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 reli-ability 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. (c) 2021 The Author(s). Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. This is an open access article under the CC BY license (http://creativecommons.org/ licenses/by/4.0/).

Automated summary

The paper develops a computationally-efficient toolchain for probabilistic modelling of NOx emission in hydrogen-enriched and lean-premixed combustion systems, utilizing a combination of 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. The calibrated model shows significant improvement in predicting exit temperature and NOx emission, and is used for global sensitivity and reliability analysis studies to optimize low-emission combustion systems.