A model-based methodology to predict the compressor behaviour for the simulation of turbocharged engines

Abstract

Modelling the flow and efficiency of turbochargers for engine system simulation and control applications is an established practice that relies on the steady-state maps provided by manufacturer suppliers. However, as often occurs in practice, only a limited fraction of data is available in the compressor and turbine operating domain. For this reason, several modelling techniques have been proposed to interpolate and extrapolate flow and efficiency data. Most of the modelling approaches, based on black- or grey-box approaches, have limited predictive ability and typically low accuracy in off-design conditions, such as at engine idle or low engine speed. The current paper presents a novel model-based approach for overcoming the sparse nature of the available compressor maps, characterizing the flow and efficiency outputs of automotive centrifugal compressors by using extrapolation methods that are physically consistent with the conservation principles and actual behaviour of the system. The approach relies on a predictive model based on the thermodynamic analysis of a centrifugal compressor stage. The model builds upon the mass, energy, and entropy balance equations for compressible fluids. Specific sub-models are then introduced to account for the effects of slip phenomena, incidence losses, friction, and heat transfer losses, leading to high fidelity and predictive ability in off-design conditions. A detailed analysis of the model calibration and validation process is presented, utilizing data from two different automotive compressors. Finally, the procedure described is applied to characterize the compressor performance in engine system simulation, in comparison with a conventional (data-driven) model.