Abstract
The flow over riblets is examined computationally using a time dependent model of the viscous wall region. This “2 1/2 D model”, developed by Hatziavramidis and Hanratty (1979) and modified by Nikolaides (1984) and Chapman and Kuhn (1981, 1986) assumes homogeneity in the streamwise direction so that the flow is solved only in the cross-sectional plane. The flow at the upper boundary of the computational domain (y + ≅ 40) is described using a streamwise eddy model consisting of two scales, one of the streak spacing (λ+ ≅ 100), which dominates vertical momentum transport, and a larger scale that accounts for the influence of large outer flow eddies.
The protrusion height concept (Bechert and Bartenwerfer, 1989) is used to define ay +=0 location for surfaces with riblets. A control volume finite element method utilizing triangular meshes is used to exactly fit the riblet cross-sectional geometry. Results obtained using fairly large riblets compare well with the limited experimental evidence available. Observations of the transient flow suggest that the riblets interact with the near-wall streamwise vortices, weakening them by the generation of intermittent secondary vortices within the riblet valleys. The riblets also appear to limit the lateral spread of inrushes towards the wall and retain low momentum fluid in the riblet valleys effectively isolating much of the wall from such inrushes.
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References
Bacher, E.V., Smith, C.R., A combined visualization-anemometry study of the turbulent drag reducing mechanisms of triangular micro-groove surface modifications. AIAA Paper 85-0548 (1985).
Bakewell, H.P., Lumley, J.L., Viscous sublayer and adjacent wall region in turgulent pipe flow.Physics Fluids 10 (1967) 1880.
Baliga, B.R., A control-volume based finite element method for convective heat and mass transfer. Ph.D. Thesis, Dept. of Mech. Eng., University of Minnesota (1978).
Baliga, B.R., Patankar, S.V., A control volume based finite element method for two-dimensional fluid flow and heat transfer.Numerical Heat Transfer (1983) 245–261.
Bechert, D.W., Bartenwerfer, M., The viscous flow on surfaces with longitudinal ribs.J. Fluid Mech. 206 (1989) 105–129.
Benhalilou, M., Anselmet, F., Liandrat, J., Fulachier, L., Experimental and numerical investigation of a turbulent boundary layer over riblets.Proc. of the 8th Symp. on Turb. Shear Flows, Munich, Sept. 9–11, 1991.
Chapman, D.R., Kuhn, G.D., Two-component Navier-Stokes computational model of viscous sublayer turbulence. AIAA Paper 81-1024 (1981).
Chapman, D.R., Kuhn, G.D., The limiting behavior of turbulence near a wall.J. Fluid Mech. 170 (1986) 265–292.
Choi, K., The wall pressure fluctuations of modified turbulent boundary layer with riblets.Proc. IUTAM Symp. on Turbulent Management and Relaminarization, Bangalore. Springer-Verlag (1987) p. 109.
Choi, K., Near-wall structure of a turbulent boundary layer with riblets.J. Fluid Mech. 208 (1989) 417–458.
Chu, D.C., A direct numerical simulation of laminar and turbulent flow over streamwise aligned riblets. M.Sc. Thesis, Dept. of Mech. and Aerospace Eng., Princeton University (1992).
Clark, D.G., Boundary layer flow visualization patterns on a riblet surface. QMC-EP-1081 Queen Mary and Westfield College, University of London (1989).
Clark, J.A., A study of turbulent boundary layers in channel flow.Trans. ASME, J. Basic Engng. 90 (1968) 455–465.
Djenidi, L., Squire, L.C., Savill, A.M., High resolution conformal mesh computations for V, U or L groove riblets in laminar and turbulent boundary layers. In: Choi (ed.),Proceedings, 5th European Drag Reduction Working Meeting, British Maritime Technology, Teddington, Middlesex. Dordrecht: Kluwer Academic Publishers (1991).
Djenidi, L., Riblet flow prediction with a low-Reynolds-number κ-ε model. 6th European Drag Reduction Working Meeting, abstract (1991).
Gallager, J.A., Thomas, A.S.W., Turbulent boundary layer characteristics over streamwise grooves. AIAA paper 84-2185 (1984).
Hatziavramidis, D.T., Hanratty, T.J., The representation of the viscous wall region by a regular eddy pattern.J. Fluid Mech. 95 (1979) 655–679.
Kline, S.J., Reynolds, W.C., Schraub, F.A., Runstadler, P.W., The structure of turbulent boundary layers.J. Fluid Mech. 30 (1967) 283–325.
Laufer, J., The structure of turbulence in fully developed pipe flow, NACA Report 1174 (1954).
Launder, B.E., Li, S.-P., Prediction of drag reduction by riblets. 6th European Drag Reduction Working Meeting, abstract (1991).
Nikolaides, C., A study of the coherent structures in the viscous wall region of a turbulent flow. Ph.D. Thesis, Dept. of Chem. Eng., University of Illinois, Urbana (1984).
Patankar, S.V.,Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Co. (1980).
Prakash, C., Patankar, S.V., A control volume based finite element method for solving the Navier-Stokes equations using equal-order velocity-pressure interpolation.Numerical Heat Transfer 8 (1985) 259–280.
Robinson, S.K., Kline, S.J., Spalart, P.R., Quasi-coherent structures in the turbulent boundary layer: Part II. Verification and new information from a numerically simulated flat-plate boundary layer. In: Afgan and Kline (eds),Zoran Zaric Memorial Seminar on Near-Wall Turbulence. Hemisphere Publishing (1988).
Saabas, H.J., A control volume based finite element method for three-dimensional, incompressible, viscous fluid flow. Ph.D. Thesis, Dept. of Mech. Eng., McGill University (1991).
Savill, A.M., Drag reduction by passive devices — a review of some recent developments.Proc. IUTAM Symp. on Structure of Turbulent and Drag Reduction. Zurich, Springer-Verlag (1989) pp. 429–465.
Smith, C.R., Walker, J.D.A., Haidari, A.H., Taylor, B.K., Hairpin vortices in turbulent boundary layers: the implications for reducing surface drag.Proc. IUTAM Symp. on Structure of Turbulent and Drag Reduction. Zurich, Springer-Verlag (1989) pp. 51–58.
Tardu, S., Investigation of the structure of the turbulence in an internal flow manipulated by riblets. Report IMHEF T-91-19, Sept. 1991, EPFL, Lausanne, Switzerland.
Tardu, S., Truong, T.V., Tanguay, B., Bursting and structure of the turbulence in an internal flow manipulated by riblets.Appl. Sci. Res. (1993).
Tiederman, W.G., The effect of dilute polymer solutions on the viscous drag and turbulence structure.Proc. IUTAM Symp. on Structure of Turbulent and Drag Reduction. Zurich, Springer-Verlag (1989) pp. 187–200.
Townsend, A.A.,The Structure of Turbulent Shear Flow, 2nd edition. Cambridge University Press (1976).
Tullis, S.W.J., Modelling the time dependent flow over riblets in the near wall region, M.Sc. Thesis, Department of Mechanical Engineering, Queen's University at Kingston (1992).
Tullis, S., Pollard, A., A numerical investigation of the turbulent flow over V and U groove riblets using a viscous wall region model. In: So, Speziale, Launder (eds),Proceedings, Near Wall Turbulent Flows. Elsevier (1993) pp. 761–770.
Ueda, H., Hinze, J.O., Fine-structure turbulence in the wall region of a turbulent boundary layer.J. Fluid Mech. 67 (1975) 125–143.
Vukoslavĉević, P., Wallace, J.M., Balint, J.-L., On the mechanism of viscous drag reduction using streamwise aligned riblets: a review with new results.Proc. RAeS Int. Conf. on Turbulent Drag Reduction by Passive Means. London, RAeS 2 (1987) pp. 290–309.
Walsh, M.J., Riblets, Viscous drag reduction in boundary layers. In: Bushnell, D.M. and Hefner, J. (eds),Progress in Astronautics and Aeronautics, Vol. 123 (1990).
Wilkinson, S.P., Anders, J.B., Lazos, B.S. and Bushnell, D.M., Turbulent drag reduction research at NASA Langley — progress and plans.Proc. RAeS Int. Conf. on Turbulent Drag Reduction by Passive Means. London, RAeS 1 (1987) p. 1.
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Tullis, S., Pollard, A. Modelling the time dependent flow over riblets in the viscous wall region. Appl. Sci. Res. 50, 299–314 (1993). https://doi.org/10.1007/BF00850563
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DOI: https://doi.org/10.1007/BF00850563