A flat plate boundary layer has been surveyed by means of time-resolved particle image velocimetry (PIV) under variable Reynolds number (Re=70000, 150000) and turbulence intensity level (Tu=1.5%, 2.5%). The PIV data were post-processed by applying Dynamic Mode Decomposition (DMD), which provides frequency based modes and their corresponding growth rate. The effects of the Re and the Tu variation on the amplification of the dominant wavelength within the separated shear layer, which is responsible for transition, is the main subject of the present work. The PIV visualizations were completed in two measuring planes, that are oriented both normal and parallel to the wall. For the wall-parallel configuration, the measuring plane is located inside the boundary layer, which separates due to the adverse pressure gradient imposed to the flow typical of low pressure turbine blades. For each combination of the flow parameters, about 8000 time-resolved PIV snapshots were collected, enabling both the statistical and the dynamic characterization of the transition process.

The DMD modes and related eigenvalues were computed with reference to the main streamwise coordinate. This allowed discussing the effects of the main flow parameters on the amplification, due to the Kelvin-Helmholtz (K-H) instability, of the dominant streamwise wavelengths within the separated shear layer. The growth of such streamwise modes ends with the formation of large scale vortices, whose breakup forces transition. In order to obtain the effective distribution of the maximum growth rate of fluctuations at different locations and times, the DMD domain was continuously extended in the streamwise direction, accounting for a specified number of periods characterizing the large scale K-H vortices. Applying the DMD directly on the whole data set provides instead globally stable modes due to nonlinearities occurring within the flow.

Then, in order to reduce the time-space dependent results obtained by the DMD procedure, a probability density function of the most unstable wavelength and the corresponding growth rate has been computed. A single unstable mode is therefore provided for each combination of the Re and the Tu level, that allows comparing the effects of these two flow parameters on the transition dynamics. For the present data set, the spatial growth rate of fluctuations is found to increase at the higher Reynolds number, while it slightly reduces with increasing the Tu level.

The procedure and findings discussed in this work shall be suitable for designing active control systems, such as harmonic blowing for separation control. Indeed, the forcing frequency that is used to promote the boundary layer transition is directly linked to the most amplified wavelength provided by the method presented in this work.


Dynamic Mode Decomposition Analysis of Separated Boundary Layers Under Variable Reynolds Number and Free-Stream Turbulence

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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