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Research Papers

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

[+] Author and Article Information
D. Lengani

DIME—Universitá di Genova,
Via Montallegro 1,
Genova I-16145, Italy
e-mail: davide.lengani@edu.unige.it

D. Simoni, M. Ubaldi, P. Zunino

DIME—Universitá di Genova,
Via Montallegro 1,
Genova I-16145, Italy

F. Bertini

GE AvioAero S.r.l.,
Via I Maggio,
Rivalta (TO) 99 I-10040, Italy

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 5, 2016; final manuscript received September 22, 2016; published online November 16, 2016. Editor: Kenneth Hall.

J. Turbomach 139(3), 031006 (Nov 16, 2016) (8 pages) Paper No: TURBO-16-1225; doi: 10.1115/1.4034917 History: Received September 05, 2016; Revised September 22, 2016

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.

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References

Figures

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Fig. 1

Sketch of the test section and PIV interrogation area

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Fig. 2

Sketch of the data set arrangement for a temporal (left) or a spatial (right) analysis (POD or DMD) (see Schmid [20])

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Fig. 3

Time-mean streamwise velocity component (top), streamwise velocity fluctuation (center), and normal to the wall velocity fluctuations (bottom)

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Fig. 4

POD modes of the streamwise velocity component and their vectorial representation

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Fig. 5

POD modes of the wall-normal velocity component and their vectorial representation

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Fig. 6

Amplitude spectra of POD temporal eigenvectors

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Fig. 7

POD eigenvector of the spatial analysis (red line on bottom). Fifth POD mode of the temporal analysis, on top.

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Fig. 8

Spatial analysis. Example of POD mode in the (y, t) plane.

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Fig. 9

Spatial analysis. Example of DMD mode in the (y, t) plane.

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Fig. 10

Growth rate obtained from DMD, spatial stability problem

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Fig. 11

Amplitude spectra of unstable DMD modes and of eigenvector of the fourth POD mode of Fig. 6

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