Theoretical solution of conical detonation waves with chemical equilibrium and variable specific heat

To advance the design of conical oblique detonation engines, this study develops a rapid and accurate method for predicting wave angles and post-wave parameters. Existing theoretical models for conical oblique detonation waves are limited by simplified heat release assumptions, restricted accuracy, or high computational costs. This work addresses these limitations by solving the Taylor–Maccoll equations integrated with chemical equilibrium calculations, incorporating variable specific heat effects induced by hypersonic inflow. The proposed method achieves enhanced accuracy under both cold and heated conditions (wave angle errors of 0.001% and 0.3%, respectively) while maintaining computational efficiency. Validation against numerical simulations and experimental data confirms the method's reliability. Analysis of detonation polar curves reveals that the stationary range of conical detonation waves is narrower and weaker than that of planar counterparts at identical geometric angles. The minimum detonation Mach number for conical configurations exhibits an inverted J-shaped distribution, with the inflow Mach number dominating stationary ranges. At fixed cone angles, the detonation wave angle decreases with rising inflow temperature or decreasing pressure and peaks near equivalence ratios slightly over 1. Furthermore, conical structures in oblique detonation engines simplify wall interaction dynamics and generate higher post-wave total pressure compared to planar configurations.