Fluid Mechanics and Acoustics Laboratory - UMR 5509

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Evaporating droplets Lagrangian tracking

In turbulent flow, a droplet of intermediairy size is submitted to velocity fluctuations, and sometimes temperature and concentration, that modify its trajectory and its evaporation rate. A Lagrangian approach is then suitable to studies evaporation of such droplets. It consists in tracking droplets along their own trajectories which are, by nature, three-dimensional. Such 3D tracking can be done by using Digital In-line Holography. Associated to a reconstruction method based on an ’inverse problems’ approach, the technique provides the highly accurate measurements of droplet position and size, with a large enough probe volume as required for this phase change study.

A quazi-homogeneous and isotropic turbulence is generated in a small volume of about 5cm side, at the intersection of synthetic jets produced by 6 woofers. Ether droplets are generated by means of a piezo-electric injector. Their initial diameters ranges from 60 to 150 µm, depending on the injection head and atomisation mode that are selected. The droplets tracking by digital in-line holography is performed by means of a continuous laser (2W) and a high speed camera (6kHz), placed at about 50 cm from the droplets.

a droplet hologram consists of a set of concentric rings. This interferometric pattern contains information on both the droplet size and its distance from the sensor. The vapor wake, produced by the droplet is clearly visible on the holograms. Its orientation is related to the orientation of the relative velocity, the air velocity as viewed by the droplet.

Inverse problem approach reconstruction

Such small droplets are perfectly spherical and they can be considered as opaque objects due to their large distance tothe sensor. As a consequence a droplet can be fully described by only 4 parameters x , y , z and d representing its 3 coordinates and its diameters. The inverse problem restitution approach consists in comparaing the experimental hologram to a model hologram which is a function of the 4 parameters. In the present conditions, a scalar diffraction model for an opaque disk, with fraunhofer approximation is enough. The 4 parameters that minimize the difference between the model and the experimental hologram are considered as a measure of the 3D location ans the size of the droplet. After one droplet has been detected and measured, the best fit model can be subtracted to the hologram in order to facilitate the next droplet detection. The vapor contribution to the hologram is clearly visible on the residual image, as a wake but also as an excessively bright center and the 2 or 3 first rings that have not completely vanished after the best fit hologram subtraction

4D trajectory sample