Influence of discrete injection on asymptotic and transient dynamics of rotating detonation engines

Rotating detonation engines (RDEs) promise improved thermodynamic efficiency over traditional combustion engines, improved energy density, mechanical simplicity, and continuous operation. Nevertheless, several questions remain on how to optimize these devices. The injection system governs the dynamics of these systems through several, crucial mechanisms. These include the creation of a spatially varying reactant field and wave scattering off injectors. However, how these dynamics influence the number of detonations, presence of counter-propagating detonations, or other wave features is not well understood. This lack of understanding prevents the creation of general guidelines for designing the injection system. To address these obstacles, we studied a 2-dimensional “unwrapped” computational model of an RDE with simplified reaction kinetics and injector physics. The inlet consisted of equally spaced zones of constant mass flux (“injectors”) separated by isothermal walls. The number and area ratio of these injectors were varied over several individual simulations, and the impacts of these parameters were assessed. Results revealed that discrete injection introduces multiple physical processes – such as variable acoustic impedance, promotion of hot spots between injectors, and periodic de- and re-coupling of detonations – that increase the propensity for multiple detonations. Higher injector numbers and decreased area ratio tend to promote more detonations. Nevertheless, this relationship was non-monotonic, and further testing showed that additional wave modes besides those observed were stable. These wave modes appear to have definite, albeit topologically complex, basins of attraction — i.e., the system favors certain modes over others, but their link to the initial conditions is difficult to characterize. We therefore hypothesize that wave number is governed by the interplay between transient chaos during the initial transient and the new physics introduced by the injection system.