Summary
The impact of a wavy surface on turbulent flow is investigated by direct numerical simulation. By means of finite differences in terrain following coordinates, the method treats the flow in a plane channel with wavy lower and flat top surfaces. Both surfaces are smooth. The lower surface wave amplitude is 0.05 and the wavelength is 1 in units of the mean channel height. The Reynolds number in terms of mean velocity and mean channel height is 6760. Parameter studies are performed with different resolution, Reynolds number and geometrical shape of the surface wave. If the vertical resolution is fine enough to resolve the viscous surface layer, a recirculation zone develops as expected for this surface geometry and Reynolds number. The comparison with existing experimental data shows good agreement when the precise details of the surface wave geometry, which deviates slightly from a sinusoidal profile, is taken into account.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. P. Almeida, D. F. G. Durão, and M. V. Heitor. Wake flows behind two-dimensional model hills. Experimental Thermal and Fluid Science, 7:87–101, 1993.
A. Andrén, A. R. Brown, J. Graf, P. J. Mason, C.-H. Moeng, F. T. M. Nieuwstadt, and U. Schumann. Large-eddy simulation of a neutrally stratified boundary layer: A comparison of four computer codes. Q. J. R. Meteorol. Soc., 120:1457–1484, 1994.
T. B. Benjamin. Shearing flow over a wavy boundary. J. Fluid Mech., 6:161–205, 1959.
M. Breuer and W. Rodi. Large-eddy simulation of complex flows of practical interest. In this publication.
J. J. Buckles, T. J. Hanratty, and R. J. Adrian. Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech., 140:27–44, 1984.
M. Dianat and I. P. Castro. Turbulence in a separated boundary layer. J. Fluid Mech., 226:91–123, 1991.
A. Dörnbrack, T. Gerz, and U. Schumann. Turbulent breaking and overturning gravity waves below a critical level. Appl. Sci. Res., 54:163–176, 1995.
A. Dörnbrack and U. Schumann. Numerical simulation of turbulent convective flow over wavy terrain. Boundary-Layer Meteorol., 65:323–355, 1993.
J. G. M. Eggels, F. Unger, M. H. Weiss, J. Westerweel, R. J. Adrian, R. Friedrich, and F. T. M. Nieuwstadt. Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech., 268:175–209, 1994.
W. Gong, P. A. Taylor, and A. Dörnbrack. Turbulent boundary-layer flow over fixed, aerodynamically rough, 2-d sinusoidal waves. J. Fluid Mech., 1996. in press.
C. Härtel and L. Kleiser. Large-eddy simulation of near-wall turbulence. In this publication.
M. Hino and T. Okumura. Coherent structure of turbulent flow over wavy walls. In Proc. 9th Turbulent Shear Flow Symp. Kyoto, Aug. 16–18, pages 14.3.1–14.3.4, 1993.
J. D. Hudson. The effect of a wavy boundary on turbulent flow. PhD thesis, Dept. Chemical Engineering, University of Illinois, Urbana, 1993.
T. Kajishima, Y. Miyake, and T. Ohta. Direct numerical simulation of turbulent flow in a wavy channel. In Proc. of The International Symp. on Mathematical Modelling of Turbulent Flows. Tokyo, Dec. 18–20, pages 176–180, 1995.
J. Kim, P. Moin, and R. Moser. Turbulence statistics in fully developed channel flow at low reynolds number. J. Fluid Mech., 177:133–166, 1987.
K. Krettenauer and U. Schumann. Numerical simulation of turbulent convection over wavy terrain. J. Fluid Mech., 237:261–299, 1992.
J. D. Kuzan, T. J. Hanratty, and R. J. Adrian. Turbulent flows with incipient separation over solid waves. Exper. in Fluids, 7:88–98, 1989.
H. Lamb. Hydrodynamics. Dover, New York, 1945.
C. Maaß, A. Dörnbrack, and U. Schumann. Grobstruktursimulationen turbulenter Strömungen über welligem Untergrund. Deutsche Meteorologen-Tagung, 16.–20.3.1992, Berlin. In Ann. Meteorol., volume 27, pages 306–307, 1992.
C. Maaß and U. Schumann. Numerical simulation of turbulent flow over a wavy boundary. In P. R. Voke, L. Kleiser, and J.-P. Chollet, editors, Direct and large-eddy simulation I: selected papers from the First ERCOFTAC Workshop on Direct and Large-Eddy Simulation, pages 287–297. Kluwer Academic Press, Dordrecht, 1994.
H. Motzfeld. Die turbulente Strömung an welligen Wänden. Z. angew. Math. Mech., 17:193–212, 1937.
W. Rodi, editor. ERCOFTAC Workshop on Data Bases and Testing of Calculation Methods for Turbulent Flows, Karlsruhe, April 3–7 1995.
U. Schumann. Large-eddy simulation of turbulent convection over flat and wavy terrain. In B. Galperin and S. A. Orszag, editors, Large-Eddy Simulation of Complex Engineering and Geophysical Flows, pages 399–421. Cambridge Univ. Press, 1993.
U. Schumann. Stochastic backscatter of turbulence energy and scalar variances by random subgrid-scale fluxes. Proc. Roy. Soc. London A, 451:293–318 and 811, 1995.
U. Schumann and M. Strietzel. Parallel solution of tridiagonal systems for the Poisson equation. J. Sci. Comput., 10:181–190, 1995.
C. B. Thorsness, P. E. Morrisroe, and T. J. Hanratty. A comparison of linear theory with measurements of the variation of shear stress along a solid wave. Chem. Eng. Sci., 33:579–592, 1978.
F. Unger. Numerische Simulation turbulenter Rohrströmungen. PhD thesis, Technische Universität, München, 1994.
N. Wood and P. Mason. The pressure force induced by neutral, turbulent flow over hills. Q. J. R. Meteorol. Soc, 119:1233–1267, 1993.
D. P. Zilker, G. W. Cook, and T. J. Hanratty. Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows. J. Fluid Mech., 82:29–51, 1977.
D. P. Zilker and T. J. Hanratty. Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 2. Separated flows. J. Fluid Mech., 90:257–271, 1979.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Maaß, C., Schumann, U. (1996). Direct Numerical Simulation of Separated Turbulent Flow over a Wavy Boundary. In: Hirschel, E.H. (eds) Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89849-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-322-89849-4_17
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-89851-7
Online ISBN: 978-3-322-89849-4
eBook Packages: Springer Book Archive