Experimental Investigation on the Time–Space Evolution of a Laminar Separation Bubble by Proper Orthogonal Decomposition and Dynamic Mode Decomposition

Abstract

A time-resolved particle image velocimetry (TR-PIV) system has been employed to investigate a laminar separation bubble which is induced by a strong adverse pressure gradient typical of ultrahigh-lift low-pressure turbine (LPT) blades. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are described and applied within this paper. These techniques allow reducing the degrees-of-freedom of complex systems producing a low-order model ranked by the energy content (POD) or by the modal contribution to the dynamics of the system itself (DMD), useful to highlight the dominant dynamics. The time–space evolution of the laminar separation bubble is characterized by rollup vortices shed in the surrounding of the bubble maximum displacement as a consequence of the Kelvin–Helmholtz (KH) instability process as well as by a low-frequency motion of the separated shear layer. The decomposition techniques proposed allow the identification of these coherent structures and the characterization of their modal properties (e.g., temporal frequency, spatial wavelength, and growth rate). The POD separates the different dynamics that induce velocity fluctuations at different frequencies and wavelength looking at their contribution to the overall kinetic energy. The DMD provides complementary information: the unstable spatial frequencies are identified with their growth (or decay) rates. DMD modes associated with the Kelvin–Helmholtz instability and the corresponding vortex shedding phenomenon clearly dominate the unsteady behavior of the laminar separation bubble, being characterized by the highest growth rate. Modes with longer wavelength describe the low-frequency motion of the laminar separation bubble and are neutrally stable. Results reported in this paper prove the ability of the present methods in extracting the dominant dynamics from a large dataset, providing robust and rapid tools for the in depth analysis of transition and separation processes.