Implementing Turbomachinery Physics into Data Map-Based Turbocharger Models

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Abstract
A convenient way of modelling turbochargers is based on data maps. These models are easy to put into place, require low CPU charge and are control-oriented. Data relative to compressor and turbine are read from tables: pressure ratio and efficiency are determined as functions of mass flow rate and rotary speed on two distinct data maps. Nevertheless, this type of model has drawbacks: Usually, only higher turbocharger speed data are mapped (> 90000 rpm) although the low rpm zone is the most useful zone for normalized driving cycles simulations. Moreover, maps are poorly discretized, leading to the use of specific extra-interpolation methods (many are identified in [5]). These methods are purely mathematical, which gives inaccurate results in extrapolation zones. Relation between pressure ratio and efficiency is then broken (i.e., if one implements a pumping model for the compressor, the pressure ratio will be affected, but not the efficiency). The present paper develops a new extra/interpolation model incorporating physical laws. An analysis of turbo-machinery equations is performed. A new approach for extra-interpolating performance maps, which satisfies the physical laws stated in turbomachinery equations, is derived from this work. Results from this new model are compared with standard methods. The major conclusions drawn from this study are: 1 - The new model improves the simulation accuracy while keeping the same easiness of use and robustness. 2 - Extrapolation in the low rpm zone is derived from physical equations. 3 -This method is applicable to both compressor and turbine. 4 - The pressure ratio and efficiency maps are now linked.

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