Chemical reaction mechanism related vibrational nonequilibrium effect on the Zel'dovich−von Neumann−Döring (ZND) detonation model

Abstract

Discrepancies in detonation cell size are always found between experiments and numerical simulations. The recent numerical simulation by Shi et al. (2016) included the vibrational relaxation effect in molecules and revealed that the vibrational nonequilibrium effect may be one of the reasons for the above discrepancy. In this study, a steady one-dimensional Zel'dovich–von Neumann–Döring (ZND) model is modified to account for the vibrational nonequilibrium effect in gaseous detonation. By introducing a new parameter α, which is defined as the ratio of translational-rotational mode of the specific heat at constant volume to the overall specific heat at constant volume, the translational-rotational energy and the vibrational energy are treated separately in the energy conservation equation. Both the single step and the two step Arrhenius models are used to describe the chemical reaction progress, and the Landau–Teller model and Park's two-temperature model are applied to describe the vibrational energy relaxation and the coupling between the molecular vibration and the chemical reaction, respectively. The parametric study on the modified ZND model is conducted and compared with the conventional ZND one, including the activation energy in chemical model, the ratio of the chemical time scale to the vibrational relaxation time scale and the characteristic vibrational temperature. The results show that the half reaction length is relatively not sensitive to the variation of characteristic vibrational temperature applied in the model (compared with the activation energy and the time ratio), but is increased to a significant extent with the increase of the activation energy and the decrease of the time ratio, when considered the vibrational nonequilibrium. The simulated half reaction lengths in the modified model are in good agreement with those in the conventional model, if the chemical time scale is larger than the vibrational relaxation time scale above a critical ratio when the vibrational nonequilibrium effect is insignificant.