Abstract

Phase-Doppler interferometry in which a probe volume that is much smaller than the droplets being measured has been shown to work well when coupled with a phase-ratio and intensity-validation scheme that is capable of eliminating trajectory-dependent scattering errors. With ray-tracing and geometric-optics models, the type and magnitude of trajectory errors were demonstrated quantitatively through stochastic trajectory calculations. Measurements with monodispersed water droplet streams and glass beads were performed to validate the model calculations and to characterize the probe volume. Scattered-light intensity has also been shown to provide a robust means of determining the probe cross-sectional area, which is critical for making accurate mass flux measurements.

© 2000 Optical Society of America

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References

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  1. S. V. Sankar, D. H. Buermann, A. S. Inenaga, K. M. Ibrahim, W. D. Bachalo, “Coherent scattering in phase Doppler interferometry: response of frequency domain processors,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.
  2. Y. Hardalupus, C. H. Liu, “Implications of the Gaussian intensity distribution of laser beams on the performance of the phase Doppler technique. Sizing uncertainties,” Prog. Energy Combust. Sci. 23, 41–63 (1997).
    [CrossRef]
  3. P. Haugen, E. I. Hayes, H.-H. von Benzon, “Size and velocity measurements of large drops in air and in a liquid–liquid two-phase flow by the phase-Doppler technique,” Part. Part. Syst. Charact. 11, 63–72 (1994).
    [CrossRef]
  4. Y. Hardalupas, A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–358 (1994).
    [CrossRef]
  5. P. A. Strakey, D. G. Talley, W. D. Bachalo, S. V. Sankar, “The use of small probe volumes with phase Doppler interferometry,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.
  6. P. A. Strakey, D. G. Talley, W. D. Bachalo, “Phase Doppler measurements in dense sprays,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.
  7. S. V. Sankar, W. D. Bachalo, “Response characteristics of the phase Doppler particle analyzer for sizing spherical particles larger than the light wavelength,” Appl. Opt. 30, 1487–1496 (1991).
    [CrossRef] [PubMed]
  8. H. Qui, C. T. Hsu, “Method of phase-Doppler anemometry free from the measurement-volume defect,” Appl. Opt. 38, 2737–2742 (1999).
    [CrossRef]
  9. G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and near-backward geometry,” Part. Part. Syst. Charact. 11, 133–144 (1994).
    [CrossRef]
  10. A. Naqwi, F. Durst, X.-Z. Liu, “An extended phase-Doppler system for characterization of multiphase flows,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 1990.
  11. G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.
  12. Y. Aizu, M. Ziema, X. Liu, S. Hohmann, F. Durst, “PDA system without Gaussian beam defects,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, August 1993.
  13. C. Tropea, T.-H. Xu, F. Onofri, G. Grehan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.
  14. S. V. Sankar, W. D. Bachalo, “Performance analysis of various phase Doppler systems,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.
  15. S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.
  16. S. V. Sankar, W. D. Bachalo, D. A. Robart, “An adaptive intensity validation technique for minimizing trajectory dependent scattering errors in phase Doppler interferometry,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.
  17. T.-H. Xu, C. Tropea, “Improving the performance of two-component phase Doppler anemometers,” Meas. Sci. Technol. 5, 969–975 (1994).
    [CrossRef]

1999 (1)

1997 (1)

Y. Hardalupus, C. H. Liu, “Implications of the Gaussian intensity distribution of laser beams on the performance of the phase Doppler technique. Sizing uncertainties,” Prog. Energy Combust. Sci. 23, 41–63 (1997).
[CrossRef]

1994 (4)

P. Haugen, E. I. Hayes, H.-H. von Benzon, “Size and velocity measurements of large drops in air and in a liquid–liquid two-phase flow by the phase-Doppler technique,” Part. Part. Syst. Charact. 11, 63–72 (1994).
[CrossRef]

Y. Hardalupas, A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–358 (1994).
[CrossRef]

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and near-backward geometry,” Part. Part. Syst. Charact. 11, 133–144 (1994).
[CrossRef]

T.-H. Xu, C. Tropea, “Improving the performance of two-component phase Doppler anemometers,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

1991 (1)

Aizu, Y.

Y. Aizu, M. Ziema, X. Liu, S. Hohmann, F. Durst, “PDA system without Gaussian beam defects,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, August 1993.

Bachalo, W. D.

S. V. Sankar, W. D. Bachalo, “Response characteristics of the phase Doppler particle analyzer for sizing spherical particles larger than the light wavelength,” Appl. Opt. 30, 1487–1496 (1991).
[CrossRef] [PubMed]

P. A. Strakey, D. G. Talley, W. D. Bachalo, “Phase Doppler measurements in dense sprays,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

S. V. Sankar, D. H. Buermann, A. S. Inenaga, K. M. Ibrahim, W. D. Bachalo, “Coherent scattering in phase Doppler interferometry: response of frequency domain processors,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

P. A. Strakey, D. G. Talley, W. D. Bachalo, S. V. Sankar, “The use of small probe volumes with phase Doppler interferometry,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

S. V. Sankar, W. D. Bachalo, “Performance analysis of various phase Doppler systems,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

S. V. Sankar, W. D. Bachalo, D. A. Robart, “An adaptive intensity validation technique for minimizing trajectory dependent scattering errors in phase Doppler interferometry,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.

Buermann, D. H.

S. V. Sankar, D. H. Buermann, A. S. Inenaga, K. M. Ibrahim, W. D. Bachalo, “Coherent scattering in phase Doppler interferometry: response of frequency domain processors,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Durst, F.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and near-backward geometry,” Part. Part. Syst. Charact. 11, 133–144 (1994).
[CrossRef]

A. Naqwi, F. Durst, X.-Z. Liu, “An extended phase-Doppler system for characterization of multiphase flows,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 1990.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

Y. Aizu, M. Ziema, X. Liu, S. Hohmann, F. Durst, “PDA system without Gaussian beam defects,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, August 1993.

Gouesbet, G.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and near-backward geometry,” Part. Part. Syst. Charact. 11, 133–144 (1994).
[CrossRef]

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

Grehan, G.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and near-backward geometry,” Part. Part. Syst. Charact. 11, 133–144 (1994).
[CrossRef]

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

C. Tropea, T.-H. Xu, F. Onofri, G. Grehan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Hardalupas, Y.

Y. Hardalupas, A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–358 (1994).
[CrossRef]

Hardalupus, Y.

Y. Hardalupus, C. H. Liu, “Implications of the Gaussian intensity distribution of laser beams on the performance of the phase Doppler technique. Sizing uncertainties,” Prog. Energy Combust. Sci. 23, 41–63 (1997).
[CrossRef]

Haugen, P.

P. Haugen, E. I. Hayes, H.-H. von Benzon, “Size and velocity measurements of large drops in air and in a liquid–liquid two-phase flow by the phase-Doppler technique,” Part. Part. Syst. Charact. 11, 63–72 (1994).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Grehan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Hayes, E. I.

P. Haugen, E. I. Hayes, H.-H. von Benzon, “Size and velocity measurements of large drops in air and in a liquid–liquid two-phase flow by the phase-Doppler technique,” Part. Part. Syst. Charact. 11, 63–72 (1994).
[CrossRef]

Hohmann, S.

Y. Aizu, M. Ziema, X. Liu, S. Hohmann, F. Durst, “PDA system without Gaussian beam defects,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, August 1993.

Hsu, C. T.

Ibrahim, K. M.

S. V. Sankar, D. H. Buermann, A. S. Inenaga, K. M. Ibrahim, W. D. Bachalo, “Coherent scattering in phase Doppler interferometry: response of frequency domain processors,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Inenaga, A. S.

S. V. Sankar, D. H. Buermann, A. S. Inenaga, K. M. Ibrahim, W. D. Bachalo, “Coherent scattering in phase Doppler interferometry: response of frequency domain processors,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

Liu, C. H.

Y. Hardalupus, C. H. Liu, “Implications of the Gaussian intensity distribution of laser beams on the performance of the phase Doppler technique. Sizing uncertainties,” Prog. Energy Combust. Sci. 23, 41–63 (1997).
[CrossRef]

Liu, X.

Y. Aizu, M. Ziema, X. Liu, S. Hohmann, F. Durst, “PDA system without Gaussian beam defects,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, August 1993.

Liu, X.-Z.

A. Naqwi, F. Durst, X.-Z. Liu, “An extended phase-Doppler system for characterization of multiphase flows,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 1990.

Naqwi, A.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and near-backward geometry,” Part. Part. Syst. Charact. 11, 133–144 (1994).
[CrossRef]

A. Naqwi, F. Durst, X.-Z. Liu, “An extended phase-Doppler system for characterization of multiphase flows,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 1990.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

Onofri, F.

C. Tropea, T.-H. Xu, F. Onofri, G. Grehan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Qui, H.

Robart, D. A.

S. V. Sankar, W. D. Bachalo, D. A. Robart, “An adaptive intensity validation technique for minimizing trajectory dependent scattering errors in phase Doppler interferometry,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.

Sankar, S. V.

S. V. Sankar, W. D. Bachalo, “Response characteristics of the phase Doppler particle analyzer for sizing spherical particles larger than the light wavelength,” Appl. Opt. 30, 1487–1496 (1991).
[CrossRef] [PubMed]

S. V. Sankar, D. H. Buermann, A. S. Inenaga, K. M. Ibrahim, W. D. Bachalo, “Coherent scattering in phase Doppler interferometry: response of frequency domain processors,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

P. A. Strakey, D. G. Talley, W. D. Bachalo, S. V. Sankar, “The use of small probe volumes with phase Doppler interferometry,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

S. V. Sankar, W. D. Bachalo, D. A. Robart, “An adaptive intensity validation technique for minimizing trajectory dependent scattering errors in phase Doppler interferometry,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

S. V. Sankar, W. D. Bachalo, “Performance analysis of various phase Doppler systems,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.

Strakey, P. A.

P. A. Strakey, D. G. Talley, W. D. Bachalo, “Phase Doppler measurements in dense sprays,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

P. A. Strakey, D. G. Talley, W. D. Bachalo, S. V. Sankar, “The use of small probe volumes with phase Doppler interferometry,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

Talley, D. G.

P. A. Strakey, D. G. Talley, W. D. Bachalo, S. V. Sankar, “The use of small probe volumes with phase Doppler interferometry,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

P. A. Strakey, D. G. Talley, W. D. Bachalo, “Phase Doppler measurements in dense sprays,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

Taylor, A. M. K. P.

Y. Hardalupas, A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–358 (1994).
[CrossRef]

Tropea, C.

T.-H. Xu, C. Tropea, “Improving the performance of two-component phase Doppler anemometers,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Grehan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

von Benzon, H.-H.

P. Haugen, E. I. Hayes, H.-H. von Benzon, “Size and velocity measurements of large drops in air and in a liquid–liquid two-phase flow by the phase-Doppler technique,” Part. Part. Syst. Charact. 11, 63–72 (1994).
[CrossRef]

Xu, T.-H.

T.-H. Xu, C. Tropea, “Improving the performance of two-component phase Doppler anemometers,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

C. Tropea, T.-H. Xu, F. Onofri, G. Grehan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Ziema, M.

Y. Aizu, M. Ziema, X. Liu, S. Hohmann, F. Durst, “PDA system without Gaussian beam defects,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, August 1993.

Appl. Opt. (2)

Exp. Fluids (1)

Y. Hardalupas, A. M. K. P. Taylor, “Phase validation criteria of size measurements for the phase Doppler technique,” Exp. Fluids 17, 253–358 (1994).
[CrossRef]

Meas. Sci. Technol. (1)

T.-H. Xu, C. Tropea, “Improving the performance of two-component phase Doppler anemometers,” Meas. Sci. Technol. 5, 969–975 (1994).
[CrossRef]

Part. Part. Syst. Charact. (2)

P. Haugen, E. I. Hayes, H.-H. von Benzon, “Size and velocity measurements of large drops in air and in a liquid–liquid two-phase flow by the phase-Doppler technique,” Part. Part. Syst. Charact. 11, 63–72 (1994).
[CrossRef]

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: study of a near-forward and near-backward geometry,” Part. Part. Syst. Charact. 11, 133–144 (1994).
[CrossRef]

Prog. Energy Combust. Sci. (1)

Y. Hardalupus, C. H. Liu, “Implications of the Gaussian intensity distribution of laser beams on the performance of the phase Doppler technique. Sizing uncertainties,” Prog. Energy Combust. Sci. 23, 41–63 (1997).
[CrossRef]

Other (10)

S. V. Sankar, D. H. Buermann, A. S. Inenaga, K. M. Ibrahim, W. D. Bachalo, “Coherent scattering in phase Doppler interferometry: response of frequency domain processors,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

P. A. Strakey, D. G. Talley, W. D. Bachalo, S. V. Sankar, “The use of small probe volumes with phase Doppler interferometry,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

P. A. Strakey, D. G. Talley, W. D. Bachalo, “Phase Doppler measurements in dense sprays,” presented at the Eleventh Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17–20 May 1998.

A. Naqwi, F. Durst, X.-Z. Liu, “An extended phase-Doppler system for characterization of multiphase flows,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 1990.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Trajectory ambiguities in phase Doppler systems: use of polarizers and additional detectors to suppress the effect,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

Y. Aizu, M. Ziema, X. Liu, S. Hohmann, F. Durst, “PDA system without Gaussian beam defects,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, August 1993.

C. Tropea, T.-H. Xu, F. Onofri, G. Grehan, P. Haugen, “Dual mode phase Doppler anemometry,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

S. V. Sankar, W. D. Bachalo, “Performance analysis of various phase Doppler systems,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.

S. V. Sankar, A. S. Inenaga, W. D. Bachalo, “Trajectory dependent scattering in phase Doppler interferometry: minimizing and eliminating sizing errors,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–24 July 1992.

S. V. Sankar, W. D. Bachalo, D. A. Robart, “An adaptive intensity validation technique for minimizing trajectory dependent scattering errors in phase Doppler interferometry,” presented at the Fourth International Congress on Optical Particle Sizing, Nurnberg, Germany, 21–23 March 1995.

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Figures (10)

Fig. 1
Fig. 1

Trajectory-dependent scattering.

Fig. 2
Fig. 2

Optical arrangement for modeling calculations.

Fig. 3
Fig. 3

(a), (b) Model calculations of φ12 and φ13 and (c), (d) normalized scattered-light intensity, diameter, and phase ratio for droplet diameters of 60 µm and 200 µm. Water droplets; optical arrangement of case 1, Table 1.

Fig. 4
Fig. 4

Illustration of the slit effect. Lighter dashed lines, beam edge; darker dashed lines, slit edge. Ray paths of reflection (p = 0) and refraction (p = 1) are shown.

Fig. 5
Fig. 5

Fraction of measurements with significant sizing errors versus droplet size for 60- and 300-µm probe diameters with and without the slit effect.

Fig. 6
Fig. 6

Histograms of (I) calculated droplet size and (II) measured droplet size for 57-µm droplets on random trajectories (a) without a phase-ratio criterion, (b) with a ±10% phase-ratio criterion, and (c) with a ±10% phase-ratio and a 10:1 intensity-validation criterion. Water droplets; optical configuration from case 1, Table 1.

Fig. 7
Fig. 7

Histograms of (I) calculated droplet size and (II) measured droplet size for 98-µm droplets on random trajectories (a) without a phase-ratio criterion, (b) with a ±10% phase-ratio criterion and (c) with a ±10% phase-ratio and a 10:1 intensity-validation criterion. Water droplets; optical configuration from case 1, Table 1.

Fig. 8
Fig. 8

Histograms of experimentally measured counts for 250 µm water droplets on random trajectories (a) without a phase-ratio criterion and (b) with a phase-ratio criterion. Noninteger detector separation; optical configuration from case 2, Table 1.

Fig. 9
Fig. 9

Experimentally measured relative volume distributions (counts × D 3) for 61-µm water droplets on random trajectories (a) without a phase-ratio criterion and (b) with a phase-ratio criterion. Noninteger detector separation; optical configuration from case 2, Table 1.

Fig. 10
Fig. 10

Contour plots of measured (a) log of the normalized intensity, (b) linear normalized intensity over a 10:1 range, (c) normalized D 10, and (d) normalized validation rate. Parallelograms; assumed probe cross sections. 330-µm glass bead; optical configuration from case 1, Table 1.

Tables (1)

Tables Icon

Table 1 Values of Parameters in Configurations for Experiments and Model Calculations

Equations (4)

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

V=πDw2Ds4 sinθ,
Pn=VNnn! e-VN,
φ13=φ13+Truncφ12S13360°S12×360°,
A=Dw10%Dssinθ.

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