In the present work the evolution of the boundary layer over a low-pressure turbine blade is studied by means of direct numerical simulations. The free-stream flow is characterized by high level of free-stream turbulence and periodically impinging wakes. To include the presence of the wake without employing an ad-hoc model, we simulate both the moving bars and the stationary blades in their respective frames of reference and the coupling of the two domains is done through appropriate boundary conditions. The presence of the wake mainly affects the development of the boundary layer on the suction side of the blade. The presence of the wake introduces alternating regions in the streamwise direction of high- and low-velocity fluctuations inside the boundary layer. The analysis of the velocity fields allows the characterization of the streaky structures forced in the boundary layer by turbulence carried by upstream wakes. Both the fluctuations induced by the migration of the wake in the blade passage and the presence of the streaks contribute to high values of the disturbance velocity inside the boundary layer with respect to a steady inflow case. It was found that the migration of the wake in the blade passage stands for the most part of the perturbations with zero spanwise wavenumber. The non-zero wavenumbers are found to be amplified in the rear part of the blade at the boundary between the low and high speed regions associated with the wakes.

The present work describes a method for the computation of the nucleation rate of turbulent spots in transitional boundary layers from particle image velocimetry (PIV) measurements. Different detection functions for turbulent events recognition were first tested and validated using data from direct numerical simulation, and this latter describes a flat-plate boundary layer under zero pressure gradient. The comparison with a previously defined function adopted in the literature, which is based on the local spanwise wall-shear stress, clearly highlights the possibility of accurately predicting the statistical evolution of transition even when the near-wall velocity field is not directly available from the measurements. The present procedure was systematically applied to PIV data collected in a wall-parallel measuring plane located inside a flat plate boundary layer evolving under variable Reynolds number, adverse pressure gradient (APG) and free-stream turbulence. The results presented in this work show that the present method allows capturing the statistical response of the transition process to the modification of the inlet flow conditions. The location of the maximum spot nucleation is shown to move upstream when increasing all the main flow parameters. Additionally, the transition region becomes shorter for higher Re and APG, whereas the turbulence level variation gives the opposite trend. The effects of the main flow parameters on the coefficients defining the analytic distribution of the nucleation rate and their link to the momentum thickness Reynolds number at the point of transition are discussed in the paper. Graphical abstract