Deflagration-to-detonation transition in an unconfined space

Whereas deflagration-to-detonation transition in confined systems is a matter of common knowledge, feasibility of the transition in unconfined space is still a matter of controversy. With a freely expanding self-accelerating spherical flame as an example, it is shown that deflagration-to-detonation transition in unconfined gaseous systems is indeed possible provided the flame is large enough. The transition is caused by positive feedback between the accelerating flame and the flame-driven pressure buildup, which results in the thermal runaway when the flame speed reaches a critical level.