Trajectory generated low-dimensional manifolds generated using the stochastic particle model

Abstract

The Trajectory Generated Low-Dimensional Manifold (TGLDM) is a way to reduce detailed chemistry based on the separation of time-scales in the chemical reaction system. At low temperatures the TGLDM is difficult to compute because of extremely low reaction rates early in the induction process. The Stochastic Particle Model (SPM) uses a probabilistic description of the reaction system and evolves the reaction system through a Markov process resolving down to the time difference between individual reactions and thus is immune to problems with stiffness in the reaction mechanism and to initial reaction rates being extremely low. Because the SPM uses a Monte Carlo method, every time a trajectory is computed, the resulting trajectory takes a different path through the composition space and a different time to move from the boundary of the composition space to equilibrium. Two different methods for incorporating trajectories calculated using the SPM into a TGLDM have been used in this work. First, many realisations have been averaged together. At high temperatures, where a trajectory can be computed using the more usual continuum approach, the average of the SPM trajectories converges to the continuum solution. Using the TGLDM that results from using the SPM to calculate the average autoignition trajectory for a stoichiometric mixture of methane and air, a significant improvement in the prediction of a perfectly stirred reactor is obtained. Second, a time filter has been applied to individual realisations to eliminate the small time-scale fluctuations. Even after the time-filtering, there is still significant variation between realisations. When different realisations are incorporated into the TGLDMs and these are used in the prediction of autoignition of a turbulent methane jet using Conditional Source-term Estimation in Reynolds averaged Navier–Stokes, there are significant variations in the predicted ignition delay times. These fluctuations are still several times smaller in magnitude than those seen in experiments, which suggests that turbulent fluctuations (which cannot be accounted for in the RANS paradigm) also have a significant influence on the fluctuations in the ignition delay time.