Symbolic Sensitivity Analysis of Math-Based Spark Ignition Engine with Two-Zone Combustion Model

This paper presents a math-based spark ignition (SI) engine model for fast simulation with enough fidelity to predict in-cylinder thermodynamic properties at each crank angle. The quasi-dimensional modelling approach is chosen to simulate four-stroke operation. The combustion model is formulated based on two-zone combustion theory with a turbulent flame propagation model [1].

Cylinder design parameters such as bore and stroke play an important role to achieve higher performance (e.g. power) and reduce undesirable in-cylinder phenomenon (e.g. knocking). A symbolic sensitivity analysis is used to study the effect of the design parameters on the SI engine performance. We used the symbolic Maple/MapleSim environment to obtain highly-optimized simulation code [3]. It also facilitates a sensitivity analysis that identifies the critical parameters for design and control purposes. Among various schemes used in the sensitivity analysis of dynamical systems, internal differentiation is used in this research project due to its reliability and robustness [4].

In this study, the symbolic sensitivity functions are generated and solved along with two-zone combustion DAEs (differential-algebraic equations) at each crank angle.