2 / 4 π 2 ) J ( x , z , α ) F ( α ) ,
J ¯ = J / J m             ( 0 J ¯ 1 ) .
F ¯ = F / F m             ( 0 F ¯ 1 ) ,
A m = G ( λ 2 / 4 π 2 ) J m F m ,
A ¯ = A / A m             ( 0 A ¯ 1 ) ,
A ¯ = J F ¯ .
C 1 = j = 1 m U Δ S 1 j N j , C i = j = 1 m U Δ S i j N j , C m = j = 1 m U Δ S m j N j , }
C = U Δ S · N .
A ¯ i + 1 = ( A ¯ i + Δ A ¯ i ) and F ¯ j + 1 = ( F ¯ j + Δ F ¯ j ) .
A ¯ k = J ¯ m F ¯ k ,
N = ( 1 / U ) Δ S - 1 · C
Δ A ¯ k A ¯ k = β = constant , i . e . , A ¯ k + 1 = ( 1 + β ) A ¯ k ( for all k ) .
( Δ F ¯ k ) / ( F ¯ k ) = β , i . e . , F ¯ k + 1 = ( 1 + β ) F ¯ k             ( for all k ) .
C i = U Δ S i k N k ,
C i = U Δ S l N m ,             l = 1 , m .
i = 1 m C i = U i = l m Δ S i N m ,
C l , m = U S l , m N m .
S l , m i = l m Δ S i .
J ¯ l = 1 ( 1 + β ) m - l = 1 ( 1 + β ) r ,
i = 1 m C i ,
P ( n , x ) x n exp ( - x ) n ! ,
x i = 1 m C i τ .
P int = 1 - exp - ( i = 1 m C i τ ) .
P int i = 1 m C i τ .
i = 1 m C i = U { N 1 Δ S m + N 2 ( Δ S m + Δ S m - 1 ) + + N m ( Δ S m + + Δ S 1 ) } = U j = 1 m N j l = m - j + 1 m Δ S l = U j = 1 m N j S ( m - j + 1 ) , m .
P int = U τ j = 1 m N j S ( m - j + 1 ) , m .
S ( m - j + 1 ) , m l = m - j + 1 m Δ S l = j Δ S ,
P int U τ Δ S j = 1 m j N j .
P int V m j = 1 m ( j / m ) N j ,
V m = L S m L m Δ S
P int V m N T ( j ¯ / m ) ,
N T = j = 1 m N j
j ¯ = j - 1 m j N j j - 1 m N j
S m = p S R l n ( d max / d min ) .
N ( d ) = k d - q ,
N j = d j d j + Δ d j N ( d ) δ d k Δ d j d j q .
Δ d j ( β / p ) d j ,
N j k ( β / p ) d j q - 1 .
N j = k ( β / p ) = constant , j ¯ = 1 m j = 1 m j = ( m + 1 ) 2 ,
N j k ( β / p ) d min ( q - 1 ) ( d max / d min ) ( j - 1 ) ( q - 1 ) / ( m - 1 ) .
j ¯ 1 [ ( d max / d max ) ( q - 1 ) / ( m - 1 ) - 1 ] + [ ( d max / d min ) ( q - 1 ) - ( m + 1 ) ] ( d max / d min ) ( q - 1 ) - 1 ] .
j ¯ ( m - 1 ) ( q - 1 ) ln ( d max / d min ) ,
P int p ( q - 1 ) L S R N T p V R N T ( q - 1 ) .
A ¯ k + 1 = ( 1 + β ) A ¯ k = F ¯ k + 1 = ( 1 + β ) F ¯ k , Δ A ¯ k A ¯ k = Δ F ¯ k F ¯ k = β }
J ¯ l + 1 = ( J ¯ l + Δ J ¯ l ) = ( 1 + β ) J ¯ l , Δ J l J l = β . }
A ¯ i = J ¯ l F ¯ j .
A ¯ i + 1 = J ¯ l F ¯ j + 1 .
Δ S i j = Δ S i + 1 , j + 1 = Δ S l ,
Δ S i j = Δ S m - ( j - i ) .
C m - r , r = U S m - r , m N m .
C k - r , k = U S k - r , k N k ,
S k - r , r = S m - R , r ,
C l = U Δ S l N m .
C i = U Δ S l N k ,
Δ S m - ( k - i ) S k - r , k = C i C k - r , k ,             i = 1 , k .

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