Identification of free-stream and boundary layer correlating events in free-stream turbulence-induced transition

Abstract

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.