A Bayesian method has been used to identify the best model strategy to describe the aerodynamic profile losses of a low pressure turbine (LPT) cascade operating under unsteady inflow. The model has been tuned with experimental data measured in a large scale cascade facility, specifically equipped with a moving bar system in order to evaluate the effects of the most influencing unsteady parameters on the losses. Tests have been carried out on two different cascades, investigating three different reduced frequencies, three mass flow coefficients and several Reynolds numbers (three to seven according with the bar system’s rotational speed limit), accounting for an overall amount of 51 different combinations of these parameters for each cascade. The predictor functions included into the model have been varied starting from a classic polynomial formulation for each influencing parameters, and then with functional relationships mimicking physical constrains and loss tendencies.

Particularly, predictor functions for the Reynolds number should include the capability in reproducing the lapse rate for laminar and/or turbulent boundary layer growth mechanisms, thus suggesting a dependency of the type proportional to Re^-0.5^ and/or Re^-0.2^. The coefficients of the model for both these terms also give a rapid view of the main boundary layer status and the dominant source, laminar or turbulent related, in the generation of viscous losses. For the mass flow coefficient, the limiting value toward infinity should be considered as a steady state condition, thus a horizontal asymptote should be reproduced by the model, suggesting a hyperbole as the most promising functional relationship. Finally, for the reduced frequency a quadratic form gives the opportunity to have a minimum distribution, as also previously shown in works available in the literature, thus allows us to check for an optimum. Different combinations of the predictors, also including different types and order of the cross-terms, have been evaluated by means of a Bayesian model selection method searching for the maximum probability of the model in fitting the cloud of experimental data. In particular, the evaluation of the Model Evidence (ME) using the Bayesian Information Criterion approximation (BIC) has allowed both to obtain sufficient accuracy and to avoid overfitting at the same time.

The best model here identified will be shown to be able to well reproduce the loss surface of a third different cascade that does not participate to the education of the model itself, especially providing realistic profile losses evolution outside of the design space tested, thus also allowing for a generalization of the structure of the model for other applications and future works.


A Bayesian Approach for the Identification of Cascade Loss Model Strategy

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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