Synchronization of multi-plane measurement data by means of POD: application to unsteady boundary layer transition

Time-resolved particle image velocimetry measurements have been performed on the suction side of a low-pressure turbine cascade perturbed by periodic unsteady incoming wakes. The flow field has been investigated in two orthogonal planes. A wall-normal and a wall-parallel plane have been considered to identify and characterize the dimensions of the coherent structures developing within the boundary layer at the different wake passing phases. A new proper orthogonal decomposition (POD)-based procedure has been developed to sort the data acquired in the two planes. Particularly, the temporal coefficients of the POD modes related to wake migration have been used to provide phase-averaged data and synchronize the information obtained in the two measurement planes. It is shown that this technique does not require an external trigger, typically requested by previous available multi-plane phase-locking strategies. Moreover, POD has been applied to sub-ensembles of data at the same relative phase within the wake passing cycle. Thanks to the proposed procedure, the characteristic dimension of the eddies caused by the wake–boundary layer interaction has been investigated: at each phase of the wake passing cycle, the POD provides the representation of the most relevant flow features. It has been possible to observe the presence of boundary layer streaks and when they first occur within the wake passing period. One-dimensional auto-correlations of the velocity fields in the wall-parallel plane have been performed following the periodic perturbation induced by the passing wake in space and time. The auto-correlation provides the spacing between streaks, that, once scaled with the local boundary layer displacement thickness measured at the same phase in the wall-normal plane, is consistent with the available literature data for steady flows. Graphical abstract:

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