Quasi-State-Specific QCT Method for Calculating the Dissociation Rate of Nitrogen in Thermal Non-Equilibrium

Abstract

The dissociation of nitrogen was studied using a quasi-classical trajectory (QCT) analysis in the context of calculating the dissociation rate surface for a dense range of temperatures for use in computational fluid dynamics (CFD) applications. By sampling rovibrational states from a Boltzmann distribution but uniformly sampling the relative speed, the dissociation rate was calculated for translational and rovibrational temperatures between 8000 K and 20000 K. The justification for this approach was verified by analyzing different sampling techniques. It was found that uniformly sampling the relative speed increased the uncertainty of the thermally averaged dissociation rate, but the same QCT results could be used for a large range of temperatures. This is in contrast to Monte Carlo sampling techniques, where a new batch of trajectories must be simulated for each desired temperature. To generate the dissociation rate surface, 500 million trajectories were simulated, and the non-equilibrium rates were compared to other models and experimental data, generally showing good agreement.

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.…”

“…The analytical PES used in this work was developed by Bender et al [50], which was an extension of the surface developed by Paukku et al from a set of approximately 17,000 ab initio data points [51]. The maximum impact parameter was set as 6 Å based on previous studies using this PES [20,26]. To define the initial state, first the rovibrational is sampled from f 0 rv for a given T t , T r , and T v , as defined in Eq.…”

“…At high temperatures, though, the rotational relaxation time scale approaches that of vibrational relaxation [17,41,43], thus indicating that T r ≈ T v . As such, the dissociation rate coefficient has also been calculated under the assumption that T r ≈ T v [26,44]. At moderate temperatures, where rotational relaxation is slow but not the same as vibrational relaxation, T r should be treated independently, as suggested by Park [41].…”

“…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.…”

Effect of thermal nonequilibrium on reactions in hydrogen combustion

“…The cutoff was chosen so as to ensure that the probability of reaction beyond b max was effectively zero. Also, uniformly sampling the impact parameter lowered the uncertainty of non-averaged quantities, e.g., the probability of reaction versus the impact parameter, because small impact parameters, where reactions are most likely to occur, were sampled significantly more often than in a Monte Carlo sampling technique [25]. In total, for 51 relative speed states, 5 vibrational temperatures per species, and 5 rotational temperatures per species, a total of 1275 cross-sections were calculated for the reactions in (7) and (8).…”