Theory of DDT in Unconfined Flames

TL;DR

This paper develops a theoretical framework to predict the onset of detonation in unconfined turbulent flames, relevant to terrestrial combustion and supernovae, based on the gradient mechanism and turbulent mixing.

Contribution

It introduces a lower-bound criterion for DDT in unconfined flames using a simplified model based on flame and detonation wave parameters.

Findings

Derived a criterion for DDT onset in unconfined conditions.

Identified parameter regions where DDT can occur.

Provided a theoretical basis applicable to both terrestrial and astrophysical flames.

Abstract

This paper outlines a theoretical approach for predicting the onset of detonation in unconfined turbulent flames which is relevant both to problems of terrestrial combustion and to thermonuclear burning in Type Ia supernovae. Two basic assumuptions are made: 1) the gradient mechanism is the inherent mechanism that leads to DDT in unconfined conditions, and 2) the sole mechanism for preparing the gradient in induction time is by turbulent mixing and local flame quenching. The criterion for DDT is derived in terms of the one-dimensional detonation wave thickness, the laminar flame speed, and the laminar flame thickness in the reactive gas. This approach gives a lower-bound criterion for DDT for conditions where shock preheating, wall effects, and interactions with obstacles are absent. Regions in parameter space where unconfined DDT can and cannot occur are determined. A subsequent paper will address these issues specifically in the astrophysical context.