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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

Mayle, R. E. , 1991, “ The Role of Laminar-Turbulent Transition in Gas Turbine Engines,” ASME J. Turbomach., 113(4), pp. 509–537. [CrossRef]
Bons, J. L. , Pluim, J. , Gompertz, K. , Bloxham, M. , and Clark, J. , 2008, “ The Application of Flow Control to an Aft-Loaded Low Pressure Turbine Cascade With Unsteady Wakes,” ASME Paper No. GT2008-50864.
Mahallati, A. , McAuliffe, B. R. , Sjolander, S. A. , and Praisner, T. J. , 2013, “ Aerodynamics of a Low-Pressure Turbine Airfoil at Low Reynolds Numbers—Part I: Steady Flow Measurements,” ASME J. Turbomach., 135(1), p. 011010. [CrossRef]
Satta, F. , Simoni, D. , Ubaldi, M. , Zunino, P. , and Bertini, F. , 2014, “ Loading Distribution Effects on Separated Flow Transition of Ultra-High-Lift Turbine Blades,” AIAA J. Propul. Power, 30(3), pp. 845–856. [CrossRef]
Jacob, R. G. , and Durbin, P. A. , 2001, “ Simulations of Bypass Transition,” J. Fluid Mech., 428, pp. 185–212. [CrossRef]
Nolan, K. , and Zaki, T. , 2013, “ Conditional Sampling of Transitional Boundary Layers in Pressure Gradients,” J. Fluid Mech., 728, pp. 306–339. [CrossRef]
Hain, R. , Kähler, C. J. , and Radespiel, R. , 2009, “ Dynamics of Laminar Separation Bubbles at Low-Reynolds-Number Aerofoils,” J. Fluid Mech., 630, pp. 129–153. [CrossRef]
Simoni, D. , Ubaldi, M. , Zunino, P. , Lengani, D. , and Bertini, F. , 2012, “ An Experimental Investigation of the Separated-Flow Transition Under High-Lift Turbine Blade Pressure Gradients,” Flow Turbul. Combust., 88(1), pp. 45–62. [CrossRef]
Wu, X. , Jacobs, R. , Hunt, J. C. R. , and Durbin, P. A. , 2001, “ Evidence of Longitudinal Vortices Evolved From Distorted Wakes in a Turbine Passage,” J. Fluid Mech., 446, pp. 199–228.
Nagabhushana Rao, V. , Tucker, P. , Jefferson-Loveday, R. , and Coull, J. , 2013, “ Large Eddy Simulations in Low-Pressure Turbines: Effect of Wakes at Elevated Free-Stream Turbulence,” Int. J. Heat Fluid Flow, 43, pp. 85–95. [CrossRef]
Lumley, J. L. , 1967, “ The Structure of Inhomogeneous Turbulent Flows,” Atmospheric Turbulence and Wave Propagation, A. M. Yaglom and V. I. Tatarski , eds., Nauka, Moscow, pp. 166–178.
Sirovich, L. , 1987, “ Turbulence and the Dynamics of Coherent Structures. Part I,” Q. Appl. Math., 45(3), pp. 561–590.
Legrand, M. , Nogueira, J. , and Lecuona, A. , 2011, “ Flow Temporal Reconstruction From Non-Time-Resolved Data—Part I: Mathematic Fundamentals,” Exp. Fluids, 51(4), pp. 1047–1055. [CrossRef]
Sarkar, S. , 2008, “ Identification of Flow Structures on a LP Turbine Blade Due to Periodic Passing Wakes,” ASME J. Fluid Eng., 130(6), p. 061103. [CrossRef]
Ben Chiekh, M. , Michard, M. , Guellouz, M. S. , and Béra, J. C. , 2013, “ POD Analysis of Momentumless Trailing Edge Wake Using Synthetic Jet Actuation,” Exp. Therm. Fluid Sci., 46, pp. 89–102. [CrossRef]
Shi, L. L. , Liu, Y. Z. , and Wan, J. J. , 2010, “ Influence of Wall Proximity on Characteristics of Wake Behind a Square Cylinder: PIV Measurements and POD Analysis,” Exp. Therm. Fluid Sci., 34(1), pp. 28–36. [CrossRef]
Berrino, M. , Lengani, D. , Simoni, D. , Ubaldi, M. , Zunino, P. , and Bertini, F. , 2015, “ Dynamics and Turbulence Characteristics of Wake-Boundary Layer Interaction in a Low Pressure Turbine Blade,” ASME Paper No. GT2015-42626.
Lengani, D. , and Simoni, D. , 2015, “ Recognition of Coherent Structures in the Boundary Layer of a Low-Pressure-Turbine Blade for Different Free-Stream Turbulence Intensity Levels,” Int. J. Heat Fluid Flow, 54, pp. 1–13. [CrossRef]
Lengani, D. , Simoni, D. , Ubaldi, M. , Zunino, P. , and Bertini, F. , 2016, “ Coherent Structures Formation During Wake-Boundary Layer Interaction on a LP Turbine Blade,” Flow Turbul. Combust., epub, pp. 1–25.
Schmid, P. J. , 2010, “ Dynamic Mode Decomposition of Numerical and Experimental Data,” J. Fluid Mech., 656, pp. 5–28. [CrossRef]
Sarmast, S. , Dadfar, R. , Mikkelsen, R. F. , Schlatter, P. , Ivanell, S. , Sørensen, J. N. , and Henningson, D. S. , 2014, “ Mutual Inductance Instability of the Tip Vortices Behind a Wind Turbine,” J. Fluid Mech., 755, pp. 705–731. [CrossRef]
Chen, K. K. , Tu, J. H. , and Rowley, C. W. , 2012, “ Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses,” J. Nonlinear Sci., 22(6), pp. 887–915. [CrossRef]
Bernardini, C. , Benton, S. I. , Chen, J.-P. , and Bons, J. P. , 2014, “ Exploitation of Subharmonics for Separated Shear Layer Control on a High-Lift Low-Pressure Turbine Using Acoustic Forcing,” ASME J. Turbomach., 136(5), p. 051018. [CrossRef]
Lou, W. , and Hourmouziadis, J. , 2000, “ Separation Bubbles Under Steady and Periodic-Unsteady Main Flow Conditions,” ASME J. Turbomach., 122(4), pp. 634–643. [CrossRef]
Berrino, M. , Lengani, D. , Simoni, D. , Ubaldi, M. , and Zunino, P. , 2015, “ POD Analysis of the Wake-Boundary Layer Unsteady Interaction in a LPT Blade Cascade,” 11th European Turbomachinery Conference (ETC11), Madrid, Spain, Mar. 23–27.
Rowley, C. W. , Mezić, I. , Bagheri, S. , Schlatter, P. , and Henningson, D. S. , 2009, “ Spectral Analysis of Nonlinear Flows,” J. Fluid Mech., 641, pp. 115–127. [CrossRef]
Alam, M. , and Sandham, N. , 2000, “ Direct Numerical Simulation of “Short” Laminar Separation Bubbles With Turbulent Reattachment,” J. Fluid Mech., 410, pp. 1–28. [CrossRef]
Wissink, W. G. , and Rodi, W. , 2003, “ DNS of a Laminar Separation Bubble in the Presence of Oscillating External Flow,” Flow Turbul. Combust., 71(1), pp. 311–331. [CrossRef]
Burgmann, S. , and Schröder, W. , 2008, “ Investigation of the Vortex Induced Unsteadiness of a Separation Bubble Via Time-Resolved and Scanning PIV Measurements,” Exp. Fluids, 45(4), pp. 675–691. [CrossRef]
Simoni, D. , Ubaldi, M. , and Zunino, P. , 2012, “ Loss Production Mechanisms in a Laminar Separation Bubble,” Flow Turbul. Combust., 89(4), pp. 547–562. [CrossRef]
Langari, M. , and Yang, Z. , 2013, “ Numerical Study of the Primary Instability in a Separated Boundary Layer Transition Under Elevated Free-Stream Turbulence,” Phys. Fluids, 25(7), p. 074106. [CrossRef]
Lengani, D. , Simoni, D. , Ubaldi, M. , and Zunino, P. , 2014, “ POD Analysis of the Unsteady Behavior of a Laminar Separation Bubble,” Exp. Therm. Fluid Sci., 58, pp. 70–79. [CrossRef]

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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