The droplet size, size distribution, refractive index, and temperature can be measured simultaneously by the rainbow technique. In the present work, the rainbow scattering diagram for a spherical droplet in the secondary rainbow region is simulated by the use of the generalized Lorenz-Mie theory. For achieving high spatial resolution in denser droplet sprays, a focused Gaussian beam is used. For droplet characterization, different inversion algorithms are investigated, which includes trough-trough (θmin1 and θmin2) method and inflection-inflection (θinf1 and θinf2) method. For the trough-trough algorithm, the absolute error of the refractive index is between ?6.4 × 10?4 and 1.7 × 10?4, and the error of the droplet radius is only between ?0.55% and 1.77%. For the inflection-inflection algorithm, the maximum absolute error of the inverted refractive index is less than ?1.1 × 10?3. The error of the droplet radius is between ?0.75% and 5.67%.
References
[1]
Tropea, C. (2011) Optical Particle Characterization in Flows. Annual Review of Fluid Mechanics, 43, 399-426. https://doi.org/10.1146/annurev-fluid-122109-160721
[2]
Sazhin, S. (2014) Droplets and Sprays. Springer, London. https://doi.org/10.1007/978-1-4471-6386-2
[3]
Dames, P., Gleich, B., Flemmer, A., Hajeket, K., Seidl, N., Wiekhorst, F., Eberbeck, D., Bittmann, I., Bergemann, C., Weyh, T., Trahms, L., Rosenecker, J. and Rudolphal, C. (2007) Targeted Delivery of Magnetic Aerosol Droplets to the Lung. Nature Nanotechnology, 2, 495-499. https://doi.org/10.1038/nnano.2007.217
[4]
Nascimento, L.F., Saldarriaga, C.V., Vanhavere, F., D’Agostino, E., Defraene, G. and Deene, Y.D. (2013) Characterization of OSL Al2O3:C Droplets for Medical Dosimetry. Radiation Measurements, 56, 200-204. https://doi.org/10.1016/j.radmeas.2013.01.048
[5]
Albrecht, H.E., Borys, M., Damaschke, N. and Tropea, C. (2003) Laser Doppler and Phase Doppler Measurement Techniques. Springer-Verlag, Heidelberg. https://doi.org/10.1007/978-3-662-05165-8
[6]
Adrian R.J. and Westerweel, J. (2010) Particle Image Velocimetry. Cambridge University Press, Cambridge UK.
[7]
Glover, A.R., Skippon, S.M. and Boyle, R.D. (1995) Interferometric Laser Imaging for Droplet Sizing: A Method for Droplet-Size Measurement in Sparse Spray Systems. Applied Optics, 34, 8409-8421. https://doi.org/10.1364/AO.34.008409
[8]
Wu, X.C., Lin, X.D., Yao, L.C., Wu, Y.C., Wu, C.Y., Chen, L.H. and Cen, K.F. (2019) Primary Fragmentation Behavior Investigation in Pulverized Coal Combustion with High-Speed Digital Inline Holography. Energy Fuels, 33, 8126-8134. https://doi.org/10.1021/acs.energyfuels.9b01521
[9]
Schäfer, W. and Tropea, C. (2014) Time-Shift Technique for Simultaneous Measurement of Size, Velocity, and Relative Refractive Index of Transparent Droplets or Particles in a flow. Applied Optics, 53, 588-597. https://doi.org/10.1364/AO.53.000588
[10]
van Beeck, J.P.A.J. and Riethmuller, M.L. (1995) Nonintrusive Measurements of Temperature and Size of Single Falling Raindrops. Applied Optics, 34, 1633-1639. https://doi.org/10.1364/AO.34.001633
[11]
Han, X.E., Ren, K.F., Wu, Z.S., Corbin, F., Gouesbet, G. and Gréhan, G. (1998) Characterization of Initial Disturbances in a Liquid Jet by Rainbow Sizing. Applied Optics, 37, 8498-8503. https://doi.org/10.1364/AO.37.008498
[12]
van Beeck, J.P.A.J., Giannoulis, D. and Zimmer, L. (1999) Global Rainbow Thermometry for Droplet-Temperature Measurement. Optics Letters, 24, 1696-1698. https://doi.org/10.1364/OL.24.001696
[13]
van Beeck, J.P.A.J., Zimmer, L. and Riethmuller, M.L. (2001) Global Rainbow Thermometry for Mean Temperature and Size Measurement of Spray Droplets. Particle & Particle Systems Characterization, 18, 196-204. https://doi.org/10.1002/1521-4117(200112)18:4<196::AID-PPSC196>3.0.CO;2-H
[14]
Vetrano, M.R., van Beeck, J.P.A.J. and Riethmuller, M.L. (2004) Global Rainbow Thermometry: Improvements in the Data Inversion Algorithm and Validation Technique in Liquid-Liquid Suspension. Applied Optics, 43, 3600-3607. https://doi.org/10.1364/AO.43.003600
[15]
Lemaitre, P., Porcheron, E., Gréhan, G. and Bouilloux, L. (2006) Development of a Global Rainbow Refractometry Technique to Measure the Temperature of Spray Droplets in a Large Containment Vessel. Measurement Science and Technology, 17, 1299-306. https://doi.org/10.1088/0957-0233/17/6/002
[16]
Wu, Y.C., Li, C., Cao, J.Z., Wu, X.C., Saengkaew, S., Chen, L.H., Gréhan, G. and Cen, K.F. (2018) Mixing Ratio Measurement in Multiple Sprays with Global Rainbow Refractometry. Experimental Thermal and Fluid Science, 98, 309-316. https://doi.org/10.1016/j.expthermflusci.2018.06.004
[17]
Yu, H.T., Sun, H. and Shen, J.Q. (2018) Measurements of Refractive Index and Size of a Spherical Drop from Gaussian Beam Scattering in the Primary Rainbow Region. Journal of Quantitative Spectroscopy and Radiative Transfer, 207, 83-88. https://doi.org/10.1016/j.jqsrt.2017.12.028
[18]
Cao, Y.Y., Wang, W.T., Yu, H.T., Shen, J.Q. and Tropea, C. (2020) Characterization of Refractive Index and Size of a Spherical Drop by Using Gaussian Beam Scattering in the Secondary Rainbow Region. Journal of Quantitative Spectroscopy and Radiative Transfer, 242, Article ID: 106785. https://doi.org/10.1016/j.jqsrt.2019.106785
[19]
Hulst, H.C.V.D. (1957) Light Scattering by Small Particles. Physics Today, 10, 28-30. https://doi.org/10.1063/1.3060205
[20]
Wang, R.T. and Hulst, H.C.V.D. (1991) Rainbows: Mie Computations and the Airy Approximation. Applied Optics, 30, 106-117. https://doi.org/10.1364/AO.30.000106