Calibration and Results of a Radial Turbine 1-D Model with Distributed Parameters

Paper #:
  • 2011-01-1146

Published:
  • 2011-04-12
Citation:
Macek, J., Vitek, O., and Zak, Z., "Calibration and Results of a Radial Turbine 1-D Model with Distributed Parameters," SAE Technical Paper 2011-01-1146, 2011, https://doi.org/10.4271/2011-01-1146.
Pages:
24
Abstract:
The physical 1-D model of a radial turbine consists in a set of gas ducts featuring total pressure and/or temperature changes and losses. This model has been developed using the basic modules of generalized 1-D manifold solver. The tools for it were presented at SAE 2008 and 2009 World Congresses.The model published before is amended by a semi-empiric mechanical loss and windage loss modules. The instantaneous power of a turbine is integrated along the rotating impeller channel using Euler turbine theorem, which respects the local unsteadiness of mass flow rate along the channel.The main aim of the current contribution is to demonstrate the use of measured turbine maps for calibration of unsteady turbine model for different lay-outs of turbine blade cascades. It is important for VG turbines for the optimal matching to different engine speeds and loads requirements. The turbine model calibration parameters (flow direction angles, loss coefficients, leakage coefficients) are identified by means of the same model applied to a steady flow turbocharger testbed simulation using optimization to find the best fit.The examples of model results at a four cylinder engine are compared to evaluation of a turbine performance at an engine in operation using measured unsteady pressures close to a turbine and turbocharger speed changes. The differences between steady-flow, lumped parameters model and the current model are demonstrated.The interpolation and extrapolation of turbine parameters to different blade cascades lay-outs is carried out in dependence on turbine pressure ratio and rack positions. The results are helpful to find the best controlled turbine for a car engine.The potential of the current model is in physical simulation of twin scroll turbines, outlet diffuser influence and the robust prediction of turbine map at low speeds. The experience from the model is being used for an unsteady flow compressor model.
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