Abstract

Improvements on the validation of a nonintrusive laser-based measurement technique are presented. This new technique, called global rainbow thermometry (GRT), is capable of determining the temperature and the size distributions of liquid droplets dispersed in a liquid or gaseous bulk. We propose a new data inversion algorithm that takes into account the whole rainbow pattern. Experimental validation of the GRT technique is performed for a liquid-liquid suspension. We performed the validation by comparing the measurements obtained with the GRT technique for the mean droplet temperature and size with the results obtained with alternative techniques.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micro-metric range,” J. Laser Appl. 2, 37–42 (1990).
    [CrossRef]
  2. S. V. Sankar, D. H. Buermann, W. D. Bachalo, “An advanced Rainbow signal processor for improved accuracy in droplet measurement,” in Proceedings of the Eighth International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 1996).
  3. J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
    [CrossRef] [PubMed]
  4. Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
    [CrossRef]
  5. P. Massoli, “Rainbow refractometry applied to radially inhomogeneous spheres: the critical case of evaporating droplets,” Appl. Opt. 37, 3227–3235 (1998).
    [CrossRef]
  6. J. P. A. J. van Beeck, D. Giannoulis, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for droplet-temperature measurement,” Opt. Lett. 24, 1696–1698 (1999).
    [CrossRef]
  7. J. P. A. J. van Beeck, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for mean temperature and size measurement of spray droplets,” Part. Part. Syst. Charact. 18, 196–204 (2001).
    [CrossRef]
  8. D. Yildiz, J. P. A. J. van Beeck, M. L. Riethmuller, “Global Rainbow Thermometry applied to a flashing two-phase R134-A jet,” in Proceedings of Eleventh International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 2002).
  9. R. Descartes, Discourse on Method, Optics, Geometry, and Meteorology, translated, with an introduction, by P. J. Olscamp, revised edition (Hackett Publishing, Indianapolis, 2001).
  10. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  11. G. Mie, “Beitrâge zur optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).
  12. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  13. J. P. A. J. van Beeck, M. L. Riethmuller, “Simultaneous determination of temperature and size of droplets from rainbow using Airy theory,” in Developments in Laser Techniques and Fluid Mechanics: Selected Papers from the 8th International Symposium, Lisbon, Portugal, 8–11 July 1996, R. J. Adrian, D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1997), pp. 330–339.
  14. J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
    [CrossRef] [PubMed]
  15. J. P. A. J. van Beeck, “Rainbow phenomena: development of a laser-based, nonintrusive technique for measuring droplet size, temperature, and velocity,” Ph.D. dissertation (Eindhoven University of Technology, Eindhoven, The Netherlands, 1997).
  16. M. R. Vetrano, J. P. A. J. van Beeck, M. L. Riethmuller, “Experimental validation of global rainbow thermometry simulations,” in Optical Technology and Image Processing for Fluids and Solid Diagnostics (Beijing University of Aeronautics and Astronautics, Beijing, China, 2002).
  17. J. P. A. J. van Beeck, T. Grosges, M. G. De Giorgi, “Global rainbow thermometry assessed by Airy and Lorenz-Mie theories and compared with phase Doppler anemometry,” Appl. Opt. 42, 4016–4022 (2003).
    [CrossRef] [PubMed]

2003 (1)

2002 (1)

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

2001 (1)

J. P. A. J. van Beeck, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for mean temperature and size measurement of spray droplets,” Part. Part. Syst. Charact. 18, 196–204 (2001).
[CrossRef]

1999 (1)

1998 (1)

1996 (1)

1995 (1)

1990 (1)

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micro-metric range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

1908 (1)

G. Mie, “Beitrâge zur optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).

Anders, K.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micro-metric range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Bachalo, W. D.

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “An advanced Rainbow signal processor for improved accuracy in droplet measurement,” in Proceedings of the Eighth International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 1996).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Buermann, D. H.

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “An advanced Rainbow signal processor for improved accuracy in droplet measurement,” in Proceedings of the Eighth International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 1996).

De Giorgi, M. G.

Descartes, R.

R. Descartes, Discourse on Method, Optics, Geometry, and Meteorology, translated, with an introduction, by P. J. Olscamp, revised edition (Hackett Publishing, Indianapolis, 2001).

Frohn, A.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micro-metric range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Giannoulis, D.

Gouesbet, G.

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Gréhan, G.

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Grosges, T.

Han, Y. P.

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Massoli, P.

Méès, L.

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Mie, G.

G. Mie, “Beitrâge zur optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).

Olscamp, P. J.

R. Descartes, Discourse on Method, Optics, Geometry, and Meteorology, translated, with an introduction, by P. J. Olscamp, revised edition (Hackett Publishing, Indianapolis, 2001).

Ren, K. F.

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Riethmuller, M. L.

J. P. A. J. van Beeck, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for mean temperature and size measurement of spray droplets,” Part. Part. Syst. Charact. 18, 196–204 (2001).
[CrossRef]

J. P. A. J. van Beeck, D. Giannoulis, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for droplet-temperature measurement,” Opt. Lett. 24, 1696–1698 (1999).
[CrossRef]

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Simultaneous determination of temperature and size of droplets from rainbow using Airy theory,” in Developments in Laser Techniques and Fluid Mechanics: Selected Papers from the 8th International Symposium, Lisbon, Portugal, 8–11 July 1996, R. J. Adrian, D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1997), pp. 330–339.

D. Yildiz, J. P. A. J. van Beeck, M. L. Riethmuller, “Global Rainbow Thermometry applied to a flashing two-phase R134-A jet,” in Proceedings of Eleventh International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 2002).

M. R. Vetrano, J. P. A. J. van Beeck, M. L. Riethmuller, “Experimental validation of global rainbow thermometry simulations,” in Optical Technology and Image Processing for Fluids and Solid Diagnostics (Beijing University of Aeronautics and Astronautics, Beijing, China, 2002).

Roth, N.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micro-metric range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Sankar, S. V.

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “An advanced Rainbow signal processor for improved accuracy in droplet measurement,” in Proceedings of the Eighth International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 1996).

van Beeck, J. P. A. J.

J. P. A. J. van Beeck, T. Grosges, M. G. De Giorgi, “Global rainbow thermometry assessed by Airy and Lorenz-Mie theories and compared with phase Doppler anemometry,” Appl. Opt. 42, 4016–4022 (2003).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for mean temperature and size measurement of spray droplets,” Part. Part. Syst. Charact. 18, 196–204 (2001).
[CrossRef]

J. P. A. J. van Beeck, D. Giannoulis, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for droplet-temperature measurement,” Opt. Lett. 24, 1696–1698 (1999).
[CrossRef]

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Simultaneous determination of temperature and size of droplets from rainbow using Airy theory,” in Developments in Laser Techniques and Fluid Mechanics: Selected Papers from the 8th International Symposium, Lisbon, Portugal, 8–11 July 1996, R. J. Adrian, D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1997), pp. 330–339.

D. Yildiz, J. P. A. J. van Beeck, M. L. Riethmuller, “Global Rainbow Thermometry applied to a flashing two-phase R134-A jet,” in Proceedings of Eleventh International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 2002).

M. R. Vetrano, J. P. A. J. van Beeck, M. L. Riethmuller, “Experimental validation of global rainbow thermometry simulations,” in Optical Technology and Image Processing for Fluids and Solid Diagnostics (Beijing University of Aeronautics and Astronautics, Beijing, China, 2002).

J. P. A. J. van Beeck, “Rainbow phenomena: development of a laser-based, nonintrusive technique for measuring droplet size, temperature, and velocity,” Ph.D. dissertation (Eindhoven University of Technology, Eindhoven, The Netherlands, 1997).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

Vetrano, M. R.

M. R. Vetrano, J. P. A. J. van Beeck, M. L. Riethmuller, “Experimental validation of global rainbow thermometry simulations,” in Optical Technology and Image Processing for Fluids and Solid Diagnostics (Beijing University of Aeronautics and Astronautics, Beijing, China, 2002).

Wu, S. Z.

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Yildiz, D.

D. Yildiz, J. P. A. J. van Beeck, M. L. Riethmuller, “Global Rainbow Thermometry applied to a flashing two-phase R134-A jet,” in Proceedings of Eleventh International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 2002).

Zimmer, L.

J. P. A. J. van Beeck, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for mean temperature and size measurement of spray droplets,” Part. Part. Syst. Charact. 18, 196–204 (2001).
[CrossRef]

J. P. A. J. van Beeck, D. Giannoulis, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for droplet-temperature measurement,” Opt. Lett. 24, 1696–1698 (1999).
[CrossRef]

Ann. Phys. (Leipzig) (1)

G. Mie, “Beitrâge zur optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–452 (1908).

Appl. Opt. (4)

J. Laser Appl. (1)

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micro-metric range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Opt. Commun. (1)

Y. P. Han, L. Méès, K. F. Ren, G. Gouesbet, S. Z. Wu, G. Gréhan, “Scattering of light by spheroids: the far field case,” Opt. Commun. 210, 1–9 (2002).
[CrossRef]

Opt. Lett. (1)

Part. Part. Syst. Charact. (1)

J. P. A. J. van Beeck, L. Zimmer, M. L. Riethmuller, “Global rainbow thermometry for mean temperature and size measurement of spray droplets,” Part. Part. Syst. Charact. 18, 196–204 (2001).
[CrossRef]

Other (8)

D. Yildiz, J. P. A. J. van Beeck, M. L. Riethmuller, “Global Rainbow Thermometry applied to a flashing two-phase R134-A jet,” in Proceedings of Eleventh International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 2002).

R. Descartes, Discourse on Method, Optics, Geometry, and Meteorology, translated, with an introduction, by P. J. Olscamp, revised edition (Hackett Publishing, Indianapolis, 2001).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “An advanced Rainbow signal processor for improved accuracy in droplet measurement,” in Proceedings of the Eighth International Symposium on Application of Laser Techniques to Fluid Mechanics (Instituto Superior Technico, Lisbon, Portugal, 1996).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

J. P. A. J. van Beeck, M. L. Riethmuller, “Simultaneous determination of temperature and size of droplets from rainbow using Airy theory,” in Developments in Laser Techniques and Fluid Mechanics: Selected Papers from the 8th International Symposium, Lisbon, Portugal, 8–11 July 1996, R. J. Adrian, D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1997), pp. 330–339.

J. P. A. J. van Beeck, “Rainbow phenomena: development of a laser-based, nonintrusive technique for measuring droplet size, temperature, and velocity,” Ph.D. dissertation (Eindhoven University of Technology, Eindhoven, The Netherlands, 1997).

M. R. Vetrano, J. P. A. J. van Beeck, M. L. Riethmuller, “Experimental validation of global rainbow thermometry simulations,” in Optical Technology and Image Processing for Fluids and Solid Diagnostics (Beijing University of Aeronautics and Astronautics, Beijing, China, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Scattering angle θ as a function of incident angle τ for different values of N.

Fig. 2
Fig. 2

Scattered light intensity distribution for a single water drop of 200-μm diameter obtained with the Lorenz-Mie approach.

Fig. 3
Fig. 3

Example of a GRT pattern: θrg, rainbow scattering angle; θ M1 and θ M2, first and second maximum scattering angles; θinf1 and θinf2, first and second inflection scattering angles; θ m1, first minimum scattering angle.

Fig. 4
Fig. 4

Comparison of the Airy diameters and the mean value of the size distribution for different values of the nondimensional dispersion factor.

Fig. 5
Fig. 5

GRT setup for liquid-liquid suspension characterization.

Fig. 6
Fig. 6

GRT interference fringes and its relative intensity pattern.

Fig. 7
Fig. 7

Comparison of the GRT experimental pattern for an oil-in-water suspension (dashed curve) with the theoretical pattern obtained with the fitting process (solid curve).

Fig. 8
Fig. 8

Image of silicon oil droplets suspended in a water bulk.

Fig. 9
Fig. 9

Postprocessing of BLT images.

Fig. 10
Fig. 10

Example of droplet size distribution obtained with the BLT and GRT.

Fig. 11
Fig. 11

Comparison of the GRT pattern obtained by fringe analysis (solid curve) and the pattern obtained from the droplet size values by means of the BLT (dashed curve).

Fig. 12
Fig. 12

Temperature variation as a function of the scattering angle for oil-in-water dispersion and for water-in-air spray.

Tables (1)

Tables Icon

Table 1 Experimental Results for Droplet Diameter and Temperature

Equations (11)

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

E s θ = - iE b   cos φ exp ik 0 r k 0 r   S 2 , E s φ = - iE b   sin φ exp ik 0 r k 0 r   S 1 , E s r = 0 ,
I = | S 1 | 2   sin 2 φ + | S 2 | 2 cos 2 φ I i k 0 r .
Ω Rnbw 2 z θ = 12 π 2 1 / 3 z θ 2 ,
z θ = - θ - θ rg - Δ θ rg 16 D 2   sin 3 τ rg cos τ rg λ 2 ,
Rnbw θ ,   D ,   σ D ,   T ,   σ T ,   σ R = D T R Ω Rnbw 2 z θ × σ D D ¯ , σ D ξ T T ¯ , σ T × ζ R R ¯ , σ R D T R .
D Airy = λ 4 cos   τ rg sin 3   τ rg 0.5 z i - z j θ i - θ j 1.5 ,
D Airy 1 = 1016.175 λ θ M 2 - θ M 1 - 1.5 ,
D Airy 2 = 531.555 λ θ inf 2 - θ inf 1 - 1.5 .
θ rg = 2 m 2 T - 1 3 - 4   arccos 1 m T cos 1 / 2 , | θ rg | = θ - c λ D Airy 2 / 3 ,
θ rg 1 = θ M 1 - 46.15 λ D Airy 1 2 / 3 ,
θ rg 2 = θ inf 1 - 13.91 λ D Airy 2 2 / 3 .

Metrics