On the Determination of Rotating Detonation Engine Wave Modes Using Limited Point Measurements

A method to determine the average modal parameters in a rotating detonation engine (RDE) for a limited set of point measurements using the 2D discrete Fourier Transform (fast Fourier transform) is described, and a new sensor placement inspired by the field of compressed sensing is identified based on success of this method in predicting the wave count m and operating frequency f_det in a suite of synthetic case studies of steady-state RDE operation. The performance of this new, “prime” sensor placement is compared to the NASA SP-194 [1] and equidistant (uniform) sensor placements, which are both in use today for determining RDE modes using point measurements. For the synthetic case studies tested, the newly proposed sensor placement is demonstrated to outperform both the SP-194 and equidistant placements for each deployed sensor count between M = 2 and 5. The performance of the proposed prime sensor placement is comparable to the SP-194 recommendations for (co-)rotating wave modes, both with and without concern for the wave direction, and outperforms the SP-194 placement strategy for more complex wave modes. Both the newly proposed and SP-194 recommended sensor placements strongly outperform the equidistant placement for all investigated sensor counts. Finally, these three sensor placement strategies are compared to one another for a representative set of experimental data that spans three RDE geometries, two propellant mixtures, and a variety of flow conditions, which yields a representative range of wave mode types, wave counts, and operating frequencies. The performance of the prime and SP-194 recommended sensor placements are shown to be comparable for these experimental cases, while the equidistant placement significantly underperforms relative to these other sensor arrangements. Key takeaways from this study include a strong argument against using the equidistant sensor placement, as well as the potential for more complex wave modes to be correctly identified using intelligent sensor placement compared to current placement approaches using reduced point measurements.