Steady-State Analysis of Rotating Detonation Engine Flowfields with the Method of Characteristics

A method for modeling the internal flowfield in a rotating detonation engine is developed using shock-expansion theory combined with the steady two-dimensional isentropic method of characteristics. An analytical model using the oblique shock relations, the Prandtl–Meyer function, and the detonation jump conditions is used to determine the basic shock structure. Once the structure is known, a shock-fitted method of characteristics solution is marched out to generate the rest of the flowfield. Reactant injection is handled analytically by solving the conservation equations for a flow undergoing a sudden expansion along with the method of characteristics compatibility relations to provide a new boundary condition. A new solution is then initialized using information from the previous solution to calculate the new shock structure. This process is repeated until the solutions converge. The converged solution is the ideal steady-state solution of a rotating detonation engine in the wave-fixed reference frame. The goal of this model is to provide ideal performance estimates one step up from a basic thermodynamic model that are still fast enough for large parametric studies.