**Author details**

relations obtained earlier [4], the conditions are found, under which the probability of a chain branching reaches unity (*δ* ¼ 1), and a fast chain reaction is started. The existence of the critical temperature *Tx* at the front of a shock wave, above which the detonation takes place, is substantiated, as well as the functional dependence (5) of the critical temperature on the Mach number. In author's opinion, the latter should be taken as a basis, while studying the processes of spherical detonation. Summarizing the results of work [4], the ondition *T*<sup>2</sup> ≥ *Tx* is found, which connects the kinetics of a chemical reaction with the detonation in a gas mixture. On the basis of the relations of the hydrodynamic theory of detonation, the region of possible values for the temperatures at the shock wave front, *T*2, and in the chemical reaction zone, *T*3, is determined. The equality *Tx* ≈*T*<sup>2</sup> ≈*T*<sup>3</sup> which couples them, corresponds to the lower limit, at which the detonation is possible. The minimum and maximum values of Mach number in reacting gas media are also determined, which enables the process of supersonic burning to be analyzed in more details and the region of physical parameters and quantities (the critical emperature, the temperature of detonation in the motionless medium, and the hydrogen content in the mixture), at which the spherical detonation is probable, to be indicated. The latter is

llustrated, by using the hydrogen-oxygen mixture as an example.

**Acknowledgements**

**Nomenclature**

Basic designations:

long-term fruitful cooperation.

*Recent Advances in Numerical Simulations*

H2 hydrogen molecule O2 oxygen molecule H2O water molecule O oxygen atom H hydrogen atom

*Tx* critical temperature

*δ* branching probability

*ES* explosive substance *DP* detonation products *CRZ* chemical reaction zone

*K* <sup>∗</sup> *universal gas constant*

*M* Mach number

*γ* adiabatic index

*μ molar mass*

**162**

*T*<sup>2</sup> temperature at the shock front

*D* shock wave velocity, detonation velocity

*P*, *T*, *ρ* pressure, temperature, density of the medium

*Q combustion energy of one mole of combustible gas*

*E*<sup>2</sup> the activation energy of the branching reaction

To summarize, it should be noted that this paper is final in a cycle of works

The author expresses his sincere gratitude to Yu.L. Birkovoi, the former head of the technological department of microelectronics of the known, in the past, production association "Rodon", as well as to the whole team of this department, for a

devoted to the study of the whole process of normal spherical detonation.

OH compound of an oxygen atom with a hydrogen atom

Myron Polatayko Kyiv National University, Kyiv, Ukraine

\*Address all correspondence to: pmm.miron@gmail.com

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
