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Intermittent turbulence in a pulsating pipe flow

Published online by Cambridge University Press:  06 March 2008

RAFFAELLA TUZI  and
PAOLO BLONDEAUX
RAFFAELLA TUZI*
Affiliation:
Department of Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genoa, Italy
PAOLO BLONDEAUX
Affiliation:
Department of Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genoa, Italy
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Abstract

Numerical simulations of the pulsating flow in a pipe of circular cross-section characterized by small imperfections are carried out to determine the conditions leading to the appearance of turbulence. The results show that in the oscillatory case (no steady velocity component of the basic flow), the critical value of the Reynolds number Rδ depends on the Womersley parameter α and, in particular, Rδ increases as α decreases. The critical value of Rδ of the plane wall case is recovered when α is larger than about 10. For moderate values of the Reynolds numbers but larger than the critical one, turbulence appears around flow reversal and breaks the symmetry of the flow, originating a steady velocity component. Moreover, turbulence is not present throughout the whole cycle and there are phases during which the flow relaminarizes. The presence of a steady pressure gradient tends to destabilize the flow and this destabilizing effect becomes larger as the steady velocity component is increased. When turbulence is present, its dynamics is similar to that of the steady case and a log-law layer can be identified both in the oscillatory and the pulsating case.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 599 , 25 March 2008 , pp. 51 - 79
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Akhavan, R., Kamm, R. D. & Shapiro, A. H. 1991a An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 1. Experiments. J. Fluid Mech. 225, 395–422.CrossRefGoogle Scholar
Akhavan, R., Kamm, R. D. & Shapiro, A. H. 1991b An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 2. Numerical simulations. J. Fluid Mech. 225, 423–444.CrossRefGoogle Scholar
Beam, R. M. & Warming, R. F. 1976 An implicit finite-difference algorithm for hyperbolic system in conservation-law form. J. Comput. Phys. 22, 87–110.CrossRefGoogle Scholar
Bedoya, J., Choksi, T., Guo, H. & Pita, A. 2003 Biofluid dynamics of the human respiratory system. In Congress on Biofluid Dynamics of Human Body Systems, Biomedical Engineering, FIU, Miami, FL D-1 (ed. Goyal, M. R.), p. 20.Google Scholar
Blennerhassett, P. J. & Bassom, A. P. 2002 The linear stability of flat Stokes layers. J. Fluid Mech. 464, 393–410.CrossRefGoogle Scholar
Blennerhassett, P. J. & Bassom, A. P. 2006 The linear stability of high-frequency oscillatory flow in a channel. J. Fluid Mech. 556, 1–25.CrossRefGoogle Scholar
Blondeaux, P. & Seminara, G. 1979 Transizione incipiente al fondo di un'onda di gravitá. Rendiconti Accad. Naz. Lincei 67, 407–417.Google Scholar
Blondeaux, P. & Vittori, G. 1994 Wall imperfections as a triggering mechanism for Stokes-layer transition. J. Fluid Mech. 264, 107–135.CrossRefGoogle Scholar
Costamagna, P., Vittori, G. & Blondeaux, P. 2003 Coherent structures in oscillatory boundary layers. J. Fluid Mech. 474, 1–33.CrossRefGoogle Scholar
Eckmann, D. & Grotberg, J. B. 1991 Experiments on transition to turbulence in oscillatory pipe flow. J. Fluid Mech. 222, 329–350.CrossRefGoogle Scholar
Gilbrech, D. A. & Combs, G. O. 1963 Developments in Theoretical and Applied Mechanics, vol. 1, p. 292. Plenum.Google Scholar
Goldschmied, F. R. 1970 On the frequency response of viscous compressible fluids as a function of the Stokes number. Trans. ASME D: J. Basic Engng 92, 333–347.CrossRefGoogle Scholar
Hall, P. 1978 The linear stability of flat Stokes layers. Proc. R. Soc. Lond. A 359, 151–166.Google Scholar
Hino, M., Sawamoto, M. & Takasu, S. 1976 Experiments on transition to turbulence in an oscillatory pipe flow. J. Fluid Mech. 75, 193–207.CrossRefGoogle Scholar
Hirschberg, A. J., Gilbert, R. M. & Wijnands, A. P. J. 1996 Shock waves in trombones. J. Acoust. Soc. Am. 99, 1754–1758.CrossRefGoogle Scholar
Jimenez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59, 308.CrossRefGoogle Scholar
Leon, D. F. & Shaver, J. A. 1974 Physiologic principles of heart sounds and murmurus. American Heart Association Monograph 46.Google Scholar
Lodhal, C. R., Sumer, B. M. & Fredsøe, J. 1998 Turbulent combined oscillatory flow and current in a pipe. J. Fluid Mech. 373, 313–348.CrossRefGoogle Scholar
Luchini, P. & Bottaro, A. 2001 Linear stability and receptivity analyses of the Stokes layer produced by an impulsively started plate. Phys. Fluids 13, 1668–1678.CrossRefGoogle Scholar
Luo, J. & Wu, X. 2004 Influence of small imperfections on the stability of plane poiseuille flow: a theoretical model and direct numerical simulation. Phys. Fluids 16, 2852–2863.CrossRefGoogle Scholar
Merkli, P. & Thomann, H. 1975 Transition to turbulence in oscillating pipe flow. J. Fluid Mech. 68, 567–576.CrossRefGoogle Scholar
Monkewitz, A. 1983 Lineare stabilitats untersuchungen an den aszillierenden grenzschichten von Stokes. PhD thesis 7297, Stabilitaets, Oszillierenden, Federal Institute of Technology, Zurich.Google Scholar
Nerem, R. M., Seed, W. A. & Wood, N. B. 1972 An experimental study of the velocity distribution and transition to turbulence in the aorta. J. Fluid Mech. 52, 137–160.CrossRefGoogle Scholar
Ojha, M., Cobbold, R. S. C., Johnston, K. W. & Hummel, R. L. 1989 Pulsatile flow through constricted tubes: an experimental investigation using photochromic tracer method. J. Fluid Mech. 203, 173–197.CrossRefGoogle Scholar
Orlandi, P. 2000 Fluid Flow Phenomena: A Numerical Toolkit. Kluwer.CrossRefGoogle Scholar
Pedley, T. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rai, M. M. & Moin, P. 1991 Direct simulations of turbulent flow using finite-difference schemes. J. Comput. Phys. 96, 15–53.Google Scholar
Ramaprian, B. R. & Tu, S. 1980 An experimental study of oscillatory pipe flow at transitional Reynolds numbers. J. Fluid Mech. 100, 513–544.CrossRefGoogle Scholar
Sarpkaya, T. 1966 Experimental determination of the critical Reynolds number for pulsating Poiseuille flow. Trans. ASME D: J. Basic Engng 88, 589–598.CrossRefGoogle Scholar
Sergeev, S. I. 1966 Fluid oscillations in pipes at moderate reynolds number. Fluid Dyn. (Merkh. Zh.) 1, 21–22.Google Scholar
Shemer, L., Wygnanski, I. & Kit, E. 1985 Pulsating flow in a pipe. J. Fluid Mech. 153, 313–337.CrossRefGoogle Scholar
Spalart, P. M. & Baldwin, B. S. 1987 Direct simulation of a turbulent oscillating boundary layer. In Symp. on Turbulent Shear Flows, Toulouse, 7–9 September (ed. Durst, F. S. F., Launder, B. & Whitelaw, J.).Google Scholar
Stettler, J. C. & Hussain, A. K. M. F. 1986 On transition of the pulsatile pipe flow. J. Fluid Mech. 170, 169–197.CrossRefGoogle Scholar
Tromans, P. 1976 The stability of oscillatory pipe flow. abstract of lecture given at Euromech 73: Oscillatory Flows in Ducts, Aix-en-Provence, April 13–15.Google Scholar
Tuzi, R. 2006 Transition in oscillatory and pulsating pipe flows. PhD thesis, Department of Environmental Engineering, University of Genova, Italy.Google Scholar
Verzicco, R. & Vittori, G. 1996 Direct simulation of transition in a Stokes boundary layer. Phys. Fluids 8, 1341–1343.CrossRefGoogle Scholar
Vittori, G. & Verzicco, R. 1998 Direct simulation o transition in an oscillatory boundary layer. J. Fluid Mech. 371, 207–232.CrossRefGoogle Scholar
von Kerczek, C. & Davis, S. H. 1974 Linear stability theory of oscillatory Stokes layers. J. Fluid Mech. 62, 753–773.CrossRefGoogle Scholar
Wu, X. 1992 The nonlinear evolution of high-frequency resonant-triad waves in an oscillatory Stokes layer at high Reynolds number. J. Fluid Mech. 245, 553–597.CrossRefGoogle Scholar
Wu, X. & Luo, J. 2006 Influence of small imperfections on the stability of plane Poiseuille flow and the limitation of Squire's theorem. Phys. Fluids 18, 044104–1–14.CrossRefGoogle Scholar
Yellin, E. L. 1966 Laminar-turbulent transition process in pulsatile flow. Circulation Res. 19, 791–804.CrossRefGoogle ScholarPubMed