Skip to main content

Advertisement

SpringerLink
Log in

Analysis of vortex splitting characteristics in the wake of an inclined flat plate using Hilbert–Huang transform

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Three-dimensional vortex dynamics in the wake behind a flat plate at 20○ angle of attack are explored by means of the Hilbert–Huang transform. While a completely regular vortex shedding is observed at Reynolds number Re = 500 with a distinct shedding frequency and only a single subharmonic frequency, a complex shedding behavior is observed at Re = 525 and above. The low-frequency variations of the energy content and frequency in time are deduced from the Hilbert spectra. The low-frequency modulations along the span of the plate are substantially increased from Re = 525 to Re = 800. The mean marginal spectra reveal that the energy in the low-frequency band increases with increasing Re. A corresponding reduction of the energy content in the high-frequency band is observed at the highest Reynolds number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A(T):

Correlation function

A i (t):

Instantaneous amplitude of each IMF (intrinsic mode functions) component

C i (t):

ith Intrinsic mode functions component

\({\tilde {C}_i (t)}\) :

Hilbert transforms of the ith intrinsic mode function component

\({\mathbb{C}_i \left(t\right)}\) :

Complex analytic signal

d :

Flat plate width (m)

e max (t):

Upper envelope for a given time series

e min (t):

Lower envelope for a given time series

E j :

Local energy of the different frequency bands

E :

Total energy

f :

Frequency (1/s)

h ij (t):

The ith intrinsic mode function component after j times sifting process

H j :

Relative energy distribution of the different frequency bands

H (ω, t):

Hilbert spectrum

h (ω):

Marginal spectrum

IE (t):

Instantaneous energy

m i (t):

Mean of the upper envelope and the lower envelope

r i (t):

Residual obtained by separating the intrinsic mode functions from the original data

Re :

Reynolds number

RP:

Real part

SD:

The standard deviation defined by two successive sifting processes

t :

Running time (s)

T :

Time lag (s)

u′:

Velocity fluctuations (m/s)

U 0 :

Uniform bulk velocity (m/s)

τ :

Total length of data analyzed

ν :

Kinematic viscosity (m2/s)

φ i (t):

Instantaneous phase

ω i (t):

Instantaneous frequency

References

  1. Eisenlohr H., Eckelmann H.: Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Phys. Fluids A 1, 189 (1989)

    Article  Google Scholar 

  2. Browand F.K., Ho C.-M.: Forced, unbounded shear flows. Nucl. Phys. B 2, 139 (1987)

    Article  Google Scholar 

  3. Williamson C.H.K.: The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393 (1992)

    Article  Google Scholar 

  4. Lewis C.G., Gharib M.: An exploration of the wake three dimensionalities caused by a local discontinuity in cylinder diameter. Phys. Fluids A 4, 104 (1992)

    Article  Google Scholar 

  5. Yang P.-M., Mansy H., Williams D.R.: Oblique and parallel wave interaction in the near wake of a circular cylinder. Phys. Fluids A 5, 1657 (1993)

    Article  Google Scholar 

  6. Williamson C.H.K.: The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31, 3165 (1988)

    Article  Google Scholar 

  7. Brede M., Eckelmann H., Rockwell D.: On secondary vortices in the cylinder wake. Phys. Fluids 8, 2117 (1996)

    Article  Google Scholar 

  8. Braza M., Faghani D., Persillon H.: Successive stages and the role of natural vortex dislocations in the three-dimensional wake transition. J. Fluid Mech. 439, 1 (2001)

    Article  MATH  Google Scholar 

  9. Prasad A., Williamson C.H.K.: Three-dimensional effects in turbulent bluff-body wakes. J. Fluid Mech. 343, 235 (1997)

    Article  MathSciNet  Google Scholar 

  10. Tombazis N., Bearman P.W.: A study of three-dimensional aspects of vortex shedding from a bluff body with a mild geometric disturbance. J. Fluid Mech. 330, 85 (1997)

    Article  Google Scholar 

  11. Bailey S.C.C., Martinuzzi R.J., Kopp G.A.: The effects of wall proximity on vortex shedding from a square cylinder: three-dimensional effects. Phys. Fluids 14, 4160 (2002)

    Article  Google Scholar 

  12. Najjar F.M., Balachandar S.: Low-frequency unsteadiness in the wake of a normal flat plate. J. Fluid Mech. 370, 101 (1998)

    Article  MATH  Google Scholar 

  13. Wu S.J., Miau J.J., Hu C.C., Chou J.H.: On low-frequency modulations and three-dimensionality in vortex shedding behind a normal plate. J. Fluid Mech. 526, 117 (2005)

    Article  MATH  Google Scholar 

  14. Breuer M., Jovicic N.: Separated flow around a flat plate at high incidence: an LES investigation. J. Turbul. 2, 1 (2001)

    Article  Google Scholar 

  15. Breuer M., Jovicic N., Mazaev K.: Comparison of DES, RANS and LES for the separated flow around a flat plate at high incidence. Int. J. Numer. Methods Fluids 41, 357 (2003)

    Article  MATH  Google Scholar 

  16. Zhang J., Liu N.-S., Lu X.-Y.: Route to a chaotic state in fluid flow past an inclined flat plate. Phys. Rev. E 79, 045306 (2009)

    Article  Google Scholar 

  17. Lam K.M., Leung M.Y.H.: Asymmetric vortex shedding flow past an inclined flat plate at high incidence. Eur. J. Mech. B/Fluids 24, 33 (2005)

    Article  MATH  Google Scholar 

  18. Yang D., Pettersen B., Andersson H.I., Narasimhamurthy V.D.: Vortex shedding in flow past an inclined flat plate at high incidence. Phys. Fluids 24, 084103 (2012)

    Article  Google Scholar 

  19. Yang D., Pettersen B., Andersson H.I., Narasimhamurthy V.D.: On oblique and parallel shedding behind an inclined plate. Phys. Fluids 25, 054101 (2013)

    Article  Google Scholar 

  20. Huang N.E., Shen Z., Long S.R., Wu M.C., Shih H.H., Zheng Q., Yen N.-C., Tung C.C., Liu H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  21. Huang N.E., Wu Z.: A review on Hilbert–Huang transform: method and its applications to geophysical studies. Rev. Geophys. 46, RG2006 (2008)

    Article  Google Scholar 

  22. Manhart M.: A zonal grid algorithm for DNS of turbulent boundary layers. Comput. Fluids 33, 435 (2004)

    Article  MATH  Google Scholar 

  23. Stone H.L.: Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J. Numer. Anal. 5, 530 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  24. Peller N., Duc A.L., Tremblay F., Manhart M.: High-order stable interpolations for immersed boundary methods. Int. J. Numer. Methods Fluids 52, 1175 (2006)

    Article  MATH  Google Scholar 

  25. Yang D., Narasimhamurthy V.D., Pettersen B., Andersson H.I.: Three-dimensional wake transition behind an inclined flat plate. Phys. Fluids 24, 094107 (2012)

    Article  Google Scholar 

  26. Peng Z.K., Tse P.W., Chu F.L.: An improved Hilbert–Huang transform and its application in vibration signal analysis. J. Sound Vib. 286, 187 (2005)

    Article  Google Scholar 

  27. Li H., Zhang Y., Zheng H.: Hilbert–Huang transform and marginal spectrum for detection and diagnosis of localized defects in roller bearings. J. Mech. Sci. Technol. 23, 291 (2009)

    Article  Google Scholar 

Download references

Author information

Author notes

  1. Vagesh D. Narasimhamurthy

    Present address: GexCon AS, P. O. Box 6015, 5892, Bergen, Norway

Authors and Affiliations

  1. Department of Marine Technology, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Dan Yang & Bjørnar Pettersen

  2. Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Helge I. Andersson & Vagesh D. Narasimhamurthy

Authors
  1. Dan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bjørnar Pettersen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Helge I. Andersson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vagesh D. Narasimhamurthy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, D., Pettersen, B., Andersson, H.I. et al. Analysis of vortex splitting characteristics in the wake of an inclined flat plate using Hilbert–Huang transform. Acta Mech 226, 1085–1104 (2015). https://doi.org/10.1007/s00707-014-1222-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-014-1222-1

Keywords

Search

Navigation