Laser Beam Interaction with Spheroidal Droplets: Computation and Measurement

• Main Author: Yu, Haitao
• Format: Others
• Language: English; en
• Published: tuprints 2013
• Online Access: https://tuprints.ulb.tu-darmstadt.de/3714/7/Dissertation.pdf; Yu, Haitao <http://tuprints.ulb.tu-darmstadt.de/view/person/Yu=3AHaitao=3A=3A.html> (2013): Laser Beam Interaction with Spheroidal Droplets: Computation and Measurement.Darmstadt, tuprints, Technische Universität, [Ph.D. Thesis]

Sprays and droplets are involved in numerous industrial processes and in nature, e.g. fuel injection in combustion chambers, painting, spray cooling, spray coating, chemical engineering, cloud physics, etc. The understanding of the light scattering features from the droplets, or particles in general, lays the foundation for extending existing techniques or devising novel techniques for particle characterization. The optical techniques are clearly advantageous over sampling, because of their non-intrusiveness and immediacy of results. Typical particle characteristics of interest include refractive index, size, velocity, and especially for non-spherical particles, some information regarding shape or form and orientation. However, most of existing optical techniques are only available for the measurement of spherical particles. In this thesis, the light scattering from a spheroid is studied and the generalized rainbow technique is proposed for droplet non-sphericity measurement. First, the vector ray tracing (VRT) model is employed to simulate the optical caustic structures in the primary rainbow region of oblate spheroidal droplets, which includes the rainbow and hyperbolic umbilic (HU) fringes. The location of cusp caustic is calculated by use of the VRT simulation and compared with that calculated by using analytic solution, exhibiting excellent agreement. Furthermore, the evolution process of the optical caustic structures is consistent with the experimental observation. It reveals that the optical caustic structures in the primary rainbow region can be used to measure the non-sphericity of oblate droplets. The VRT model can also be used to simulate and predict the optical caustic structures observed in higher-order rainbows. As a further validation, the cusp location and optical caustic structures in the secondary rainbow region also have been studied using the VRT method. The secondary rainbow fringe, as well as the location and opening rate of the cusp caustic provide a further avenue for non-sphericity measurement of oblate droplets. Then the character of the generalized rainbow pattern from a spheroidal water droplet is investigated experimentally. In the experiment, light scattering from spheroidal water droplets in the vicinity of the primary rainbow region has been observed to contain a variety of characteristic interference patterns which are the generalization of the rainbow from a sphere. These patterns start from being a fold rainbow, change to transverse cusp caustics and then to hyperbolic umbilic catastrophe as the aspect ratio of the droplet increases. A comparison of the intensity distribution of the observed rainbow patterns in the horizontal equatorial plane with those of Airy simulation reveals that these patterns can be used for characterizing droplets, in particular for determining the refractive index and the diameter of the spheroidal droplet in the equatorial plane. According to the generalized rainbow patterns and Airy approximation, the refractive index and equatorial diameter of water droplets can be inverted from the corresponding generalized rainbow patterns. A comparison of the refractive indices inverted from the corresponding generalized rainbow patterns with that of pure water shows good agreement with absolute errors less than 0.5x10-4. The water droplet diameters in the horizontal equatorial plane are calculated from the generalized rainbow patterns and compared to that measured by direct imaging. It is shown that the relative errors of droplet diameters associated with the generalized rainbow patterns lie between -5% and 5%; hence reliable diameter estimations of droplets can be obtained from the generalized rainbow patterns. The curvatures of simulated rainbow fringes are compared with observed ones from the generalized rainbow patterns, in which good agreement is also shown. Since for a given type of droplet, the curvatures of the rainbow fringes are only a function of the aspect ratios, the non-sphericity (in terms of aspect ratio) of water droplets are inferred from the relevant generalized rainbow patterns. The relative errors of aspect ratios calculated from the generalized rainbow pattern lie between -1% and 1%. Accordingly, the complete informations of a spheroidal water droplet in terms of geometric and optical properties are obtained. Then, the evolution of the optical caustic structures for tilted spheroidal droplets is investigated. The rainbow fringes are tilted counterclockwise as the spheroidal droplet is tilted counterclockwise and vice versa. The changes of the fringes depend on the aspect ratio and tilt angle. A preliminary experiment for tilted spheroidal droplet is shown. Furthermore, Mobius’s approximation is modified to calculate the deviation between the geometrical rainbow angle for an ellipse and that for a sphere. And the vector ray tracing model is also used to compute the rainbow angle deviation for an ellipse, which agrees with modified Mobius equation for small eccentricity. Moreover, the application range of Mobius’s approximation is also investigated. It is demonstrated that, for small eccentricity (0.95≤a/c ≤1.05), the Mobius approximation can predict the rainbow angle difference of ellipse.