Skip to main content
SpringerLink
Log in

On the scaling of streamwise streaks and their efficiency to attenuate Tollmien–Schlichting waves

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

Streaky boundary layers generated by an array of miniature vortex generators (MVGs) mounted on a flat plate have recently shown to have a stabilizing effect on both two- and three-dimensional disturbances. An experimental study on the effect of the geometrical parameters of MVGs on the generated streamwise streaks in the flat plate boundary layer is carried out, and the corresponding stabilizing effect on Tollmien–Schlichting (TS) wave disturbances is quantified. The new experimental configurations have led to an improved empirical scaling law, which includes additional geometrical parameters of the MVGs compared to the previously reported relation. It is found that the MVG configuration can be optimized with respect to the attenuation of disturbances. In addition, the streamwise location of branch I of the neutral stability curve, with regard to the location of the MVG array, is found to be correlated with the initial receptivity of TS waves on the MVG array and the attenuation of the TS wave amplitude in the unstable region.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Cossu C, Brandt L (2002) Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys Fluids 14:L57–L60

    Article  Google Scholar 

  • Cossu C, Brandt L (2004) On Tollmien–Schlichting-like waves in streaky boundary layers. Eur J Mech B Fluids 23:815–833

    Article  MATH  MathSciNet  Google Scholar 

  • Downs RS, Fransson JHM (2014) Tollmien–Schlichting wave growth over spanwise-periodic surface patterns. J Fluid Mech 754:39–74

    Article  Google Scholar 

  • Fransson JHM, Talamelli A (2012) On the generation of steady streamwise streaks in flat-plate boundary layers. J Fluid Mech 698:211–234

    Article  MATH  Google Scholar 

  • Fransson JHM, Brandt L, Talamelli A, Cossu C (2004) Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer. Phys Fluids 16(10):3627–3638

    Article  Google Scholar 

  • Fransson JHM, Brandt L, Talamelli A, Cossu C (2005) Experimental study of the stabilisation of Tollmien–Schlichting waves by finite amplitude streaks. Phys Fluids 17(054):110

    Google Scholar 

  • Fransson JHM, Talamelli A, Brandt L, Cossu C (2006) Delaying transition to turbulence by a passive mechanism. Phys Rev Lett 96(064):501

    Google Scholar 

  • Johansson AV, Alfredsson PH (1982) On the structure of turbulent channel flow. J Fluid Mech 122:295–314

    Article  Google Scholar 

  • Klingmann BGB, Boiko A, Westin KJA, Kozlov VV, Alfredsson PH (1993) Experiments on the stability of Tollmien–Schlichting waves. Eur J Mech B Fluids 12:493–514

    Google Scholar 

  • Lindgren B, Johansson AV (2002) Evaluation of the flow quality in the mtl wind-tunnel. Tech Rep KTH/MEK/TR-02/13-SE, KTH Mechanics, Stockholm

  • Lögdberg O, Fransson JHM, Alfredsson PH (2009) Streamwise evolution of longitudinal vortices in a turbulent boundary layer. J Fluid Mech 623:27–58

    Article  MATH  Google Scholar 

  • Luchini P (1996) Reynolds-number independent instability of the boundary layer over a flat surface. J Fluid Mech 327:101–115

    Article  MATH  Google Scholar 

  • Sattarzadeh SS, Fransson JHM (2014) Experimental investigation on the steady and unsteady disturbances in a flat plate boundary layer. Phys Fluids 26:124103

    Article  Google Scholar 

  • Sattarzadeh SS, Fransson JHM, Talamelli A, Fallenius BEG (2014) Consecutive turbulence transition delay with reinforced passive control. Phys Rev E 89:061001(R)

    Article  Google Scholar 

  • Schlichting H (1933) Berechnung der anfachung kleiner störungen bei der plattenströmung. Z Angew Math Mech 13:171–174

    Article  MATH  Google Scholar 

  • Schubauer GB, Skramstad HK (1947) Laminar boundary layer oscillations and the stability of laminar flow. J Aeronaut Sci 14:69–78

    Article  Google Scholar 

  • Shahinfar S, Sattarzadeh SS, Fransson JHM, Talamelli A (2012) Revival of classical vortex generators now for transition delay. Phys Rev Lett 109:074501

    Article  Google Scholar 

  • Shahinfar S, Fransson JHM, Sattarzadeh SS, Talamelli A (2013) Scaling of streamwise boundary layer streaks and their ability to reduce skin-friction drag. J Fluid Mech 733:1–32

    Article  MATH  MathSciNet  Google Scholar 

  • Shahinfar S, Sattarzadeh SS, Fransson JHM (2014) Passive boundary layer control of oblique disturbances by finite amplitude streaks. J Fluid Mech 749:1–36

    Article  Google Scholar 

  • Siconolfi L, Camarri S, Fransson JHM (2015) Boundary layer stabilization using free-stream vortices. J Fluid Mech 764:R2

    Article  Google Scholar 

  • Squire HB (1933) On the stability for three-dimensional disturbances of viscous fluid flows between parallel walls. Proc R Soc Lond A 142(847):621–628

    Article  MATH  Google Scholar 

  • Tollmien W (1929) Über die entstehung der turbulenz. Nachr Ges Wiss Göttingen 21–24, English translation NACA TM 609, 1931

  • White EB (2002) Transient growth of stationary disturbances in a flat plate boundary layer. Phys Fluids 14:4429–4439

    Article  MathSciNet  Google Scholar 

  • White EB, Rice JM, Ergin FG (2005) Receptivity of stationary transient disturbances to surface roughness. Phys Fluids 17(064):109

    Google Scholar 

Download references

Acknowledgments

J. H. M. F. acknowledges the European Research Council for its financial support of the AFRODITE project through a Starting Independent Researcher Grant.

Author information

Authors and Affiliations

  1. Linné Flow Centre, KTH Royal Institute of Technology, 10044, Stockholm, Sweden

    Sohrab S. Sattarzadeh & Jens H. M. Fransson

Authors
  1. Sohrab S. Sattarzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jens H. M. Fransson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jens H. M. Fransson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sattarzadeh, S.S., Fransson, J.H.M. On the scaling of streamwise streaks and their efficiency to attenuate Tollmien–Schlichting waves. Exp Fluids 56, 58 (2015). https://doi.org/10.1007/s00348-015-1930-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-015-1930-x

Keywords

Search

Navigation