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On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug

Published online by Cambridge University Press:  29 March 2006

I. J. Wygnanski  and
F. H. Champagne
I. J. Wygnanski
Affiliation:
Boeing Scientific Research Laboratory, Seattle, Washington Present address: School of Engineering, Tel-Aviv University.
F. H. Champagne
Affiliation:
Boeing Scientific Research Laboratory, Seattle, Washington Present address: Department of Applied Mechanics and Engineering Sciences, University of California, San Diego.
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Abstract

Conditionally sampled hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence. The pipe was smooth and carefully aligned so that turbulent slugs appeared naturally at Re > 5 × 104. Transition could be initiated at lower Re by introducing disturbances into the inlet. For smooth or only slightly disturbed inlets, transition occurs as a result of instabilities in the boundary layer long before the flow becomes fully developed in the pipe. This type of transition gives rise to turbulent slugs which occupy the entire cross-section of the pipe, and they grow in length as they proceed downstream. The leading and trailing ‘fronts’ of a turbulent slug are clearly defined. A unique relation seems to exist between the velocity of the interface and the velocity of the fluid by which relaminarization of turbulent fluid is prevented. The length of slugs is of the same order of magnitude as the length of the pipe, although the lengths of individual slugs differ at the same flow conditions. The structure of the flow in the interior of a slug is identical to that in a fully developed turbulent pipe flow. Near the interfaces, where the mean motion changes from a laminar to a turbulent state, the velocity profiles develop inflexions. The total turbulent intensity near the interfaces is very high and it may reach 15% of the velocity at the centre of the pipe. A turbulent energy balance was made for the flow near the interfaces. All of the terms contributing to the energy balance must vanish identically somewhere on the interface if that portion of the interface does not entrain non-turbulent fluid. It appears that diffusion which also includes pressure transport is the most likely mechanism by which turbulent energy can be transferred to non-turbulent fluid. The dissipation term at the interface is negligible and increases with increasing turbulent energy towards the interior of the slug.

Mixed laminar and turbulent flows were observed far downstream for \[ 2000 < Re < 2700 \] when a large disturbance was introduced into the inlet. The flow in the vicinity of the inlet, however, was turbulent at much lower Re. The turbulent regions which are convected downstream at a velocity which is slightly smaller than the average velocity in the pipe we shall henceforth call puffs. The leading front of a puff does not have a clearly defined interface and the trailing front is clearly defined only in the vicinity of the centre-line. The length and structure of the puff is independent of the character of the obstruction which created it, provided that the latter is big enough to produce turbulent flow at the inlet. The puff will be discussed in more detail later.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 2 , 19 June 1973 , pp. 281 - 335
Copyright
© 1973 Cambridge University Press

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References

Coles, D. 1962 In Mécanique de la Turbulence (ed. A. Favre), pp. 229. Paris: C.N.R.S.
Corrsin, S. & Kistler, A. 1955 N.A.C.A. Rep. no. 1244.
Crow, S. C. & Champagne, F. H. 1971 J. Fluid Mech. 48, 547.
Elder, J. W. 1960 J. Fluid Mech. 9, 235.
Goldstein, S. (ed.) 1938 Modern Developments in Fluid Dynamics. Oxford University Press.
Kibens, V. 1968 Ph.D. dissertation, Department of Mechanics, Johns Hopkins University.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 J. Fluid Mech. 12, 1.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741.
Kovasznay, L. S. G., Komoda, H. & Vesudeva, B. R. 1962 Proc. Heat Trans. & Fluid Mech. Inst. Stanford University Press.
Laufer, J. 1954 N.A.C.A. Rep. no. 1174.
Lindgren, E. R. 1957 Arkiv Fys. 12, 1.
Lindgren, E. R. 1969 Phys. Fluids, 12, 418.
Lowson, M. V. 1964 J. Roy. Aero. Soc. 68, 343.
Michalke, A. & Wille, R. 1964 Proc. of the 11th Int. Cong. Appl. Mech. (ed. H. Görtler). Springer.
Morkovin, M. V. 1969 Viscous Drag Reduction. Plenum Press.
Patel, R. R. 1968 McGill Univ. Dept. Mech. Engng Rep. no. 68-7.
Patel, V. C. & Head, M. R. 1969 J. Fluid Mech. 38, 181.
Reshotko, E. 1958 Jet Propulsion Lab., Pasadena, Prog. Rep. no. 20–364.
Reynolds, O. 1883 Phil. Trans. 174, 935.
Rotta, J. 1956 Ing. Arch. 24, 258.
Schubauer, G. B. & Klebanoff, P. S. 1956 N.A.C.A. Rep. no. 1289.
Smith, A. M. O. 1960 J. Fluid Mech. 7, 565.
Tatsumi, T. 1952 J. Phys. Soc. Japan, 7, 489.
Theodorsen, T. 1955 In Fifty Years of Boundary Layer Research (ed. H. Görtler), pp. 55–63. Braunschweig: Friedr. Vieweg.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1966 J. Fluid Mech. 26, 689.
Valerani, E. 1964 Engineer's thesis, Guggenheim Aero. Lab., Calif. Inst. Tech.
Willmarth, W. W. & Lu, S. S. 1970 Bull. Am. Phys. Soc. Ser. II, 15, 1545.
Wygnanski, I. 1971 Israel J. Tech. 9, 105.
Wygnanski, I. & Fiedler, H. 1970 J. Fluid Mech. 41, 327.