Abstract
The well-known formula for the flat detonation wave velocity derived from the Hugoniot system of equations faces difficulties, if being applied to a spherical reactor. A similar formula has been obtained in the framework of the theory of explosion in reacting gas media with the use of a special model describing the transition of an explosive wave in the detonation. The derived formula is very simple, being also more suitable for studying the limiting processes of volume detonation. The conditions for the transition of a shock wave to a detonation wave are studied. Initial detonation conditions required for fast chemical reactions to take place at the front of a spherical explosive wave have been determined. A simple relation describing the critical detonation temperature for various pressures in the hydrogen-oxygen mixture was obtained. Using the known formulas for a shock transition, the critical temperature was coupled with the initial conditions in a static environment, such as the pressure, temperature, and hydrogen content in the mixture.
Highlights
Direct Numerical Simulations - An Introduction and Applications where r is the current radius, Rx is the critical radius, А is a constant, Dп is the velocity of a plane wave, and D is the velocity of a spherical wave
Using expression (79), let us calculate the critical temperature for two Mach numbers, (i) M 1⁄4 2:15 and (ii) M 1⁄4 4:78, i.e. for shock waves of two types, but at the fixed initial pressure P0 1⁄4 60 mm Hg
Experimental data indicate that detonation is not observed at M < 2:15, weak shock waves become waves of compression and rarefaction
Summary
The strong explosion in a small volume of a detonating gas mixture has been studied well in modern physics [1, 2]. The work is aimed at analyzing the development of the process at the time moment, when the energy of a point explosion is equal to the energy of a burned gas, r 1⁄4 Rx, but provided that Rx 61⁄4 ∞. The model supposes that the pressures at the front and in the explosion region are equal, which results in the appearance of a high temperature at the transition point behind the shock front, since the main part of the substance mass is concentrated in a thin layer of the blast wave. There are no works in the scientific literature dealing with the influence of initial conditions on the detonation process, when the blast wave propagates in the gas environment. In this paper it was possible to obtain the necessary results by studying the chain reactions [9] of the interaction of hydrogen with oxygen
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