# Study of Deformation and Breakup of Submillimeter Droplets' Spray in a Supersonic Nozzle Flow
## Materials and Methods  
The behavior of liquid drops introduced into a gradually accelerating air flow in a converging-diverging nozzle was investigated. A converging-diverging nozzle with a rectangular cross-section and a throat size of 8 \(\times\) 10 mm was employed for the study. Optical access to the measurement area was provided by transparent flat side walls of the nozzle. A compressor supplied constant airflow through the air supply line at the rate of 36 L/s. Air flow temperature and pressure were measured in the settling chamber preceding the converging part of the nozzle. The nozzle was operated in a choked regime with the formation of a Mach disk inside the divergent part of the nozzle, at a distance of 11.5 mm from the nozzle throat. Droplets were introduced into the flow by atomization of the coaxial liquid jet of distilled water issued from the tube with an inner diameter of 0.5 mm. The exit of the tube was fixed in the settling chamber at a distance of 35 mm upstream of the nozzle throat. A fiber atomization regime of the round jet, described, e.g., in the review by [PERSON] and [PERSON] [PERSON] (2018), was observed at the exit of the tube. Large liquid clusters formed at the distance of 3-5 mm from the tube exit. Primary atomization was generally finished at the distance of 10-12 mm, the size of resulting drops mainly varied in the range from 10 to 100 \(\upmu\)m. A scheme of the setup and the flow inside the nozzle is shown in Figures 1 and 2, respectively. Figure 1: Scheme of the setup. 1—turboprop compressor, 2—pressure and temperature measurement sensors, 3—converging–diverging nozzle, 4—water supply tank, 5—pressure regulator, 6—pressure tank. Figure 2: Schematic of the underexpanded gas flow with injected droplets in the converging–diverging nozzle. Direct visualization of droplet's behavior in the flow using shadow photography (SP) played a key role in the work. To acquire a sharp image of a small-scale droplet in a supersonic flow, a high spatial resolution and short exposure are required. In the present work, short exposure was provided by a Rhodamine-B fluorescent background screen (thin cuvette filled with dyed ethanol), excited by 5-7 ns duration Nd:YAG laser (Quantel Evergreen EVG00200, Lannion, France) pulses. The fluorescent screen provided background lighting without speckles, which allowed visual analysis of small droplets. Images were captured by a CCD-camera (Bobcat B2020, Imperx, Boca Raton, FL, USA) with an Infinity K2/SC long-distance microscope (Infinity photo-optical, Centennial, CO, USA) with the optical magnification of 4.6:1, which is 1.6 \(\upmu\)m/pix. An example of the SP image is shown in Figure 3.  
The spatial resolution of the images was enough to measure the size of droplets larger than 15 \(\upmu\)m and to qualitatively analyze the morphology of droplets in the state of the breakup. At the same time, fine details and small droplets remained unresolved. An increase in spatial resolution could be useful for such tasks as the estimation of the breakup products' size distribution and analysis of the droplets' surface shape in the state of the breakup. An increase in resolution in future works can be achieved through the employment of cameras with smaller pixel size and employment of higher magnification optics, although considerations for the optics diffraction limit should be taken into account. During the exposure time, droplets' displacement was less than one pixel, and the motion blur of the droplets' images was negligible. The use of a dual-head laser and a CCD-camera in double-frame exposure mode allowed capturing pairs of images with a short interframe delay (down to 300 ns), fetching not only instant images but also an evolution of the droplets over two frames. A small depth-of-field (DOF) of the microscope, which was about a few hundreds of micrometers, allowed to localize the measurement region in the central plane of the nozzle. At the same time, out-of-focus droplets significantly hindered the evaluation.