Qualitative modeling of the dynamics of detonations with losses

TL;DR

This paper introduces a simplified PDE model for one-dimensional detonations with losses, capturing key unsteady behaviors like pulsations and chaos, and presents a novel method for steady-state solutions.

Contribution

It proposes a new simplified PDE model for detonation dynamics with losses and a novel approach to solve the eigenvalue problem avoiding sonic point issues.

Findings

Model reproduces pulsating and chaotic detonation behaviors

New numerical method improves steady-state solution computation

Unsteady simulations reveal stability properties of solutions

Abstract

We consider a simplified model for the dynamics of one-dimensional detonations with generic losses. It consists of a single partial differential equation that reproduces, at a qualitative level, the essential properties of unsteady detonation waves, including pulsating and chaotic solutions. In particular, we investigate the effects of shock curvature and friction losses on detonation dynamics. To calculate steady-state solutions, a novel approach to solving the detonation eigenvalue problem is introduced that avoids the well-known numerical difficulties associated with the presence of a sonic point. By using unsteady numerical simulations of the simplified model, we also explore the nonlinear stability of steady-state or quasi-steady solutions.