Unsteady 1D Simulation of a Turbocharger Compressor

The one-dimensional (1D) modeling of a turbocharged engine requires the availability of the turbine and compressor characteristic maps. This leads to two main problems: • performance maps of the turbocharger device are usually limited to a reduced number of rotational speeds, pressure ratios and mass flow rates. Extrapolation of maps’ data is commonly required; • performance maps are experimentally derived on stationary test benches, while the turbocharger usually operates under unsteady conditions, when coupled to an internal combustion engine (ICE). To overcome the above problems, in the present paper the flow inside a rotating pipe of a centrifugal compressor is simulated within a 1D modeling approach, with the aim of predicting its characteristic map. The main improvement with respect to the employment of a steady experimental map consists in the absence of data extrapolation and in the possibility of fully characterizing the unsteady operation of the component. In this way it is also possible to handle on a physical point of view surge phenomena (backflows) which may arise particularly at low engine speed and high load. To this aim, the actual evolution of the blade-to-blade duct profile is specified through the assignment of proper data which define the duct orientation in the space along its curvilinear abscissa. Flow equations are next generalized to include additional terms arising as a consequence of pipe rotation. The whole compressor is schematized as a number of rotating channels in parallel, linked at the impeller inlet and outlet by a constant pressure boundary condition. The velocity triangles are employed to handle the transition between the absolute and the relative motion occurring at the impeller inlet and outlet. The presence of a vaneless diffuser is also considered at the exit section of the rotor blades. The procedure includes some correlations to keep into account slip effects, incidence and distributed losses. The above methodology is utilized to directly compute the stationary map of the device, starting from the specification of its geometry and rotating speed. A comparison with experimental data shows a good agreement with the predicted performance curves. The same procedure can be easily extended to the simulation of a radial turbine, too. A one-dimensional model of a centrifugal compressor was described in detail under both isentropic and real flow conditions. Classical correlations for the various flow losses and slip effects were introduced in the model, and their effect on the computed results was discussed with reference to a test compressor. The model was then applied to the simulation of a backswept vanes compressor constituting the turbocharger of a small displacement SI engine. The numerical procedure, after a limited adjustment of few tuning constants, was proven to furnish the steady performance map of the device all over its operating region. Both the pressure ratio and the outlet temperature showed a very good agreement with the test data. The stable operating limit of the compressor was also estimated with good accuracy. The proposed methodology was proven to overcome some of the limitations related to the employment of the steady performance map, to compute the engine-turbocharger matching conditions. The direct calculation of the performance map in fact allows avoiding the need of map’s extrapolation and can be realized with the present model basing on few geometrical data of the device. The intrinsic unsteadiness of the methodology also gives the possibility to fully characterize the transient operation of the component. A first example of the model capabilities in describing the unsteady operation of the compressor was included in the paper. The presented results authorize to further develop the model with the objective to describe the unstable operating regime of the compressor. In this way, it will be also possible to handle on a physical point of view surge phenomena (backflows) which may arise particularly at low engine speed and high load.