Method of characteristics for curved-detonation by inverse design

Research on detonation has traditionally focused on forward solutions, with limited attention to inverse design methods, which has significantly hindered the development of detonation engines. In this paper, the Method of characteristics for Curved-Detonation (MOCD) is proposed to enable the inverse design of detonation waves. MOCD is based on the Method of Curved-shock Characteristics (MOCC) and integrates higher-order aerodynamic parameters from Curved Detonation Equations (CDE), allowing the calculation of the wedge angle given specific wave angle. The effectiveness of MOCD is validated using both oblique and curved detonation waves with single-step and detailed chemical reactions. Various applications demonstrate the ability to meet the inverse design requirements of detonation engines. For example, inverse design for given wave angles can optimize engine thrust and prevent Mach reflections. Additionally, inverse design schemes tailored to incoming flow conditions, such as varying Mach numbers and equivalence ratios, enhance the feasibility of detonation engines. Applying the method to given post-wave aerodynamic parameters enables more precise engine design, which is crucial for improving propulsion performance and effective thermal protection. In summary, the advantages of MOCD include not only performing a fast solution of the detonation flow field, but also allowing the inverse design of the detonation wave.