Abstract

A theoretical model based on the Lorenz-Mie theory was used to study the response characteristics of the Aerometrics phase Doppler particle analyzer (PDPA). The validity of the model was verified experimentally, and its suitability for calculating measurement uncertainties was established. The theoretical and experimental results suggest that size resolutions of the order of ±0.3 μm are possible when the PDPA is used to measure small spherical particles (< 10 μm). We show that the optical configuration of the PDPA plays an important role in establishing the sizing uncertainty of the instrument.

© 1991 Optical Society of America

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References

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  1. F. Durst, M. Zare, “Laser Doppler measurements in two-phase flows,” presented at the LDA Symposium, Copenhagen, 1975.
  2. W. D. Bachalo, M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
    [CrossRef]
  3. K. Bauckhage, H. H. Flogel, “Simultaneous measurements of droplet size and velocity in nozzle sprays,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).
  4. M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).
  5. S. A. M. Al-Chalabi, Y. Hardalupas, A. R. Jones, A. M. K. P. Taylor, “Calculation of calibration curves for the phase Doppler technique: comparison between Mie theory and geometrical optics,” in Proceedings of the International Symposium on Optical Particle Sizing: Theory and Practice (Université de Rouen, Rouen, France, 1987).
  6. Y. Hardalupas, A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).
  7. S. R. Martin, L. E. Drain, M. L. Yeoman, D. M. Livesley, “Resolution limits of the phase Doppler technique and its-extension to monitor non-ideal particles in two phase flows,” in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).
  8. W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,”in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).
  9. W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast, vector-speed computer codes,” Rep. NCAR/ TN-140 STR (National Center for Atmospheric Research, Boulder, Colo., June1979).
  10. M. Saffman, “The Use of Polarized Light for Optical Particle Sizing,” in Proceedings of the Third International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1986).

1988 (1)

Y. Hardalupas, A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

1984 (1)

W. D. Bachalo, M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

Al-Chalabi, S. A. M.

S. A. M. Al-Chalabi, Y. Hardalupas, A. R. Jones, A. M. K. P. Taylor, “Calculation of calibration curves for the phase Doppler technique: comparison between Mie theory and geometrical optics,” in Proceedings of the International Symposium on Optical Particle Sizing: Theory and Practice (Université de Rouen, Rouen, France, 1987).

Bachalo, W. D.

W. D. Bachalo, M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,”in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

Bauckhage, K.

K. Bauckhage, H. H. Flogel, “Simultaneous measurements of droplet size and velocity in nozzle sprays,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).

Buchhave, P.

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).

Drain, L. E.

S. R. Martin, L. E. Drain, M. L. Yeoman, D. M. Livesley, “Resolution limits of the phase Doppler technique and its-extension to monitor non-ideal particles in two phase flows,” in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

Durst, F.

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flows,” presented at the LDA Symposium, Copenhagen, 1975.

Flogel, H. H.

K. Bauckhage, H. H. Flogel, “Simultaneous measurements of droplet size and velocity in nozzle sprays,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).

Hardalupas, Y.

Y. Hardalupas, A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

S. A. M. Al-Chalabi, Y. Hardalupas, A. R. Jones, A. M. K. P. Taylor, “Calculation of calibration curves for the phase Doppler technique: comparison between Mie theory and geometrical optics,” in Proceedings of the International Symposium on Optical Particle Sizing: Theory and Practice (Université de Rouen, Rouen, France, 1987).

Houser, M. J.

W. D. Bachalo, M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

Jones, A. R.

S. A. M. Al-Chalabi, Y. Hardalupas, A. R. Jones, A. M. K. P. Taylor, “Calculation of calibration curves for the phase Doppler technique: comparison between Mie theory and geometrical optics,” in Proceedings of the International Symposium on Optical Particle Sizing: Theory and Practice (Université de Rouen, Rouen, France, 1987).

Livesley, D. M.

S. R. Martin, L. E. Drain, M. L. Yeoman, D. M. Livesley, “Resolution limits of the phase Doppler technique and its-extension to monitor non-ideal particles in two phase flows,” in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

Martin, S. R.

S. R. Martin, L. E. Drain, M. L. Yeoman, D. M. Livesley, “Resolution limits of the phase Doppler technique and its-extension to monitor non-ideal particles in two phase flows,” in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

Saffman, M.

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).

M. Saffman, “The Use of Polarized Light for Optical Particle Sizing,” in Proceedings of the Third International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1986).

Sankar, S. V.

W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,”in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

Tanger, H.

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).

Taylor, A. M. K. P.

Y. Hardalupas, A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

S. A. M. Al-Chalabi, Y. Hardalupas, A. R. Jones, A. M. K. P. Taylor, “Calculation of calibration curves for the phase Doppler technique: comparison between Mie theory and geometrical optics,” in Proceedings of the International Symposium on Optical Particle Sizing: Theory and Practice (Université de Rouen, Rouen, France, 1987).

Wiscombe, W. J.

W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast, vector-speed computer codes,” Rep. NCAR/ TN-140 STR (National Center for Atmospheric Research, Boulder, Colo., June1979).

Yeoman, M. L.

S. R. Martin, L. E. Drain, M. L. Yeoman, D. M. Livesley, “Resolution limits of the phase Doppler technique and its-extension to monitor non-ideal particles in two phase flows,” in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

Zare, M.

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flows,” presented at the LDA Symposium, Copenhagen, 1975.

Exp. Fluids (1)

Y. Hardalupas, A. M. K. P. Taylor, “The identification of LDA seeding particles by the phase-Doppler technique,” Exp. Fluids 6, 137–140 (1988).

Opt. Eng. (1)

W. D. Bachalo, M. J. Houser, “Phase Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

Other (8)

K. Bauckhage, H. H. Flogel, “Simultaneous measurements of droplet size and velocity in nozzle sprays,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).

M. Saffman, P. Buchhave, H. Tanger, “Simultaneous measurements of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings of the Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1984).

S. A. M. Al-Chalabi, Y. Hardalupas, A. R. Jones, A. M. K. P. Taylor, “Calculation of calibration curves for the phase Doppler technique: comparison between Mie theory and geometrical optics,” in Proceedings of the International Symposium on Optical Particle Sizing: Theory and Practice (Université de Rouen, Rouen, France, 1987).

S. R. Martin, L. E. Drain, M. L. Yeoman, D. M. Livesley, “Resolution limits of the phase Doppler technique and its-extension to monitor non-ideal particles in two phase flows,” in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

W. D. Bachalo, S. V. Sankar, “Analysis of the light scattering interferometry for spheres larger than the light wavelength,”in Proceedings of the Fourth International Symposium on the Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1988).

W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast, vector-speed computer codes,” Rep. NCAR/ TN-140 STR (National Center for Atmospheric Research, Boulder, Colo., June1979).

M. Saffman, “The Use of Polarized Light for Optical Particle Sizing,” in Proceedings of the Third International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Instituto Superior Técnico, Lisbon, 1986).

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flows,” presented at the LDA Symposium, Copenhagen, 1975.

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Figures (14)

Fig. 1
Fig. 1

Coordinate system chosen for the theoretical analyses.

Fig. 2
Fig. 2

Schematic of the receiving aperture of the PDPA showing the three areas from which useful information is obtained.

Fig. 3
Fig. 3

Experimental setup for dispersing PSL particles in air.

Fig. 4
Fig. 4

Predicted PDPA response curves for sizing fine water droplets at a mean scattering angle of 30°. The PDPA optical configuration consists of a 500-mm focal length, f/4.7 receiver lens and laser beam (λ = 0.6328-μm) intersection angle of 1.39°.

Fig. 5
Fig. 5

Predicted PDPA response curves for sizing fine water droplets at a mean scattering angle of 74°. The PDPA optical configuration consists of a 238-mm focal length, f/2.25 receiver lens and laser beam (λ = 0.6328-μm) intersection angle of 13.74°.

Fig. 6
Fig. 6

Predicted PDPA response curves for sizing fine glass beads at a mean scattering angle of 30°. The PDPA optical configuration consists of a 500-mm focal length, f/4.7 receiver lens and laser beam (λ = 0.6328-μm) intersection angle of 1.39°.

Fig. 7
Fig. 7

Predicted PDPA response curves for sizing fine glass beads at a mean scattering angle of 67.4°. The PDPA optical configuration consists of a 238-mm focal length, f/2.25 receiver lens and laser beam (λ = 0.6328-μm) intersection angle of 13.74°.

Fig. 8
Fig. 8

Predicted and measured phase differences for PSL particles dispersed in water. The PDPA optical configuration consists of θ = 20°, γ = 13.74°, λ = 0.6328 μm, and a 238-mm focal length, f/2.25 receiver lens.

Fig. 9
Fig. 9

Predicted and measured phase differences for PSL particles dispersed in water. The PDPA optical configuration consists of θ = 30°, γ = 13.74°, λ = 0.6328 μm, and a 238-mm focal length, f/2.25 receiver lens.

Fig. 10
Fig. 10

Predicted and measured phase differences for PSL particles dispersed in water. The PDPA optical configuration consists of θ = 50°, γ = 13.74°, λ = 0.6328 μm, and a 238-mm focal length, f/2.25 receiver lens.

Fig. 11
Fig. 11

Predicted and measured phase differences for PSL particles dispersed in water. The PDPA optical configuration consists of θ = 70°, γ = 13.74°, λ = 0.6328 μm, and a 238-mm focal length, f/2.25 receiver lens.

Fig. 12
Fig. 12

Measured size distribution of a mixture of classified PSL particles dispersed in distilled water.

Fig. 13
Fig. 13

Predicted and measured phase differences for sizing PSL particles in air. The PDPA optical configuration consists of θ = 30°, γ = 13.74°, λ = 0.6328 μm, and a 238-mm focal length, f/2.25 receiver lens.

Fig. 14
Fig. 14

Predicted and measured phase differences for sizing PSL particles in air. The PDPA optical configuration consists of Θ = 60°, γ = 13.74°, λ = 0.6328 μm, and a 238-mm focal length, f/2.25 receiver lens.

Equations (6)

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E 1 n = i k n r exp ( k n r + i ω n t ) cos ϕ n S 1 n ( θ n ) ,
E 2 n = i k n r exp ( k n r + i ω n t ) sin ϕ n S 2 n ( θ n ) .
I p ( x , z ) = ( | E p 1 | 2 + | E p 2 | 2 ) / 2 + | E p 1 | | E p 2 | cos ( ω D t + β p 2 β p 1 ) for p = 1 , 2 , 3 .
T j = 1 A j x z p = 1 3 I p ( x , z ) Δ x Δ z = D j + C j cos ( ω D t + η j ) for j = 1 , 2 , 3 ,
η 12 = η 1 η 2 ,
η 13 = η 1 η 3 ,

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