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TECHNICAL PAPERS

The Effect of Finite Amplitude Disturbance Magnitude on Departures From Laminar Conditions in Impulsively Started and Steady Pipe Entrance Flows

[+] Author and Article Information
E. A. Moss, A. H. Abbot

School of Mechanical Engineering, University of the Witwatersrand, Johannesburg, Private Bag 3, WITS 2050, South Africa

J. Fluids Eng 124(1), 235-240 (Nov 07, 2001) (6 pages) doi:10.1115/1.1445137 History: Received February 16, 1999; Revised November 07, 2001
Copyright © 2002 by ASME
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References

Lessen,  M., Sadler,  S. G., and Liu,  T. Y., 1968, “Stability of pipe Poiseuille Flow,” Phys. Fluids, 11, pp. 1404–1409.
Salwen,  H., and Grosch,  C. E., 1972, “The stability of Poiseuille flow in a pipe of circular cross-section,” J. Fluid Mech., 54, Part 1, pp. 93–112.
Salwen,  H., Cotton,  F. W., and Grosch,  C. E., 1980, “Linear stability of Poiseuille flow in a circular pipe,” J. Fluid Mech., 98, Part 2, pp. 273–284.
Abbot,  A. H., and Moss,  E. A., 1994, “The existence of critical Reynolds numbers in pipe entrance flows subjected to infinitesimal axisymmetric disturbances,” Phys. Fluids, 6, No. 10, pp. 3335–3340.
Gaster,  M., 1962, “A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamics stability,” J. Fluid Mech., 14, pp. 222–224.
Huang,  L. M., and Chen,  T. S., 1974, “Stability of the developing pipe flow subjected to non-axisymmetric disturbances,” J. Fluid Mech., 63, Part 1, pp. 183–193.
Garg,  V. K., 1981, “Stability of developing flow in a pipe: non-axisymmetric disturbances,” J. Fluid Mech., 110, pp. 209–216.
da Silva,  D. F., and Moss,  E. A., 1993, “The stability of pipe entrance flows subjected to axisymmetric disturbances,” ASME J. Fluids Eng., 116, pp. 61–65.
Jordinson,  R., 1970, “The flat plate boundary layer. Part 1. Numerical Integration of the Orr-Sommerfeld equation,” J. Fluid Mech., 43 , Part 4, pp. 801–811.
Drazin P. G., and Reid W. M., 1981, Hydrodynamic Stability, Cambridge University Press, Cambridge.
Sarpkaya,  T., 1975, “A note on the stability of developing laminar pipe flow subjected to axisymmetric and non-axisymmetric disturbances,” J. Fluid Mech., 68, Part 2, pp. 345–351.
Van de Sande E., Belde A. P., Hamer B. J. G., and Hiemstra W., 1980, “Velocity profiles in accelerating pipe flows started from rest,” Proc. of the Third Int. BHRA Conf. on Pressure Surges, Canterbury, England, pp. 1–14.
Lefebvre,  P. J., and White,  F. M., 1989, “Experiments on transition to turbulence in a constant-acceleration pipe flow,” ASME J. Fluids Eng., 111, pp. 428–432.
Moss,  E. A., 1989, “The identification of two distinct laminar to turbulent transition modes in pipe flows accelerated from rest,” Exp. Fluids, 7, pp. 271–274.
Rubin Y., Wygnanski I., and Haritonidis J. H., 1979, “Further observations on transition in a pipe,” IUTAM Conf. on Laminar-Turbulent Transition, Stuttgart, Germany, pp. 17–26.
Abbot A. H., 1995, “The transition to turbulence in strongly accelerated pipe flows,” PhD thesis, University of the Witwatersrand, Johannesburg.
Mayle,  R. E., 1991, “The role of laminar-turbulent transition in gas turbine engines,” ASME J. Turbomach., 113, pp. 509–519.
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Figures

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Schematic of test rig used in the current investigation
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Typical voltage variation with time, as an output of the shear stress probe
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Variations of wall shear stress with cross-sectional mean velocity immediately prior to transition
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Variation of displacement thickness Reynolds number with dimensionless time, showing departures from laminar flow for the current experiments
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Variation of displacement thickness Reynolds number with dimensionless axial co-ordinate, showing the experimental onset of instabilities (Sarpkaya 11) for axisymmetric and non-axisymmetric disturbances
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Variation of Reynolds number with velocity profile shape parameter, showing:- the current transition data for impulsively started pipe flows flows; Sarpkaya’s 11 stability measurements for steady pipe entrance flows; the respective linear stability predictions for each type of flow; and the possible large disturbance pipe-Poiseuille limit
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Variation of displacement thickness Reynolds number with velocity profile shape parameter, showing: The current transition data for impulsively started pipe flows flows; Sarpkaya’s 11 stability measurements for steady pipe entrance flows; the respective linear stability predictions and boundary layer limits for each type of flow; the possible large disturbance pipe-Poiseuille limit; the possible large disturbance Blasius boundary layer limit; and the possible large disturbance error function boundary layer limit
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Variation of displacement thickness Reynolds number with velocity profile shape parameter, showing asymptotic limits, the experimental data of Sarpkaya 11, and the expected qualitative dependence of steady pipe flow entrance stability on disturbance level
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Variation of displacement thickness Reynolds number with velocity profile shape parameter, showing asymptotic limits, the current experimental data, and the expected qualitative dependence of impulsively started pipe flow stability on disturbance level

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