Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T14:48:40.192Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of turbulent flow over a modeled riblet covered surface

Published online by Cambridge University Press:  26 April 2006

D. Goldstein ,
R. Handler  and
L. Sirovich
D. Goldstein
Affiliation:
Center for Fluid Mechanics, Brown University, Providence, RI 02912, USA Present address: Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin, Austin, TX 78712, USA.
R. Handler
Affiliation:
Naval Research Laboratory, Washington, DC 20375, USA
L. Sirovich
Affiliation:
Center for Fluid Mechanics, Brown University, Providence, RI 02912, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An immersed boundary technique is used to model a riblet covered surface on one wall of a channel bounding fully developed turbulent flow. The conjecture that the beneficial drag reduction effect of riblets is a result of the damping of cross-flow velocity fluctuations is then examined. This possibility has been discussed by others but is unverified. The damping effect is explicitly modelled by applying a cross-flow damping force field in elongated streamwise zones with a height and spacing corresponding to the riblet crests. The same trends are observed in the turbulence profiles above both riblet and damped surfaces, thus supporting cross-flow damping as a beneficial mechanism. It is found in the examples presented that the effect of the riblets on the mean flow field quantities (mean velocity profile, velocity fluctuations, Reynolds shear stress, and low–speed sreak spacing) is small. The riblests cause a relatively small drag reduction of about 4%, a figure that is in rough agreement with experiments and other computations. The simulations also suggest a mechanism for the observed displacement of the turbulence quantities away from the wall.

The immersed boundary technique used to model the riblets consists of creating an externally imposed spatially localized body force which opposes the flow velocity and creates a riblet-like surface. For unstead viscous flow the calculation of the force is done with a feedback scheme in which the velocity is used to iteratively determine the desired value. In particular, the surface body force is determined by the relation f(xs, t) = α ∫ t0U(xs,t′)dt′ + βU(xs, t) for surface points xs, velocity U time t and negative constants α and β. All simulations are done with a spectral code in a single computational domain without any mapping of the mesh. The combination of the immersed boundary and spectral techniques can potentially be used to solve other problems having complex geometry and flow physics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 302 , 10 November 1995 , pp. 333 - 376
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bacher, E. V. & Smith, C. R. 1985 A combined Visualization-anemometry study of the turbulent drag reducing mechanisms of triangular micro-groove surface modifications. AIAA Paper 85–0548.Google Scholar
Bechert, D. W. 1985 Experiments on three-dimensional riblets. Presented at Turbulent Drag Reduction by Passive Means Conf. 15–17 Sept., London Royal Aeronautical Society.
Bechert, D. W. & Bartenwerfer, M. 1989 The viscous flow on surfaces with longitudinal ribs. J. Fluid Mech. 206, 105–129.Google Scholar
Bechert, D. W. Bartenwerfer, M. & Hoppe, G. 1990 Turbulent drag reduction by nonplanar surfaces- a survey on the research at TU/DLR Berlin. In Structure of Turbulence and Drag Reduction: IUTAM Symp., Zurich, 1989 (ed. A. Gyr), pp. 525–543. Springer.
Bechert, D. W. Bartenwerfer, M., Hoppe, G. & Reif W. E. 1986 Drag reduction mechanism derived from shark skin. 15th Congress of the Intl Council of Aeronautical Sciences, Sept. 7–12, London, U. K. ICAS-86-1.8.3.
Bechert, D. W., Hoppe, G. & Reif, W. E. 1985 On the drag reduction of the shark skin. AIAA Paper 85–0546.Google Scholar
Bernard, P. S., Thomas, J. T. & Handler, R. A. 1993 Vortex dynamics and the production of Reynolds stress. J. Fluid Mech. 253, 385–413.Google Scholar
Brooke, J. W. & Hanratty, T. J. 1993 Origin of turbulence-producing eddies in a channel flow. Phys. Fluids A 5, 1011–1022.Google Scholar
Bruse, M., Bechert, D. W., Hoeven, J. G. TH. VAN DER, Hage, W. & Hoppe, G. 1993 Experiments with conventional and with novel adjustable drag-reducing surfaces. In Near-Wall Turbulent Flows (ed. R. M. C. So, C. G. Speziale & B. E. Launder), pp. 719–738. Elsevier.
Choi, H., Moin, P. & Kim, J.1991a On the effect of riblets in fully developed laminar channel flows. Phys. Fluids A 3, 1892–1896.Google Scholar
Choi, H., Moin, P. & Kim, J. 1991b Turbulence control in wall-bound flows using direct numerical simulation. In Proc. Turbulence Structure and control, April 1–3, Columbus, OH pp. 68–73.
Chu, D., Henderson, R. & Karniadakis, G. 1992 Parallel spectral-element-Fourier simulation of trubulent flow over riblet-mounted surfaces.. Theor. Comput. Flud Dyn. 3 219–229.Google Scholar
Chu, D., Henderson, G. 1993 The direct numerical simulation of laminar and turbulent flow over riblets. J. Fluid Mech. 250, 1–42.Google Scholar
Coustols, E. & Savill, A. M. 1992 Turbulent skin-friction drag reduction by active and passive means: parts 1 and 2. In AGARD Rep. 768. Special Course on Skin-Friction Drag Reduction, March 2–6 pp. 8–1 to 8–55.
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow.. Trans ASME I: J. Fluids Engng 100, 215–223Google Scholar
Djenidi, L., Squire, L. C. & Savill, A. M. 1991 High resolution conformal mesh computations for V, U or L groove ribelts in laminar and turbulent boundary layers, In Recent Developments in turbulence Management (ed. K. S. Choi), p. 239. Kluwer.
Dorf, R. C. 1983 Modern Control Systems. Addition-Wesley.
Fauci, L. J. 1991 A grid-free method for high Reynolds number flow around an immersed elastic structure. Armstrong Lab Rep. AL-TR-1991-0045, May, pp. 1–21.
Fauci, L. J. & Peskin, C. S. 1988 A computational model of aquatic animal locomotion. J. Comput. Phys. 77, 85–108.Google Scholar
Fogelson, A. L. & Peskin, C. S. 1988 A fast numerical method for solving the three-dimensional Stockes equations in the presence of suspended particles. J. Comput. Phys. 79, 50–69.Google Scholar
Goldstein, D., Handier, R. & Sirovich, L., 1993a Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105, 354–366.Google Scholar
Goldstein, D., Adachi, T. & Izumi, H., 1993b Modeling flow between concentric vibrating cylinders with an external force field. Proc. AIAA CFD Meeting. Orlando, FL.
Gottlieb, D., Hussaini, M. Y. & Orszag, S. 1984 In Spectral Methods for Partial Differential Equations (ed. R. G. Voigt, D. D. Gottlieb, & M. Y. Hussaini). SAIM.
Handler, R. A., Hendricks, E. W. & Leighton, R. I. 1989 Low Reynolds number calculation of turbulent channel flow: A general discussion. NRL Memorandum Rep. 6410, pp. 1–103.
Handler, R. A., Levich, E. & Sirovich, L. 1993 Drag reduction in turbulent channel flow by phase randomization Phys. Fluids A. 5 686–694.Google Scholar
Jimenez, J. & Moin, P.1991 The minimal flow unit in near-wall turbulence J. Fluid Mech. 225, 213–240.Google Scholar
Johansen, J. B. & Smith, C. R.1983 The effects of cylindrical surface modifications on turbulent boundary layers. Rep. FM-3 pp. 1–127. Dept of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA.
Johansen, J. B. & Smith, C. R.1986 The effects of Cylindrical surface modifications on turbulent boundary layers. AIAA J. 24, 1081–1087.Google Scholar
Kennedy, J. F., Hsu, S. T. & Liu, J. T. 1973 Turbulent flows past boundaries with small streamwise fins.. J. Hydraul. Div. ASCE 99 (HY4), 605–616.Google Scholar
Khan, M. M. S. 1986 A numerical investigation of the drag reduction by riblet surfaces. AIAA Paper 86–1127.
Kim, J., Moin, P. & Moser, R.1987 Turbulence statistics in fully developed channel flow at low Reynolds number.. J. Fluid Mech 177, 133–166.Google Scholar
Kramer, M.1937 Einrichtung zur Verminderurg des reibungswide stands (Device for reducing the frictional resistance). German Patent no. 66987, March 17.
Lee, M. J., Kim, J. & Moin, P.1990 Structure of turbulence at high shear.. J. Fluid Mech. 216, 516–583.Google Scholar
Liu, C. K., Kline, S. J. & Johnston, J. P. 1966 An experimental study of turbulent boundary layer on rough walls. Rep. MD-15., pp 1–171. Thermosciences Div., Dept of Mech, Engng, Stanford Uniersity, July.
Luchini, P., Manzo, F. & Pozzi, A. 1991 Resistance of a grooved surface to parallel and cross-flow. J. Fluid Mech. 228, 87–109.Google Scholar
Mcqueen, D. M. & Peskin, C. S.1989 A three-dimensional computational method for blood-flow in the heart. II. Contractile fibers.. J. Comput. Phys. 82, 289–297.Google Scholar
Moin, P., Kim, J. & Choi, H. 1989 On the active control of wall-bound turbulent flows. AIAA Paper 89–0960.Google Scholar
Orszag, S. A. 1980 Spectra methods for problems in comples geometries. J. Comput. Phys. 37, 70–92.Google Scholar
Peskin, C. S. 1972 Flow patterns around heart valves: anumerical method. J. Comput. Phys. 10, 252–271.Google Scholar
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220–252.Google Scholar
Peskin, C. S. & Mcqueen, D. M. 1980 Modeling prosthetic heart valves for mumerical analysis of blood flow in the heart. J. Comput. Phys. 37, 113–132.Google Scholar
Peskin, C. S. & Mcqueen, D. M. 1989 A three-deminsional co0mputational method for blood-flow in the heart, I. Imeeersed elastic fibers in a viscous incompressible fluid. J. Comput. Phys. 81, 372–405.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech. 81, 601–639.Google Scholar
Saiki, E. & Biringen, S. 1995 Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method J. Comput. Phys. (to appear).
Salathe, E. P. & Sirovich, L. 1967 Boundary-value problems in compressible megnetohydrodynamics. Phys. Fluins 10, 1477–1491.Google Scholar
Schraub, F. A. & Kline, S. J. 1965 A study of the structure of the turbulent boundary layer with and without longitudinal pressure gradients. Rep. MD-12 Dept. of Mech. Engng. Stanford University.
Sirovich, L. 1967 Initial and boundary-value problems in dissipative gas dynamics. Phys. Fluids 10, 24–34.Google Scholar
Sirovich, L. 1968 Steady gasdynmic flows. Phys. Fluids 11, 1424–1439.Google Scholar
Sirovich, L. Ball, K. & Handler, R. A 1991 Propagating structures in wall-bounded turbulent flows.. Theor. Comput. Fluid Dyn. 2 307–317.Google Scholar
Smith, C. R. Metzler, S. P. 1983 The characteristics of low-speed streaks in the wall region of the turbulent boundary layer. J. Fluid Mech. 129, 339–368.Google Scholar
Sulsky, D. & Brackbill, J. U. 1991 A numerica method for suspension flows. J. Comput. Phys. 96, 339–368.Google Scholar
Tu, C. & Peskin, C. S. 1992 Stability and instability in the computation of flows with moving immersed boundaries : a comparison of three methods. SIAM J. Sci. Statist. Comput. 13, 1361–1376.Google Scholar
Tsinober, A. 1990 MHD flow drag reduction. In Vismous Drag Reduction in Boundary Layers (ed. D. Bushnell & J. Hefner). Progress in Astronautics and Aeronautics, vol. 123, p. 327. AIAA.
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys 100, 25–27.Google Scholar
Viecelli, J. A. 1969 A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique. J. Comput. Phys. 4 543–551.Google Scholar
Vieelli, J. A. 1971 A computing method for incompressible flows bounded by moving walls. J. Comput. Phys. 8, 119–143.Google Scholar
Vukoslavcevic, P. Wallace, J. M. & Balint, J. L. 1992 Viscous drag reduction using streamwisealigned riblets.. AIAA J. 30 1119–1122.Google Scholar
Wallace, J. M. & Balint, J. L. 1988 Viscous drag reduction using streamwise aligned riblets: Survey and new results. In Turbulence Mangagement and Relaminarisation IUTAM Symp., Bangalore, India, 1987 (ed. H. W. Liepmann & R. Narasimha), pp. 133–147. Springer.
Walsh, M. J. 1990 Riblets. In Visous Drag Reduction in Boundary Layers (ed. D. Bushnell & J. H. Hefner). Progress in Astronautica and Aeronautics, vol. 123, pp. 203–259. AIAA.