Experimental Research of Gasdynamic Liquid Drops Breakup in the Supersonic Flow with an Oblique Shock Wave

Abstract

This paper is devoted to understanding gasdynamic liquid drops breakup in a supersonic flow with presence of an oblique shock wave. An experimental facility, diagnostic tools and an experimental methodology are presented as well as numerical simulations results. Computations and experiments were used to get flow parameters in the duct with supersonic flow at Mach numbers 2.0, 2.5, and 3.0. The droplets were made to interact with a single oblique shock wave generated by a wedge in the test section. Experimental data are obtained for the change in diameter of the droplets and the change in speed of droplets in a supersonic flow at the three Mach numbers. The data are presented for an initial Weber number over the range of 16–115. It is shown that the mass loss rate of droplets are quadratically related to the Weber number, irrespective of the presence of oblique shock.

INTRODUCTION

Two-phase supersonic flows often occur in propulsion systems and technological devices of different functions [1–4], when there is a need to inject liquid into a high speed stream. It is necessary to note that understanding of injection of liquid, drops formation and their subsequent destruction due to gasdynamic breakup is an important scientific and technical problem. Solving this problem can help predict distribution of droplets of various disperse composition in a supersonic flow. The close relation of liquids spray process with efficiency of the power propulsion systems and technological devices renders this problem important and relevant [5–7].

The modern physical and mathematical models used for the description of trajectory, the time history of weight and sizes of drops are based on different empirical data, some of which are presented in [8–15]. This data is obtained in the core for single drops in streams with high, short-time pressure gradients. However, use of these models requires application of some significant assumptions and results interpolation. It can lead to considerable differences between complex physical processes in two-phase flows and the predictions of the model.

Besides, as shown in earlier studies, on the injections of a liquid in subsonic streams with the Mach number in range from 0.24 to 0.55 [16], the destruction of droplets have significant impact on not only the average values of flow parameters (like pressure, speed, gas density), but also gasdynamic properties of flow. It was shown that [16], for those regimes considered, non-uniform distribution of gasdynamic properties, intense velocity fluctuations, and also recirculation zones, all of which can lead to an intensification of droplet breakup. Utheza et al. [17] investigated the interaction of an oblique shock with a two phase flow and found breakup of droplets weakens the shock wave when compared to shock wave in single phase flow. Ren and Wang [18] analysed the aerodynamic and thermal response of droplets, post oblique shock wave. They found that small sized droplets responded well to shock wave when compared with large size droplets. It was also found that aerodynamic response of the droplets were more prominent than their corresponding thermal response. Ren et al. [19] examined the distortion of the incident shock by supersonic mixing layer which resulted in a refracted shock, a reflected shock and a transmitted shock wave. In the vortex, refracted shocks are broken and connected with upper and lower portion of the vortex. Kailasanath et al. [20] investigated interaction of shock wave with particles and liquid fuel droplets. In case of liquid droplets, attenuation rate is accelerated due to vaporization, compared to solid particles.

The generalization of the available computational and experimental data [6, 8] made it possible to show that two main mechanisms participate in the gas-dynamic droplets breakup: the breakdown of the boundary layer and the mechanism based on the separation of microparticles from the ridges of wave disturbances on the side surface of the droplet formed as a result of the development of the Kelvin-Helmholtz instability. In some cases, there is even an effect of reverse coagulation of detached particles on the surface of the drop. At the same time, the intensity of gas-dynamic crushing is significantly reduced.

Another earlier study [21] indicates that, for supersonic flows considerable influence on gasdynamic breakup of droplets and their spatial distribution renders presence of shock wave structure. However, it is necessary to note that at present there are not enough experimental data for definition of regularity of liquid injection, formation of drops and their destruction in a supersonic flow with oblique shock waves. This is due to the complexity of the experiment itself, diagnostics of two-phase flows and the acquisition of quantitative parameters to quantify drops breakup.

Considering the aforesaid, this work aims to obtain new experimental data related to gasdynamic droplet breakup in supersonic flows inclusive of oblique shock waves. Such data can allow to specify uniformity and reveal features of physical processes of a two-phase mixing. Further, results of research can be used for development and validation of physical and mathematical models used in high-level numerical simulations and at engineering calculations also.

EXPERIMENTAL FACILITY AND DIAGNOSTIC TOOLS

The atmospheric-vacuum wind tunnel facility ST-4 in Moscow Institute of Physics and Technology (MIPT) was modified to investigate gasdynamic breakup of droplets in a supersonic flow. The duct design and experimental facility are presented in Fig. 1. Initially, the flow starts by opening of a valve 1. Air from atmosphere enters the settling chamber 2, passes through the flow straightener lattice 3 and then the turbulence grid 4 to arrive at the model chamber 5. The aerodynamic nozzle (ADN) 6 accelerates the flow to supersonic speeds. The relevant modifications to the experimental facility using different profiles of ADN center body were presented in [16]. Flow speed was changed by changing the central body ADN. In the tail of each central body of the ADN, channels are provided with an outlet of 0.5 mm diameter through which water is injected. This center body nozzle configuration was chosen since this causes minimum disturbance to the core supersonic flow due to liquid injection. Necessary operating time of the tunnel with constant flow parameters in the test section was provided. The air exit the test section through a low pressure chamber 9 connected to vacuum pump system. The air then exhausts through vacuum pumps. Water was used as the injected liquid in experiments. After ADN, the test section of the model chamber had a constant square cross section with area 56 cm². Sizes of flow straightener lattice cell and the grid cell were 5 mm × 5 mm, and 0.8 mm × 0.8 mm, respectively. Static pressure sensors 10 were placed along the flow path after the ADN. Transparent windows 8 were provided for optical diagnostics of the two phase flow. A wedge insert 11 was used to generate an oblique shock wave for this study.

Fig. 1.

The experimental installation duct design: (1) valve, (2) an entrance section, (3) a flow straightener lattice, (4) a turbulence grid, (5) model chamber, (6) ADN with the central body, (7) injector, (8) transparent windows, (9) a pressure chamber, (10) pressure sensors, (11) a wedge-shaped insert.

For finding the flow structure behind the aerodynamic nozzle using optical diagnostics, high-speed camera and shadow device IAB-451 [22] were used. These equipment’s gave monochrome shadowgraph images with the resolution of 1024 × 1024 px with speed of 3600 frame/s.

Determination of the instantaneous velocity field of the gas flow behind the aerodynamic nozzle (without liquid injection) was done by Particle Image Velocimetry (PIV) [23]. Oil tracer particles of size less than 1 μm, from Laskin nozzle [23], were used for this purpose. PIV images were recorded by a double exposure (exposition delay was of 3 to 8 μs) camera with resolution of 1600 × 1200 was used. This gave the spatial resolution of 1052 pixel/mm. The particles were illuminated by a laser sheet from frequency doubled Nd:YAG laser (532 nm) and energy in one pulse up to 125 mJ was used. The frequency of measurements was 10 Hz.

As done in earlier studies, for high-speed streams [16] shadowgraph method was chosen to obtain parameters of liquid drops in experiments (Fig. 2) [24]. For this purpose, one side of the test section had a special optical objective diffuser, which transformed the coherent laser beam into incoherent and provide uniform back illumination of the two-phase stream. Incoherent plane-parallel light beam is passed through the transparent windows into the test section and then is captured by the camera. The presence of droplets alters the light intensity reaching the camera array. In this case the darkening region represents the shape of the drops. Use of the dual pulse laser allows to obtain two images with a short time delay, which gives the ability to measure the velocity of the droplets in the two phase flow. In Fig. 2, the segment of the characteristic photo obtained by system during experiment is presented.

Fig. 2.

(a) Schematic of the shadow method for droplet measurement and (b) a typical image of a two-phase flow with droplet sizes in μm: (1) test section, (2) windows, (3) optical diffuser, (4) lens and camera.

CHARACTERIZATION OF THE SUPERSONIC AIR FLOW IN THE EXPERIMENTAL SETUP

Profile of central bodies of ADN has been obtained from method of characteristics [25] proceeding from criterion of maximum uniformity of a stream before the liquid injection location. Three different central bodies were made with design Mach numbers on the exit M = 2.0 (no. 1), 2.5 (no. 2), 3.0 (no. 3). To have better understanding of the flow structure, 2D numerical simulation of the flow was also performed by solving the equations of conservation of mass, impulse and energy for viscous perfect gas. Calculated distributions of Mach number near the central body are presented in Fig. 3. The nozzle configuration was selected based on profiling by the method of characteristics, taking into account the growth of the boundary layer. It should be noted that for the selected nozzles in the flow core the Mach number unevenness is less than 1%. From calculations, it is seen that in the exit cross section of ADN the flow is reasonably uniform. It should be noted that a boundary layer is formed along the central body, and after the trailing edge it forms a shear layer behind the ADN. The flow in this shear layer is accelerated by the supersonic streams on both sides, which increased the gas velocity from subsonic to supersonic, in less than 10 mm.

Fig. 3.

Mach number fields in symmetry plane for different ADNs obtained from the simulations of air flow: (a) ADN no. 1, M = 2.0; (b) no. 2, M = 2.5; (c) no. 3 M = 3.0.

In order to experimentally confirm calculated flow parameters, static pressure measurements along the test section of experimental setup were performed. These static pressure measurements were used to calculate the flow Mach number near the pressure ports, which were behind the ADN at distances x/h = 1.6 and 4.8. Here, x is the longitudinal co-ordinate from nozzle exit cross section and h is the height of the flowing path of experimental setup. Assuming the total pressure is the atmospheric pressure for this tunnel and using isentropic relations, Mach numbers were evaluated from static pressures at those port locations.

The maximum operating time for the experimental setup, t_max is defined as the time during which the flow path is guaranteed to retain supersonic flow. Table 1 presents the measured pressure data for the three ADNs, the calculated values of Mach numbers and the Mach number obtained from pressure data. Table 1 shows that the difference between the calculated and experimental values of the Mach number is not more than 13%. The difference may be due to the influence of real geometry of experimental setup, and the spatial 3D effects, which are not considered in numerical calculations. Experimental values of t_max show the tunnel has same flow for more than 83 s, suggesting that there is sufficient time for diagnostics, and appropriate data averaging for PIV measurements and a shadow imaging (for diagnostic of drops).

Table 1.   Calculated and experimental data

For characterizing the transverse distribution of velocity and its fluctuations, PIV measurements were performed. Typical plots of the time-averaged velocity magnitude $\left| {\mathbf{u}} \right|$ and its root-mean-square (RMS) fluctuation σ along the axis of the experimental setup and in different cross sections are shown in Fig. 4. In these plots, the maximum values of time averaged velocity magnitude $\left| {\mathbf{u}} \right|$_max, a difference between minimum and maximum values of time averaged velocity magnitude Δ$\left| {\mathbf{u}} \right|$ and the maximum values of RMS fluctuations of the velocity magnitude σ_max are depicted.

Fig. 4.

Typical plots of the time-averaged velocity module |u| and its mean-square deviation behind ADN on a channel axis (a) and in a cross sections (b).

Lower values of velocity magnitude and the high fluctuations were observed along the centerline of the test section downstream of the nozzle as shown in Fig. 4. This is due to the ADN center body boundary layer leaving the body at the trailing edge and forming a shear layer. These type of shear layers are unstable and have vortex roll up and shedding causing fluctuations in the flow. This shear layer continues to spread downstream, as is evidenced by a slightly lower value of the velocity, as well as a markedly increased value of its fluctuations. The RMS fluctuations reach a maximum value σ_max at a distance x/h ~ 0.2 and then decrease at higher distances. In cross section normal to flow, the velocity is almost uniform and decreases only near the walls due to frictional force on the walls. The Δ|u| is observed to decrease along the flow direction.

For further ease of analysis of gasdynamic droplet breakup, it is easier to average the flow velocity in various cross sections and to define, for each cross section, a characteristic average Mach number. The following relation can be used for this purpose:

$${\text{M}} = \frac{1}{{\sqrt {\frac{{{\kern 1pt} \gamma R{{T}_{0}}}}{{\mu {{{\left| {{\mathbf{\bar {u}}}} \right|}}^{2}}}} - \frac{{\gamma - 1}}{2}} }}.$$

Here, $\left| {{\mathbf{\bar {u}}}} \right|$ is the cross section averaged flow velocity magnitude; R is universal gas constant; μ the molar weight of air; T₀ the stagnation temperature of air.

Values $\left| {{\mathbf{\bar {u}}}} \right|$, M, |u|_max/$\left| {{\mathbf{\bar {u}}}} \right|$, Δ|u|/$\left| {{\mathbf{\bar {u}}}} \right|$, and σ_max/$\left| {{\mathbf{\bar {u}}}} \right|$, obtained with use of PIV method for cross section x/h ≈ 1 are presented in Table 2.

Table 2.   Experimental data, obtained with use of PIV method

The values of Mach number obtained from PIV measurements can be compared to the data converted from static pressure measurements (see Table 1). It is necessary to note that for ADN nos. 1 and 3, data has correlated well (a difference no more than 6%). However, for ADN no. 2 the difference is about 12%. This difference could be due to experimental errors, small location differences, as well as the geometric features of the experimental setup. Averaging the data obtained from the different methods of estimating the Mach number, we can estimate the Mach numbers of the flow to be equal to 1.74, 2.29, and 2.74 for ADN nos. 1, 2, and 3, respectively.

The maximum velocity |u|_max exceeds averaged value $\left| {{\mathbf{\bar {u}}}} \right|$ no more than 2% for all ADNs. Value Δ|u| makes up to 8.4% of $\left| {{\mathbf{\bar {u}}}} \right|$ for ADN1 and lesser for higher Mach number ADNs. These parameters specify in uniform enough air flow in the flowing path. The value σ_max/$\left| {{\mathbf{\bar {u}}}} \right|$, characterizing fluctuations in velocity, is in the range 0.075 to 0.087 and grows with Mach number increase. It is necessary to note that relative variations of velocity for a supersonic flow is essentially less than the similar data presented for a subsonic flow in [16]. This fluctuation is inevitable and is a consequence of stabilization of flow and minimization of reverse flows behind the central body of the ADN.

In order to study the influence of oblique shock waves on gasdynamic breakup of droplets in a supersonic flow, wedge-shaped insert with an angle of 10° was installed in the experimental setup. The distance between the nozzle trailing edge and wedge-shaped insert back step is about 24 mm. The presence of the insert leads to change of the structure of the flow. Its pattern is presented in Fig. 5 (as example the Mach number field in the plane of symmetry for ADN1 is shown). It is evident that there is an oblique shock wave generated from the leading edge of the wedge and is reflected at the walls to form a system of shock waves. One can also note that there is an expansion wave generated from the trailing edge of the wedge.

Fig. 5.

Mach number distribution in a plane of symmetry for ADN no. 1 with a wedge: (1) oblique shock wave, (2) expansion wave, (3) reflected shock wave.

Shadowgraph imaging of flow with various ADN (Fig. 6) shows that there is an oblique shock wave interacting with the trailing edge shear layer of the ADN as desired. One can notice that there are weak oblique shock waves inside the ADNs. These are most likely due to geometrical irregularities of the flow path. This can also be the reason for differences between the design and experimental fixed values of a Mach number in the flowing path behind ADN (see Tables 1 and 2). Further, it can be noted that at the trailing edge of the ADNs there is a system of expansion and shock system on each side due to the end of the wall and recirculation region behind it. The wavy disturbances seen on the nozzle contour are due to optical illusion caused window glass deformation. Another flow feature shown by the shadow imaging is the relatively low velocity wake behind the ADNs. This may slightly influence the flow behavior and structure. In Figs. 5 and 6 one can see some difference in the position of the shock wave. This is due to differences in the Mach number in the calculations and in the experiment.

Fig. 6.

Shadow pictures of the flow with the installed wedge-shaped insert for various ADNs: no. 1 (a), no. 2 (b), and no. 3 (c).

Thus the flow facility is characterized well to be used for the study of gasdynamic breakup of droplets of a liquid.

ANALYSIS OF GASDYNAMIC CRUSHING OF DROPS

In the experiments the differential pressure of the water from 0.45 to 1.55 MPa was studied. For the realized pressure drops in the nozzle, the calculated initial droplet diameters range from 80 to 400 μm.

In order to understand the influence of flow parameters on gasdynamic breakup of drops for all ADNs, experiments were performed with various mass flow rates of liquid water. Thus, for each mass flow rate of liquid the droplet parameters (velocities and diameter distributions) in two small regions of the flow were measured. Region 1 (Fig. 7) is an area of 1 mm × 1 mm located on the axis of the flow, 20 mm from the trailing edge of the center body. Region 2 is a similar area located 100 mm downstream of region 1. This distance is chosen so that for all the nozzles, for the wedge insert used, region 2 will be downstream of the oblique shock, while region 1 will be upstream. Experiments were performed for three Mach numbers, with and without the wedge, for various mass flow rates of water. It is to be noted that at various mass flow rates of liquid region 1 can have droplets of various speeds and diameters. Such an approach at conducting of experiments and measurements gives the chance to understand the rate of droplet mass loss during gasdynamic breakup in a supersonic flow, and to estimate the influence of presence of an oblique shock wave on the intensity of this process.

Fig. 7.

An example of the shadow pattern as the fluid spray with the specified fields of measurements: (1) region 1, (2) region 2.

It should be noted that the intensity of mass loss by drops was not evaluated in the area after the nozzle to the region 1.

Examples of distribution of droplet parameters in region 1 and region 2 for the cases with and without wedge for ADN no. 1 are presented in Fig. 8. Histograms show the quantitative distribution of droplets by diameters D and average values of droplet velocity V magnitude. Also the range of magnitudes of average droplet velocity V ± σ_d/2 are presented, where σ_d is RMS variation of velocity.

Fig. 8.

Distributions of diameters (left) and velocities (right) of droplets for ADN no. 1 case in two regions: (a) 1, (b) 2 without wedge, and (c) 2 with wedge installed; water pressure was 5 bar; (1) V + σ_d/2, (2) V, (3) V – σ_d/2, figures at the left are drawn for (a) N = 52 291, D₁₀ = 13.33 μm, D₃₂ 37.88; (b) 91 124, 9.76, 19.63; (c) 113 725, 7.96, 14.01.

From the histograms presented, it can be seen that the distribution of D in region 2 has a much larger number of small drops than region 1, which indicates an intense gasdynamic breakup of droplets. It is seen from region 1 to region 2 that the average droplet velocity magnitude, V increases due to flow drag for the case without shock. This is seen to be faster for small D as the values are closer to the gas velocity magnitude, while for large droplets, a significant velocity non-equilibrium between expected flow and the droplet velocity can be observed. Averaged results V are quite reliable considering the large number of droplets used for measurement (more than 50 000) in the course of every run (with most of them very small droplets).

Further, it can be seen that in the presence of a shock wave the number of small droplets (less than 25 μm) in region 2 is increased further. This suggests that the droplets are broken into smaller sizes by the oblique shock. This is explained by a sudden decrease in the flow rate more enhanced breakup of drops and a decrease in the velocity non-equilibrium of the two-phase flow.

The rate of droplet mass m loss during gasdynamic breakup can be estimated as the relation of the difference of drops mass of average dimensions in region 1 M_d1 and region 2 M_d2 to a characteristic residence time of drops based on spatial average of velocities between the two locations t_res:

$$m = \frac{{{{M}_{{d1}}} - {{M}_{{d2}}}}}{{{{t}_{{{\text{res}}}}}}}.$$

As an estimate of average dimension of droplets for this purpose, Sauter mean diameter ${{D}_{{32}}} = {{\sum\nolimits_{i = 1}^N {D_{i}^{3}} } \mathord{\left/ {\vphantom {{\sum\nolimits_{i = 1}^N {D_{i}^{3}} } {\sum\nolimits_{i = 1}^N {D_{i}^{2}} }}} \right. \kern-0em} {\sum\nolimits_{i = 1}^N {D_{i}^{2}} }}$ in each region was used. Here, N is the total number of registered drops. Between the two locations considered, a characteristic residence time can be estimated from the following ratio:

$${{t}_{{{\text{res}}}}} = \frac{{2\left( {{{x}_{2}} - {{x}_{1}}} \right)}}{{\left( {{{V}_{2}} + {{V}_{1}}} \right)}},$$

where x₁, V₁ are the longitudinal coordinate and the magnitude of velocity of the droplets of size D₃₂ in region 1, and x₂, V₂ are the longitudinal coordinate of the region 2 center and the magnitude of velocities of droplets with diameter D₃₂ in region 2.

The experimental data obtained in the case of the installed wedge insert and without it are presented in Tables 3 and 4.

Table 3.   Characteristics of drops breakup with wedge-shaped insert

Table 4.   Characteristics of drops breakup without wedge insert

On the basis of the analysis of the literature data [8–11] and previously carried out computational and experimental studies [6, 7, 13] it was found that the most significant effect on the intensity of the droplet breakup is provided by the Weber number, which relates the ratio of external gasdynamic forces acting on the drop and the surface tension forces of the liquid.

In order to summarize the data we introduce the initial Weber number based on properties of droplets of average size, in the region 1:

$${\text{W}}{{{\text{e}}}_{{\text{1}}}} = \frac{{{{\rho }_{{\text{g}}}}{{D}_{{{\text{32}}}}}{{{\left( {\left| {{\mathbf{\bar {u}}}} \right| - V} \right)}}^{2}}}}{\lambda },$$

where λ is surface tension, ρ_g is gas density.

As a result of data processing, the regularities of We₁ influence on the rate of droplet breakup in the presence and absence of wedge-shaped insert are obtained (Fig. 9). The curves in Fig. 9 are obtained by the following function:

$$m = (3 \times {{10}^{{ - 3}}}{\text{We}}_{1}^{2} + 0.36{\text{W}}{{{\text{e}}}_{1}}) \times {{10}^{{ - 10}}}.$$

Fig. 9.

Dependence of rate of drops breakup on initial Weber number: (1) with wedge and (2) without it.

The obtained values of the initial Weber number for droplets with diameters D₃₂ = 37.88 to 206.70 μm (for different injection pressure and injectors diameters) are in the range We₁ = 16 to 115. The maximum obtained drop mass loss rate was m < 3.7 × 10^–9 kg/s. The plot also shows quadratic fits to the data as dashed and dot-dashed curves. It can be seen that the mass loss rate m depends quadratically on We₁. The presented trend is the same for all flow Mach numbers tested here.

The plots with and without wedge insert show that the oblique shock wave from the wedge enhances the gasdynamic breakup of droplets. Thus, by introducing an oblique shock in the flow the drop mass loss rate can be increased to 1.8 times of that of breakup of drops in a supersonic flow without shock wave. This is due to the significant change in the flow velocity along the trajectory of the droplets and the local increase in the gasdynamic forces that leads to the acceleration of the droplet breakup. It is necessary to note here that the oblique shock wave also deflects the fluid stream from the axis a little. This is clearly seen in the shadow image (see Fig. 7).

To generalize the data and take into account the presence of shock-wave structure, the average Weber number We_av calculated along the trajectories of droplets can be introduced. Using the obtained computational and experimental data, the parameters of the gas flow, the averaged values of D₃₂ and the droplet velocities along the base trajectory were determined. Thus one can define We_av according to the relation

$$\begin{gathered} {\text{W}}{{{\text{e}}}_{{{\text{av}}}}} = \frac{{\int\limits_{x = {{x}_{1}}}^{{{x}_{2}}} {{{\rho }_{{\text{g}}}}{{D}_{{{\text{32}}}}}{{{\left( {\left| {\mathbf{u}} \right| - V} \right)}}^{2}}dx} }}{{\lambda \left( {{{x}_{2}} - {{x}_{1}}} \right)}} - {\text{W}}{{{\text{e}}}_{{{\text{cr}}}}} \\ \approx \frac{{\overline {{{D}_{{{\text{32}}}}}} \int\limits_{x = {{x}_{1}}}^{{{x}_{2}}} {{{\rho }_{{\text{g}}}}{{{\left( {\left| {\mathbf{u}} \right| - \overline V } \right)}}^{2}}dx} }}{{\lambda \left( {{{x}_{2}} - {{x}_{1}}} \right)}} - {\text{W}}{{{\text{e}}}_{{{\text{cr}}}}}, \\ \end{gathered} $$

where $\overline V$, $\overline {{{D}_{{{\text{32}}}}}}$ are trajectory-averaged values of droplet velocity and diameter D₃₂; We_cr is critical Weber number [26].

Using the newly defined Weber number, the two curves of rate of droplet break up can be collapsed onto a single quadratic curve as show in Fig. 10. This suggests that the rate of droplet mass loss is dependent on the parameter We_av.

Fig. 10.

Dependence of rate of gasdynamic breakup of drops on average Weber number.

The obtained dependence with a sufficiently high accuracy can be approximated by a quadratic equation in the form of m = (4.35 × 10^–3${\text{We}}_{{{\text{av}}}}^{2}$ + 0.16We_av) × 10^–10 kg/s (Fig. 10). The given dependence is characteristic for all observed flow Mach number and can be used as in cases with or without an oblique shock wave.

CONCLUSIONS

From the experimental study of gasdynamic breakup of droplets in supersonic flow, the following can be established:

(1) Mach numbers of the supersonic flow in the experimental setup are M = 1.74, 2.29, and 2.74. A low-speed wake of the central body of the ADN was observed for the sections under consideration, but the difference between the maximum and minimum velocities was utmost 8.4% of the average velocity. The relative value of the standard deviation of the velocity was from 7.5% to 8.7%, which indicates a relatively low level of velocity fluctuations in the flow.

(2) The obtained values of the initial Weber number for the studied drops with average diameters of 37.88 to 206.70 μm are in the range from 16 to 115. It was also found that in the study region, the rate of drops mass loss during their gasdynamic breakup can achieve up to 3.7 × 10^–9 kg/s. It was shown that the oblique shock wave arising from the wedge can increase the rate of drops mass loss by 1.8 times of one without a shock wave.

(3) It was established that the quadratic dependence can be used to describe the gas-dynamic breakup of droplets in the flow with/without the shock wave m = (0.435 × 10³${\text{We}}_{{{\text{av}}}}^{2}$ + 0.016We_av) × 10^–9 kg/s, which makes it possible to determine the rate of loss of droplets mass from the averaged Weber number along its trajectory.

The obtained data can be used at the stage of choosing the configuration of liquid injection systems in high-speed flow, as well as for the validation of mathematical models of gasdynamic breakup of droplets.