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A comparative study of data-driven modal decomposition analysis of unforced and forced cylinder wakes

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Abstract

The present study on the recognition of coherent structures in flow fields was conducted using three typical data-driven modal decomposition methods: proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and Fourier mode decomposition (FMD). Two real circular cylinder wake flows (forced and unforced), obtained from two-dimensional particle image velocimetry (2D PIV) measurements, were analyzed to extract the coherent structures. It was found that the POD method could be used to extract the large-scale structures from the fluctuating velocity in a wake flow, the DMD method showed potential for dynamical mode frequency identification and linear reconstruction of the flow field, and the FMD method provided a significant computational efficiency advantage when the dominant frequency of the flow field was known. The limitations of the three methods were also identified: The POD method was incomplete in the spatial–temporal decomposition and each mode mixed multiple frequencies leading to unclear physics, the DMD method is based on the linear assumption and thus the highly nonlinear part of the flow field was unsuitable, and the FMD method is based on global power spectrum analysis while being overwhelmed by an unknown high-frequency flow field.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

2D, 3D:

Two-dimensional

DFT:

Discrete Fourier transform

DMD:

Dynamic mode decomposition

FMD:

Fourier mode decomposition

PIV:

Particle image velocimetry

POD:

Proper orthogonal decomposition

ROM:

Reduced-order model

RSS:

Reynolds shear stress

SVD:

Singular value decomposition

TKE:

Turbulent kinetic energy

\(\varepsilon\) :

Relative error

Β :

Blockage ratios

\({\omega }_{r},{\omega }_{i}\) :

Critical values of the quadratic mappings

\({\omega }_{z}\) :

Spanwise vorticity

\({\lambda }_{1},{\lambda }_{2},{\lambda }_{N}\) :

Eigenvalue

\({\phi }_{n}\) :

POD modal decomposition substrate

c k :

Global spectral information

D :

Characteristic diameter of the square cylinder

E j :

Mode energy

f e :

Excitation frequency

f 0 :

Vortex shedding domain frequency

\({F}_{j}\) :

Dmd modal frequency

\({G}_{j}\) :

Growth rate

L :

Span-wise length of the mode

m, n :

Temporal and special index

Re:

Reynolds number

St:

Strouhal number

T :

Vortex shedding period

\({u}^{\mathrm{^{\prime}}}\) :

Fluctuation flow

U 0 :

Incoming airflow velocity

\(\overline{U}\) :

Mean velocity of x direction

\(\overline{V}\) :

Mean velocity of y direction

[u,v]:

Profile of flow direction and lateral velocity fluctuations

Y :

Correlation matrix

X/D, Y/D:

X, Y direction dimensionless length

References

  • Chang X, Chen W, Huang Y, Gao D (2022) Dynamics of the forced wake of a square cylinder with embedded flapping jets. Appl Ocean Res 23:120

    Google Scholar 

  • Donglai Gao X, Chang GC, Chen W (2022) Fluid dynamics behind a circular cylinder embedded with an active flapping jet actuator. J Fluids Eng. https://doi.org/10.1115/1.4051312

    Article  Google Scholar 

  • Feng L-H, Wang J-J, Pan C (2011) Proper orthogonal decomposition analysis of vortex dynamics of a circular cylinder under synthetic jet control. Phys Fluids 23(1):014106

    Article  Google Scholar 

  • Gao D, Chen W, Eloy C, Li H (2018) Multi-mode responses, rivulet dynamics, flow structures and mechanism of rain-wind induced vibrations of a flexible cable. J Fluids Struct 82:154–172

    Article  Google Scholar 

  • Gao D, Chen W-L, Zhang R-T, Huang Y-W, Li H (2019) Multi-modal vortex- and rain–wind- induced vibrations of an inclined flexible cable. Mech Syst Signal Process 118:245–258

    Article  Google Scholar 

  • Gao D, Deng Z, Yang W, Chen W (2021a) Review of the excitation mechanism and aerodynamic flow control of vortex-induced vibration of the main girder for long-span bridges: a vortex-dynamics approach. J Fluids Struct 105:103348

    Article  Google Scholar 

  • Gao D, Meng H, Huang Y, Chen G, Chen W-L (2021b) Active flow control of the dynamic wake behind a square cylinder using combined jets at the front and rear stagnation points. Phys Fluids 33(4):047101

    Article  Google Scholar 

  • Gao D, Zhang S, Ning Z, Chen W-L, Li H (2021c) On the coupling mechanism of rain–wind two-phase flow induced cable vibration: a wake-dynamics perspective. Phys Fluids 33(11):117102

    Article  Google Scholar 

  • Ghavamian F, Tiso P, Simone A (2017) POD–DEIM model order reduction for strain-softening viscoplasticity. Comput Methods Appl Mech Eng 317:458–479

    Article  MathSciNet  MATH  Google Scholar 

  • Konstantinidis E, Balabani S, Yianneskis M (2007) Bimodal vortex shedding in a perturbed cylinder wake. Phys Fluids 19(1):011701

    Article  MATH  Google Scholar 

  • Le Clainche S, Vega JM (2017) Higher Order dynamic mode decomposition. SIAM J Appl Dyn Syst 16(2):882–925

    Article  MathSciNet  MATH  Google Scholar 

  • Liu Y, Long J, Wu Q, Huang B, Wang G (2021) Data-driven modal decomposition of transient cavitating flow. Phys Fluids 33(11):113316

    Article  Google Scholar 

  • Lumley JL (1967) The structure of inhomogeneous turbulent flows. In: Yaglom T (ed) Proc Atm Turb and Radio Wave Prop. Nauka, Moscow, pp 166–178

    Google Scholar 

  • Ma L, Feng L, Pan C, Gao Q, Wang J (2015) Fourier mode decomposition of PIV data. SCIENCE CHINA Technol Sci 58(11):1935–1948

    Article  Google Scholar 

  • Mendez MA, Balabane M, Buchlin J-M (2019) Multi-scale proper orthogonal decomposition of complex fluid flows. J Fluid Mech 870:988–1036

    Article  MathSciNet  MATH  Google Scholar 

  • Meyer KE, Pedersen JM, Özcan O (2007) A turbulent jet in crossflow analysed with proper orthogonal decomposition. J Fluid Mech 583:199–227

    Article  MathSciNet  MATH  Google Scholar 

  • Mezić I (2013) Analysis of fluid flows via spectral properties of the koopman operator. Annu Rev Fluid Mech 45(1):357–378

    Article  MathSciNet  MATH  Google Scholar 

  • Nathan Kutz J, Brunton SL, Brunton BW, Proctor JL (2016) Dynamic mode decomposition: data-driven modeling of complex systems. Society for industrial and applied mathematics, Philadelphia. https://doi.org/10.1137/1.9781611974508

    Book  MATH  Google Scholar 

  • Pan C, Wang H, Wang J (2013) Phase identification of quasi-periodic flow measured by particle image velocimetry with a low sampling rate. Meas Sci Technol 24(5):055305

    Article  Google Scholar 

  • Park J, Derrandji-Aouat A, Wu B, Nishio S, Jacquin E (2006) Uncertainty analysis: particle imaging velocimetry. In ITTC recommended procedures and guidelines, international towing tank conference

  • Rowley CW, Dawson STM (2017) Model reduction for flow analysis and control. Annu Rev Fluid Mech 49(1):387–417

    Article  MathSciNet  MATH  Google Scholar 

  • Rowley CW, Mezić I, Bagheri S, Schlatter P, Henningson DS (2009) Spectral analysis of nonlinear flows. J Fluid Mech 641:115–127

    Article  MathSciNet  MATH  Google Scholar 

  • Schmid PJ (2010) Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 656:5–28

    Article  MathSciNet  MATH  Google Scholar 

  • Schmid PJ (2011) Application of the dynamic mode decomposition to experimental data. Exp Fluids 50(4):1123–1130. https://doi.org/10.1007/s00348-010-0911-3

    Article  Google Scholar 

  • Schmid PJ (2022) Dynamic mode decomposition and its variants. Annu Rev Fluid Mech 54(1):225–254

    Article  MATH  Google Scholar 

  • Sirovich L (1987) Turbulence and the dynamics of coherent structures. I. Coherent structures. Quar Appl Math 8(45):561–571

    Article  MathSciNet  MATH  Google Scholar 

  • van Oudheusden BW, Scarano F, van Hinsberg NP, Watt DW (2005) Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence. Exp Fluids 39(1):86–98

    Article  Google Scholar 

  • Weiss J (2019) A tutorial on the proper orthogonal decomposition. In AIAA Aviation 2019 Forum, 3333. 2022-06-15

  • Xu Z, et al. (2022) Structured porous surface for drag reduction and wake attenuation of cylinder flow. Ocean Eng 110444

  • Zhang Q, Liu Y, Wang S (2014) The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition. J Fluids Struct 49:53–72

    Article  Google Scholar 

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Acknowledgements

The present study was funded by the National Natural Science Foundation of China (52278494, 52008140, U2106222).

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Authors and Affiliations

  1. Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin, 150090, China

    Xu Chang & Donglai Gao

  2. Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin, 150090, China

    Xu Chang & Donglai Gao

Authors
  1. Xu Chang
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  2. Donglai Gao
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XC contributed to experiments; data and figures; and writing of the manuscript. DG contributed to conceptualization; supervision; methodology; funding acquisition; and editing of the manuscript.

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Correspondence to Donglai Gao.

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Chang, X., Gao, D. A comparative study of data-driven modal decomposition analysis of unforced and forced cylinder wakes. J Vis 26, 755–777 (2023). https://doi.org/10.1007/s12650-023-00912-8

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