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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.

Boundary layer receptivity to free-stream disturbances plays a crucial role in forming coherent structures, whose breakup drives the laminar to turbulent flow transition. In the present work, an extended proper orthogonal decomposition (E-POD) procedure is applied to particle image velocimetry (PIV) data to identify correlating events between the free-stream velocity field and transitional boundary layers for flow configurations typical of low-pressure turbine blades. Data collected in two wall-parallel planes were ordered along the homogeneous spanwise coordinate so that the dominant POD coefficients provide the most energetic spanwise wavelengths in the free-stream and the near-wall regions. Then, the cross-correlation matrix of the POD spanwise coefficients computed independently in both measuring planes directly identifies the free-stream scales showing the highest degree of correlation with the boundary layer structures. Low-order reconstructions of the original PIV data show that the most correlating events are directly linked to the formation and the successive breakup process of streaky structures. Otherwise, larger-scale structures which are not involved in the transition process are filtered out. Interestingly, free-stream disturbances appear as organized wave packets with significant elongation in the streamwise direction when the velocity fields are reconstructed considering only the most correlating modes. The effect due to the Reynolds numbers, the pressure gradient, and the free-stream turbulence variation on the free-stream modes affecting the formation of coherent structures in the boundary layer is discussed in the paper.

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