**5. Conclusions**

The dependences between the temperature, Mach number, the hydrogen content in the hydrogen-oxygen mixture as the main parameters characterizing the process of transformation of a shock wave into a detonation one and affecting the chemical reactions between reacting components are studied. On the basis of

Making allowance for Eqs. (29) and (30), relation (33) can be simplified to the

The corresponding family of curves is shown in **Figure 7**, according to **Table 4**. While analyzing the plots, the attention should be drawn to the following facts. (i) Every temperature *T*<sup>1</sup> of the gas mixture is associated with a specific dependence

*Diagrams of the dependence of the detonation temperature T*<sup>1</sup> *on the hydrogen content c in an explosive gas*

173°K *T*<sup>1</sup> 680 542 456 398 346 313 280 258 232 217 200 188 173 273°K 658 568 500 442 409 372 345 320 302 280 266 250 373°K 626 576 516 477 436 412 381 360 340 328 310 473°K 620 572 535 500 467 436 416 392 378 360 573°K 660 616 580 540 508 476 458 432 418 398 673°K 652 616 576 543 512 492 470 454 438 773°K 644 609 580 548 526 504 484 470 800°K 658 625 600 570 548 523 507 493

*Values of the detonation temperature T*<sup>1</sup>*, depending on the specific content of hydrogen c at T*<sup>1</sup> <sup>¼</sup> *const,*

*c* 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.66

*mixture H*<sup>2</sup> þ *O*<sup>2</sup> *(P* ¼ 60 *mm Hg) for different temperatures in a stationary environment, T*1*.*

� exp � *<sup>E</sup>*2ð Þ *<sup>γ</sup>* <sup>þ</sup> <sup>1</sup> <sup>2</sup>

*K* <sup>∗</sup> *T*<sup>1</sup>

*η*с

*:*

(34)

ð Þ 2*γη*с � *γ* þ 1 ð Þ 2 þ ð Þ *γ* � 1 *η*с

!

following form:

**Figure 7.**

**Table 4.**

**160**

*P*<sup>0</sup> ¼ 60 *mm Hg.*

*<sup>T</sup>*<sup>1</sup> � �<sup>2</sup> <sup>¼</sup> <sup>2</sup>*:*<sup>5</sup> � <sup>10</sup><sup>5</sup>

*T*0*T*1ð Þ *γ* þ 1

*cP*0ð Þ 2*γηc* � *γ* þ 1

*Recent Advances in Numerical Simulations*

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.

*d* the chemical reaction zone width

front

*T*<sup>3</sup> temperature at the Jouguet point

*vg* the gas velocity behind the reaction front

*b*<sup>1</sup> the sound velocity in the motionless medium in front of the

*Determination of Values Range of Physical Quantities and Existence Parameters of Normal…*

*c* coefficient of flammable gas content in the mixture

Δ*t* the reaction duration

*DOI: http://dx.doi.org/10.5772/intechopen.96285*

*W* chemical reaction rate *T*<sup>1</sup> detonation temperature *Mmax* maximum Mach number *Mmin* minimum Mach number *f x*ð Þ function of the variable x exp xð Þ exponential function Δ*x* increment of variable x

*m* gas mass

≪ much less ≫ much more ≈ almost equal ½ � *a*; *b* line segment

**Author details**

Myron Polatayko

**163**

Kyiv National University, Kyiv, Ukraine

provided the original work is properly cited.

\*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,

To summarize, it should be noted that this paper is final in a cycle of works devoted to the study of the whole process of normal spherical detonation.

## **Acknowledgements**

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 long-term fruitful cooperation.
