Exploring the controlling mechanisms for gradient evolution in unsteady detonation flows

Proper characterization of the transient interaction between shock front motion and chemical energy release is the key for further understanding of unsteady detonation dynamics. We have shown that the gradients could be the adequate intermediate quantities to reflect the transient interaction between shock front motion and chemical energy release through the Lagrangian particle analysis of the simulated direct detonation initiation (DDI) process in H₂-O₂-Ar mixtures. Specifically, the "shock change equations" are verified to describe the direct relation between the shock front motion and the gradients immediately behind the shock. Moreover, given the time derivatives of shock speed, the gradient evolution in the induction zone can be reproduced by the gradient evolution equations that are deduced from the Euler equations, no matter if the shock front undergoes rapid deceleration or acceleration. While in the reaction zone where the heat release is significant, it is demonstrated that the evolutions of velocity, pressure, and their gradients can be described by the Zel'dovich-von Neumann-Döring model with a constant wave speed that is below the Chapman-Jouguet speed, no matter if the shock front undergoes rapid deceleration or acceleration. These two distinct controlling mechanisms are verified in both planar and spherical DDI processes, showing their general applicability. This work suggests a new perspective, in terms of gradient evolution, for further understanding the unsteady detonation dynamics.