Control of the deflagration-to-detonation transition in systems with resistance

This paper develops an approach to controlling gas combustion, including deflagration-to-detonation transition, based on using systems with resistance, such as porous media, periodic obstacles, rough tubes, etc. Gas combustion in these systems involves various physicochemical interactions: interfacial heat transfer, including combustion failure, flame quenching in fast pulsations (jets), transition to turbulence, generation of pressure waves in the flame zone, formation of hotspots, etc. These interactions result in a number of steady-state regimes with a uniform velocity of propagation of thermal waves – low-, high-, and sonic-velocity regimes, low-velocity detonation, and normal detonation with heat and momentum losses. Systems with porous media and periodic obstacles are considered as examples of systems with resistance. It is shown that with the effects of Lewis numbers taken into account, the steady-state velocities in the high-velocity regime for $\mathrm{CH}_4$/Air, $\mathrm{C}_3\mathrm{H}_8$/air, and $\mathrm{H}_2$/air systems over wide parameter ranges can be represented by a single relation $\mathrm{Re} = 6\cdot 10^{-4}\mathrm{Pe}^3$ in the coordinates $(\mathrm{Re}-\mathrm{Pe})$ for systems with porous media. Steady-state velocities in the sonic velocity regime for $\mathrm{C}_3\mathrm{H}_8$/air and $\mathrm{H}_2$/air systems are described in the same coordinates by a single function $\mathrm{Re} = 120\mathrm{Pe}^{4/3}$ for systems with porous media and periodic obstacles. A condition for pressure generation in the flame zone at sonic velocities was obtained analytically. Problems involved in the implementation of the approach of controlling high-velocity combustion processes in systems with resistance are discussed.