Data-driven Modeling of Rotating Detonation Waves

TL;DR

This paper introduces machine learning-based methods to develop reduced-order models for rotating detonation engines, enabling efficient analysis of complex wave dynamics and interactions that are computationally expensive to simulate with traditional CFD methods.

Contribution

It leverages machine learning to discover moving coordinate frames, overcoming translational invariance limitations in ROMs for RDEs, and applies dynamic mode decomposition and Koopman embeddings for better modeling.

Findings

Machine learning effectively identifies moving frames for RDE data.

ROMs with ML techniques capture complex shock wave dynamics.

Deep Koopman embeddings provide new insights into wave interactions.

Abstract

The direct monitoring of a rotating detonation engine (RDE) combustion chamber has enabled the observation of combustion front dynamics that are composed of a number of co- and/or counter-rotating coherent traveling shock waves whose nonlinear mode-locking behavior exhibit bifurcations and instabilities which are not well understood. Computational fluid dynamics simulations are ubiquitous in characterizing the dynamics of RDE's reactive, compressible flow. Such simulations are prohibitively expensive when considering multiple engine geometries, different operating conditions, and the long-time dynamics of the mode-locking interactions. Reduced-order models (ROMs) provide a critically enabling simulation framework because they exploit low-rank structure in the data to minimize computational cost and allow for rapid parameterized studies and long-time simulations. However, ROMs are inherently limited by translational invariances manifest by the combustion waves present in RDEs. In this work, we leverage machine learning algorithms to discover moving coordinate frames into which the data is shifted, thus overcoming limitations imposed by the underlying translational invariance of the RDE and allowing for the application of traditional dimensionality reduction techniques. We explore a diverse suite of data-driven ROM strategies for characterizing the complex shock wave dynamics and interactions in the RDE. Specifically, we employ the dynamic mode decomposition and a deep Koopman embedding to give new modeling insights and understanding of combustion wave interactions in RDEs.