Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T00:37:39.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment

Published online by Cambridge University Press:  26 April 2006

J. G. M. Eggels ,
F. Unger ,
M. H. Weiss ,
J. Westerweel ,
R. J. Adrian ,
R. Friedrich  and
F. T. M. Nieuwstadt
J. G. M. Eggels
Affiliation:
Delft University of Technology, Laboratory for Aero- and Hydrodynamics, Rotterdamseweg 145, 2628 AL Delft, The Netherlands
F. Unger
Affiliation:
Lehrstuhl für Fluidmechanik, Technische Universität München, Arcisstrasse 21, 8000 München 2, Germany
M. H. Weiss
Affiliation:
Novacor Research & Technology Corporation, 2928 – 16th Street NE, Calgary, Alberta T2E 7K7, Canada
J. Westerweel
Affiliation:
Delft University of Technology, Laboratory for Aero- and Hydrodynamics, Rotterdamseweg 145, 2628 AL Delft, The Netherlands
R. J. Adrian
Affiliation:
University of Illinois at Urbana-Champaign, Department of Theoretical and Applied Mechanics, 104 South Wright Street, Urbana, IL 61801, USA
R. Friedrich
Affiliation:
Lehrstuhl für Fluidmechanik, Technische Universität München, Arcisstrasse 21, 8000 München 2, Germany
F. T. M. Nieuwstadt
Affiliation:
Delft University of Technology, Laboratory for Aero- and Hydrodynamics, Rotterdamseweg 145, 2628 AL Delft, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) and experiments are carried out to study fully developed turbulent pipe flow at Reynolds number Rec ≈ 7000 based on centreline velocity and pipe diameter. The agreement between numerical and experimental results is excellent for the lower-order statistics (mean flow and turbulence intensities) and reasonably good for the higher-order statistics (skewness and flatness factors). To investigate the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, the present DNS results are compared to those obtained from a channel flow simulation. Beside the mean flow properties and turbulence statistics up to fourth order, the energy budgets of the Reynolds-stress components are computed and compared. The present results show that the mean velocity profile in the pipe fails to conform to the accepted law of the wall, in contrast to the channel flow. This confirms earlier observations reported in the literature. The statistics on fluctuating velocities, including the energy budgets of the Reynolds stresses, appear to be less affected by the axisymmetric pipe geometry. Only the skewness factor of the normal-to-the-wall velocity fluctuations differs in the pipe flow compared to the channel flow. The energy budgets illustrate that the normal-to-the-wall velocity fluctuations in the pipe are altered owing to a different ‘impingement’ or ‘splatting’ mechanism close to the curved wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 268 , 10 June 1994 , pp. 175 - 210
Copyright
© 1994 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

Andersson, H. I. & Kristoffersen, R., 1992 Statistics of numerically generated turbulence. Acta Applicandae Mathematicae 26, 293–314.Google Scholar
Antonia, R. A., Teitel, M., Kim, J. & Browne, L. W. B. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579–605.Google Scholar
Bradshaw, P. 1973 The effects of streamline curvature on turbulent flow. AGARDograph 169.Google Scholar
Eckelmann, H. 1974 The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech. 65, 439–459.Google Scholar
Eggels, J. G. M. 1994 Direct and large eddy simulation of turbulent flow in a cylindrical pipe geometry. PhD thesis, Delft University of Technology, the Netherlands.
Eggels, J. G. M., Westerweel, J., Nieuwstadt, F. T. M. & Adrian, R. J. 1993 Comparison of vortical flow structures in DNS and PIV studies of turbulent pipe flow. In Near-Wall Turbulent Flows (ed. R. M. C. So et al.), pp. 413–422. Elsevier.
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101–129.Google Scholar
Gilbert, N. & Kleiser, L. 1991 Turbulence model testing with the aid of direct numerical simulation results. Proc. 8th Symp. on Turbulent Shear Flows, Sept. 9-11, Munich, Germany.
Grötzbach, G. 1983 Spatial resolution requirements for direct numerical simulation of the Rayleigh-Bénard convection. J. Comput. Phys. 49, 241–264.Google Scholar
Huffman, G. D. & Bradshaw, P. 1972 A note on von Kármán's constant in low Reynolds number turbulent flows. J. Fluid Mech. 53, 45–60.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (referred to herein as KMM).Google Scholar
Kreplin, H. & Eckelmann, H. 1979 Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids 22, 1233–1239.Google Scholar
Kristoffersen, R. & Andersson, H. I. 1993 Direct simulations of low Reynolds number turbulent flow in a rotating channel. J. Fluid Mech. 256, 163–197.Google Scholar
Landreth, C. C. & Adrian, R. J. 1990 Measurement and refinement of velocity data using high image density analysis in particle image velocimetry. In Applications of Laser Anemometry to Fluid Mechanics (ed. R. J. Adrian et al.), pp. 484–497. Springer.
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NACA Rep. 1174.
Lawn, C. J. 1971 The determination of the rate of dissipation in turbulent pipe flow. J. Fluid Mech. 48, 477–505.Google Scholar
Lekakis, I. C. 1988 Coherent structures in fully developed turbulent pipe flow. Thesis University of Illinois.
Löfdahl, L., Glavmo, M., Johansson, B. & Stemme, G. 1993 A silicon transducer for the determination of wall-pressure fluctuations in turbulent boundary layers. Appl. Sci. Res. 51, 203–207.Google Scholar
Lyons, S. L., Hanratty, T. J. & McLaughlin, J. B. 1991 Large-scale computer simulation of fully developed turbulent channel flow with heat transfer. Intl J. Numer. Meth. Fluids 13, 999–1028.Google Scholar
Mansour, N. N., Kim, J. & Moin, P. 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44.Google Scholar
Moser, R. D. & Moin, P. 1984 Direct numerical simulation of curved turbulent channel flow. Rep. TF-20. Stanford University.
Patel, V. C. & Head, M. R. 1969 Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J. Fluid Mech. 38, 181–201.Google Scholar
Rai, M. M. & Moin, P. 1989 Direct simulations of turbulent flow using finite difference schemes. AIAA Paper 89-0369 (also in J. Comput. Phys. 96, 15–53, 1991).
Schewe, G. 1983 On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow. J. Fluid Mech. 134, 311–328.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn., pp. 596–612. McGraw-Hill.
Schumann, U. 1973 Ein Verfahren zur direkten numerischen Simulation turbulenter Strömungen in Platten- und Ringspaltkanälen und über seine Anwendung zur Untersuchung von Turbulenzmodellen. PhD thesis, KFK 1854, TH Karlsruhe, Germany.
Schumann, U. 1975 Linear stability of finite difference equations for three-dimensional flow problems. J. Comput. Phys. 18, 465–470.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Reθ = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Unger, F. & Friedrich, R. 1993 Large eddy simulation of fully-developed turbulent pipe flow. In Flow Simulation of High Performance Computers I (ed. E. H. Hirschel), NNFM, Vol. 38, pp. 201–216. Vieweg (also in Proc. 8th Symp. on Turbulent Shear Flows, Sept. 9–11, 1991, Munich, Germany, pp. 19/3/1–19/3/6).
Wei, T. & Willmarth, W. W. 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57–95.Google Scholar
Weiss, M. H. 1993 Drag reduction with riblets in pipe flow. PhD thesis, University of Calgary, Canada.
Westerweel, J. 1993 Digital particle image velocimetry: theory and application. PhD thesis, Delft University of Technology, the Netherlands.
Westerweel, J., Adrian, R. J., Eggels, J. G. M. & Nieuwstadt, F. T. M. 1993 Measurements with particle image velocimetry of fully developed turbulent pipe flow at low Reynolds number. In Laser Applications in Fluid Mechanics (ed. R. J. Adrian et al.) Springer. (also in Proc. 6th Intl Symp. on Applications of Laser Techniques to Fluid Mechanics, July 20–23, 1992, Lisbon, Portugal Paper 1.2).
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281–335.Google Scholar