Effects of activation energy on the instability of oblique detonation surfaces with a one-step chemistry model

A numerical study was performed to investigate the detailed effects of activation energy E_a on the oblique detonation wave surface instability. Numerical simulations were performed using an ideal reactive flow model given by the inviscid Euler equations with one-step irreversible Arrhenius reaction kinetics. The numerical results demonstrate two types of unstable structures following the initial smooth surface after detonation initiation. One exhibits by a "saw-tooth" reactive front and the other exhibits by a "keystone" feature. To quantify the destabilization processes, two characteristic length scales, L₁ and L₂, are defined statistically to be the length of the smooth detonation surface before the appearance of instabilities and the length of the unstable surface before the first cellular structure with the onset of right-running transverse waves, respectively. Their dependence on E_a was simulated and analyzed. In general, both lengths decrease with increasing E_a, making the surface more unstable. However, with increasing E_a, the high temperature sensitivity of the mixture causes an abrupt explosion in the initiation region, introducing a high overdriven surface and suppressing the instability. With the balance between the destabilizing effect of E_a and the stabilizing effect of increasing overdrive factor, both L₁ and L₂ are found to approach a near-constant value in the high E_a limit.