# Physical and Mathematical Modeling of the Interaction of Water Droplets and High-Speed Gas Flow
## 2 Research Methodology  
### Experimental Data  
The experimental data were used for the analysis published by the authors earlier in [29] as well as the results of new experiments obtained with the usage of a similar experimental setup. The working part of the experimental setup (Figure 1) is a channel of constant cross-section (transverse dimensions 75 \(\times\) 75 mm) with a supersonic air flow. To obtain a supersonic flow at the inlet to the test section of the experimental setup, three different central aerodynamic nozzles were installed (the setup scheme is shown in Figure 2). These nozzles were designed to generate a flow with Mach numbers in the range from 2 to 3 with a step of 0.5. Let us take the following designations in the text: nozzle 1 corresponds to the calculated Mach number M = 2, nozzle 2 corresponds to the calculated Mach number M = 2.5, nozzle 3 corresponds to the calculated Mach number M = 3. The configuration of the nozzles is selected on the profiling basis by the method of characteristics with respect to the growth of the boundary layer. The criterion for choosing the nozzle profile was the uniformity of the flow in the outlet section. To implement the flow with oblique shock waves the special wedge with an angle of 10\({}^{\circ}\) relative to the axis of the experimental setup working part was installed on the upper wall of the channel behind the nozzle. In the end part of all aerodynamic nozzles, there was an orifice with a diameter of d = 0.7 mm, through which water was injected co-directionally with the air flow at supply pressures from \(\mathrm{P_{liquid}}\) = 0.6 MPa to \(\mathrm{P_{liquid}}\) = 1.6 MPa. The length of the orifice in all nozzles was \(\sim\)100 mm. Particle Image Velocimetry (PIV) measurements were carried out to confirm the distribution of the flow velocity in the duct during preliminary investigation without liquid injection [30]. To register tracers a video camera with a resolution of 1600 \(\times\) 1200 pixels was installed in the mode of the double exposure with a delay of 3... 8 \(\upmu\)s. To illuminate the tracers we used a laser knife based on a double Nd:YAG laser with a 532 nm second harmonic generator and an energy in one pulse up to 125 mJ. The measurement frequency was up to 10 Hz. Taking into account the preliminary approach carried out for high velocity flows the shadow method was used in the experiments at the diagnostic method of liquid droplet parameters [31]. The mentioned method makes it possible to determine the droplet velocity vector and droplet diameter. The minimum recognizable droplet size that can be recognized by the equipment was 5 \(\upmu\)m. The measurements were carried out in two areas (1 initial, 2 final). The dimensions of each measurement area were up to 2 mm \(\times\) 2 mm. The  
Figure 1: General view of the experimental setup: 1—pneumatic valve; 2—receiver; 3—working chamber with the supersonic insert and water supply to the stream; 4—vacuum chamber, 5—vacuum seal, 6–gas flow path, 7—gas tanks. Figure 2: The layout of the wedge in the experimental setup: 1—central aerodynamic nozzle; 2—nozzle for water supply; 3—wedge; 4—water supply channel. coordinates of the centers of the measuring regions for different modes are presented in Table 1. Some differences in the coordinates of the measuring regions are associated with the peculiarities of the flow (shock wave and droplet trajectories). The position of the water injector nozzle corresponds to the coordinate (0,0). Within the framework of the present work 6 experiments without water supply (M = 2, M = 2.5, M = 3; without wedge and with it) were carried out to confirm the correspondence of the gas-dynamic flow parameters to the calculated ones, as well as three starts for each nozzle with different water injection pressures. The launches were carried out both with the installed wedge and without it (18 modes). Each of the experiments was repeated several times to obtain reliable data and their averaging.