Fluid Dynamics

, Volume 41, Issue 6, pp 916–922 | Cite as

Effect of the pattern of initial perturbations on the steady pipe flow regime

  • A. A. Pavelyev
  • A. I. Reshmin
  • V. V. Trifonov


The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other.

The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes.

In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet.

The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.


Reynolds number turbulent flow laminar flow transition to turbulence in a pipe experiment 


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  1. 1.
    O. Reynolds, “On the dynamical theory of incompressible viscous fluids and the determination of the criterion,” Phil. Trans. Roy. Soc., A 186, 123–164 (1895).ADSGoogle Scholar
  2. 2.
    V. V. Kolyada and A. A. Pavel’ev, “Transition to turbulence on the initial section of a circular pipe,” Fluid Dynamics, 20, No. 4, 538–541 (1985).CrossRefGoogle Scholar
  3. 3.
    A. G. Darbyshire and T. Mullin, “Transition to turbulence in constant-mass-flux pipe flow,” J. Fluid Mech., 289, 83–114 (1995).CrossRefADSGoogle Scholar
  4. 4.
    A. A. Draad, G. D. C. Kuiken, and F. T. M. Nieuwstadt, “Laminar-turbulent transition in pipe flow for Newtonian and non-Newtonian fluids,” J. Fluid Mech., 377, 267–312 (1998).MATHCrossRefADSGoogle Scholar
  5. 5.
    S. Eliahou, A. Tumin, and I. Wygnanski, “Laminar-turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall,” J. Fluid Mech., 361, 333–349 (1998).MATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    V. G. Lushchik, A. A. Pavelyev, and A. E. Yakubenko, “Analysis of turbulent transition in a boundary layer with high-intensity external perturbations using a three-parameter model,” Problems of Contemporary Mechanics [in Russian], Pt 1, Moscow University Press, Moscow, 127–138 (1983).Google Scholar
  7. 7.
    N. V. Nikitin, “Numerical Analysis of Laminar-Turbulent Transition in a Circular Pipe with Periodic Inflow Perturbations,” Fluid Dynamics, 36, No. 2, 204–216 (2001).MATHCrossRefGoogle Scholar
  8. 8.
    A. A. Pavelyev and A. I. Reshmin, “Turbulent Transition in the Inlet Region of a Circular Pipe,” Fluid Dynamics, 36, No. 4, 626–633 (2001).CrossRefGoogle Scholar
  9. 9.
    A. A. Pavelyev, A. I. Reshmin, S. Kh. Teplovodskii and S. G. Fedoseev, “On the Lower Critical Reynolds Number for Flow in a Circular Pipe,” Fluid Dynamics, 38, No. 4, 545–551 (2003).CrossRefGoogle Scholar
  10. 10.
    A. S. Monin and A. M. Yaglom, Statistical Hydrodynamics. Turbulence Mechanics [in Russian], Pt 1, Nauka, Moscow (1965).Google Scholar
  11. 11.
    L. Prandtl, Führer durch die Strömungslehre, Vieweg, Braunschweig (1949).Google Scholar
  12. 12.
    A. E. Samuel and P. N. Joubert, “A boundary layer developing in an increasingly adverse pressure gradient,” J. Fluid Mech., 66, Pt 3, 481–505 (1974).CrossRefADSGoogle Scholar
  13. 13.
    N. V. Nikitin and A. A. Pavel’ev, “Turbulent flow in a channel with permeable walls. Direct numerical simulation and results of three-parameter model,” Fluid Dynamics, 33, No. 6, 826–832 (1998).MATHCrossRefGoogle Scholar

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© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. A. Pavelyev
  • A. I. Reshmin
  • V. V. Trifonov

There are no affiliations available

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