Theoretical and numerical investigation on vibrational nonequilibrium effect in detonation

Abstract

This thesis attempts to elucidate the effect of vibrational nonequilibrium in detonation by theoretically modelling. A simplified vibrational-chemical coupling mechanism is constructed by correlating single-step/two-step Arrhenius equations (denoting chemical reaction) and the Landau-Teller model (denoting vibrational relaxation) with Park's two-temperature model. Two issues are demonstrated based on these coupling kinetics, which include 1) the extension of the ZND detonation model to predict half-reaction length when detonation is under significant vibrational nonequilibrium and 2) the stability behaviour of detonation under significant vibrational nonequilibrium. A time ratio denoting the ratio of chemical reaction time scale and the vibrational relaxation time scale is utilized throughout this study and it represents the different state of vibrational nonequilibrium. In the first half of the thesis, it is concluded that the elongation of half reaction length at the state of nonequilibrium is observed due to the reduction of overall chemical reaction rate, whereas in the second half of the thesis, it is shown that the detonation is stabilized at vibrational nonequilibrium state through a normal mode linear stability analysis. The results obtained in the analytical approach are compared with that using a numerical approach by CE/SE scheme, and these findings are well verified. The theoretical derivation in the detonation model indicates that vibrational nonequilibrium and thus the vibrational-chemical coupling mechanism plays an important role in gaseous detonation physics and should be examined further in future detonation simulations.