Stochastic simulation of hydrogen–oxygen auto-ignition at the microscale

Abstract

A hybrid stochastic simulation method is developed to study H2–O2 auto-ignition at the microscale. Simulation results show that the discrete and stochastic characteristics of reaction collisions have notable impacts on the ignition process, particularly in the early stages when only a few radicals exist. The statistical properties of ignition delay time, which reflect the accumulated stochasticity during ignition, are obtained and analyzed for different initial temperatures and total molecular numbers. It is found that the average and standard deviation of ignition delay time increase as the total molecular number decreases, with this phenomenon being particularly pronounced near the crossover temperature. When the total molecular number is sufficiently small, the chain initiation reaction becomes crucial to the stochastic properties, as its average firing time exhibits an inverse proportionality to the total molecular number. As the total molecular number increases, the influence of other chain reactions intensifies, causing the power law relation between standard deviation and total molecular number to shift from −1 power to −0.5 power. Owing to different chain reaction paths for high- and low-temperature auto-ignition, the strongest relative fluctuation occurs near the crossover temperature. A theoretical equation for the standard deviation of ignition delay time is obtained based on dimensional analysis, giving excellent agreement with the simulation results in both high- and low-temperature modes.