Comprehensive uncertainty analysis of a Wiebe function-based combustion model for pilot-ignited natural gas engines

Abstract

This paper presents a comprehensive uncertainty analysis of a Wiebe function-based combustion model for advanced low-pilot-ignited natural gas (ALPING) combustion in a single-cylinder research engine. The sensitivities, uncertainty magnification factors (UMFs), and uncertainty percentage contributions (UPCs) of different experimental input variables and model parameters were investigated. First, the Wiebe function model was validated against experimental heat release/mass burned fraction profiles and cylinder pressure histories for three pilot injection timings (start of injection (SOI)): −20°, −40°, and −60° after top dead center (ATDC). Second, the sensitivities and UMFs of predicted cylinder pressure histories were determined. Finally, crank angle-resolved uncertainties were quantified and mapped as ‘uncertainty bounds’ in predicted pressures, which were compared with measured pressure curves with error bars for cyclic variations. The Wiebe function-based combustion model with a quadratic interpolation equation for the specific heat ratio ( γ) provided reasonable cylinder pressure and heat release/mass burned fraction predictions for all SOIs (better for −20° and −60° ATDC SOIs compared with −40° ATDC). Uncertainty analysis results indicated that γ (parameters in the quadratic interpolation equation), compression ratio, mass and lower heating value of natural gas trapped in the cylinder, overall trapped mass, and ignition delay were important contributors to the overall uncertainty in predicted cylinder pressures. For all SOIs, γ exhibited the highest UPC values (80–90 per cent) and therefore, γ must be determined with the minimum possible uncertainty to ensure satisfactory predictions of cylinder pressure histories. While the importance of γ in single-zone combustion models is well recognized, the specific contribution of the present analysis is quantification of the crank angle-resolved UPCs of γ and other model parameters to the overall model uncertainty. In this paper, it is shown that uncertainty analysis provides a unique methodology for quantitative validation of crank angle-resolved predictions from any type of engine combustion model with the corresponding experimental results. It is also shown that uncertainties in both predicted and measured cylinder pressures and heat release rates must be considered while validating any engine combustion model.