**2. Experimental equipment for hypersonic flow generation and optical diagnostics**

In most cases, to implement a hypersonic gas flow with a high Mach number, a shock tube equipped at the end with a diaphragm and a Laval nozzle is used [18–20]. In this case, the hot gas behind the front of the reflected shock wave flows out through the nozzle into the vacuum reservoir at a hypersonic speed. However, due to the large expansion of the gas, its density turns out to be rather low, which greatly complicates the visualization of the flow. Thus, it is possible to estimate the angles of deflection *ε<sup>x</sup>* and *ε<sup>y</sup>* of the probe light beam in geometrical optics approach while schlieren method of hypersonic flow visualization is used [21].

$$\varepsilon\_{\varepsilon} = \frac{1}{n\_0} \int \frac{\partial n(\varkappa, \jmath)}{\partial \varkappa} d\varpi; \qquad \varepsilon\_{\jmath} \frac{1}{n\_0} \int \frac{\partial n(\varkappa, \jmath)}{\partial \jmath} d\varpi. \tag{1}$$

At the same time gradients of gas refraction index *<sup>∂</sup>n x*ð Þ , *<sup>y</sup> ∂y* and *<sup>∂</sup>n x*ð Þ , *<sup>y</sup> <sup>∂</sup><sup>x</sup>* are very small when the light gas outflows into vacuum. If helium is used as a light gas and the residual pressure in the vacuum chamber is 1 Torr and the characteristic scale of the streamlined body is �10�<sup>2</sup> m, then the characteristic gradients of the refractive index do not exceed 5 � <sup>10</sup>�<sup>6</sup> <sup>m</sup>‐1. Under these conditions, the use of shadow methods and interference diagnosis becomes almost impossible. Therefore, in such cases, it is necessary to use the methods of multipass interferometry, multibeam interferometry, interferometry in polarized light, holographic methods or shadow methods with a large focal length and special imaging diaphragms [22]. On the other hand, the use of light-gas launcher where accelerating chan-nel is replaced with Laval nozzle allows to receive a hypersonic flow with high optical density and to apply Tepler method to its visualization. Hypersonic flow facility studied in this research is a modified light-gas launcher we used for ballistic tests and described in details in article [23]. The scheme of the experimental setup is shown in **Figure 1**.

*Investigation of Hypersonic Conic Flows Generated by Magnetoplasma Light-Gas Gun Equipped… DOI: http://dx.doi.org/10.5772/intechopen.99457*

**Figure 1.** *Scheme of experimental facility.*

This light-gas gun allows to accelerate balls with a diameter of 2.5 mm to 4 mm made of high-alloy steel to speeds of 2.5–4 km/s.

During the experiments, the light gas section was filled with helium to a pressure of 40 bar. Experiments on hypersonic flow around cones were carried out in a vacuum chamber with a residual gas pressure of 1 Torr. As a result of a high-current discharge in a magnetoplasma accelerator filled with gunpowder, the piston is set in motion and causes an adiabatic compression of the light gas. The capacitor bank of 1 200 *μ*F was charged to the voltage 4.5 kV. In front of the confuser of Laval nozzle 5 brass diaphragms 100 *μ*m thick each were placed. The rupture of diaphragms occurred when pressure in light-gas section reaches �1 600 bars. Compression rate and temperature of working gas can be calculated from the Poisson equation:

$$\frac{T\_2}{T\_1} = \left(\frac{V\_1}{V\_2}\right)^{r-1} = \left(\frac{P\_2}{P\_1}\right)^{r-1/r},\tag{2}$$

where *<sup>T</sup>* is gas temperature, *<sup>V</sup>* is gas volume, *<sup>P</sup>* is gas pressure and *<sup>γ</sup>* <sup>¼</sup> <sup>5</sup> <sup>3</sup> for the monoatomic gas. Subscript 1 corresponds to initial state of gas and subscript 2 is for state of gas at diaphragms rupture. When diaphragms rupture compression rate of the working gas is about 10 and temperature is about 1500 K. With the simultaneous outflow of gas through the critical section of the Laval nozzle, further compression of the gas continues until the piston reaches the end point. The maximum compression ratio is about 50 and can be calculated as the ratio of the volume of the light gas section to the volume of the confuser of the Laval nozzle. The ratio of the throat to the outlet of the diffuser in the Laval nozzle for a Mach number of 18 was calculated using the formula [22, 24]:

$$\frac{A}{A\*} = \left(\frac{2}{\gamma+1}\right)^{\frac{r+1}{2(r-1)}} \frac{1}{M} \left(1 + \frac{\gamma-1}{2} M^2\right)^{\frac{r+1}{2(r-1)}},\tag{3}$$

where *A* is area of Laval nozzle exit section and *A* ∗ is area of Laval nozzle throat. The test cones were fixed coaxially with the nozzle at a distance of 20 mm from the nozzle outlet. To visualize the hypersonic gas flow, the shadow knife-and-slit method was used. Width of a slit was 0.16 mm. Foucault's knife was placed in the focal plane of a receiving part of the shadow device and shaded a half of the image of a slit. The 150 W halogen lamp was used as a light source. The focal length of the shadow device was 1 000 mm. Registration of shadow patterns was carried out using high-speed camera Photron Fastcam (300 000 fps) with an exposure time of 1 *μ*s (**Figure 2**).
