Analysis of a Quasi-Steady Extension to the Turbine Model in Mean Value Engine Models

The aim to reduce fuel consumption and CO₂ emissions has been targeted by several approaches. One of them is downsizing, where a small engine is equipped with a turbocharger in order to give the same power as a larger engine, but with less fuel consumption. This in turn requires advanced control systems to take full benefit from the downsizing. Recent hardware advancements have enabled the use of variable geometry turbochargers also on SI engines, pushing the control demands further. This paper investigates possible extensions to control-oriented mean value engine models for turbocharged SI engines, focusing on the turbine. Mean value models do not take the pulsating phenomena in the exhaust manifold into account. This is assumed to cause large model errors, especially for the turbine efficiency and turbine power. The main contribution of this paper is to present an investigation of the effects of incorporating pressure pulses in the mean value model, together with an analysis of the effects of the pulsation on the turbine performance maps. An evaluation of the extended mean value model using measurements on a four-cylinder SI engine with a variable geometry turbocharger is also presented. The evaluation shows little difference between using pressure pulses and mean values. An analysis of the expression for turbine power shows that, when treating the maps quasi-steady, the calculated turbine power is almost the same when using pressure pulsations as when using just the mean pressure ratio. The analysis also indicates that this is due to the fact that the turbine power is an approximately linear function of the turbine pressure ratio.