The Darrieus-Landau instability in fast deflagration and laser ablation

TL;DR

This paper rigorously analyzes the Darrieus-Landau instability in compressible flows with a focus on fast deflagration and laser ablation, revealing how compression effects weaken the instability and lead to its disappearance in certain regimes.

Contribution

It derives a new boundary condition considering the internal structure of the front, clarifying the influence of energy sources on the instability in compressible flows.

Findings

Compression effects weaken the Darrieus-Landau instability.

The instability growth rate is reduced in laser ablation scenarios.

The instability vanishes in the Chapman-Jouguet regime.

Abstract

The problem of the Darrieus-Landau instability at a discontinuous deflagration front in a compressible flow is solved. Numerous previous attempts to solve this problem suffered from the deficit of boundary conditions. Here, the required additional boundary condition is derived rigorously taking into account the internal structure of the front. The derived condition implies a constant mass flux at the front; it reduces to the classical Darrieus-Landau condition in the limit of an incompressible flow. It is demonstrated that in general the solution to the problem depends on the type of energy source present in the system. In the common case of a strongly localized source, compression effects make the Darrieus-Landau instability considerably weaker. In particular, the Darrieus-Landau instability growth rate is reduced for laser ablation in comparison with the classical incompressible case. The instability disappears completely in the Chapman-Jouguet regime of ultimately fast deflagration.