Investigations on Projection-Based Reduced Order Model Development for Rotating Detonation Engine

The current study aims to evaluate and investigate the development of projection-based reduced-order models (ROMs) for efficient and accurate RDE simulations. Specifically, we focus on assessing the projection-based ROM construction utilizing three different approaches: the linear static basis, nonlinear quadratic basis, and an adaptive model order reduction (MOR) formulation. First, an ~\textit{a priori} analysis is performed to evaluate the effectiveness of the linear static and nonlinear quadratic bases in representing the detonation-wave dynamics. The~\textit{a priori} analysis reveals that compared to the linear basis, the nonlinear quadratic basis provides significantly improved representation of detonation-wave dynamics within the training regime. However, it exhibits limited capabilities in representing the dynamics beyond the training regime, either in the future state or under a different operating parameter (i.e., inlet velocity). Second, the investigations proceed to the adaptive MOR formulation, which constructs an \textit{online} adaptive ROM with a small amount of offline training data. It is demonstrated that the adaptive ROM can provide significantly enhanced predictive capabilities in modeling the RDE dynamics in the future state, and subject to parametric variations. More importantly, the adaptive ROM is shown to be capable of capturing the initial transience in establishing the detonation wave.