Skip to main content
Log in

Riblet modelling using a second-moment closure

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

A low Reynolds number second-moment closure has been used to calculate a turbulent boundary layer which develops over a riblet surface with zero pressure gradient. The calculated mean velocity distributions compare favourably with measurements. Calculated Reynolds stresses away from the riblet surface region are also in agreement with measurements. In the vicinity of the riblets, the model reflects the increased anisotropy of the Reynolds stress tensor inadequately. Possible reasons for this shortcoming are discussed and suggestions for improving the model are made.

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. and Kim, J., Low Reynolds number effects on the near-wall turbulence.J. Fluid Mech. 276 (1994) 61–80.

    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., Anselmet, F., Fulachier, L. and Antonia, R.A., Experimental investigation of a turbulent boundary layer manipulated by a ribbed surface. In:Proc. Ninth Symposium on Turbulent Shear Flows (1993) Paper P107-1.

  • Benhalilou, M., Anselmet, F., Liandrat, J. and Fulachier, L., Experiments and numerical investigation of a turbulent boundary layer over riblets. In:Proc. Eighth Symposium on Turbulent Shear Flows (1991) Paper 18-5.

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

    Google Scholar 

  • Choi, H., Moin, P. and Kim, J., Turbulent drag reduction: Studies of feedback control and flow over riblets. CTR Report TF-55, Stanford University (1992).

  • Choi, H., Moin, P. and Kim, J., Direct numerical simulation of turbulent flow over riblets.J. Fluid Mech. 255 (1993) 503–539.

    Google Scholar 

  • Chu, D.C. and Karniadakis, G.E., A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces.J. Fluid Mech. 250 (1993) 1–42.

    Google Scholar 

  • Djenidi, L. and Antonia, R.A., Riblet flow calculation with a low Reynolds number κ — ε model.Appl. Sci. Res. 50 (1993) 267–282.

    Google Scholar 

  • Djenidi, L. and Antonia, R.A., Numerical study of laminar flow over riblets. Report T.N. FM 94/1, Department of Mechanical Engineering, University of Newcastle (1994).

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

    Google Scholar 

  • Gibson, M.M. and Launder, B.E., Ground effects on pressure fluctuations in the atmospheric boundary layer.J. Fluid Mech. 86 (1978) 491–511.

    Google Scholar 

  • Hallbäck, M., Groth, J. and Johansson, A.V., An algebraic model for nonisotropic turbulent dissipation rate in Reynolds stress closure.Phys. Fluids A 2 (1990) 1859–1866.

    Google Scholar 

  • Kawamura, H., A κ — ε —\(\overline {v^2 } \) model with special reference to near-wall turbulence. In:Proc. Eighth Symposium on Turbulent Shear Flows (1991) Paper 26.4.1.

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

  • Launder, B.E. and Li, S.P., The prediction of riblet behaviour with a low Reynolds numberk - ε model.Aero. Jnl. 96 (1992) 351–355.

    Google Scholar 

  • Launder, B.E. and Li, S.P., On the prediction of riblet performance with engineering turbulence models,Appl. Sci. Res. 50 (1993a) 283–298.

    Google Scholar 

  • Launder, B.E. and Li, S.P., On the prediction of flow over riblets in a second moment closure. In: So, R.M.C., Speziale, C.G. and Launder, B.E. (eds),Near Wall Turbulent Flows, Amsterdam: Elsevier Science Publishers (1993b) 739–748.

    Google Scholar 

  • Launder, B.E. and Li, S.P., On the elimination of wall topography parameters from second-moment closure.Phys. Fluids 6 (1994) 999–1006.

    Google Scholar 

  • Launder, B.E. and Shima, N., Second-moment closure for the near-wall sublayer: Development and application.AIAA Jnl. 27 (1989) 1319–1325.

    Google Scholar 

  • Lumley, J.L. and Newman, G.R., The return to isotropy of homogeneous turbulence,J. Fluid Mech. 82 (1977) 161–178.

    Google Scholar 

  • Mansour, N.N., Kim, J. and Moin, P., Reynolds-stress and dissipation-rate budgets in a turbulent channel flow.J. Fluid Mech. 194 (1988) 15–44.

    Google Scholar 

  • Park, S.R. and Wallace, J.M., Flow alteration and drag reduction by riblets in a turbulent boundary layer.AIAA Jnl. 32 (1994) 31–38.

    Google Scholar 

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

    Google Scholar 

  • Perkins, H.J., The formation of streamwise vorticity in turbulent flow,J. Fluid Mech. 44 (1970) 721–740.

    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 a turbulent boundary layer up toR θ=1410.J. Fluid Mech. 187 (1988) 61–98.

    Google Scholar 

  • Suzuki, Y. and Kasagi, N., On the turbulent drag reduction mechanism above a riblet surface. AIAA Paper 93-3257 (1993).

  • Vukoslavecevic, 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. International Conference on Turbulent Drag Reduction by Passive Means, Vol. 2, The Royal Aero. Soc. (1987) pp. 290–309.

  • Vukoslavcevic, P., Wallace, J.M. and Balint, J.L., Viscous drag reduction using streamwise aligned riblets.AIAA Jnl. 30 (1992) 1119–1122.

    Google Scholar 

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

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 modelling using a second-moment closure. Appl. Sci. Res. 54, 249–266 (1995). https://doi.org/10.1007/BF00863512

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00863512

Key words

Navigation