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Parallel spectral-element-Fourier simulation of turbulent flow over riblet-mounted surfaces. (English) Zbl 0747.76074
Summary: The flow in a channel with its lower wall mounted with streamwise \(V\)- shaped riblets is simulated using a highly efficient spectral-element- Fourier method. The range of Reynolds numbers investigated is 500 to 4000, which corresponds to laminar, transitional, and turbulent flow states. Our results suggest that in the laminar regime there is no drag reduction, while in the transitional and turbulent regimes drag reduction up to 10% exists for the riblet-mounted wall in comparison with the smooth wall of the channel. For the first time, we present detailed turbulent statistics in a complex geometry. These results are in good agreement with available experimental data and provide a quantitative picture of the drag-reduction mechanism of the riblets.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
76F10 Shear flows and turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] Frisch, U., and Orszag, S.A. Turbulence: Challenges for theory and experiment. Physics Today, p. 22, January 1990.
[2] Patera, A.T. A spectral-element method for fluid dynamics: Laminar flow in a channel expansion. Journal of Computational Physics, 54:468, 1984. · Zbl 0535.76035
[3] Karniadakis, G.E., Bullister, E.T., and Patera, A.T. A spectral-element method for solution of two- and three-dimensional time dependent Navier-Stokes equations. Finite-Element Methods for Nonlinear Problems, Springer-Verlag, New York, p. 803, 1985.
[4] Karniadakis, G.E. Spectral-element simulations of laminar and turbulent flows in comlex geometries. Applied Numerical Mathematics, 6:85, 1989. · Zbl 0678.76050
[5] Henderson, R.D., and Karniadakis, G.E. A hybrid spectral-element-finite-difference method for parallel computers. Unstructured Scientific Computations on Scalable Multi-processors, M.I.T. Press, Cambridge, MA, to appear.
[6] Walsh, M.J. Riblets. In Viscous Drag Reduction in Boundary Layers, Progress in Astronautics and Aeronautics, vol. 123, eds. Bushnell, D., and Hefner, J., 1990.
[7] 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. Turbulent Drag Reduction by Passive Means, 1987.
[8] Chu, D., and Karniadakis, G.E. Numerical Investigation of Drag Reduction in Flow over Surfaces with Streamwise Aligned Riblets. AIAA-91-0518, 1991.
[9] Karniadakis, G.E., Israeli, M., and Orszag, S.A. High-order splitting methods for the incompressible Navier-Stokes equations. Journal of Computational Physics, to appear. · Zbl 0738.76050
[10] Karniadakis, G.E., Spectral-element?Fourier methods for incompressible turbulent flows. Computer Methods in Applied Mechanics and Engineering, 80:367, 1990. · Zbl 0722.76053
[11] Tomboulides, A.G., Israeli, M., and Karniadakis G.E. Efficient removal of boundary-divergence errors in time-splitting methods. Journal of Scientific Computing, 4(3):291, 1989.
[12] Wallace, J.M., and Balint, J.L. Viscous drag reduction using streamwise aligned riblets: Survey and new results. In Turbulence Management and Relaminarisation, eds. Liepmann, H.W., and Narasimha, R., p. 133, 1987.
[13] Zores, R. Numerische untersuchungen mit einem grobauflosenden simulationsmodell fur die turbulente kanalstromung. Technical Report IB 221-89 A 24, Institut für Theoretische Stromungsmechanik, DLR Gottingen, 1989.
[14] Gupta, A.K., and Kaplan, R.E. Statistical characteristics of Reynolds stress in a turbulent boundary layer. Physics of Fluids, 15:981, 1972.
[15] Hooshmand, A. An Experimental Investigation of the Influence of a Dray Reducing, Longitudinally Alighed, Triangular Riblet Surface on the Velocity and Streamwise Vorticity Fields of a Zero-Pressure Gradient Turbulent Boundary Layer. Ph.D. thesis, University of Maryland, 1985.
[16] Dean, R.B. Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Journal of Fluids Engineering, 100:215, 1978.
[17] Henderson, R.D. Ph.D. thesis, Princeton University, in progress.
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