Mode transitions have been observed in rotating detonation engines at a variety of flow conditions and across many different engine geometries. This is particularly true for rotating detonation rocket engines (RDRE's), where the number of waves in the annulus has shown variation from as few as two waves, to as many as fourteen waves. While instantaneous behavior of these mode transitions has been examined in a previous work by our group, the global engine performance effects accompanied with these mode transitions have not yet been reported. This study presents an in-depth analysis of the changes in system pressures and global performance for multiple ascending mode transitions from two waves to three waves, all occuring at similar flow conditions. There are distinct behaviors associated with each operating mode, where one mode produces a notable increase in thrust and specific impulse. Specifically, the mode transition from 2 to 3 waves is accompanied by a 12% decrease in the detonation wave speed, a 2.2% decrease in the chamber pressure, and a 5.3% increase in the thrust and specific impulse. Most notably, this study challenges the commonly held belief that detonation wave speed and engine performance are tightly coupled, such that they increase or decrease together. An accompanying thermodynamic analysis is performed in order to show that the correlation between detonation wave speed and global performance holds a more complex relationship, where for non-ideal detonation modes seen in RDRE's, it is possible for a decrease in the wave speed to result in an increase in global performance, due to the complexity of heat addition at various portions of the thermodynamic cycle (i.e., detonative heat release vs. deflagrative heat release). This implies that there is some optimization between the detonation wave speed and the number of waves, possibly due a decrease in the spacing between the waves corresponding with a decrease in the amount of parasitic deflagration in the annulus. Therefore, future efforts to optimize the performance of an RDRE should consider the optimal number of waves for a particular chamber size, as the wave speed and global engine performance are still expected to be directly correlated when controlling for a given number of waves.
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