To resolve the discrepancy between the numerical detonation cell size and experimental observations, simulations are conducted with a detailed thermochemical reaction model for a premixed argondiluted hydrogen-oxygen mixture. Four different scenarios are considered: (i) The whole system is in thermodynamic equilibrium; (ii) the vibrational relaxation is considered and the translational-rotational temperature is used as the dominant temperature of the chemical reactions; (iii) the same non-equilibrium effect as in the second scenario is used along with Park's two-temperature model to account for the effect of vibrational temperature on chemical reaction rates; and (iv) a more physically consistent vibration-chemistry-vibration coupling model is adopted. The simulated detonation cell widths for the first and second scenarios are significantly lower than the experimental measurements, whereas reasonable agreement is observed for the third and fourth scenarios. These results confirm that the involvement of vibrational relaxation in the chemical reactions is an important mechanism in gaseous detonation. ARTICLE HISTORY

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The linear stability of one-dimensional detonations with one-reaction chemistry coupled with molecular vibration nonequilibrium is investigated using the normal mode approach. The chemical kinetics in the Arrhenius form depend on an averaged temperature model that consists of translational–rotational mode and vibrational mode. The Landau–Teller model is applied to specify the vibrational relaxation. A time ratio is introduced to denote the ratio between the chemical time scale and the vibrational time scale in this study, which governs the vibrational relaxation rate in this coupling kinetics. The stability spectrum of disturbance eigenmodes is obtained by varying the bifurcation parameters independently at a different time ratio. These parameters include the activation energy, the degree of overdrive, the characteristic vibrational temperature, and the heat release. The results indicate that the neutral stability limit shifts to higher activation energy on the vibrational nonequilibrium side with a smaller time ratio, implying that the detonation is stabilized. A similar observation is seen at a lower degree of overdrive. Compared with the above two parameters, the characteristic vibrational temperature plays a minor role in the stabilization of detonation, and no change in the number of eigenmodes is identified throughout the selected range. By plotting the neutral stability curves relating the heat release to the above parameters, the decreases in instability ranges are obviously seen under vibrational nonequilibrium. The thermal nonequilibrium effect on detonation stability is clearly demonstrated. The analysis presented in this paper is ultimately justified by comparing the results with numerical simulation.

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As depicted in Chap. 2, the interface between the two sub-CEs (CD in Fig. 2.7), belongs to the SE of (j, n). The flux FC needs to be calculated through the Taylor expansion at point (j, n) toward the inverse time direction. As a result, the a scheme is reversible. This violates the second law of thermodynamics. Thus, the non-dissipative core suffers from the unphysical oscillations for practical applications.