Steady Modeling of a Turbocharger Turbine for Automotive Engines

Nowadays the turbocharging technique is playing a fundamental role in improving automotive engine performance and reducing fuel consumption and the exhaust emissions, in spark-ignition and compression ignition engines, as well. To this end, one-dimensional (1D) modeling is usually employed to compute the engine-turbocharger matching, to select the boost level in different operating conditions, and to estimate the low-end torque level and the transient response. However, 1D modeling of a turbocharged engine requires the availability of the turbine and compressor characteristic maps. This leads to some typical drawbacks: (1) Performance maps of the turbocharger device are usually limited to a reduced number of rotational speeds, pressure ratios, and mass flow rates because of turbine/compressor matching limits; (2) as a consequence of previous issue, unphysical extrapolation of maps' data is commonly required; and (3) heat transfer conditions may strongly differ between test bench measurements and actual operation, where turbocharger is coupled to an internal combustion engine. To overcome the above problems, in the present paper a numerical procedure is introduced: It solves 1D steady flow equations inside the turbine components with the aim of accurately reproducing the experimentally derived characteristic maps. The steady procedure describes the main phenomena and losses arising within the stationary and rotating channels constituting the turbine. It is utilized to directly compute the related steady maps, starting from the specification of a reduced set of geometrical data. An optimization process is employed to identify a number of tuning constants included in the various loss correlations. The procedure is applied to the simulation of five different turbines: three waste-gated turbines, a twin-entry turbine, and a variable geometry turbine. The numerical results show good agreement with the experimentally derived maps for all the tested devices. The model is, hence, used to evaluate the turbine performance in the whole operating domain.