The present article attempts to describe the behavior of wastegated turbines under various steady and pulsating flow conditions. For this, meanline and one-dimensional numerical codes including appropriate modeling approaches for wastegated turbines have been developed with the FORTRAN language. These codes were validated against experiments with an established test rig at the National School of Engineers of Sfax. The discharge coefficient map of the wastegate was determined with a developed correlation built from experiments, and it was served as an input to the developed codes for interpolations during computation. This correlation is based on a two-dimensional non-linear dose-response fitting relationship instead of classical polynomial function which is one novelty of the article in addition to the one-dimensional modeling methodology. The normalized root mean square error (NRMSE) of both cycle-averaged efficiency and mass flow parameter (MFP) remains below 2% which confirms the validity of the proposed calculation approach. The results indicated a large deviation in the turbine performance under pulsating flow conditions compared to the steady state ones. The shape of the hysteresis loop of the turbine efficiency remains unchanged toward the variation of the wastegate valve angle at the same pulse frequency. The mass flow hystereses loop area is decreased by around 50% as the pulse frequency increases from 33 up to 133.33 Hz. An increase of less than 1% of the cycle-averaged efficiency has been reported when the bypass flow through the wastegate increases. The fluctuation of the efficiency is decreased by 1.5% when the wastegate valve becomes fully opened under the whole range of the pulse frequency.

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Mixed flow turbines are widely used in several industrial applications covering turbomachinery, automotive engineering and electricity production. For decades, it is well known that mixed flow turbines are a seat of several loss phenomena such as the volute to rotor interspace loss, subject of this paper. Commonly, the meanline approach is the first step solution for building a preliminary design of such turbines and estimating subsequent losses. The accuracy of the code used in the meanline modeling is crucial for building an optimized turbine design with a minimized loss generation. This paper presents an improved validated meanline code, written in the newest object-oriented version of the FORTRAN language, for turbomachinery performance prediction. Unlike commercially available codes, the code allows the calculation of the rotor passage loss coefficient given the turbine expansion ratio without the need for additional test data. The standard deviation value between the code and test data is less than 10%, for all studied cases which ensure the validity of the developed model. Then, the developed code is exploited to investigate the effect of the volute to rotor interspace geometry on the loss generation and performance of a mixed flow turbine. Indeed, a performance distribution over a wide range of rotational speed and an energy loss breakdown are depicted and discussed showing a significant impact of the volute to rotor interspace. The results revealed an improvement in the turbine efficiency up to 2.9% with a volute to rotor interspace radii ratio of 0.59 at 80% of the design speed.

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