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.

The impact mechanism of sideslip angle on shock wave interference structures at the V-Shaped Blunt Leading Edge (VSBLE) of a three-dimensional inward-turning inlet is studied through numerical simulationand theoretical analysis. The focus is on examining the types of shock wave interference at the VSBLE with a radius ratio of R/r = 4.5and the variation trends of peak wall heat fluxand pressure under conditions of Mach number 6and sideslip angles ranging from 0° to 8°. Numerical simulation results show that regarding wave system interference structures, the types of primary shock interferenceand secondary shock interference on the windward side of the model do not change with the increase of the sideslip angle, whereas the type of secondary shock interference on the leeward side transitions from regular reflection to Mach reflection. To effectively predict the transition boundary of the secondary shock interference type, a theoretical analysis method of shock wave interference at the VSBLE under sideslip conditions is established based on the inviscid shock theory. It is found that with the increase of the sideslip angle, the flow parameters in the secondary shock interference regions on the windwardand leeward sides shift towards values lower than the von Neumann boundaryand higher than the detachment boundary, respectively. In terms of wall heat fluxand pressure, changes in the sideslip angle lead to alterations in the heating/pressure peak values on the windwardand leeward sides, displaying different variation patterns. The results from both theoreticaland numerical simulations indicate that the variations of transmitted shock intensityand heating/pressure peak values with changes of sideslip angle are generally consistent. This shows that the change in transmitted shock intensity caused by variations in the sideslip angle is the key factor leading to different variation patterns in the heating/pressure peak values on the windwardand leeward sides. This study can provide a reference for the aerodynamic heating/pressure load required for structural design at the VSBLE.