Bayesian inference and uncertainty quantification for hydrogen-enriched and lean-premixed combustion systems

Development of probabilistic modelling tools to perform Bayesian inference and uncertainty quantification (UQ) is a challenging task for practical hydrogen-enriched and low-emission combustion systems due to the need to take into account simultaneously simulated fluid dynamics and detailed combustion chemistry. A large number of evaluations is required to calibrate models and estimate parameters using experimental data within the framework of Bayesian inference. This task is computationally prohibitive in high-fidelity and deterministic approaches such as large eddy simulation (LES) to design and optimize combustion systems. Therefore, there is a need to develop methods that: (a) are suitable for Bayesian inference studies and (b) characterize a range of solutions based on the uncertainty of modelling parameters and input conditions. This paper aims to develop a computationally-efficient toolchain to address these issues for probabilistic modelling of NOx emission in hydrogen-enriched and lean-premixed combustion systems. A novel method is implemented into the toolchain using a chemical reactor network (CRN) model, non-intrusive polynomial chaos expansion based on the point collocation method (NIPCE-PCM), and the Markov Chain Monte Carlo (MCMC) method. First, a CRN model is generated for a combustion system burning hydrogen-enriched methane/air mixtures at high-pressure lean-premixed conditions to compute NOx emission. A set of metamodels is then developed using NIPCE-PCM as a computationally efficient alternative to the physics-based CRN model. These surrogate models and experimental data are then implemented in the MCMC method to perform a two-step Bayesian calibration to maximize the agreement between model predictions and measurements. The average standard deviations for the prediction of exit temperature and NOx emission are reduced by almost 90% using this method. The calibrated model then used with confidence for global sensitivity and reliability analysis studies, which show that the volume of the main-flame zone is the most important parameter for NOx emission. The results show satisfactory performance for the developed toolchain to perform Bayesian inference and UQ studies, enabling a robust and consistent process for designing and optimising low-emission combustion systems.