Analysis of Quasi-steady, Transitional, and Short Timescale Galloping within Rotating Detonation Engines

Abstract

Various cases of unsteady detonation wave behavior, commonly referred to as “galloping”, are presented and analyzed for test times exceeding twenty seconds in a water-cooled rotating detonation engine (RDE). Galloping waves exhibit cyclic acceleration and deceleration, resulting in oscillating wave spacing at unique process conditions. In previous studies, galloping waves have been studied as microsecond scale instabilities leading to ascending or descending modal transitions. In the current work, however, galloping waves are considered a stable wave mode, occupying unique portions of the operational envelope adjacent to those of their equally spaced counterparts. These occurrences of galloping are repeatable, enduring behaviors. Indications of galloping wave modes present in time series data are explored. A method to generate shifted contour surfaces specifically intended to extract and analyze wave spacing variation through time, termed galloping surfaces, is presented. Galloping surfaces representing quasi-steady, short timescale, and transitional galloping modes are leveraged to understand the relationship between fill height, wave strength, local wave acceleration, and subsequent galloping wave spacing for individual wave sets. Quasi-steady multiples of four and five galloping waves display wave spacing oscillations between equal spacing values associated with ±1 wave across runs exceeding 18 and 13 seconds, respectively. In addition to the stable nature of galloping modes across extended run times, of particular interest are transitional cases, where galloping wave modes transition to and from equally spaced wave modes in response to actively changing equivalence ratios. These transient process conditions may be reflective of future demands required of a turbine-integrated RDE expected to achieve flexible load responsiveness.