Evaluating Emissions in a Modern Compression Ignition Engine Using Multi-Dimensional PDF-Based Stochastic Simulations and Statistical Surrogate Generation

Abstract

Digital engineering workflows, involving physico-chemical simulation and advanced statistical algorithms, offer a robust and cost-effective methodology for model-based internal combustion engine development. In this paper, a modern Tier 4 capable Cat ® C4.4 engine is modelled using a digital workflow that combines the probability density function (PDF)-based Stochastic Reactor Model (SRM) Engine Suite with the statistical Model Development Suite (MoDS). In particular, an advanced multi-zonal approach is developed and applied to simulate fuels, in-cylinder combustion and gas phase as well as particulate emissions characteristics, validated against measurements and benchmarked with respect to the predictive power and computational costs of the baseline model. The multizonal SRM characterises the combustion chamber on the basis of different multi-dimensional PDFs dependent upon the bulk or the thermal boundary layer in contact with the cylinder liner. In the boundary layer, turbulent mixing is significantly weaker and heat transfer to the liner alters the combustion process. The integrated digital workflow is applied to perform parameter estimation based on the in-cylinder pressure profiles and engine-out emissions (i.e. NOx, CO, soot and unburnt hydrocarbons; uHCs) measurements. Four DoE (design-of-experiments) datasets are considered, each comprising measurements at a single load-speed point with various other operating conditions, which are then used to assess the capability of the calibrated models in mimicking the impact of the input variable space on the combustion characteristics and emissions. Both model approaches predict in-cylinder pressure profiles, NOx, and soot emissions satisfactorily well across all four datasets. Capturing the physics of emission formation near the cylinder liner enables the multi-zonal SRM approach to provide improved predictions for intermediates, such as CO and uHCs, particularly at low load operating points. Finally, fast-response surrogates are generated using the High Dimensional Model Representation (HDMR) approach, and the associated global sensitivities of combustion metrics and emissions are also investigated.

Evaluation of zero-dimensional stochastic reactor modelling for a Diesel engine application

“…From a practical application perspective, an additional challenge that needs to be considered is the suitability of a single SRM model for the entire operating space of an engine and a particular application of that engine. Previously, SRM has been used to model light duty [33], [34] and heavy duty [33], [35] engines operating domains, reporting good performance throughout. However, it is important to note that neither of these sources considered more than two injections per cycle, which is now common in light duty engine applications, as the combustion and control strategies are becoming more complicated, and the NOx model performance was not evaluated in all studies.…”

A Process for an Efficient Heat Release Prediction at Multiple Engine Speeds and Valve Timings in the Early Stage of Gasoline Engine Development

“…[27][28][29]. Regarding the SRM, different studies have shown how the SRM coupled with a 0-D turbulence model can be used to predict the engine combustion rate for an entire engine map [31][32][33]. The methodology was successfully used to predict the RoHR and carry a virtual engine calibration out thanks to an initial model training against multiple engine operating points.…”

Deep kernel learning approach to engine emissions modeling

“…Popular choices for the basis functions include ordinary polynomials (Li et al, 2002) and Lagrange polynomials (Baran and Bieniasz, 2015). Apart from applications in chemical kinetics, HDMR has been applied in process engineering (Sikorski et al, 2016) and also in engine emissions modeling (Lai et al, 2018).…”