Skip to main content
Log in

Riblet flow calculation with a low Reynolds number κ - ε model

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

A low Reynolds number κ - ε model has been used to calculate the turbulent boundary layer over riblets. Calculated mean velocity, Reynolds shear stress and kinetic energy distributions are generally in good agreement with available experimental data. The comparison between these distributions and those in a corner flow points to a significant difference between the two flows and the unlikelihood of counter-rotating vortices within the riblet grooves. One shortcoming of the present κ - ε model is the relatively slow return to a two-dimensional turbulence state as the distance from the riblet surface increases.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Antonia, R.A., Teitel, M., Kim, J. and Browne, L.W.B., Low Reynolds number effects in a fully developed turbulent duct flow.J. Fluid Mech. 236 (1992) 579–605.

    Google Scholar 

  • Bechert, D.W. and Bartenwerfer, M., The viscous flow on surfaces with longitudinal ribs.J. Fluid Mech. 206 (1989) 105–129.

    Google Scholar 

  • Benhalilou, M., Etude Experimentale et Numerique d'une Couche Limite Turbulente sur Paroi Rainuree, Ph.D. Dissertation, I.M.S.T., France (1992).

    Google Scholar 

  • Benhalilou, M., Anselmet, F., Liandriat, J. and Fulachier, L., Experimental and numerical investigation of a turbulent boundary layer over riblets.Turbulent Shear Flows 8 Munich (1991).

  • Bragg, G.M., The turbulent boundary layer in a corner.J. Fluid Mech 36 (1969) 485–503.

    Google Scholar 

  • Buleev, N.I., Theoretical model of the mechanism of turbulent exchange in fluid flows.AERE Trans. 957, Harwell (1963) 1–39.

    Google Scholar 

  • Chien, K.Y., Predictions of channel and boundary-layer flows with a low-Reynolds number turbulence model.AIAA Jnl. 20 (1982) 33–38.

    Google Scholar 

  • Choi, H., Moin, P. and Kim, J., On the effect of riblets in fully developed laminar channel flows.Phys. Fluids A 3 (1991) 1892–1896.

    Google Scholar 

  • de St. Victor, X., Resolution des Equations de Navier-Stokes Bi- ou Tridimensionelles par Méthodes de Marches—Application au Calcul de Melange d'Ecoulements Cisailles, Ph.D. Dissertation, I.N.P.T., France (1986).

    Google Scholar 

  • Djenidi, L. and Antonia, R.A., LDA measurements in low Reynolds number turbulent boundary layer.Expts. in Fluids [to appear].

  • Djenidi, L., Liandriat, J., Anselmet, F. and Fulachier, L., Laminar boundary layer over riblets.Phys. Fluids A [submitted].

  • Djenidi, L., Squire, L.C. and Savill, A.M., High resolution conformal mesh computation for V, U and L-groove riblets in laminar and turbulent boundary layer. In: K. S. Choi (ed.),Recent Development in Turbulence Management. Dordrecht: Kluwer, Academic Publishers (1991) pp. 65–92.

    Google Scholar 

  • Durbin, P.A., Near wall turbulence closure modeling without damping function.CTR Manuscript 112, Stanford University (1990).

  • Granville, P.S., Similarity-law analysis and turbulence modeling for riblet drag reduction.J. Ship Res. 36 (1992) 55–58.

    Google Scholar 

  • Hooshmand, D., Youngs, R., Wallace, J.M. and Balint, J.L., An experimental study of changes in the structure of a turbulent boundary layer due to surface geometry changes.AIAA Paper 83-0230 (1983).

  • Kawamura, H., Ak − ε −\(\overline {\upsilon ^2 } \) model with special relevance to the near wall turbulence.Proc. Eighth Symposium on Turbulent Shear Flows Munich (1991) pp. 26-4-1 to 26-4-6.

  • Khan, M.M.S., A numerical investigation of the drag reduction by riblet surface.AIAA paper 86-1127 (1986).

  • Kim, J., Study of turbulence structure through numerical simulations: the perspective of drag reduction.AGARD Report 786 (Special Course on Skin Friction Drag Reduction) (1992) pp. 7-1 to 7-14.

  • Klebanoff, P.S., Characteristics of turbulence in a boundary layer with zero pressure gradient.NACA Report 1247 (1955).

  • Lam, C.K.G. and Bremhorst, K.A., Modified form of thek - ε model for predicting wall turbulence.J. Fluids Eng. 103 (1981) 456–460.

    Google Scholar 

  • Launder, B.E. and Li, S.P., Prediction of drag reduction by riblets. Presentation at the 6th Drag Reduction Meeting, Eindhoven (1991).

  • Launder, B.E. and Sharma, B.I., Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc.Letters in Heat Mass Transfer 1 (1974) 131–138.

    Google Scholar 

  • Launder, B.E. and Tselepidakis, D.P., Contribution to the second-moment modeling of sublayer turbulent transport. In: Kline, S. J. and Afgan, N. H. (eds),Near-Wall Turbulence. New York: Hemisphere (1990) pp. 818–833.

    Google Scholar 

  • Mansour, N.N., Kim, J. and Moin, P., Near-wallk - ε turbulence modelling.AIAA Jnl. 27 (1989) 1068–1073.

    Google Scholar 

  • Nakamura, I., Miyata, M., Kushoda, T. and Kagiya, K., Some measurements in the intermittent region of a turbulent boundary layer along a corner. In: Fernholz, H. H. and Drause, E. (eds),Three Dimensional Turbulent Boundary Layers. Berlin: Springer (1982) pp. 118–209.

    Google Scholar 

  • Nash, J.F. and Patel, V.C.,Three Dimensional Turbulent Boundary Layers. SBC Technical Books (1972).

  • Patankar, S.V.,Numerical Heat Transfer and Fluid Flow. Series in Computational Methods in Mechanics and Thermal Sciences. McGraw-Hill (1980).

  • Patel, V.C., Rodi, W. and Scheuerer, G., Turbulence models for near-wall and low-Reynolds number flows: a review.AIAA Jnl. 23 (1985) 1308–1319.

    Google Scholar 

  • Rodi, W. and Mansour, N.N., Low Reynolds numberk - ε modelling with the aid of direct simulation data. In:Proc. of the Summer Program 1990. Stanford University: Center for Turbulence Research (1990) pp. 85–106.

    Google Scholar 

  • Schneider, G.E. and Zedan, M., A modified strongly implicit procedure for the numerical solution of field problems.Num. Heat Transfer 4 (1981) 1–19.

    Google Scholar 

  • Spalart, P.R., Direct simulation of turbulent boundary layer up toR θ=1410.J. Fluid Mech. 187 (1988) 61–98.

    Google Scholar 

  • Vukoslavcevic, P., Wallace, J.M. and Balint, J.L., On the mechanism of viscous drag reduction using streamwise aligned riblets: a review with new results. In:Proc. R.A.S. Int. Conf. on Turbulent Drag Reduction by Passive Means, Vol. 2. The Royal Aero. Soc. (1987) pp. 290–309.

  • Walsh, M.J., Turbulent boundary layer drag reduction using riblets.AIAA Paper 82-0169 (1982).

  • Walsh, M.J. and Weinstein, L.M., Drag and heat transfer on surfaces with small longitudinal fins.AIAA Paper 78-1161, presented at AIAA 11th Fluid and Plasma Dynamics Conference, Seattle, WA (1978).

  • Wei, T. and Willmarth, W.W., Reynolds-number effects on the structure of a turbulent channel flow.J. Fluid Mech. 204 (1989) 57–95.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Djenidi, L., Antonia, R.A. Riblet flow calculation with a low Reynolds number κ - ε model. Appl. Sci. Res. 50, 267–282 (1993). https://doi.org/10.1007/BF00850561

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00850561

Keywords

Navigation