Abstract

Part 1 describes a model to account for the effect of particles on laser sheet attenuation in flows where particles are heterogeneously distributed and where particles are small compared with the imaged volume. Here we extend the model to account for the effect of a strongly diverging light sheet, which is desirable when investigating many turbulent flows, e.g., in two-phase combustion problems. A calibration constant, Cκ, is derived to account for the attenuation of the incident laser sheet due to extinction of the laser beam through a seeded medium. This is shown to be effective in correcting both the effect of in-plane laser sheet attenuation and out-of-plane signal trapping due to particles in a jet flow heavily seeded with 5g/s of 2540  μm spherical particles. In the uncorrected case, attenuation causes up to 15% error in the mean concentration and 35% error on the rms fluctuations. Selecting an appropriate Cκ was found to remove the error in the mean concentration and reduce error on the rms fluctuation by half. Methods to estimate or measure an appropriate value of Cκ are also presented.

© 2007 Optical Society of America

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References

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  1. S. Dhodapkar, L. Bates, G. Klinzing, and P. Wypych, "Guidelines for solids storage, feeding and convening," Chem. Eng. 113, 26-33 (2006).
  2. N. L. Smith, G. J. Nathan, D. K. Zhang, and D. S. Nobes, "The significance of particle clustering in pulversied coal flames," Proc. Combust. Inst. 29, 797-804 (2002).
    [CrossRef]
  3. H. M. Cassel and I. Leibman, "The cooperative mechanism in the ignition of dust dispersions," Combust. Flame 3, 467-472 (1959).
  4. W. Fulkerson, R. R. Judkins, and M. K. Sanghvi, "Energy from fossil fuels," Sci. Am. (September 1990), pp. 83-89.
  5. L. L. Baxter, L. Ip, and K. Cen, "Distinguishing biomass combustion characteristics and their implications for sustainable energy," in 5th Asia-Pacific Conference on Combustion, G. J. Nathan, B. B. Dally, and P. A. M. Kalt, eds. (The Combustion Institute, 2005), pp. 496-474.
  6. N. L. Smith, "The influence of the spectrum of jet turbulence on the stability, NOx emissions and heat release profile of pulverised coal flames," Ph.D. dissertation (Department of Mechanical Engineering, University of Adelaide, 2000).
  7. C. H. Birzer, P. A. M. Kalt, G. J. Nathan, and N. L. Smith, "The influence of mass loading on particle distribution in the near field of a co-annular jet," in 15th Australasian Fluid Mechanics Conference (The University of Adelaide, 2004), pp. AFMC00205.
  8. H. A. Becker, H. C. Hottel, and G. C. Williams, "On the light-scatter technique for the study of turbulence and mixing," J. Fluid Mech. 30, 259-284 (1967).
    [CrossRef]
  9. P. A. M. Kalt and C. H. Birzer, "Calibrations for planar nephelometry in densely seeded two-phase flows," in Fourth Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion, Z. T. Alwahabi, B. B. Dally, P. A. M. Kalt, G. J. Nathan, and C. Y. Wong, eds. (University of Adelaide, 2005).
  10. P. A. M. Kalt, C. H. Birzer, and G. J. Nathan, "Corrections to facilitate planar imaging of particle concentration in particle-laden flows using Mie-scattering, Part 1: Collimated laser sheets," Appl. Opt. 46, 5823-5834 (2007).
    [CrossRef] [PubMed]
  11. C. H. Birzer, P. A. M. Kalt, G. J. Nathan, and N. L. Smith, "Planar measurements of the distribution of particles in a two-phase precessing jet flow," in Proceedings of the 5th Asia-Pacific Conference on Combustion, B. B. Dally, G. J. Nathan, and P. A. M. Kalt, eds. (The Combustion Institute, 2005), pp. 105-108.
  12. C. H. Birzer, P. A. M. Kalt, and G. J. Nathan, "The influence of particle mass-loading on mean particle distributions in the near field of a co-annular jet," Int. J. of Multiphase Flows (to be published).
  13. J. Fan, H. Zhao, and K. Cen, "An experimental study of two-phase turbulent coaxial jets," Exp. Fluids 13, 279-287 (1992).
    [CrossRef]
  14. P. R. Medwell, P. A. M. Kalt, and B. B. Dally, "Simultaneous imaging of OH, formaldehyde, and temperature of turbulent nonpremixed jet flames in a heated and diluted coflow," Combust. Flame 148, 48-61 (2007).
    [CrossRef]
  15. M. C. Jermy and D. A. Greenhalgh, "Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase doppler measurement," Appl. Phys. B , 71, 703-710 (2000).
    [CrossRef]

2007 (2)

P. A. M. Kalt, C. H. Birzer, and G. J. Nathan, "Corrections to facilitate planar imaging of particle concentration in particle-laden flows using Mie-scattering, Part 1: Collimated laser sheets," Appl. Opt. 46, 5823-5834 (2007).
[CrossRef] [PubMed]

P. R. Medwell, P. A. M. Kalt, and B. B. Dally, "Simultaneous imaging of OH, formaldehyde, and temperature of turbulent nonpremixed jet flames in a heated and diluted coflow," Combust. Flame 148, 48-61 (2007).
[CrossRef]

2006 (1)

S. Dhodapkar, L. Bates, G. Klinzing, and P. Wypych, "Guidelines for solids storage, feeding and convening," Chem. Eng. 113, 26-33 (2006).

2002 (1)

N. L. Smith, G. J. Nathan, D. K. Zhang, and D. S. Nobes, "The significance of particle clustering in pulversied coal flames," Proc. Combust. Inst. 29, 797-804 (2002).
[CrossRef]

2000 (1)

M. C. Jermy and D. A. Greenhalgh, "Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase doppler measurement," Appl. Phys. B , 71, 703-710 (2000).
[CrossRef]

1992 (1)

J. Fan, H. Zhao, and K. Cen, "An experimental study of two-phase turbulent coaxial jets," Exp. Fluids 13, 279-287 (1992).
[CrossRef]

1967 (1)

H. A. Becker, H. C. Hottel, and G. C. Williams, "On the light-scatter technique for the study of turbulence and mixing," J. Fluid Mech. 30, 259-284 (1967).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

M. C. Jermy and D. A. Greenhalgh, "Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase doppler measurement," Appl. Phys. B , 71, 703-710 (2000).
[CrossRef]

Chem. Eng. (1)

S. Dhodapkar, L. Bates, G. Klinzing, and P. Wypych, "Guidelines for solids storage, feeding and convening," Chem. Eng. 113, 26-33 (2006).

Combust. Flame (1)

P. R. Medwell, P. A. M. Kalt, and B. B. Dally, "Simultaneous imaging of OH, formaldehyde, and temperature of turbulent nonpremixed jet flames in a heated and diluted coflow," Combust. Flame 148, 48-61 (2007).
[CrossRef]

Exp. Fluids (1)

J. Fan, H. Zhao, and K. Cen, "An experimental study of two-phase turbulent coaxial jets," Exp. Fluids 13, 279-287 (1992).
[CrossRef]

Int. J. of Multiphase Flows (1)

C. H. Birzer, P. A. M. Kalt, and G. J. Nathan, "The influence of particle mass-loading on mean particle distributions in the near field of a co-annular jet," Int. J. of Multiphase Flows (to be published).

J. Fluid Mech. (1)

H. A. Becker, H. C. Hottel, and G. C. Williams, "On the light-scatter technique for the study of turbulence and mixing," J. Fluid Mech. 30, 259-284 (1967).
[CrossRef]

Proc. Combust. Inst. (1)

N. L. Smith, G. J. Nathan, D. K. Zhang, and D. S. Nobes, "The significance of particle clustering in pulversied coal flames," Proc. Combust. Inst. 29, 797-804 (2002).
[CrossRef]

Sci. Am. (1)

W. Fulkerson, R. R. Judkins, and M. K. Sanghvi, "Energy from fossil fuels," Sci. Am. (September 1990), pp. 83-89.

Other (6)

L. L. Baxter, L. Ip, and K. Cen, "Distinguishing biomass combustion characteristics and their implications for sustainable energy," in 5th Asia-Pacific Conference on Combustion, G. J. Nathan, B. B. Dally, and P. A. M. Kalt, eds. (The Combustion Institute, 2005), pp. 496-474.

N. L. Smith, "The influence of the spectrum of jet turbulence on the stability, NOx emissions and heat release profile of pulverised coal flames," Ph.D. dissertation (Department of Mechanical Engineering, University of Adelaide, 2000).

C. H. Birzer, P. A. M. Kalt, G. J. Nathan, and N. L. Smith, "The influence of mass loading on particle distribution in the near field of a co-annular jet," in 15th Australasian Fluid Mechanics Conference (The University of Adelaide, 2004), pp. AFMC00205.

H. M. Cassel and I. Leibman, "The cooperative mechanism in the ignition of dust dispersions," Combust. Flame 3, 467-472 (1959).

P. A. M. Kalt and C. H. Birzer, "Calibrations for planar nephelometry in densely seeded two-phase flows," in Fourth Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion, Z. T. Alwahabi, B. B. Dally, P. A. M. Kalt, G. J. Nathan, and C. Y. Wong, eds. (University of Adelaide, 2005).

C. H. Birzer, P. A. M. Kalt, G. J. Nathan, and N. L. Smith, "Planar measurements of the distribution of particles in a two-phase precessing jet flow," in Proceedings of the 5th Asia-Pacific Conference on Combustion, B. B. Dally, G. J. Nathan, and P. A. M. Kalt, eds. (The Combustion Institute, 2005), pp. 105-108.

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Figures (11)

Fig. 1
Fig. 1

(Color online) Schematic showing ray-trace model for diverging laser sheet of fixed thickness.

Fig. 2
Fig. 2

(Color online) Magnitude of divergence errors based on relative position of virtual origin.

Fig. 3
Fig. 3

(Color online) (a) Imaged plane of an n × m CCD, (b) imaged pixel volume, δx and δy are in-plane resolution, δz is laser sheet thickness.

Fig. 4
Fig. 4

(Color online) Beam path between virtual origin and pixel [i, j] as a one-dimensional array of interpolated pixel values.

Fig. 5
Fig. 5

(Color online) Schematic of diverging light passing through a pixel volume.

Fig. 6
Fig. 6

(Color online) Two-phase wind tunnel setup including lasers and optics.

Fig. 7
Fig. 7

Size distribution of Q-cell hollow glass particles used for validation.

Fig. 8
Fig. 8

(Color online) Corrections for profile: (a) Smoke image with location of virtual origin shown, (b) smoke image corrected for attenuation and divergence, (c) smoothed laser sheet profile response, and (d) plot of laser intensity along arc A–A.

Fig. 9
Fig. 9

(Color online) Instantaneous image corrections: (a) Original instantaneous Mie image, (b) laser sheet profile (response), (c) divergence (with virtual origin at [ 2118 , 865 ] ), (d) transmittance ( C κ = 1.5 ) , and (e) corrected instantaneous image.

Fig. 10
Fig. 10

(Color online) Effect of corrections of ensemble statistics for C κ = 1.5 : (a) mean images, (b) rms variance image. Dashed line indicates the location of profiles shown in Fig. 11.

Fig. 11
Fig. 11

(Color online) Effect of attenuation corrections on signal profiles through the neck region indicated in Fig. 10: (a) mean, (b) rms.

Equations (12)

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Γ ( x ) = ( 1 π r p 2 / A laser ( x ) ) ,
I 1 I 0 = i = 0 n p Γ ( x ) .
Φ [ i , j ] = C κ ( π r p 2 ¯ ) n p [ i , j ] I [ i , j ] .
Φ ˜ = C κ ( π r p 2 ¯ ) n ˜ p I ˜ .
π r 1 2 + π r 2 2 + + π r n p 2 ( π r p 2 ¯ ) n p = π 4 d p ( 2 , 0 ) 2 n p .
I ˜ = I 0 × ( κ ˜ div × κ ˜ trans × κ ˜ prof × ) .
κ ˜ div = I ˜ out / I ˜ in = ( d 1 / 2 ) ( d + 1 / 2 ) ,
I ˜ n = ( i = 1 n κ div [ i ] ) I 0
= κ div [ n ] I ˜ n 1 .
κ ˜ trans = ( 1 π r p 2 ¯ x z cos θ ) n ˜ p ,
I ˜ n = ( i = 1 n Γ n p [ i ] ) I 0
= κ trans [ n ] I ˜ n 1 .

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