Characteristic timescales for detonation-based rocket propulsion systems

Characteristic timescales for rotating detonation rocket engines (RDREs) are described in this study. Traveling detonations within RDREs create a complex reacting flow field involving processes spanning a range of timescales. Specifically, characteristic times associated with combustion kinetics (detonation and deflagration), injection (e.g., flow recovery), flow (e.g., mixture residence time), and acoustic modes are quantified using first-principle analyses to characterize the RDRE-relevant physics. Three fuels are investigated including methane, hydrogen, and rocket-grade kerosene RP-2 for equivalence ratios from 0.25 to 3 and chamber pressures from 0.51 to 10.13 MPa, as well as for a case study with a standard RDRE geometry. Detonation chemical timescales range from 0.05 to 1000 ns for the induction and reaction times; detonation-based chemical equilibrium, however, spans a larger range from approximately 0.5 to \(200~\upmu \) $200\mathrm{\mu }$ s for the flow condition and fuel. This timescale sensitivity has implications regarding maximizing detonative heat release, especially with pre-detonation deflagration in real systems. Representative synthetic detonation wave profiles are input into a simplified injector model that describes the periodic choking/unchoking process and shows that injection timescales typically range from 5 to \(50~\upmu \) $50\mathrm{\mu }$ s depending on injector stiffness; for detonations and low-stiffness injectors, target reactant flow rates may not recover prior to the next wave arrival, preventing uniform mixing. This partially explains the detonation velocity deficit observed in RDREs, as with the standard RDRE analyzed in this study. Finally, timescales tied to chamber geometry including residence time are on the order of 100–10,000  \(\upmu \) $\mathrm{\mu }$ s and acoustic resonance times are 10– \(1000~\upmu \) $1000\mathrm{\mu }$ s. Overall, this work establishes characteristic time and length scales for the relevant physics, a valuable step in developing tools to optimize future RDRE designs.