A Bayesian method has been used to identify the best model strategy to describe the profile losses of low pressure turbine (LPT) cascades operating under unsteady inflow. The model has been tuned with experimental data measured in a large scale cascade facility, equipped with a moving bar system. Tests have been carried out on two different cascades, investigating three different reduced frequencies, three mass flow coefficients and several Reynolds numbers (up to eight) per condition, 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 parameter, and then with functional relationships mimicking physical constrains and loss tendencies.
Different combinations of the predictors, also including different types and orders 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 obtaining sufficient accuracy and avoiding 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 model selection. Realistic profile loss evolutions outside of the design space tested are provided, thus also allowing for a generalization of the structure of the model for other applications and future works.