Effect of thermal nonequilibrium on reactions in hydrogen combustion

Abstract

The presence of shocks in scramjet internal flows introduces nonequilibrium of internal energy modes of the molecules. Here, the effect of vibrational nonequilibrium on key reactions of hydrogen-air combustion is studied. A quasi-classical trajectory (QCT) approach is used to derive reaction probability for nonequilibrium conditions using ab initio-derived potential energy surfaces. The reaction rates under nonequilibrium are studied using a two-temperature description, where the vibrational modes are assumed to be distributed according to a Boltzmann distribution at a characteristic vibrational temperature, in addition to a translational temperature describing the translational and rotational population distribution. At scramjet-relevant conditions, it is found that the nonequilibrium reaction rate depends not only on the level of vibrational excitation, but also on the reactants involved. Conventional two-temperature models for reaction rates, often derived using empirical means, were found to be inaccurate under these conditions, and modified parameters are proposed based on the QCT calculations. It is also found that models that include details of the reaction process through dissociation energy, for instance, provide a better description of nonequilibrium effects.

Multitemperature Dissociation Rate of N2+N2→N2+N+N Calculated Using Selective Sampling Quasi-Classical Trajectory Analysis

“…Using the selective sampling technique, the dissociation rate coefficient of nitrogen was calculated using an in-house QCT program optimized for message passing interface (MPI)-based parallel simulations on high-performance computing clusters. Details are presented in [26,42]. The numerical ODE solver was the adaptive Runge-Kutta Prince-Dormand method [49] as implemented in the open-source GNU Scientific Library.…”

“…(24). The set of directly calculated rate coefficients was then projected onto a dense grid of temperatures using the interpolation scheme presented by Wang et al [54] as implemented in [26,42]. The temperature increment of the interpolated set was 1000 K, resulting in 166,375 (i.e., 55 3 ) total rate coefficients, which is dense enough to be directly imported into CFD programs.…”

“…At low temperatures, the necessary energy for dissociation is in the tails of the initial energy distributions, and so the conventional sampling strategy is highly inefficient. Uniform sampling over a wide domain of energies will ensure that the tails are sufficiently sampled, but doing so will also increase the uncertainty of the dissociation rate [42]. Second, for rate coefficients calculated using conventional sampling, the minimum observable dissociation probability corresponds to the inverse of the number of trajectories simulated (i.e., 1∕N).…”

“…Park [7,8] used a square-root model, where T e T t T v p . This straightforward model performs reasonably well at high temperatures [7,8,29,30,40,41], and it has been compared to rate coefficients derived from quasi-classical trajectory (QCT) simulations [12,14,19,20,36,42]. However, the model neglects the possibility of rotational nonequilibrium and implicitly assumes that T r T t .…”

“…For this purpose, the quasi-classical trajectory (QCT) analysis method is used [45][46][47]. This approach has been used to study other hypersonic-relevant reactions [12,19,22,33,[36][37][38]42], including this reaction [20,26,44]. For instance, regarding the title reaction, with the same potential energy surface (PES) used in this work, Bender et al [20] calculated the dissociation rate coefficient as a function of T T t T r and T v at 25 unique temperature combinations.…”