On the dynamics of self-sustained one-dimensional detonations: A numerical study in the shock-attached frame

TLDR

The concept of an embedded information boundary is fundamental to both steady detonations and the more common unsteady detonation theories. This study investigates self‑sustained detonation waves whose dynamics are governed by a finite region adjacent to the lead shock and introduces the boundary as a separatrix generalizing the sonic locus to unsteady detonations. The authors formulate the boundary mathematically, develop a new numerical algorithm for reactive Euler equations in a shock‑attached frame, and employ a nonreflecting far‑field condition to suppress spurious reflections. Using the algorithm, they demonstrate that the unsteady sonic locus acts as an information boundary, revealing its key properties.

Abstract

In this work we investigate the dynamics of self-sustained detonation waves that have an embedded information boundary such that the dynamics is influenced only by a finite region adjacent to the lead shock. We introduce the boundary of such a domain, which is shown to be the separatrix of the forward characteristic lines, as a generalization of the concept of a sonic locus to unsteady detonations. The concept plays a fundamental role both in steady detonations and in theories of much more frequently observed unsteady detonations. The definition has a precise mathematical form from which its relationship to known theories of detonation stability and nonlinear dynamics can be clearly identified. With a new numerical algorithm for integration of reactive Euler equations in a shock-attached frame, that we have also developed, we demonstrate the main properties of the unsteady sonic locus, such as its role as an information boundary. In addition, we introduce the so-called “nonreflecting” boundary condition at the far end of the computational domain in order to minimize the influence of the spurious reflected waves.