Small-size rotating detonation engine: scaling and minimum mass flow rate

Rotating detonation engines (RDEs) have been observed to exhibit several operating modes and instabilities under different operation conditions (reactant mixture, injection pressure, engine geometry, injection mass flow rate, etc.). We develop the simplest model possible describing the operation of an RDE. This model takes into account the dependence of detonation properties on engine conditions, the injection process, and the geometric constraints. Using this model, we predict the lowest allowable reactant injection rates that allow an RDE to operate with a single detonation wave propagating in the annular combustion chamber. This model is compared with experimental results of engines running on H $${}_2$$ /O $${}_2$$ and C $${}_2$$ H $${}_4$$ /O $${}_2$$ .