A physically based methodology to extrapolate performance maps of radial turbines

Abstract

This paper details a physical based methodology to perform an extrapolation of the radial turbine performance maps, both mass flow characteristics and the efficiency curve. This method takes into account a narrow range of experimental data, which is usually the data available when such turbines are part of a turbocharger. Therefore, the extrapolation methodology is especially useful when data from third parties are being used or when the compressor of a turbocharger is used as turbine brake in a gas stand. The nozzle equation is used to develop an interpolation and extrapolation of the mass flow rate trough the turbine. Then, specific information is extracted from this extrapolation and is fed into a total-to-static efficiency equation to carry out an extension of the efficiency curve. This equation is developed using the definition of the total-to-static efficiency, velocity triangles and thermodynamic and fluid fundamental equations.This procedure has been applied to five radial turbines of different sizes and types. Results are compared against experimental information available in the literature or provided by the turbine manufacturers and a good agreement has been found between theoretical and experimentally estimated data.Keywords: Turbochargers, radial turbines, efficiency and mass flow rate maps extrapolation, physical equations based extrapolation. ------------------------------- Greek --------------------------------- Subscripts INTRODUCTIONA way to characterize the performance of a radial inflow turbine widely used in a turbocharger is via a turbine map. Turbine maps usually are presented using two separate plots: one for the mass flow rate and one for the energy conversion efficiency, which usually is taken as the total-to-static efficiency. The former chart is presented as the corrected mass flow ( * m  ) as a function of the totalto-static expansion ratio (ER). The corrected mass flow ( * m  ) is defined as the mass flow rate multiplied by a ratio between the square root of the turbine stagnation inlet temperature and the turbine stagnation inlet pressure [1]. The other chart is the total-to-static efficiency ( ts ) as a function of the blade to jet speed ratio (), which is a ratio of the rotor tip linear velocity to the isentropic velocity through the turbine stage, for different turbine rotational speeds [1]. [5] used a radial compressor instead of a dynamometer to enable increased power of larger turbines to be absorbed. Szymko [6] developed an installation where an eddy current dynamometer was used in order to absorb the power of the turbine and for providing a low known inertia of the rotating assembly, which increases the measurement accuracy of the instantaneous torque.In the continuous flow test bench at Universidad Politécnica de Valencia, the approach is to use a compressor as a braking device [7]. In this last case, a collection of only a narrow range of data is possible, due to the surge and choke limits of the compressor, so a limited widespread of the data is availabl...

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