A stochastic and bayesian inference toolchain for uncertainty and risk quantification of rare autoignition events in DLE premixers

Quantification of aleatory uncertainties due to the inherent variabilities in operating conditions and fuel composition is essential for designing and improving premixers in dry low emissions (DLE) combustion systems. Advanced stochastic simulation tools require a large number of evaluations in order to perform this type of uncertainty quantification (UQ) analysis. This task is computationally prohibitive using high-fidelity computational fluid dynamic (CFD) approaches such as large eddy simulation (LES). In this paper, we describe a novel and computationally-efficient toolchain for stochastic modelling using minimal input from LES, to perform uncertainty and risk quantification of a DLE system. More specially, high-fidelity LES, chemical reactor network (CRN) model, beta mixture model, Bayesian inference and sequential Monte Carlo (SMC) are integrated into the toolchain. The methodology is applied to a practical premixer of low-emission combustion system with dimethyl ether (DME)/methane-air mixtures to simulate autoignition events at different engine conditions. First, the benchmark premixer is simulated using a set of LESs for a methane/air mixture at elevated pressure and temperature conditions. A partitioning approach is employed to generate a set of deterministic chemical reactor network (CRN) models from LES results. These CRN models are then solved at the volume-average conditions and validated by LES results. A mixture modelling approach using the expectation-method of moment (E-MM) is carried out to generate a set of beta mixture models and characterise uncertainties for LES-predicted temperature distributions. These beta mixture models and a normal distribution for DME volume fraction are used to simulate a set of stochastic CRN models. The Bayesian inference approach through Sequential Monte Carlo (SMC) method is then implemented on the results of temperature distributions from stochastic CRN models to simulate the probability of autoignition in the benchmark premixer. The results present a very satisfactory performance for the stochastic toolchain to compute the autoignition propensity for a few events with a particular combination of inlet temperature and DME volume fraction. Characterisation of these rare events is computationally prohibitive in the conventional deterministic methods such as high-fidelity LES.