Abstract

The size and the position of individual particles in a falling spray crossing a horizontal plane are measured simultaneously with a shadowgraph imaging setup. An original method for measurement of drop sizes based on a prescribed analytical form of the luminance distribution of the objects (i.e., the drops) is presented. The processing time is strongly reduced compared with that for the usual inversion techniques. The turbulent dispersion of drops in a grid-generated turbulence is studied. Evidence for the presence of coalescence in the spray is presented.

© 1998 Optical Society of America

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References

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  1. P. Bruna, “Mise au point d’une méthode originale de détermination des probabilités de présence particulaire dans un écoulement turbulent,” Ph.D. dissertation (University of Rouen, Rouen, France, 1988).
  2. J. B. Blaisot, D. Allano, C. Ozkul, M. Ledoux.“Détermination de la position 2d et de la taille d’objets dans un volume de mesure dynamique par balayage d’images incohérentes à l’aide de barrettes de photodiodes,” in OPTO’91: 11èmes Journées Professionnelles Optoélectronique (ESI Publications, Paris, 1991).
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  4. B. M. Welsh, R. N. VonNiederhausern, “Performance analysis of the self-referenced speckle-holography image reconstruction technique,” Appl. Opt. 32, 5071–5078 (1993).
    [CrossRef] [PubMed]
  5. C. E. Shannon, “A mathematical theory of information,” Bell Syst. Tech. J. 27, 623–656 (1948).
  6. E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev. 106, 620–630 (1957).
    [CrossRef]
  7. E. T. Jaynes, “Information theory and statistical mechanics. II,” Phys. Rev. 108, 171–190 (1957).
    [CrossRef]
  8. N. L. Bonavito, J. E. Dorband, T. Busse, “Maximum entropy restoration of blurred and oversaturated hubble space telescope imagery,” Appl. Opt. 32, 5768–5774 (1993).
    [CrossRef] [PubMed]
  9. R. A. Gonsalves, H. M. Kao, “Entropy-based algorithm for reducing artifacts in image restoration,” Opt. Eng. 26, 617–622 (1987).
    [CrossRef]
  10. B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc. of Am. 62, 511–518 (1972).
    [CrossRef]
  11. V. M. Bove, “Entropy-based depth from focus,” Opt. Soc. Am. A 10, 561–566 (1993).
    [CrossRef]
  12. A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Analy. Mach. Intell. PAMI-5, 523–531 (1987).
    [CrossRef]
  13. A. Maréchal, M. Françon, Diffraction, Structure des Images (Masson, Paris, 1970).
  14. J. B. Blaisot, D. Allano, M. Ledoux, “Simultaneous determination of the position and size of a particle through an imaging technique,” in ILASS-Europe92: Eighth Annual European Conference on Liquid Atomization and Spray Systems, M. Afghan, ed. (Shell Laboratorium, Amsterdam, 1992), pp. 271–276.
  15. R. Clift, J. R. Grace, M. E. Weber, Bubbles, Drops and Particles (Academic, New York, 1978).
  16. J. B. Blaisot, “Développement d’une méthode de mesure simultanée de la taille et de la position de particules dans un écoulement turbulent,” Ph.D. dissertation (University of Rouen, Rouen, France, 1992).
  17. J. B. Blaisot, M. Ledoux, D. Allano, C. Ozkul, “Measurement of droplet size distribution and dispersion by an imaging technique,” in ILASS-Europe91: Sprays and Aerosols’91, W. Balachandran, ed. (Guildford U. Press, Guildford, University of Surrey, 1991), pp. 37–41.
  18. L. Rayleigh, “On the instability of jets,” Proc. London Math. Soc. 10, 5–18 (1879).
  19. J. M. Schneider, C. D. Hendricks, “Source of uniform-sized droplets,” Rev. Sci. Instrum. 35, 1349–1350 (1964).
    [CrossRef]
  20. N. R. Lindblad, J. M. Schneider, “Production of uniformed-sized liquid droplets,” J. Sci. Instrum. 42, 635–638 (1965).
    [CrossRef]
  21. C. Maquet, M. Trinité, M. Ledoux, “Dispersion of monosized heavy particles in grid turbulence. effects of body forces,” Part. Part. Syst. Charact. 7, 136–143 (1990).
    [CrossRef]
  22. J. O. Hinze, Turbulence: An Introduction to Its Mechanism and Theory (McGraw-Hill, New York, 1959).

1993 (3)

1990 (1)

C. Maquet, M. Trinité, M. Ledoux, “Dispersion of monosized heavy particles in grid turbulence. effects of body forces,” Part. Part. Syst. Charact. 7, 136–143 (1990).
[CrossRef]

1987 (2)

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Analy. Mach. Intell. PAMI-5, 523–531 (1987).
[CrossRef]

R. A. Gonsalves, H. M. Kao, “Entropy-based algorithm for reducing artifacts in image restoration,” Opt. Eng. 26, 617–622 (1987).
[CrossRef]

1972 (1)

B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc. of Am. 62, 511–518 (1972).
[CrossRef]

1965 (1)

N. R. Lindblad, J. M. Schneider, “Production of uniformed-sized liquid droplets,” J. Sci. Instrum. 42, 635–638 (1965).
[CrossRef]

1964 (1)

J. M. Schneider, C. D. Hendricks, “Source of uniform-sized droplets,” Rev. Sci. Instrum. 35, 1349–1350 (1964).
[CrossRef]

1957 (2)

E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev. 106, 620–630 (1957).
[CrossRef]

E. T. Jaynes, “Information theory and statistical mechanics. II,” Phys. Rev. 108, 171–190 (1957).
[CrossRef]

1948 (1)

C. E. Shannon, “A mathematical theory of information,” Bell Syst. Tech. J. 27, 623–656 (1948).

1879 (1)

L. Rayleigh, “On the instability of jets,” Proc. London Math. Soc. 10, 5–18 (1879).

Allano, D.

J. B. Blaisot, D. Allano, C. Ozkul, M. Ledoux.“Détermination de la position 2d et de la taille d’objets dans un volume de mesure dynamique par balayage d’images incohérentes à l’aide de barrettes de photodiodes,” in OPTO’91: 11èmes Journées Professionnelles Optoélectronique (ESI Publications, Paris, 1991).

J. B. Blaisot, D. Allano, M. Ledoux, “Simultaneous determination of the position and size of a particle through an imaging technique,” in ILASS-Europe92: Eighth Annual European Conference on Liquid Atomization and Spray Systems, M. Afghan, ed. (Shell Laboratorium, Amsterdam, 1992), pp. 271–276.

J. B. Blaisot, M. Ledoux, D. Allano, C. Ozkul, “Measurement of droplet size distribution and dispersion by an imaging technique,” in ILASS-Europe91: Sprays and Aerosols’91, W. Balachandran, ed. (Guildford U. Press, Guildford, University of Surrey, 1991), pp. 37–41.

Blaisot, J. B.

J. B. Blaisot, “Développement d’une méthode de mesure simultanée de la taille et de la position de particules dans un écoulement turbulent,” Ph.D. dissertation (University of Rouen, Rouen, France, 1992).

J. B. Blaisot, M. Ledoux, D. Allano, C. Ozkul, “Measurement of droplet size distribution and dispersion by an imaging technique,” in ILASS-Europe91: Sprays and Aerosols’91, W. Balachandran, ed. (Guildford U. Press, Guildford, University of Surrey, 1991), pp. 37–41.

J. B. Blaisot, D. Allano, C. Ozkul, M. Ledoux.“Détermination de la position 2d et de la taille d’objets dans un volume de mesure dynamique par balayage d’images incohérentes à l’aide de barrettes de photodiodes,” in OPTO’91: 11èmes Journées Professionnelles Optoélectronique (ESI Publications, Paris, 1991).

J. B. Blaisot, D. Allano, M. Ledoux, “Simultaneous determination of the position and size of a particle through an imaging technique,” in ILASS-Europe92: Eighth Annual European Conference on Liquid Atomization and Spray Systems, M. Afghan, ed. (Shell Laboratorium, Amsterdam, 1992), pp. 271–276.

Bonavito, N. L.

Bove, V. M.

V. M. Bove, “Entropy-based depth from focus,” Opt. Soc. Am. A 10, 561–566 (1993).
[CrossRef]

Bruna, P.

P. Bruna, “Mise au point d’une méthode originale de détermination des probabilités de présence particulaire dans un écoulement turbulent,” Ph.D. dissertation (University of Rouen, Rouen, France, 1988).

Busse, T.

Clift, R.

R. Clift, J. R. Grace, M. E. Weber, Bubbles, Drops and Particles (Academic, New York, 1978).

Dorband, J. E.

Françon, M.

A. Maréchal, M. Françon, Diffraction, Structure des Images (Masson, Paris, 1970).

Frieden, B. R.

B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc. of Am. 62, 511–518 (1972).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, H. M. Kao, “Entropy-based algorithm for reducing artifacts in image restoration,” Opt. Eng. 26, 617–622 (1987).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Grace, J. R.

R. Clift, J. R. Grace, M. E. Weber, Bubbles, Drops and Particles (Academic, New York, 1978).

Hendricks, C. D.

J. M. Schneider, C. D. Hendricks, “Source of uniform-sized droplets,” Rev. Sci. Instrum. 35, 1349–1350 (1964).
[CrossRef]

Hinze, J. O.

J. O. Hinze, Turbulence: An Introduction to Its Mechanism and Theory (McGraw-Hill, New York, 1959).

Jaynes, E. T.

E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev. 106, 620–630 (1957).
[CrossRef]

E. T. Jaynes, “Information theory and statistical mechanics. II,” Phys. Rev. 108, 171–190 (1957).
[CrossRef]

Kao, H. M.

R. A. Gonsalves, H. M. Kao, “Entropy-based algorithm for reducing artifacts in image restoration,” Opt. Eng. 26, 617–622 (1987).
[CrossRef]

Ledoux, M.

C. Maquet, M. Trinité, M. Ledoux, “Dispersion of monosized heavy particles in grid turbulence. effects of body forces,” Part. Part. Syst. Charact. 7, 136–143 (1990).
[CrossRef]

J. B. Blaisot, M. Ledoux, D. Allano, C. Ozkul, “Measurement of droplet size distribution and dispersion by an imaging technique,” in ILASS-Europe91: Sprays and Aerosols’91, W. Balachandran, ed. (Guildford U. Press, Guildford, University of Surrey, 1991), pp. 37–41.

J. B. Blaisot, D. Allano, M. Ledoux, “Simultaneous determination of the position and size of a particle through an imaging technique,” in ILASS-Europe92: Eighth Annual European Conference on Liquid Atomization and Spray Systems, M. Afghan, ed. (Shell Laboratorium, Amsterdam, 1992), pp. 271–276.

Ledoux., M.

J. B. Blaisot, D. Allano, C. Ozkul, M. Ledoux.“Détermination de la position 2d et de la taille d’objets dans un volume de mesure dynamique par balayage d’images incohérentes à l’aide de barrettes de photodiodes,” in OPTO’91: 11èmes Journées Professionnelles Optoélectronique (ESI Publications, Paris, 1991).

Lindblad, N. R.

N. R. Lindblad, J. M. Schneider, “Production of uniformed-sized liquid droplets,” J. Sci. Instrum. 42, 635–638 (1965).
[CrossRef]

Maquet, C.

C. Maquet, M. Trinité, M. Ledoux, “Dispersion of monosized heavy particles in grid turbulence. effects of body forces,” Part. Part. Syst. Charact. 7, 136–143 (1990).
[CrossRef]

Maréchal, A.

A. Maréchal, M. Françon, Diffraction, Structure des Images (Masson, Paris, 1970).

Ozkul, C.

J. B. Blaisot, M. Ledoux, D. Allano, C. Ozkul, “Measurement of droplet size distribution and dispersion by an imaging technique,” in ILASS-Europe91: Sprays and Aerosols’91, W. Balachandran, ed. (Guildford U. Press, Guildford, University of Surrey, 1991), pp. 37–41.

J. B. Blaisot, D. Allano, C. Ozkul, M. Ledoux.“Détermination de la position 2d et de la taille d’objets dans un volume de mesure dynamique par balayage d’images incohérentes à l’aide de barrettes de photodiodes,” in OPTO’91: 11èmes Journées Professionnelles Optoélectronique (ESI Publications, Paris, 1991).

Pentland, A. P.

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Analy. Mach. Intell. PAMI-5, 523–531 (1987).
[CrossRef]

Rayleigh, L.

L. Rayleigh, “On the instability of jets,” Proc. London Math. Soc. 10, 5–18 (1879).

Schneider, J. M.

N. R. Lindblad, J. M. Schneider, “Production of uniformed-sized liquid droplets,” J. Sci. Instrum. 42, 635–638 (1965).
[CrossRef]

J. M. Schneider, C. D. Hendricks, “Source of uniform-sized droplets,” Rev. Sci. Instrum. 35, 1349–1350 (1964).
[CrossRef]

Shannon, C. E.

C. E. Shannon, “A mathematical theory of information,” Bell Syst. Tech. J. 27, 623–656 (1948).

Trinité, M.

C. Maquet, M. Trinité, M. Ledoux, “Dispersion of monosized heavy particles in grid turbulence. effects of body forces,” Part. Part. Syst. Charact. 7, 136–143 (1990).
[CrossRef]

VonNiederhausern, R. N.

Weber, M. E.

R. Clift, J. R. Grace, M. E. Weber, Bubbles, Drops and Particles (Academic, New York, 1978).

Welsh, B. M.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of information,” Bell Syst. Tech. J. 27, 623–656 (1948).

IEEE Trans. Pattern Analy. Mach. Intell. (1)

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Analy. Mach. Intell. PAMI-5, 523–531 (1987).
[CrossRef]

J. Opt. Soc. of Am. (1)

B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc. of Am. 62, 511–518 (1972).
[CrossRef]

J. Sci. Instrum. (1)

N. R. Lindblad, J. M. Schneider, “Production of uniformed-sized liquid droplets,” J. Sci. Instrum. 42, 635–638 (1965).
[CrossRef]

Opt. Eng. (1)

R. A. Gonsalves, H. M. Kao, “Entropy-based algorithm for reducing artifacts in image restoration,” Opt. Eng. 26, 617–622 (1987).
[CrossRef]

Opt. Soc. Am. A (1)

V. M. Bove, “Entropy-based depth from focus,” Opt. Soc. Am. A 10, 561–566 (1993).
[CrossRef]

Part. Part. Syst. Charact. (1)

C. Maquet, M. Trinité, M. Ledoux, “Dispersion of monosized heavy particles in grid turbulence. effects of body forces,” Part. Part. Syst. Charact. 7, 136–143 (1990).
[CrossRef]

Phys. Rev. (2)

E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev. 106, 620–630 (1957).
[CrossRef]

E. T. Jaynes, “Information theory and statistical mechanics. II,” Phys. Rev. 108, 171–190 (1957).
[CrossRef]

Proc. London Math. Soc. (1)

L. Rayleigh, “On the instability of jets,” Proc. London Math. Soc. 10, 5–18 (1879).

Rev. Sci. Instrum. (1)

J. M. Schneider, C. D. Hendricks, “Source of uniform-sized droplets,” Rev. Sci. Instrum. 35, 1349–1350 (1964).
[CrossRef]

Other (9)

A. Maréchal, M. Françon, Diffraction, Structure des Images (Masson, Paris, 1970).

J. B. Blaisot, D. Allano, M. Ledoux, “Simultaneous determination of the position and size of a particle through an imaging technique,” in ILASS-Europe92: Eighth Annual European Conference on Liquid Atomization and Spray Systems, M. Afghan, ed. (Shell Laboratorium, Amsterdam, 1992), pp. 271–276.

R. Clift, J. R. Grace, M. E. Weber, Bubbles, Drops and Particles (Academic, New York, 1978).

J. B. Blaisot, “Développement d’une méthode de mesure simultanée de la taille et de la position de particules dans un écoulement turbulent,” Ph.D. dissertation (University of Rouen, Rouen, France, 1992).

J. B. Blaisot, M. Ledoux, D. Allano, C. Ozkul, “Measurement of droplet size distribution and dispersion by an imaging technique,” in ILASS-Europe91: Sprays and Aerosols’91, W. Balachandran, ed. (Guildford U. Press, Guildford, University of Surrey, 1991), pp. 37–41.

P. Bruna, “Mise au point d’une méthode originale de détermination des probabilités de présence particulaire dans un écoulement turbulent,” Ph.D. dissertation (University of Rouen, Rouen, France, 1988).

J. B. Blaisot, D. Allano, C. Ozkul, M. Ledoux.“Détermination de la position 2d et de la taille d’objets dans un volume de mesure dynamique par balayage d’images incohérentes à l’aide de barrettes de photodiodes,” in OPTO’91: 11èmes Journées Professionnelles Optoélectronique (ESI Publications, Paris, 1991).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. O. Hinze, Turbulence: An Introduction to Its Mechanism and Theory (McGraw-Hill, New York, 1959).

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Figures (13)

Fig. 1
Fig. 1

Imaging system. The dashed line represents the limit of the illuminated zone.

Fig. 2
Fig. 2

Types of PSF used in computing the image profiles.

Fig. 3
Fig. 3

Comparison of computed and experimental image profiles: a/σ = 0.84. Theoretical profiles are computed for four PSF shapes.

Fig. 4
Fig. 4

Comparison of computed and experimental image profiles: a/σ = 0.54. Theoretical profiles are computed for four PSF shapes.

Fig. 5
Fig. 5

Theoretical contrast C and nondimensional image width L* versus object width a*.

Fig. 6
Fig. 6

Comparison of computed and experimental image parameters a/ L versus C.

Fig. 7
Fig. 7

Comparison of estimated image width and real image width for objects of known size.

Fig. 8
Fig. 8

Geometrical arrangement of the two optical sets used in measuring a spherical object.

Fig. 9
Fig. 9

Injection spray nozzle and wind tunnel. The vibrating wire is sufficiently small that the flow is not perturbed.

Fig. 10
Fig. 10

ppf of 240-μm droplets at streamwise location y/ M = 30.

Fig. 11
Fig. 11

Displacement variance of 240-μm droplet position versus streamwise location y/ M.

Fig. 12
Fig. 12

Histogram of size population at streamwise location y/ M = 70.

Fig. 13
Fig. 13

Coalescence effect. Comparison of the population of 310- and 240-μm droplets. A 310-μm droplet corresponds to the coalescence of two 240-μm droplets.

Tables (1)

Tables Icon

Table 1 Measurement of Coalescence Diameters

Equations (23)

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i x = o x s x ,
I ν = O ν S ν ,
o x ,   a = o * x / a ,
o * x / a = o * x / a = 1   | x / a | > 1 / 2 τ   otherwise .
s x ,   σ = s * x / σ .
i x ,   a ,   σ = - +   s * ξ σ o * x - ξ a d ξ .
i x ,   a ,   σ = σ   - +   s * η o * x / σ - η a / σ d η .
U x = - x   s * η d η ,
U = - +   s * η d η .
i * x σ ,   a σ = i x ,   a ,   σ σ U .
U i * x * ,   a * = U - 1 - τ U x * + a * 2 - U x * - a * 2 .
i * x * ,   a * = 1 - 1 - τ U ¯ x * + a * 2 - U ¯ x * - a * 2 ,
s 1 * x * = circ α 1 x * ,
circ x = 1   | x | < 1 / 2 0   otherwise .
s 2 * x * = sin 2 α 2 x * α 2 x * 2 = sinc 2 α 2 x *
s 3 * x * = J 1 2 α 3 x * α 3 x * 2
s 4 * x * = exp - α 4 x * 2 .
i min = 1 - 1 - τ 2 U ¯ a * / 2 - 1 ) , i mid = 1 - 1 - τ 2   [ 2 U ¯ a * / 2 - 1 .
C = 1 2 1 - τ 2 U ¯ a * / 2 - 1 - 1 .
i * x * = L 2 σ ,   a * = i mid ,
U ¯ L * + a * 2 - U ¯ L * - a * 2 = U ¯ a * 2 - 1 2 .
a * / L * = f 1 a * , C = f 2 a * .
a max 2 - a min 2 4 Δ y 2 ,

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