**3. Experimental results and discussion**

The analysis of shadow pictures sequence shows that at initial time the flow contains some particles formed as a result of diaphragm destruction and about each of which Mach cone (**Figure 2**) is observed. Further there is an increase of speed of a flow during 700 *μ*s and its subsequent recession during 3 400 *μ*s. At the maximum speed of the flow in shadow pictures the most acute angle of a shock wave inclination is observed. In **Figures 3** and **4** shadow pictures of a hypersonic flow over

#### **Figure 2.**

*Shadowgraph images of a hypersonic flow over cone with half-angle τ*<sup>2</sup> ¼ 12°*.*

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

**Figure 4.** *Shadowgraph of hypersonic flow over the cone with a half-angle τ*<sup>2</sup> ¼ 12°*.*

cones with half-angles *τ*<sup>1</sup> ¼ 3° and *τ*<sup>2</sup> ¼ 12° are presented at maximum speed of the hypersonic flow.

Correlation of Mach number and shock wave inclination angle observed on shadow images of hypersonic flow over sharp cone was described in details by [25] for the first time. Calculation of Mach number was carried out on the basis of measurement of shock wave inclination angle *σ* observed on shadow pictures (**Figures 3** and **4**) using formula [26]:

$$M\_1 = \csc \sigma \sqrt{\frac{2(B+C-\sec \sigma)}{(\chi+1)\left(B+C+\frac{\cos \sigma}{\sin^2 \sigma}\right) - (\chi-1)(B+C-\sec \sigma)}} \tag{4}$$

where

$$B = -\ln\left(\frac{\sin\pi}{1-\cos\pi}\right) - \frac{\cos\pi}{\sin^2\pi}; \qquad C = \ln\left(\frac{\sin\sigma}{1-\cos\sigma}\right). \tag{5}$$

The Mach number calculation results were M1 = 18 for hypersonic flow over cone with half-angle *τ*<sup>1</sup> ¼ 3° and *M*<sup>2</sup> ¼ 14*:*4 for the cone with *τ*<sup>2</sup> ¼ 12°.
