Uncertainty propagation in field inversion for turbulence modelling in turbomachinery

The simulation of turbulent flows in turbomachinery requires to describe a wide range of scales and non-linear phenomena. Since the cost of scale resolving simulations is prohibitive for several configurations, turbulence closure models are still widely used in the framework of Reynolds-averaged Navier-Stokes (RANS) equations. In order to improve the prediction capability of these models, several machine learning strategies have been proposed. Among them, the field inversion approach allows to find a correction field which can be applied to the source term of the turbulence model in order to match experimental data: the correction field can then be generalised and expressed as a function of some flow features in order to extract modelling knowledge from the data.However, the reference experimental data are affected by uncertainty and this propagates to the correction field and to the final data-augmented model. In this work, the uncertainty propagation from the reference experimental data to the correction field is investigated. In particular, the flow field around a low pressure gas turbine cascade is studied in a challenging working condition characterised by laminar separation and transition to turbulence. The original RANS results are improved by the application of the field inversion algorithm in which the required gradients are computed by means of an adjoint approach. A sensitivity analysis is performed in order to provide a linearised propagation of the uncertainty from the experimental wall isentropic Mach number to the correction field.