# Study of Deformation and Breakup of Submillimeter Droplets' Spray in a Supersonic Nozzle Flow
## Materials and Methods
Automatic and manual processing of shadow images was employed for different purposes. Images of droplets in the state of the breakup were extracted and analyzed manually. Automatic processing was used to detect non-disrupting droplets in the images and to aggregate the statistical data for such droplets. The automatic image processing procedure was implemented using Python 3.6 programming language with Numpy 1.13.3 and OpenCV 3.3 open-source libraries. The processing procedure consisted of several steps. In the first step, a custom local variance filter [23] was applied to detect edges in the image. After that, a blob detector method from the OpenCV kit was employed to find contours (connected areas) in the image. The blob detector method performs multiple threshold binarization of images and extracts connected areas (contours) from each binary image using the border traversal algorithm implemented by the FindContours class of the OpenCV module. The blob detection procedure yielded a center of mass, the area and perimeter length of each detected contour. Variance filter and blob detector processing parameters were fine-tuned to detect only sharp contours of  
Figure 3: Fragment of a typical shadow photography (SP) image. the droplets. No DOF correction method [24] was employed in the experiments, but, as the processing parameters were tuned specifically to reject even slightly blurred out-of-focus droplets, and the droplets' size range was rather small, the statistical bias due to DOF effect could be ignored. Additional filtering was applied to the extracted contours. Contours with the area smaller than 30 pixels2 (corresponding to the area of the droplet with equivalent sphere diameter \(d\) of 10 \(\upmu\)m) were filtered out. Lower size threshold was set because smaller droplets were not expected to feature breakup or significant deformation. The second filter employed the isoperimetric quotient \(Q\) of the contour as the parameter:  
\[Q=\frac{4\pi S}{p^{2}} \tag{8}\]  
where \(S\) is the area of the contour, and \(P\) is the perimeter of the contour. Isoperimetric quotient shows a ratio of the contour's area to the area of a circle with the same boundary length. Contours with \(Q<0.6\) were rejected. Such filtering passed elongated or slightly deformed droplets, but reliably rejected fibers, ligaments and droplets in the state of breakup. The filter with the threshold of \(Q=0.6\) passed the droplets with \(d_{max}\)/\(d<1.8\), considering a deformed droplet as an ellipse. The processing method was tested on generated images and experimentally on the images of monodisperse glass microspheres (Whitehouse Scientific Ltd., Waverton, Cheshire, UK) of \(d=25.6\)\(\upmu\)m and \(d=84.3\)\(\upmu\)m, and yielded an RMS error of about 1.7 \(\upmu\)m in the conditions similar to the present experiments. Additionally, particle image velocimetry (PIV) and particle tracking velocimetry (PTV) techniques were used to assess the gas and droplets' velocity fields in the nozzle. Water-glycerol tracing particles of the size of about one \(\upmu\)m were produced by the Laskin-nozzle type aerosol generator and were introduced into the air supply line immediately after the outlet of the compressor. Gas and droplets velocities were acquired in separate experiments. Gas velocity distribution was measured in the flow without droplets, as droplets' images, which are much brighter than the images of tracer particles, made a proper evaluation of PIV data impossible. It is important to note for further consideration, that PIV tracer's response to the abrupt deceleration of the flow after the shock wave front is not instant because of the tracer's inertia. In the described experimental conditions. Relaxation length of the tracers after the shock wave (SW) front was about 2 mm, and the gas velocity data in this region were overestimated.