Formation of near-Chapman-Jouguet oblique detonation wave over a dual-angle ramp

A study on the formation of oblique detonation waves (ODW) over a non-uniform ramp is presented, and a method for obtaining a Chapman-Jouguet (CJ) ODW has been explored. In particular, the method is discussed for practical application in a propulsion system. A dual-angle ramp that is inclined at two subsequent angles, overdriven and CJ, supports an induction oblique shock wave (OSW), an expansion wave, and an ODW. Conditions for reaction initiation are achieved across a strong OSW followed by the formation of an ODW attached to a weaker OSW. The CJ ramp and ODW angles for the upstream flow conditions are calculated analytically for a stoichiometric H2-air mixture. Numerical simulation is carried out using an unsteady compressible reactive flow solver in OpenFOAM, with detailed chemistry and thermodynamics. Results are obtained for plain and dual-angle ramp cases, and compared in terms of combustion efficiency and total pressure recovery. With a dual-angle ramp, the induction length can be significantly reduced through a high overdriven ramp angle. Despite a strong induction OSW, the near-CJ ODW that forms over the CJ ramp section does not suffer from higher loss in total pressure or combustion efficiency. This is contributed by lower ODW angle, and a further decrease in induction length is possible over a dual-angle ramp. The method allows for obtaining an ODW of required induction delay or strength at any given upstream flow condition. This study proposes a simple and practical method of obtaining near-CJ ODW that is beneficial for propulsive applications.