**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

doi: 10.17586/2226-1494-2015-15-5-930-941

doi: 10.17586/2226-1494-2015-15-5-930-941

# INTERFERENCE HYSTERESIS OF COUNTERPROPAGATING SHOCK WAVES AT A CHANGE IN MACH NUMBER

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**Article in**Russian

**For citation:**Bulat P.V., Denissenko P.V., Prodan N.V., Upyrev V.V. Interference hysteresis of counterpropagating shock waves at a change in Mach number.

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*, 2015, vol. 15, no. 5, pp. 930–941.

**Abstract**

**Subject of Study.** We study the interference of counterpropagating shock waves and oblique shock reflection from the wall. There are two fundamentally different interaction modes of counterpropagating shocks: four-wave regular and five-wave irregular ones. The transition from one mode to another can be abrupt or smooth; it can also be accompanied by hysteresis. Hysteresis is the existence of two different types of shock-wave structures with the same parameters of interference. The implementation of a particular decision depends on the direction and perhaps the rate of change of parameters. Hysteresis in the interference of counterpropagating shocks and oblique shock wave reflection from the wall has been studying since the mid-60s of the XX-th century, the most actively in the past 20 years. This is due to the development of new types of internal and mixed compression intakes, in particular, intended for high supersonic and hypersonic speeds. Despite of problem research for many years, many questions still remain unclarified and among them nonconcurrence of the numerical and physical experiment results with the data obtained by analytical theory of interference stationary gas-dynamic discontinuities, the effect of the rate change for parameters, the accuracy of calculations, the difference grid density. The present paper deals with the impact of two factors: the rank of difference grid and blurring degree of shock waves front. **Main Results**. Analytical and numerical calculations have shown that blurring of shock waves and the transition from small difference grid to a coarser one is accompanied by narrowing of the hysteresis domain, i.e. the transitions from regular to irregular reflection and backwards are more different from those predicted by the theory. Reducing the size of the difference grid cells leads to solution convergence to the results of interference theory of stationary gas-dynamic discontinuities. **Practical Relevance.** Obtained findings complement the interference theory of stationary gas-dynamic discontinuities and are usable in the design of advanced models of supersonic and hypersonic aircrafts.

**Keywords:**shock wave, Mach reflection, counterpropagating shock waves, shock-wave structures, hysteresis.

**Acknowledgements.**The work was carried out under financial support from the Ministry of Education and Science of the Russian Federation (Agreement No.14.575.21.0057).

**References**