Investigations of Parametric Reduced Order Modeling Framework for Rotating Detonation Engines

This study aims to evaluate and investigate the potential techniques to construct reduced order models (ROMs) for parametric predictions of rotating detonation engine (RDE) dynamics, which feature convection-dominated physics challenging for ROM development. Specifically, we focus on two promising methods: 1) a quadratic nonlinear manifold to construct the trial basis for ROM; and 2) a recently developed adaptive ROM formulation that update the trial basis on -the -fly. To achieve this, a two-dimensional (2D) RDE configuration is established to conduct numerical simulations with different inlet velocities to allow for detailed assessment of the two ROM techniques. It has been shown that though improved low-rank approximation of the detonation wave dynamics can be achieved through the quadratic nonlinear basis, it exhibits limitations in providing accurate representations of dynamics not included in the training dataset. On the other hand, the adaptive ROM has been demonstrated to provide significantly enhanced predictive capabilities in modeling the RDE dynamics in future state, during transience, and subject to parametric variations, which seems to indicate a promising path for ROM construction in RDE applications.