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On transition of the pulsatile pipe flow

Published online by Cambridge University Press:  21 April 2006

J. C. Stettler  and
A. K. M. Fazle Hussain
J. C. Stettler
Affiliation:
Department of Mechanical Engineering, University of Houston-University Park, Houston, TX 77004, USA Present address: Brown, Boveri & Cie., Abt. ZXE, CH-5401, Baden, Switzerland.
A. K. M. Fazle Hussain
Affiliation:
Department of Mechanical Engineering, University of Houston-University Park, Houston, TX 77004, USA
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Abstract

Transition in a pipe flow with a superimposed sinusoidal modulation has been studied in a straight circular water pipe using laser-Doppler anemometer (LDA) techniques. This study has determined the stability–transition boundary in the three-dimensional parameter space defined by the mean and modulation Reynolds numbers Rem, Remω and the frequency parameter λ. Furthermore, it documents the mean passage frequency Fp of ‘turbulent plugs’ as functions of Rem’ Remω and λ. This study also delineates the conditions when plugs occur randomly in time (as in the steady flow) or phase-locked with the excitation. The periodic flow requires a new definition of the transitional Reynolds number Rer, identified on the basis of the rate of change of Fp with Rem. The extent of increase or decrease in Rer from the corresponding steady flow value depends on λ and Remω. At any Rem and Remω, maximum stabilization occurs at λ ≈ 5. With increasing Remω, the ‘stabilization bandwidth’ of modulation frequencies increases and then abruptly decreases after levelling off. The maximum stabilization bandwidth depends strongly on Rem, decreasing with increasing Rem. Previously reported observations of turbulence during deceleration, followed by a relaminarization during acceleration, can be explained in terms of a new phenomenon: namely, periodic modulation produces longitudinally periodic cells of turbulent fluid ‘plugs’ which differ in structural details from ‘puffs’ or ‘slugs’ in steady transitional pipe flows and are called patches. The length of a patch could be increased continuously from zero to the entire pipe length by increasing Rem. This tends to question the concept that all turbulent plugs (and even the fully-turbulent pipe flow) consists of many identical elementary plugs as basic ‘building blocks’.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 169 - 197
Copyright
© 1986 Cambridge University Press

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References

Anliker M., Casty M., Friedli P., Keller, H. & Kubli R.1977 In Cardiovascular Flow Dynamics and Measurements (ed. N. H. C. Hwang & N. Normann). Baltimore. MD: University Park Press.
Bandyopadhyay, P. & Hussain A. K. M. F.1985 In Flow Visualization III (ed. W. J. Yang), p. 521. Hemisphere.
Benney, D. J. & Bergeron R. F.1969 Stud. Appl. Maths 48, 181.
Brown, S. N. & Stewartson K.1980 Geophys. Astrophys. Fluid Dyn. 16, 171.
Cantwell B.1981 Ann. Rev. Fluid Mech. 13, 457.
Coles D.1981 Proc. Indian Acad. Sci. (Engng Sci.) 4, 111.
Davey, A. & Drazin P. G.1969 J. Fluid Mech. 36, 209.
Davey, A. & Nguyen H. P. F.1971 J. Fluid Mech. 45, 701.
Davis R. E.1969 J. Fluid Mech. 36, 337.
Davis S. H.1976 Ann. Rev. Fluid Mech. 8, 57.
Drazin, P. G. & Reid W. H.1981 Hydrodynamic Stability. Cambridge University Press.
Garg, V. K. & Rouleau W. T.1972 J. Fluid Mech. 54, 113.
Gilbrech, D. A. & Combs G. O.1963 In Developments in Theoretical and Applied Mechanics, vol. I, p. 292. Plenum.
Gill A. E.1965 J. Fluid Mech. 21, 503.
Gill A. E.1973 J. Fluid Mech. 61, 97.
Greenspan, H. P. & Benney D. J.1963 J. Fluid Mech. 15, 133.
Grosch, C. E. & Salwen H.1968 J. Fluid Mech. 34, 177.
Haberman R.1972 Stud. Appl. Maths 51, 139.
Hall P.1975 Proc. R. Soc. Lond. A 344, 453.
Herbert D. M.1972 J. Fluid Mech. 56, 73.
Hino M., Sawamoto, M. & Takasu S.1976 J. Fluid Mech. 75, 193.
Hocking L. M.1977 Q. J. Mech. Maths 30, 343.
Hussain A. K. M. F.1977 In Cardiovascular Flow Dynamics and Measurements (ed. N. H. C. Hwang & N. Normann), p. 541. Baltimore, MD: University Park Press.
Itoh N.1977 J. Fluid Mech. 82, 469.
Kerczek, C. H. Von & Davis S. H.1974 J. Fluid Mech. 62, 753.
Kerczek C. H. Von1982 J. Fluid Mech. 116, 91.
Landahl M. T.1967 J. Fluid Mech. 29, 441.
Leite R. J.1959 J. Fluid Mech. 5, 81.
Leitko, A. D. & Hussain A. K. M. F.1983 Bull. Am. Phys. Soc. 28, 1402.
Lessen M., Sadler, S. G. & Liu T. Y.1968 Phys. Fluids 11, 1404.
Lin C. C.1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Lindgren E. R.1957 Ark. Fys. 12, 1.
Mackrodt P. A.1976 J. Fluid Mech. 73, 153.
Merkli, P. & Thomann H.1975 J. Fluid Mech. 68, 567.
Morkovin M. V.1977 AGARDograph no. 236.
Nerem, R. M. & Seed N. A.1972 Cardiovascular Res. 6, 1.
Patera, A. T. & Orszag S. A.1981 J. Fluid Mech. 112, 467.
Ramaprian, B. R. & Tu S. W.1980 J. Fluid Mech. 100, 513.
Reynolds, W. C. & Hussain A. K. M. F.1972 J. Fluid Mech. 54, 263.
Rosenblat, S. & Davis, S. H. 1979 SIAM J. Appl. Maths 37, 1.
Roshko A.1976 AIAA J. 10, 1349.
Rotta J.1956 Ing. Arch. 24, 258.
Rubin Y., Wygnanski, I. & Haritonidis, J. H. 1980 In IUTAM Symp. on Laminar Turbulent Transition (ed. R. Eppler & H. Fasel), p. 17. Springer.
Sarpkaya T.1966 Trans. ASME D: J. Basic Engng 88, 589.
Schultz-Grunow F.1940 Forschung 11, 170–187, (NASA Tech. Transl. NASA-TT-F-14881, 1973).
Sergeev S. I.1966 Fluid Dyn. (Mekh 2H) 1, 21.
Shemer, I. & Wygnanski I.1981 3rd symp. on turbulent shear flows. University of California. Davis.
Smith F. T.1979 Mathematika 26, 187.
Smith, F. T. & Bodonyi R. J.1982 Proc. R. Soc. Lond. A 384, 463.
Stettler J. C., Zaman, K. B. M. Q. & Hussain A. K. M. F.1986 J. Fluid Mech. (in preparation).
Stettler J. C., Niederer, P. & Anliker M.1981 Ann. Biomed. Engng 9, 145.
Stuart J. T.1960 J. Fluid Mech. 9, 352.
Tatsumi T.1952 J. Phys. Soc. Japan 1, 489.
Tozzi J. T.1982 Ph.D. thesis, Catholic University.
Uchida S.1956 Z. angew. Math. Phys. 7, 403.
Watson J.1960 J. Fluid Mech. 9, 371.
Wygnanski, I. J. & Champagne F. H.1973 J. Fluid Mech. 59, 281.
Wygnanski I., Sokolov, M. & Friedman D.1975 J. Fluid Mech. 69, 283.
Yellin E. L.1966 Circulation Res. 19, 791.