The design of low-pressure turbines (LPT) must account for the losses generated by the unsteady interaction with the upstream blade row. The estimation of such unsteady wake induced losses requires the accurate prediction of the incoming wake dynamics and decay. Machine-learnt, non-linear turbulence closures (stress-strain relationships) have therefore been developed for LPT flows with unsteady inflow conditions using a zonal based model development approach with an aim to enhance the wake mixing prediction for unsteady Reynolds-averaged Navier-Stokes calculations. Phase-lock averaged data from large eddy simulations at a realistic isentropic exit Reynolds number and two reduced frequencies have been used as a reference in order to create explicit algebraic Reynolds stress models based on gene expression programming, using three different model-generation approaches. These models have been tested in an a priori sense and have been found to improve the stress-strain relationship significantly over the Boussinesq approximation. The models generated have been correlated with certain physical phenomena taking place in the LPT flow domain and have been found to enhance the prediction of the wake-mixing by an average amount of 50% when compared to the Boussinesq approximation. These models developed are found to be robust as they enhance the wake-mixing predictions across different reduced frequencies over the Boussinesq approximation by similar amounts. This study aids blade designers in selecting the non-linear closures capable of mimicking the physical mechanisms responsible for loss generation.

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