Physics-based turbine power models for a Variable Geometry Turbocharger

Control-oriented models for Variable Geometry Turbochargers (VGT) typically calculate the turbine power based on isentropic assumptions with a fixed or a map based value for the turbocharger mechanical efficiency. While the fixed efficiency assumption is an obvious over simplification, the map based approach, on the other hand, may not be globally accurate due to the need for interpolation between varying vane positions and extrapolation when the turbocharger is operating outside the mapped region. In this paper physics-based models of turbine power as well as the power loss are developed, utilizing the VGT vane position and the shaft speed. This makes it possible to define the mechanical efficiency as a function of the vane position thereby eliminating the above mentioned uncertainties as well as allowing a smooth extension over the entire operating range. The proposed model is validated against a few sets of test data from both steady state and transient operations.