Abstract

The Phase Doppler Anemometer (PDA) technique measures particle diameter assuming sphericity. A means for detecting nonsphericity has usually been implemented in commercial PDA systems to avoid sizing errors if the sphericity assumption is not valid. In the present research the response of standard and planar PDA systems is examined experimentally in more detail by passing nonspherical droplets of known shape through the measurement volume. The effectiveness of nonsphericity detection schemes can be evaluated, and furthermore the influence of the droplet oscillations on the frequency and phase evolution of individual signals can be quantified. The light scattering from such particles has been simulated by using geometric optics, and the computed response of standard and planar PDA systems agrees well with the experimental observations. We conclude with some remarks concerning the possibilities of characterizing the nonsphericity with PDA systems.

© 1998 Optical Society of America

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References

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  1. C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
    [CrossRef]
  2. A. Naqwi, F. Durst, X. Liu, “Two optical methods for simultaneous measurement of particle size, velocity, and refractive index,” Appl. Opt. 30, 4949–4959 (1991).
    [CrossRef] [PubMed]
  3. D. R. Alexander, K. J. Wiles, S. A. Schaub, M. P. S. A. Seeman, “Effects of non-spherical drops on a phase Doppler spray analyzer,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. SPIE573, 67–72 (1985).
    [CrossRef]
  4. P. Lehmann, Th. Wriedt, A. Schöne, “Time-resolved laser Doppler and phase Doppler signal processing,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Cha, J. O. Trolinger, eds., Proc. SPIE2546, 246–257 (1995).
    [CrossRef]
  5. C. Hoff, T. Meyer, P. Lehmann, Th. Wriedt, “Influence of nonspherical particles on phase Doppler anemometry,” in Fourth International Congress of Optical Particle Sizing (NürnbergMesse GmbH, Nürnberg, Germany, 1995), pp. 235–244.
  6. R. D. Rajaona, P. Sulmont, “A method of spectral analysis applied to periodic and pseudoperiodic signals,” J. Comput. Phys. 61, 186–193 (1985).
    [CrossRef]
  7. R. N. Berglund, B. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
    [CrossRef]
  8. G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a phase Doppler system using generalized Lorenz-Mie Theory,” in International Conference on Multiphase Flows 1991 (Japan Society of Multiphase Flow, University of Tsukuba, Japan, 1991), pp. 291–296.
  9. F. Durst, C. Tropea, T.-H. Xu, “The Slit Effect in Phase Doppler Anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Application, (Xijiu, Beijing, 1994).
  10. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  11. E. Becker, W. J. Hiller, T. A. Kowalewski, “Experimental and theoretical investigation of large amplitude oscillations of liquid droplets,” J. Fluid Mech. 231, 189–210 (1991).
    [CrossRef]
  12. T. S. Lundgren, N. N. Mansour, “Oscillations of droplets in zero gravity with weak viscous effects,” J. Fluid Mech. 194, 479–510 (1988).
    [CrossRef]
  13. S. Asano, S. Makoto, “Light scattering by randomly orientated spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
    [CrossRef] [PubMed]
  14. J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995).
    [CrossRef] [PubMed]
  15. J. A. Lock, “Ray scattering by an arbitrary oriented spheroid. Parts I and II,” Appl. Opt. 35, 500–531 (1996).
    [CrossRef] [PubMed]
  16. H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometer,” Appl. Opt. 35, 5180–5190 (1996).
    [CrossRef] [PubMed]
  17. E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991).
    [CrossRef] [PubMed]
  18. H. Mignon, “Anémométrie phase Doppler et particules non spheriques: Cas des cylindres et des ellipoîdes,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1997).

1996 (3)

1995 (1)

1991 (3)

1988 (1)

T. S. Lundgren, N. N. Mansour, “Oscillations of droplets in zero gravity with weak viscous effects,” J. Fluid Mech. 194, 479–510 (1988).
[CrossRef]

1985 (1)

R. D. Rajaona, P. Sulmont, “A method of spectral analysis applied to periodic and pseudoperiodic signals,” J. Comput. Phys. 61, 186–193 (1985).
[CrossRef]

1980 (1)

1973 (1)

R. N. Berglund, B. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

Alexander, D. R.

D. R. Alexander, K. J. Wiles, S. A. Schaub, M. P. S. A. Seeman, “Effects of non-spherical drops on a phase Doppler spray analyzer,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. SPIE573, 67–72 (1985).
[CrossRef]

Asano, S.

Barton, J. P.

Becker, E.

E. Becker, W. J. Hiller, T. A. Kowalewski, “Experimental and theoretical investigation of large amplitude oscillations of liquid droplets,” J. Fluid Mech. 231, 189–210 (1991).
[CrossRef]

Berglund, R. N.

R. N. Berglund, B. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

Durst, F.

A. Naqwi, F. Durst, X. Liu, “Two optical methods for simultaneous measurement of particle size, velocity, and refractive index,” Appl. Opt. 30, 4949–4959 (1991).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a phase Doppler system using generalized Lorenz-Mie Theory,” in International Conference on Multiphase Flows 1991 (Japan Society of Multiphase Flow, University of Tsukuba, Japan, 1991), pp. 291–296.

F. Durst, C. Tropea, T.-H. Xu, “The Slit Effect in Phase Doppler Anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Application, (Xijiu, Beijing, 1994).

Gouesbet, G.

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometer,” Appl. Opt. 35, 5180–5190 (1996).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a phase Doppler system using generalized Lorenz-Mie Theory,” in International Conference on Multiphase Flows 1991 (Japan Society of Multiphase Flow, University of Tsukuba, Japan, 1991), pp. 291–296.

Gréhan, G.

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometer,” Appl. Opt. 35, 5180–5190 (1996).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a phase Doppler system using generalized Lorenz-Mie Theory,” in International Conference on Multiphase Flows 1991 (Japan Society of Multiphase Flow, University of Tsukuba, Japan, 1991), pp. 291–296.

Grèhan, G.

C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

Haugen, P.

C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

Hiller, W. J.

E. Becker, W. J. Hiller, T. A. Kowalewski, “Experimental and theoretical investigation of large amplitude oscillations of liquid droplets,” J. Fluid Mech. 231, 189–210 (1991).
[CrossRef]

Hoff, C.

C. Hoff, T. Meyer, P. Lehmann, Th. Wriedt, “Influence of nonspherical particles on phase Doppler anemometry,” in Fourth International Congress of Optical Particle Sizing (NürnbergMesse GmbH, Nürnberg, Germany, 1995), pp. 235–244.

Hovenac, E. A.

Kowalewski, T. A.

E. Becker, W. J. Hiller, T. A. Kowalewski, “Experimental and theoretical investigation of large amplitude oscillations of liquid droplets,” J. Fluid Mech. 231, 189–210 (1991).
[CrossRef]

Lehmann, P.

C. Hoff, T. Meyer, P. Lehmann, Th. Wriedt, “Influence of nonspherical particles on phase Doppler anemometry,” in Fourth International Congress of Optical Particle Sizing (NürnbergMesse GmbH, Nürnberg, Germany, 1995), pp. 235–244.

P. Lehmann, Th. Wriedt, A. Schöne, “Time-resolved laser Doppler and phase Doppler signal processing,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Cha, J. O. Trolinger, eds., Proc. SPIE2546, 246–257 (1995).
[CrossRef]

Liu, B. Y. H.

R. N. Berglund, B. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

Liu, X.

Lock, J. A.

Lundgren, T. S.

T. S. Lundgren, N. N. Mansour, “Oscillations of droplets in zero gravity with weak viscous effects,” J. Fluid Mech. 194, 479–510 (1988).
[CrossRef]

Makoto, S.

Mansour, N. N.

T. S. Lundgren, N. N. Mansour, “Oscillations of droplets in zero gravity with weak viscous effects,” J. Fluid Mech. 194, 479–510 (1988).
[CrossRef]

Meyer, T.

C. Hoff, T. Meyer, P. Lehmann, Th. Wriedt, “Influence of nonspherical particles on phase Doppler anemometry,” in Fourth International Congress of Optical Particle Sizing (NürnbergMesse GmbH, Nürnberg, Germany, 1995), pp. 235–244.

Mignon, H.

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometer,” Appl. Opt. 35, 5180–5190 (1996).
[CrossRef] [PubMed]

H. Mignon, “Anémométrie phase Doppler et particules non spheriques: Cas des cylindres et des ellipoîdes,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1997).

Naqwi, A.

A. Naqwi, F. Durst, X. Liu, “Two optical methods for simultaneous measurement of particle size, velocity, and refractive index,” Appl. Opt. 30, 4949–4959 (1991).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a phase Doppler system using generalized Lorenz-Mie Theory,” in International Conference on Multiphase Flows 1991 (Japan Society of Multiphase Flow, University of Tsukuba, Japan, 1991), pp. 291–296.

Onofri, F.

C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

Rajaona, R. D.

R. D. Rajaona, P. Sulmont, “A method of spectral analysis applied to periodic and pseudoperiodic signals,” J. Comput. Phys. 61, 186–193 (1985).
[CrossRef]

Schaub, S. A.

D. R. Alexander, K. J. Wiles, S. A. Schaub, M. P. S. A. Seeman, “Effects of non-spherical drops on a phase Doppler spray analyzer,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. SPIE573, 67–72 (1985).
[CrossRef]

Schöne, A.

P. Lehmann, Th. Wriedt, A. Schöne, “Time-resolved laser Doppler and phase Doppler signal processing,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Cha, J. O. Trolinger, eds., Proc. SPIE2546, 246–257 (1995).
[CrossRef]

Seeman, M. P. S. A.

D. R. Alexander, K. J. Wiles, S. A. Schaub, M. P. S. A. Seeman, “Effects of non-spherical drops on a phase Doppler spray analyzer,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. SPIE573, 67–72 (1985).
[CrossRef]

Stieglmeier, M.

C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

Sulmont, P.

R. D. Rajaona, P. Sulmont, “A method of spectral analysis applied to periodic and pseudoperiodic signals,” J. Comput. Phys. 61, 186–193 (1985).
[CrossRef]

Tropea, C.

C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometer,” Appl. Opt. 35, 5180–5190 (1996).
[CrossRef] [PubMed]

F. Durst, C. Tropea, T.-H. Xu, “The Slit Effect in Phase Doppler Anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Application, (Xijiu, Beijing, 1994).

van de Hulst, H. C.

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

Wiles, K. J.

D. R. Alexander, K. J. Wiles, S. A. Schaub, M. P. S. A. Seeman, “Effects of non-spherical drops on a phase Doppler spray analyzer,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. SPIE573, 67–72 (1985).
[CrossRef]

Wriedt, Th.

P. Lehmann, Th. Wriedt, A. Schöne, “Time-resolved laser Doppler and phase Doppler signal processing,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Cha, J. O. Trolinger, eds., Proc. SPIE2546, 246–257 (1995).
[CrossRef]

C. Hoff, T. Meyer, P. Lehmann, Th. Wriedt, “Influence of nonspherical particles on phase Doppler anemometry,” in Fourth International Congress of Optical Particle Sizing (NürnbergMesse GmbH, Nürnberg, Germany, 1995), pp. 235–244.

Xu, T. H.

Xu, T.-H.

C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

F. Durst, C. Tropea, T.-H. Xu, “The Slit Effect in Phase Doppler Anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Application, (Xijiu, Beijing, 1994).

Appl. Opt. (6)

Environ. Sci. Technol. (1)

R. N. Berglund, B. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

J. Comput. Phys. (1)

R. D. Rajaona, P. Sulmont, “A method of spectral analysis applied to periodic and pseudoperiodic signals,” J. Comput. Phys. 61, 186–193 (1985).
[CrossRef]

J. Fluid Mech. (2)

E. Becker, W. J. Hiller, T. A. Kowalewski, “Experimental and theoretical investigation of large amplitude oscillations of liquid droplets,” J. Fluid Mech. 231, 189–210 (1991).
[CrossRef]

T. S. Lundgren, N. N. Mansour, “Oscillations of droplets in zero gravity with weak viscous effects,” J. Fluid Mech. 194, 479–510 (1988).
[CrossRef]

Part. Part. Syst. Charact. (1)

C. Tropea, T.-H. Xu, F. Onofri, G. Grèhan, P. Haugen, M. Stieglmeier, “Dual-mode phase Doppler anemometer,” Part. Part. Syst. Charact. 13, 165–170 (1996).
[CrossRef]

Other (7)

H. Mignon, “Anémométrie phase Doppler et particules non spheriques: Cas des cylindres et des ellipoîdes,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1997).

G. Gréhan, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a phase Doppler system using generalized Lorenz-Mie Theory,” in International Conference on Multiphase Flows 1991 (Japan Society of Multiphase Flow, University of Tsukuba, Japan, 1991), pp. 291–296.

F. Durst, C. Tropea, T.-H. Xu, “The Slit Effect in Phase Doppler Anemometry,” in Proceedings of the Second International Conference on Fluid Dynamic Measurement and Its Application, (Xijiu, Beijing, 1994).

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

D. R. Alexander, K. J. Wiles, S. A. Schaub, M. P. S. A. Seeman, “Effects of non-spherical drops on a phase Doppler spray analyzer,” in Particle Sizing and Spray Analysis, N. Chigier, G. W. Stewart, eds., Proc. SPIE573, 67–72 (1985).
[CrossRef]

P. Lehmann, Th. Wriedt, A. Schöne, “Time-resolved laser Doppler and phase Doppler signal processing,” in Optical Techniques in Fluid, Thermal, and Combustion Flow, S. S. Cha, J. O. Trolinger, eds., Proc. SPIE2546, 246–257 (1995).
[CrossRef]

C. Hoff, T. Meyer, P. Lehmann, Th. Wriedt, “Influence of nonspherical particles on phase Doppler anemometry,” in Fourth International Congress of Optical Particle Sizing (NürnbergMesse GmbH, Nürnberg, Germany, 1995), pp. 235–244.

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Figures (14)

Fig. 1
Fig. 1

Schematic representation of a planar and a standard PDA optical arrangement.

Fig. 2
Fig. 2

Graphical representation of sphericity validation criteria.

Fig. 3
Fig. 3

PDA measurements of various deformed droplets; d G = 91.4 μm, f G = 52 kHz.

Fig. 4
Fig. 4

Relative error of measured phase difference as a function of a droplet aspect ratio when a conventional three-detector PDA is used; (a) Φ12, (b) Φ13.

Fig. 5
Fig. 5

Scatter diagram of phase-difference measurements when a conventional three-dimensional PDA is used. Each droplet was measured 10,000 times.

Fig. 6
Fig. 6

Validation as a function of the droplet aspect ratio and acceptance percent for a conventional three-detector PDA.

Fig. 7
Fig. 7

Relative error of phase-difference measurements as a function of the droplet aspect ratio when a dual-mode PDA is used; (a) standard detectors Φ12, (b) planar detectors Φ13, (c) planar detectors with an error normalized with equatorial diameter a G .

Fig. 8
Fig. 8

Scatter diagram of phase-difference measurements using a dual PDA. Each measurement contains 50,000 samples.

Fig. 9
Fig. 9

Validation as a function of droplet aspect ratio and acceptance percent for a dual-mode PDA.

Fig. 10
Fig. 10

Evolution of phase-difference Φ12 for a droplet with r = 0.95 (d G = 110 μm, f G = 35.3 kHz).

Fig. 11
Fig. 11

Evolution of (a) phase-difference Φ12 and (b) signal frequencies for an oscillating droplet with r = 0.94 (d G = 171 μm, f G = 20.7 kHz).

Fig. 12
Fig. 12

Evolution of phase-difference Φ12 for an oscillating droplet with r = 0.95 (d G = 170 μm, f G = 21.0 kHz).

Fig. 13
Fig. 13

Computed phase differences for spheroidal droplets of various aspect ratios measured when a standard three-detector PDA (d G = 91.4 μm) is used.

Fig. 14
Fig. 14

Computed phase differences for spheroidal droplets of various aspect ratios measured when a dual-mode PDA (d G = 91.4 μm) is used.

Tables (2)

Tables Icon

Table 1 Optical Parameters of PDA Systemsa

Tables Icon

Table 2 Summary of Optical Parameters of PDA Used to Investigate Phase Evolution in Individual Signals

Equations (3)

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a G = 6 π   V G r 1 / 3 ,     b G = 6 π V G r 2 1 / 3 .
D Φ / Dt = Φ t + U   Φ x .
Φ ¯ = Φ 0 + t 0 - Δ t / 2 t 0 + Δ t / 2 Φ t d t ,

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