Explosion criteria for a three-step Gray and Yang, non-isothermal branching reaction scheme in fluids with natural convection

Explosions may occur owing to thermal and branching effects in combustion processes. The ignition limits of a system are affected by the presence of natural convection, which develops inevitably in terrestrial systems. This work investigates the explosion criterion, through parametric sensitivity, for systems with a Gray and Yang, three-step, non-isothermal branching reaction scheme with natural convection. Ignition is identified with the maximum sensitivity of the non-dimensional temperature rise Tmax′ to the ratio of branching and termination reaction rates (τb/τt)(τb/τt). The effects of self-heating, branching and natural convection on the time to ignition are analysed. A value of dimensionless temperature rise T′=5T′=5 is found to be an appropriate explosion criterion for this system.