A physics-based, control-oriented turbocharger compressor model for the prediction of pressure ratio at the limit of stable operations

Downsizing and boosting is currently the principal solution to reduce fuel consumption in automotive engines without penalizing the power output. A key challenge for controlling the boost pressure during highly transient operations lies in avoiding to operate the turbocharger compressor in its instability region, also known as surge. While this phenomenon is well known by control engineers, it is still difficult to accurately predict during transient operations. For this reason, the scientific community has directed considerable efforts to understand the phenomena leading to the onset of unstable behavior, principally through experimental investigations or high-fidelity CFD simulations. On the other hand, less emphasis has been placed on creating control-oriented models that adopt a physics-based (rather than data-driven) approach to predict the onset of instability phenomena. This work describes a centrifugal compressor model that focuses on predicting the behavior at operating conditions close to the stability limit. The objective of the model is to facilitate the development of estimation and control algorithms to optimize the boost pressure in a wider set of operating conditions. The model captures some of the key thermodynamic effects associated to the transition from stable to unstable operations in turbocharger centrifugal compressors. Starting from the well-known Moore-Greitzer surge model, a physics-based 1D compressor model is integrated to calculate the steady state characteristic curves from conservation of mass, energy and angular momentum. The sudden drop of pressure ratio that occurs during transition into the unstable region is predicted by coupling a mean-line analysis with correlations that consider the losses generated by the jet and wake phenomena, as well as the effects of these phenomena on the pressure and velocity distribution at the exit of the impeller. The model is calibrated and verified against experimental data acquired during tests performed on a turbocharger test bench at the University of Genoa, which include an analysis of the effects of shaft speed and circuit geometry on the onset of instabilities.