A Physics-Based Control-Oriented Model for the Turbine Power of a Variable-Geometry Turbo-Charger

In this paper, we discuss the development of a control-oriented model for the power developed by a Variable Geometry Turbine (VGT). The turbine exit flow velocity, C_ex, is obtained based on a polytropic process assumption for the full turbine stage. The rotor inlet velocity, C_in, is estimated, through an empirical relationship between C_ex and C_in as a function of a dimensionless parameter ψ. The turbine power is developed based on Euler’s equations of Turbomachinery under the assumptions of zero exit swirl and alignment between the nozzle orientation and the C_in velocity vector. A power loss sub-model is also designed to account for the transmission loss associated with the power transfer between the turbine and compressor. The loss model is an empirical model and accounts for bearing friction and windage losses. Model validation results, for both steady state and transient operation, are shown.