Model-order reduction for wave propagation dynamics in internal combustion engine air path systems

Abstract

With the advancements in engine design, the air path systems have become so complex that advanced optimization and control design methods are nowadays needed to fully exploit the potential of technologies such as flexible valve actuation. While the automotive industry is employing model-based methodologies for the engine air path system control design process, control-oriented engine air path models are currently limited in their accuracy and predictive ability and rely significantly on calibration. As the engine system complexity increases, there is considerable interest for accurate yet computationally efficient control-oriented engine system models that are able to predict the cylinder charge composition and the thermodynamic conditions with limited calibration effort. This article presents a novel model-order reduction approach for lumped-parameter modeling of pressure wave propagation dynamics in fluids, with application to full-engine simulation. Instead of approximating the geometry of the system to a simple control volume (as typically done in control-oriented engine air path models), this modeling methodology reduces the governing equations for compressible fluid flows and allows for systematically handling both complex geometries, such as sudden area changes and pipe elbows, as well as complex boundary conditions. The model-order reduction procedure projects the partial differential equations governing the air and gas flows onto a set of eigenfunctions, resulting in a set of ordinary differential equations that can be easily implemented in forward-looking simulation software. The modeling approach presented in this article is applied to characterize the wave propagation dynamics in the air path system of a single-cylinder engine, specifically predicting the crank-angle-resolved intake and outlet pressure, as well as the cylinder air charge and volumetric efficiency. The results are benchmarked against both experimental data and simulation results from a well-established one-dimensional gas dynamic model.