Data Driven Modeling of Nonlinear Dynamics in a Rotating Detonation Combustor via Finite Dimensional Approximations of the Koopman Operator
2026-07-24 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors studied a special engine part called a Rotating Detonation Combustor (RDC), which uses fast-moving explosion waves to burn fuel efficiently. They used a math tool called the Koopman operator, combined with video data of the flames, to analyze how these explosion waves behave and interact. By improving existing methods with time-delay techniques, they could better understand complex wave patterns and reduce measurement noise. Their approach helps break down the flame behavior into simpler parts, offering clearer insights into how the RDC operates under different conditions.
Rotating Detonation Combustordetonation wavesKoopman operatorDynamic Mode Decompositiontime-delay embeddingnonlinear dynamicsannular combustion chamberwave interactionsensor noiseflame luminosity
Authors
David Oexle, Tobias Breiten, Myles D. Bohon
Abstract
A Rotating Detonation Combustor (RDC) is a promising technology for increasing efficiency in propulsion and power generation applications. The dynamics of the RDC are governed by continuously propagating detonation waves within an annular combustion chamber. Multiple operating modes can be observed, including nonlinear interactions between counter-rotating waves and the emergence of standing wave patterns. Koopman operator theory provides a framework to globally linearize nonlinear dynamical systems by representing their evolution in the space of observables rather than states. In this work, finite-dimensional approximations of the Koopman operator are constructed using variants of Dynamic Mode Decomposition (DMD) applied to high-speed video data capturing the natural flame luminosity of the detonation waves in the RDC at the Technical University (TU) Berlin. By introducing time-delay embeddings as a dictionary of observables, this approach overcomes the limitations of standard DMD methods, particularly for accurate reconstruction of standing wave patterns and for capturing nonlinear interactions. In addition, a technique is presented to mitigate the influence of sensor noise in the luminosity measurements. Finally, it is shown that the DMD-based models provide insight into the dynamics of different operating modes by decomposing the reconstructed signal into its characteristic features.