Effect of degree of reaction on critical conditions and times to ignition of a gas mixture explosion

The effect of degree of reaction on critical conditions and times to ignition of a gas-mixture explosion is theoretically examined in detail. The Arrhenius form of the chemical kinetic rate and the Frank-Kamenetskii approximation for that form is considered. The study offers analytical and numerical solutions of the problem in pressure-time, temperature-time, and temperature-pressure planes. The analytical solution presented analytical detailed expressions, which relate between the critical parameters at critical point. The fractional order of reaction (n < 1) and order of reaction (n > 1) are studied. The effect of different parameters such as ambient temperature (theta(a)), exothermicity of reaction (B), modified Semenov number (psi) on critical conditions for explosion are investigated. A direct numerical solution of the governing equations of the problem is given in different planes. Different trajectories of subcritical (non-ignition), supercritical (ignition), and critical states are illustrated. The relationships between the critical parameters from the numerical solutions are confirmed with those have been obtained from the analytical one. The effect of order of reaction on the critical parameters and so on the ignition times is also investigated.