Abstract

A near backscattered laser Doppler system was presented to carry out velocity and size distribution measurements for irregular particles in two-phase flows. The technique uses amplitudes of particles Doppler signals to estimate the particle size distribution in a statistical manner. Holve's numerical inversion scheme is employed to unfold the dependence of the scattered signals on both particle trajectory and orientation through the measurement volume. The performance and error level of the technique were simulated, and several parameters including the number of particle samples, the fluctuation of irregular particle response function, inversion algorithms, and types of particle size distribution were extensively investigated. The results show that the size distributions for those irregular particles even with strong fluctuations in response function can be successfully reconstructed with an acceptable error level using a Phillips–Twomey-non-negative least-squares algorithm instead of a non-negative least-squares one. The measurement system was then further experimentally verified with irregular quartz sands. Using inversion matrix obtained from the calibration experiment, the average measurement error for the mixing quartz sands with a size range of 200560μm are found to be about 23.3%, which shows the reliability of the technique and the potential for it to be applied to industrial measurement.

© 2007 Optical Society of America

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References

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  1. F. Durst and M. Zaré, "Laser Doppler measurements in two-phase flows," in Proceedings of LDA-75 Symposium (Technical University of Denmark, Copenhagen, 1975), pp. 403-429.
  2. W. D. Bachalo and M. J. Houser, "Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions," Opt. Eng. 23, 583-590 (1984).
  3. D. Blondel, "Conception et réalisation d'une sonde de métrologie optique pour l'étude de milieux industriels complexes," Ph.D. dissertation (Université de Rouen, 1999).
  4. D. Blondel, H. Bultynck, G. Gouesbet, and G. Gréhan, "Phase Doppler measurements with compact monoblock configurations," Part. Part. Syst. Charact. 18, 79-90 (2001).
    [CrossRef]
  5. H. Bultynck, G. Gouesbet, and G. Gréhan, "A miniature monoblock backward phase-Doppler unit," Meas. Sci. Technol. 9, 161-170 (1998).
    [CrossRef]
  6. H. Bultynck, "Développements de sondes laser Doppler miniatures pour la mesure de particules dans des écoulements réels complexes," Ph.D. dissertation (Université de Rouen, 1998).
  7. N. Damaschke, G. Gouesbet, G. Gréhan, H. Mignon, and C. Tropea, "Response of phase Doppler anemeometer systems to nonspherical particles," Appl. Opt. 37, 1752-1761 (1998).
    [CrossRef]
  8. H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, and C. Tropea, "Measurement of cylindrical particles with phase Doppler anemometry," Appl. Opt. 35, 5180-5190 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. Y. Hardalupas, K. Hishida, M. Maeda, H. Morikita, A. M. K. P. Taylor, and J. H. Whitelaw, "Shadow Doppler technique for sizing particles of arbitrary shape," Appl. Opt. 33, 8417-8426 (1994).
    [CrossRef] [PubMed]
  11. H. Morikita, K. Hishida, and M. Maeda, "Measurement of size and velocity of arbitrary shaped particles by LDA based shadow image technique," in 7th International Symposium on Application of Laser Techniques to Fluid Mechanics (Lisbon, Portugal, 1994).
  12. P. Pandey, R. Turton, P. Yue, and L. Shadle, "Evaluation of a backscatter imaging LDV system and its application to a pilot-scale Circulating Fluidized bed," Part. Sci. Technol. 24, 1-22 (2006).
    [CrossRef]
  13. D. Holve and S. A. Self, "Optical particle sizing for in situ measurements. Part 2," Appl. Opt. 18, 1646-1652 (1979).
    [CrossRef] [PubMed]
  14. D. Holve and S. A. Self, "Optical particle sizing for in situ measurements. Part 1," Appl. Opt. 18, 1632-1645 (1979).
    [CrossRef] [PubMed]
  15. C. F. Hess, "Nonintrusive optical single-particle counter for measuring the size and velocity of droplets in a spray," Appl. Opt. 23, 4375-4382 (1984).
    [CrossRef] [PubMed]
  16. C. F. Hess, "A technique to measure the size of particles in laser Doppler velocimetry applications," in Proceedings of the International Symposium on Laser Anemometry (American Society of Mechanical Engineers, 1985), pp. 119-125.
  17. J. C. F. Wang and K. R. Hencken, "in situ particle size measurements using a two-color laser scattering technique," Appl. Opt. 25, 653-657 (1986).
    [CrossRef] [PubMed]
  18. A. J. Yule, P. R. Ereaut, and A. Ungut, "Droplet sizes and velocities in vaporizing sprays," Combust. Flame 54, 15-22 (1983).
    [CrossRef]
  19. D. Allano, G. Gouesbet, G. Gréhan, and D. Lisiecki, "Droplet sizing using a top-hat laser beam technique," J. Phys. D 17, 43-58 (1984).
    [CrossRef]
  20. G. Gréhan and G. Gouesbet, "Simultaneous measurements of velocities and sizes of particles in flows using a combined system incorporating a top-hat beam technique," Appl. Opt. 25, 3527-3538 (1986).
    [CrossRef] [PubMed]
  21. H. E. Albrecht, M. Borys, and W. Fuchs, "The cross sectional area difference method--a new technique for determination of particle concentration by laser Doppler anemometry," Exp. Fluids 16, 61-69 (1993).
    [CrossRef]
  22. N. Damaschke, H. Nobach, N. Semidetnov, and C. Tropea, "Cross sectional area difference method for backscatter particle sizing," in Proceedings of 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Springer, 2004), p. 11.
  23. D. J. Holve, "Transit timing velocimetry (TTV) for two-phase reacting flows," Combust. Flame 48, 105-107 (1982).
    [CrossRef]
  24. G. Gréhan, G. Gouesbet, A. Naqwi, and F. Durst, "Trajectory ambiguities in phase Doppler systems: study of a near forward and a near-backward geometry," Part. Part. Syst. Charact. 11, 133-144 (1994).
    [CrossRef]
  25. G. Gréhan, G. Gouesbet, A. Naqwi, and F. Durst, "Particle trajectory effects in phase Doppler systems: computations and experiments," Part. Part. Syst. Charact. 10, 332-338 (1993).
    [CrossRef]
  26. S. Twomey, "Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions," J. Comput. Phys. 18, 188-200 (1975).
    [CrossRef]
  27. D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Mach. 9, 84-97 (1962).
    [CrossRef]
  28. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, 1977).
  29. G. H. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics 21, 215-223 (1979).
    [CrossRef]
  30. G. Wahba, "Practical approximate solutions to linear operator equations when the data are noisy," SIAM (Soc. Ind. Appl. Math) J. Numer. Anal. 14, 651-667 (1977).

2006 (1)

P. Pandey, R. Turton, P. Yue, and L. Shadle, "Evaluation of a backscatter imaging LDV system and its application to a pilot-scale Circulating Fluidized bed," Part. Sci. Technol. 24, 1-22 (2006).
[CrossRef]

2001 (1)

D. Blondel, H. Bultynck, G. Gouesbet, and G. Gréhan, "Phase Doppler measurements with compact monoblock configurations," Part. Part. Syst. Charact. 18, 79-90 (2001).
[CrossRef]

1998 (2)

H. Bultynck, G. Gouesbet, and G. Gréhan, "A miniature monoblock backward phase-Doppler unit," Meas. Sci. Technol. 9, 161-170 (1998).
[CrossRef]

N. Damaschke, G. Gouesbet, G. Gréhan, H. Mignon, and C. Tropea, "Response of phase Doppler anemeometer systems to nonspherical particles," Appl. Opt. 37, 1752-1761 (1998).
[CrossRef]

1996 (2)

1994 (2)

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

Y. Hardalupas, K. Hishida, M. Maeda, H. Morikita, A. M. K. P. Taylor, and J. H. Whitelaw, "Shadow Doppler technique for sizing particles of arbitrary shape," Appl. Opt. 33, 8417-8426 (1994).
[CrossRef] [PubMed]

1993 (2)

G. Gréhan, G. Gouesbet, A. Naqwi, and F. Durst, "Particle trajectory effects in phase Doppler systems: computations and experiments," Part. Part. Syst. Charact. 10, 332-338 (1993).
[CrossRef]

H. E. Albrecht, M. Borys, and W. Fuchs, "The cross sectional area difference method--a new technique for determination of particle concentration by laser Doppler anemometry," Exp. Fluids 16, 61-69 (1993).
[CrossRef]

1986 (2)

1984 (3)

C. F. Hess, "Nonintrusive optical single-particle counter for measuring the size and velocity of droplets in a spray," Appl. Opt. 23, 4375-4382 (1984).
[CrossRef] [PubMed]

D. Allano, G. Gouesbet, G. Gréhan, and D. Lisiecki, "Droplet sizing using a top-hat laser beam technique," J. Phys. D 17, 43-58 (1984).
[CrossRef]

W. D. Bachalo and M. J. Houser, "Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions," Opt. Eng. 23, 583-590 (1984).

1983 (1)

A. J. Yule, P. R. Ereaut, and A. Ungut, "Droplet sizes and velocities in vaporizing sprays," Combust. Flame 54, 15-22 (1983).
[CrossRef]

1982 (1)

D. J. Holve, "Transit timing velocimetry (TTV) for two-phase reacting flows," Combust. Flame 48, 105-107 (1982).
[CrossRef]

1979 (3)

1977 (1)

G. Wahba, "Practical approximate solutions to linear operator equations when the data are noisy," SIAM (Soc. Ind. Appl. Math) J. Numer. Anal. 14, 651-667 (1977).

1975 (1)

S. Twomey, "Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions," J. Comput. Phys. 18, 188-200 (1975).
[CrossRef]

1962 (1)

D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Mach. 9, 84-97 (1962).
[CrossRef]

Appl. Opt. (8)

Combust. Flame (2)

A. J. Yule, P. R. Ereaut, and A. Ungut, "Droplet sizes and velocities in vaporizing sprays," Combust. Flame 54, 15-22 (1983).
[CrossRef]

D. J. Holve, "Transit timing velocimetry (TTV) for two-phase reacting flows," Combust. Flame 48, 105-107 (1982).
[CrossRef]

Exp. Fluids (1)

H. E. Albrecht, M. Borys, and W. Fuchs, "The cross sectional area difference method--a new technique for determination of particle concentration by laser Doppler anemometry," Exp. Fluids 16, 61-69 (1993).
[CrossRef]

J. Assoc. Comput. Mach. (1)

D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Mach. 9, 84-97 (1962).
[CrossRef]

J. Comput. Phys. (1)

S. Twomey, "Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions," J. Comput. Phys. 18, 188-200 (1975).
[CrossRef]

J. Phys. D (1)

D. Allano, G. Gouesbet, G. Gréhan, and D. Lisiecki, "Droplet sizing using a top-hat laser beam technique," J. Phys. D 17, 43-58 (1984).
[CrossRef]

Meas. Sci. Technol. (1)

H. Bultynck, G. Gouesbet, and G. Gréhan, "A miniature monoblock backward phase-Doppler unit," Meas. Sci. Technol. 9, 161-170 (1998).
[CrossRef]

Opt. Eng. (1)

W. D. Bachalo and M. J. Houser, "Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distributions," Opt. Eng. 23, 583-590 (1984).

Part. Part. Syst. Charact. (4)

D. Blondel, H. Bultynck, G. Gouesbet, and G. Gréhan, "Phase Doppler measurements with compact monoblock configurations," Part. Part. Syst. Charact. 18, 79-90 (2001).
[CrossRef]

A. A. Naqwi, "Sizing of irregular particles using a phase Doppler system," Part. Part. Syst. Charact. 13, 343-349 (1996).
[CrossRef]

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

G. Gréhan, G. Gouesbet, A. Naqwi, and F. Durst, "Particle trajectory effects in phase Doppler systems: computations and experiments," Part. Part. Syst. Charact. 10, 332-338 (1993).
[CrossRef]

Part. Sci. Technol. (1)

P. Pandey, R. Turton, P. Yue, and L. Shadle, "Evaluation of a backscatter imaging LDV system and its application to a pilot-scale Circulating Fluidized bed," Part. Sci. Technol. 24, 1-22 (2006).
[CrossRef]

SIAM (Soc. Ind. Appl. Math) J. Numer. Anal. (1)

G. Wahba, "Practical approximate solutions to linear operator equations when the data are noisy," SIAM (Soc. Ind. Appl. Math) J. Numer. Anal. 14, 651-667 (1977).

Technometrics (1)

G. H. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics 21, 215-223 (1979).
[CrossRef]

Other (7)

C. F. Hess, "A technique to measure the size of particles in laser Doppler velocimetry applications," in Proceedings of the International Symposium on Laser Anemometry (American Society of Mechanical Engineers, 1985), pp. 119-125.

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, 1977).

N. Damaschke, H. Nobach, N. Semidetnov, and C. Tropea, "Cross sectional area difference method for backscatter particle sizing," in Proceedings of 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Springer, 2004), p. 11.

H. Morikita, K. Hishida, and M. Maeda, "Measurement of size and velocity of arbitrary shaped particles by LDA based shadow image technique," in 7th International Symposium on Application of Laser Techniques to Fluid Mechanics (Lisbon, Portugal, 1994).

H. Bultynck, "Développements de sondes laser Doppler miniatures pour la mesure de particules dans des écoulements réels complexes," Ph.D. dissertation (Université de Rouen, 1998).

F. Durst and M. Zaré, "Laser Doppler measurements in two-phase flows," in Proceedings of LDA-75 Symposium (Technical University of Denmark, Copenhagen, 1975), pp. 403-429.

D. Blondel, "Conception et réalisation d'une sonde de métrologie optique pour l'étude de milieux industriels complexes," Ph.D. dissertation (Université de Rouen, 1999).

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Figures (13)

Fig. 1
Fig. 1

Example of hypothetical response function for irregular particles.

Fig. 2
Fig. 2

Calculated ΔS matrix for ideal or spherical particles.

Fig. 3
Fig. 3

ΔS Matrix data for irregular ( κ 1 = 20 % , κ 2 = 20 % ) particles.

Fig. 4
Fig. 4

Average error variation as a function of total number of particles N ( κ 1 = 20 % , κ 2 = 20 % , unimodal distribution, NNLS algorithm).

Fig. 5
Fig. 5

Comparison of inversion results using NNLS and Phillips–Twomey–NNLS algorithms ( κ 1 = 30 % , κ 2 = 30 % , unimodal distribution, N = 10 4 ).

Fig. 6
Fig. 6

Effects of oscillation coefficients on the inversion results (unimodal distribution, P-T-NNLS algorithm, N = 10 4 ).

Fig. 7
Fig. 7

Simulated result for a bimodal distribution particle flow ( κ 1 = 20 % , κ 2 = 20 % , P-T-NNLS algorithm, N = 10 4 ). (a) The real (hollow column) and simulated (solid column) particle size distributions and (b) its amplitude distribution.

Fig. 8
Fig. 8

(Color online) Optical layout and experimental setup of the LDV sizing system.

Fig. 9
Fig. 9

(Color online) Picture of the probe unit.

Fig. 10
Fig. 10

(Color online) Particle supply unit.

Fig. 11
Fig. 11

Amplitude distribution of 400 450 μ m size class. A max = 360   mV , A min = 40   mV .

Fig. 12
Fig. 12

Average response function of quartz sands from calibration experiment.

Fig. 13
Fig. 13

Measurement results for particle flow mixed in equal-particle number of 315–355 and 500 560 μ m size classes. (a) Its amplitude distribution and (b) the real (hollow column) and measured (solid column) particle size distributions.

Tables (4)

Tables Icon

Table 1 Particle Size Classes Used for Simulation

Tables Icon

Table 2 Size Classes of Quartz Sands Used in Experiment

Tables Icon

Table 3 Error Analysis of Reconstructed Size Distributions for Each Particle Size Group

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Table 4 Error Analysis of the Technique for Mixed Particle Flows

Equations (6)

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

F max ( d ) = F 0 ( d ) · ( 1 + κ 1 ) · [ 1 + 2 · ( random 0 .5 ) · κ 2 ] ,
F min ( d ) = F 0 ( d ) · ( 1 κ 1 ) · [ 1 + 2 · ( random 0 .5 ) · κ 2 ] ,
F ( d ) = F min ( d ) + random · [ F max ( d ) F min ( d ) ] .
I = I 0   exp { 2 [ random 2 + random 2 ] } ,
A = G · I · F ( d ) ,
σ = | C ( d ) C c ( d ) | C ( d ) × 100 % .

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