Enhanced detonation shock dynamics prediction for curvature-driven detonation propagation in annular channels

Abstract

This study extends the Detonation Shock Dynamics (DSD) theory, originally developed for condensed-phase explosives, to predict the steady propagation of curved gaseous detonation waves in an annular channel filled with C₂H₂/O₂/Ar mixtures. The theory framework couples a steady-state level-set formulation with a D_n − κ relationship derived from a generalized ZND model, and incorporates shock polar analysis to impose the outer wall boundary condition. This enables the computation of the detonation shock front’s steady shape and angular velocity. The model is validated against two-dimensional simulations using the same detailed chemical kinetics. Results show that, for a fixed inner radius of the annular channel and initial pressures from 10 to 80 kPa, when outer radius of the annular channel (r_o) is larger than a critical radius (r_cr1), the angular velocity of propagating detonation wave predicted by the DSD method remains invariant with respect to variations in r_o or the outer wall normal angle (φ_o). To address underprediction of the angular velocity at low pressures, an enhanced D_n − κ relationship is proposed to account for effect induced by transverse wave collisions. The improved model demonstrates excellent agreement with simulations across all tested pressures. Two critical outer radii are identified: a lower limit radius (r_cr1) reflecting the extent of the Detonation-Driven Zone (DDZ) and an upper limit radius (r_cr2) associated with the transition in shock reflection modes. These radii define the annular width range that supports self-similar detonation propagation. The results underscore the potential of the DSD method as a fast and reliable tool for optimizing annular combustion chamber design in rotating detonation engines (RDEs).