Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-31T16:14:28.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Final stages of transition to turbulence in plane channel flow

Published online by Cambridge University Press:  20 April 2006

S. Biringen
S. Biringen
Affiliation:
Department of Mechanical Engineering, University of New Hampshire, Durham, New Hampshire 03824
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper involves a numerical simulation of the final stages of transition to turbulence in plane channel flow at a Reynolds number of 1500. Three-dimensional incompressible Navier–Stokes equations are numerically integrated to obtain the time evolution of two- and three-dimensional finite-amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32 × 51 × 32 grid. Solutions indicate the existence of structures similar to those observed in the laboratory and characteristic of the various stages of transition that lead to final breakdown. In particular, evidence points to the formation of a A-shaped vortex and the subsequent system of horsehoe vortices inclined to the main flow direction as the primary elements of transition. Details of the resulting flow field after breakdown indicate the evolution of streaklike formations found in turbulent flows. Although the flow field does approach a steady state (turbulent channel flow), the introduction of subgrid-scale terms seems necessary to obtain fully developed turbulence statistics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 148 , November 1984 , pp. 413 - 442
Copyright
© 1984 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

Benney, D. J. & Lin, C. C. 1960 On the secondary motion induced by oscillations in a shear flow. Phys. Fluids 4, 656.Google Scholar
Biringen, S. & Maestrello, L. 1984 Development of spot-like turbulence in plane channel flow. Phys. Fluids 27, 318.Google Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457.Google Scholar
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 A flow-visualization study of transition in plane Poiseuille flow. J. Fluid Mech. 121, 487.Google Scholar
Craik, A. D. D. 1971 Non-linear resonant instability in boundary layers. J. Fluid Mech. 50, 393.Google Scholar
Fasel, H., Bestek, H. & Schefenacker, R. 1977 Numerical simulation studies of transition phenomena in incompressible, two-dimensional flows. In Laminar—Turbulent Transition: AGARD Conf. Proc. 224, p. 14.
George, W. D. & Hellums, J. D. 1972 Hydrodynamic stability in plane Poiseuille flow with finite-amplitude disturbances. J. Fluid Mech. 12, 1.Google Scholar
Kama, F. R. & Nutant, J. 1963 Detailed flow field observations in the transition process in a thick boundary layer. In Proc. 1963 Heat Transfer and Fluid Mechanics Institute. Stanford University Press.
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297.Google Scholar
Herbert, T. 1981 Stability of plane Poiseuille flow—Theory and experiment. Dept Engng Sci. and Mech., Virginia Poly. Inst. and State Univ. Rep. VPI-E-21-35.Google Scholar
Herbert, T. 1983 Secondary instability of plane channel flow to subharmomic three-dimensional disturbances. Phys. Fluids 26, 871.Google Scholar
Kao, T. W. & Park, C. 1970 Experimental investigations of the stability of channel flows. Part 1. Flow of a single liquid in a rectangular channel. J. Fluid Mech. 43, 145.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1.Google Scholar
Kleiser, L. 1982 Spectral simulations of laminar—turbulent transition in plane Poiseuille flow and comparison with experiments. In Proc. 8th Intl Conf. on Numerical Methods in Fluid Dynamics, Aachen (ed. E. Krause). Lecture Notes in Physics, vol. 170, p. 280. Springer.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.Google Scholar
Komoda, H. 1967 Nonlinear development of disturbance in laminar boundary layer. Phys. Fluids Suppl. 10, 87.Google Scholar
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in transition. In Proc. 1962 Heat Transfer and Fluid Mech. Inst., p. 1.
Mansour, N. N., Ferziger, J. H. & Reynolds, W. C. 1978 Large eddy simulation of a turbulent mixing layer. Dept Mech. Engng, Stanford Univ. Rep. TF-11.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341.Google Scholar
Moin, P., Reynolds, W. C. & Ferziger, J. H. 1978 Large eddy simulation of incompressible turbulent channel flow. Dept Mech. Engng, Stanford Univ. Rep. TF-12.Google Scholar
Nishioka, M., Asai, M. & Iida, S. 1980 An experimental investigation of the secondary instability. In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), p. 37. Springer.
Nishioka, M., Asai, M. & Iida, S. 1981 Wall phenomena in the final stage of transition to turbulence. In Transition and Turbulence (ed. R. E. Meyer), p. 113. Academic.
Orszag, S. A. 1976 Turbulence and transition: A progress report. In Proc. 5th Intl Conf. on Numerical Methods in Fluid Dynamics (ed. A. I. van de Vooren & P. J. Zandbergen). Lecture Notes in Physics, vol. 59, p. 32. Springer.
Orszag, S. A. 1972 Comparison of pseudo spectral and spectral approximation. Stud. Appl. Maths 51, 253.Google Scholar
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159.Google Scholar
Orszag, S. A. & Patera, A. T. 1981 Subcritical transition to turbulence in planar shear flows. Phys. Rev. Lett. 45, 989.Google Scholar
Perry, A. E., Lim, T. T. & Teh, E. W. 1981 A visual study of turbulent spots. J. Fluid Mech. 104, 381.Google Scholar
Reynolds, W. C. 1967 A Fortran IV program for solution of the Orr—Sommerfeld equation. Dept Mech. Engng, Stanford Univ. Rep. FM-4.Google Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27.Google Scholar
Smith, C. R. & Schwartz, S. R. 1983 Observation of streamwise rotation in the near-wall region of a turbulent boundary layer. Phys. Fluids 26, 641.Google Scholar
Tani, I. 1969 Boundary layer transition. Ann. Rev. Fluid Mech. 1, 169.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Theodorsen, T. 1955 The structure of turbulence. In 50 Jahre Grenzschichtforschung, p. 55. Vieweg.
Wray, A. & Hussaini, M. Y. 1984 Numerical experiments in boundary-layer stability. Proc. R. Soc. Lond. A 392, 373.Google Scholar