Chemical Timescale Effects on Detonation Convergence

Abstract

Numerical simulations of detonation-containing flows have emerged as crucial tools for designing next-generation power and propulsion devices. As these tools mature, it is important for the combustion community to properly understand and isolate grid resolution effects when simulating detonations. To this end, this work provides a comprehensive analysis of the numerical convergence of unsteady detonation simulations, with focus on isolating the impacts of chemical timescale modifications on convergence characteristics in the context of operator splitting. With the aid of an adaptive mesh refinement based flow solver, the convergence analysis is conducted using two kinetics configurations: (1) a simplified three-step model mechanism, in which chemical timescales in the detonation are modified by adjusting activation energies, and (2) a detailed hydrogen mechanism, in which chemical timescales are adjusted through ambient pressure modifications. The convergence of unsteady self-sustained detonations in one-dimensional channels is then analyzed with reference to steady-state theoretical baseline solutions using these mechanisms. The goal of the analysis is to provide a detailed comparison of the effects of grid resolution on both macroscopic (peak pressures and detonation wave speeds) and microscopic (detonation wave structure) quantities of interest, drawing connections between the deviations from steady-state baselines and minimum chemical timescales. This work uncovers resolution-dependent unsteady detonation regimes, and highlights the important role played by not only the chemical timescales, but also the ratio between chemical timescale and induction time in the detonation wave structure on simulation convergence properties.