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Experimental data describing laminar separation bubbles developing under strong adverse pressure gradients, typical of ultra-high-lift turbine blades, have been analyzed to define empirical correlations able to predict the main features of the separated flow transition. Tests have been performed for three different Reynolds numbers and three different free-stream turbulence intensity levels. For each condition, around 4000 particle image velocimetry (PIV) snapshots have been acquired. A wavelet-based intermittency detection technique, able to identify the large scale vortices shed as a consequence of the separation, has been applied to the large amount of data to efficiently compute the intermittency function for the different conditions. The transition onset and end positions, as well as the turbulent spot production rate, are evaluated. Thanks to the recent advancements in the understanding on the role played by Reynolds number and free-stream turbulence intensity on the dynamics leading to transition in separated flows, guest functions are proposed in the paper to fit the data. The proposed functions are able to mimic the effects of Reynolds number and free-stream turbulence intensity level on the receptivity process of the boundary layer in the attached part, on the disturbance exponential growth rate observed in the linear stability region of the separated shear layer, as well as on the nonlinear later stage of completing transition. Once identified the structure of the correlation functions, a fitting process with own and literature data allowed us to calibrate the unknown constants. Results reported in the paper show the ability of the proposed correlations to adequately predict the transition process in the case of separated flows. The correlation for the spot production rate here proposed extends the correlations proposed in literature for attached (by-pass like) transition process, and could be used in γ–Reϑ codes, where the spot production rate appears as a source term in the intermittency function transport equation.

This work reports the application of an extended proper orthogonal decomposition (E-POD) procedure to multi-plane particle image velocimetry (PIV) measurements describing the evolution of laminar separation bubbles (LSBs). Measurements were performed over a flat plate installed between adjustable end-walls providing a prescribed adverse pressure gradient for two Reynolds numbers (Re = 70 000, 150 000) and free-stream turbulence intensity levels (Tu = 1.5%, 2.5%). A wall-normal and two wall-parallel measuring planes located at different distance from the wall were considered. POD was applied to the entire PIV planes as well as on their sub-domains, showing the main flow features occurring in the different regions of the LSB. Then, the application of E-POD on different plane partitions revealed the existing correlation between the main dynamics observed in the forward part of the bubble and the breakup events occurring in the reattachment region. The E-POD modes computed in the breakup region resemble streaky structures when PIV snapshots are projected onto the POD eigenvectors of the near wall plane. Otherwise, Kelvin–Helmholtz rolls dominate the E-POD modes obtained by projection of the snapshot matrices on the basis computed in the plane located far from the wall. The main scales of the coherent structures highlighted by the E-POD modes were also characterized by means of the streamwise and spanwise autocorrelation functions of E-POD filtered fields. Data in this work clearly highlight the similarity properties of the main flow features observed in LSBs once scaled with the momentum thickness of the boundary layer at the separation position.