Final Work : Reduced Order Modelling Of Rotating Detonation Engines using Dynamic Mode Decomposition

Abstract

Rotating detonation Engines (RDE) are a novel technique in pressure gain combustion. In this type of combustion the theoretical efficiency gain achievable is not possible using traditional combustion techniques. The dynamics of the rotating detonation engines is complex, and high dimensional. Reduced order modelling are tools that can be used to reduce the high dimensional nature of these systems. Dynamic Mode Decomposition is one such technique. Dynamics in the rotating detonation engine manifests itself in two major forms. The first is a spinning wave form in which a single detonation wave that travels around the annulus of the engine at a very fast rate. The second is a clapping wave form which is obtained when two counterrotating waves interact with each other around the annulus. A robust dynamic mode decomposition algorithm is developed and it is benchmarked using synthetic data generated using mathematical formulations. Synthetic data is generated to mimic the dynamics present in the rotating detonation engine. Once the algorithm has been sufficiently tested and validated it is applied to the experimental data. High speed images of the aft end of the rotating detonation engine is used, the dynamic mode decomposition algorithm is then applied to this data and it is demonstrated that the dynamics of the system can be predicted using few dynamic modes and frequencies. However it was found that the error is still large and has to be reduced in order to create a reliable and accurate reduced order model of the engine. The images are then modified to isolate the region where the detonation wave operates. DMD on reduced set of images produces degenerate modes. The number of snapshot taken for analysis was shown to affect the accuracy and presence of so called degenerate modes. It was shown that the best accuracy value was achieved when the number of snapshots is equal to the number of the modes taken. It was further shown that for this test case the best accuracy was obtained using just 50 snapshots and 50 singular modes. Long term validity of the parameters obtained i.e. the number of snapshots and number of modes retained was demonstrated. It was seen that the frequencies and reconstruction error converge and oscillate around a mean. The maximum deviation of these parameters was within acceptable limits. The mode shapes also converge thus indicating that the parameters are valid for the whole test case. This also proved that there are no transients in the test case.