Dimensionless Quantification of Small Radial Turbine Transient Performance

Turbochargers are inherently dynamic devices, comprising internal flow volumes, mechanical inertias and thermal masses. When operating under transient conditions within an engine system, these dynamics need to be better understood. In this paper, a new non-dimensional modelling approach to characterise the turbocharger is proposed. Two new dimensionless quantities are defined with respect to mechanical and thermal transient behaviour, which are used in conjunction with the Strouhal number for flow transients. The modelling approach is applied to a small wastegated turbocharger and validated against experimental results. The model is used to simulate the turbocharger mass flow rate, turbine housing temperature and shaft speed responses to different excitation frequencies for different sizes of turbine. The results highlight the influence of turbocharger size on the dynamic behaviour of the system, which is particularly marked for the turbine housing temperature. At certain frequency ranges, the system behaviour is quasi-steady, allowing modelling through static maps in these operating regions. Outside these ranges, however, transient elements play a more important role. The simulation study shows that the proposed dimensionless parameters can be used to normalise the influence of turbine size on the dynamic response characteristics of the system. The model and corresponding dimensionless parameters can be applied in future simulation studies as well as for turbocharger matching in industry.