Flow, Turbulence and Combustion

, Volume 89, Issue 4, pp 691–711 | Cite as

An Updated Portrait of Transition to Turbulence in Laminar Pipe Flows with Periodic Time Dependence (A Correlation Study)

  • Melda Özdinç ÇarpinlioğluEmail author
  • Emrah Özahi


Transition to turbulence in axially symmetrical laminar pipe flows with periodic time dependence classified as pure oscillating and pulsatile (pulsating) ones is the concern of the paper. The current state of art on the transitional characteristics of pulsatile and oscillating pipe flows is introduced with a particular attention to the utilized terminology and methodology. Transition from laminar to turbulent regime is usually described by the presence of the disturbed flow with small amplitude perturbations followed by the growth of turbulent bursts. The visual treatment of velocity waveforms is therefore a preferred inspection method. The observation of turbulent bursts first in the decelerating phase and covering the whole cycle of oscillation are used to define the critical states of the start and end of transition, respectively. A correlation study referring to the available experimental data of the literature particularly at the start of transition are presented in terms of the governing periodic flow parameters. In this respect critical oscillating and time averaged Reynolds numbers at the start of transition; Re os,crit and Re ta,crit are expressed as a major function of Womersley number, \(\sqrt {\omega ^\prime } \) defined as dimensionless frequency of oscillation, f. The correlation study indicates that in oscillating flows, an increase in Re os,crit with increasing magnitudes of \(\sqrt {\omega ^\prime } \) is observed in the covered range of \(1<\sqrt {\omega ^\prime } <72\). The proposed equation (Eq. 7), \({\rm{Re}}_{os,crit} ={\rm{Re}}_{os,crit} \left( {\sqrt {\omega ^\prime } } \right)\), can be utilized to estimate the critical magnitude of \(\sqrt {\omega ^\prime }\) at the start of transition with an accuracy of ±12 % in the range of \(\sqrt {\omega ^\prime } <41\). However in pulsatile flows, the influence of \(\sqrt {\omega ^\prime }\) on Re ta,crit seems to be different in the ranges of \(\sqrt {\omega ^\prime } <8\) and \(\sqrt {\omega ^\prime } >8\). Furthermore there is rather insufficient experimental data in pulsatile flows considering interactive influences of \(\sqrt {\omega ^\prime } \) and velocity amplitude ratio, A 1. For the purpose, the measurements conducted at the start of transition of a laminar sinusoidal pulsatile pipe flow test case covering the range of 0.21< A 1 <0.95 with \(\sqrt {\omega ^\prime } <8\) are evaluated. In conformity with the literature, the start of transition corresponds to the observation of first turbulent bursts in the decelerating phase of oscillation. The measured data indicate that increase in \(\sqrt {\omega ^\prime } \) is associated with an increase in Re ta,crit up to \(\sqrt {\omega ^\prime } =3.85\) while a decrease in Re ta,crit is observed with an increase in \(\sqrt {\omega ^\prime } \) for\(\sqrt {{\omega }'} >3.85\). Eventually updated portrait is pointing out the need for further measurements on i) the end of transition both in oscillating and pulsatile flows with the ranges of \(\sqrt {\omega ^\prime } <8\) and \(\sqrt {\omega ^\prime } >8\), and ii) the interactive influences of \(\sqrt {\omega ^\prime } \) and A 1 on Re ta,crit in pulsatile flows with the range of \(\sqrt {\omega ^\prime } >8\).


Periodic flow Transition to turbulence  Time averaged Reynolds number Womersley number  Velocity amplitude ratio Oscillation Reynolds number 


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  1. 1.
    Akhavan, R., Kamm, R.D., Shapiro, A.H.: An investigation of transition to turbulence in bounded oscillatory stokes flows Part 1: Experiments. J. Fluid Mech. 225, 395–422 (1991)CrossRefGoogle Scholar
  2. 2.
    Çarpınlıoğlu, M.Ö.: An approach for transition correlation of laminar pulsatile pipe flows via frictional field characteristics. Flow Meas. Instrum. 14, 233–242 (2003)CrossRefGoogle Scholar
  3. 3.
    Çarpınlıoğlu, M.Ö., Gündoğdu, M.Y.: A critical review on pulsatile pipe flow studies directing towards future research topics. Flow Meas. Instrum. 12, 163–174 (2001)CrossRefGoogle Scholar
  4. 4.
    Çarpınlıoğlu, M.Ö., Özahi, E.: Laminar flow control via utilization of pipe entrance inserts (a comment on entrance length concept). Flow Meas. Instrum. 22, 165–174 (2011)CrossRefGoogle Scholar
  5. 5.
    Clamen, M., Minton, P.: An experimental investigation of flow in an oscillating pipe. J. Fluid Mech. 81, 421–431 (1977)CrossRefGoogle Scholar
  6. 6.
    Das, D., Arakeri, J.H.: Transition of unsteady velocity profiles with reverse flow. J. Fluid Mech. 374, 251–283 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Durst, F., Heim, U., Ünsal, B., Kullik, G.: Mass flow rate control system for time-dependent laminar and turbulent flow investigations. Meas. Sci. Technol. 14, 893–902 (2003)CrossRefGoogle Scholar
  8. 8.
    Durst, F., Ray, S., Ünsal, B., Bayoumi, O.A.: The development lengths of laminar pipe and channel flows. Trans. ASME 127, 1154–1160 (2005)Google Scholar
  9. 9.
    Eckhardt, B., Schneider, T.M., Hof, B., Westerweel, J.: Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Eckmann, D.M., Grotberg, J.B.: Experiments on transition to turbulence in oscillatory pipe flow. J. Fluid Mech. 222, 329–350 (1991)CrossRefGoogle Scholar
  11. 11.
    Einav, S., Sokolov, M.: An experimental study of pulsatile pipe flow in the transition range. Trans. ASME 115, 404–411 (1993)Google Scholar
  12. 12.
    Fedele, F., Hitt, D.L., Prabhu, R.D.: Revisiting the stability of pulsatile pipe flow. Eur. J. Mech. B-Fluid 24, 237–254 (2005)zbMATHCrossRefGoogle Scholar
  13. 13.
    Gerrard, J.H.: An experimental investigation of the pulsating turbulent water flow in a tube. J. Fluid Mech. 46, 43–64 (1971)CrossRefGoogle Scholar
  14. 14.
    Gündoğdu, M.Y.: An experimental investigation on pulsatile pipe flows. Ph. D. Thesis, University of Gaziantep, Department of Mechanical Engineering, Turkey (2000)Google Scholar
  15. 15.
    Gündoğdu, M.Y., Çarpınlıoğlu, M.Ö.: Present state of art on pulsatile flow theory part I: laminar and transitional flow regimes. JSME Int. J. 42, 384–397 (1999)CrossRefGoogle Scholar
  16. 16.
    Hershey, D., Im, C.S.: Critical Reynolds number for sinusoidal flow of water in rigid tubes. AIChE J. 14, 807–809 (1968)CrossRefGoogle Scholar
  17. 17.
    Hino, M., Sawamoto, M., Takasu, S.: Experiments on transition to turbulence in an oscillatory pipe flow. J. Fluid Mech. 75, 193–207 (1976)CrossRefGoogle Scholar
  18. 18.
    Iguchi, M., Ohmi, M.: Transition to turbulence in a pulsatile pipe flow. Part 3: flow regimes and the conditions describing the generation and decay of turbulence. Bull JSME 27, 1873–1880 (1984)CrossRefGoogle Scholar
  19. 19.
    Ito, H.: On the pressure loss of turbulent flow through curved pipes. Rep. Inst. High Speed Mech. Tohoku Univ., Sendai Jpn. 7, 63–76 (1952)Google Scholar
  20. 20.
    Kusama, H.: Study of pulsating flow (pulsating flow in a circular pipe). Soc. Mech. Eng. Trans. 18, 27 (1952)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Leite, R.J.: An experimental investigation of the stability of Poiseuille flow. J. Fluid Mech. 5, 81–96 (1959)zbMATHCrossRefGoogle Scholar
  22. 22.
    Lessen, M., Singh, P.J.: The stability of axisymmetric free shear layers. J. Fluid Mech. 60, 433–457 (1973)zbMATHCrossRefGoogle Scholar
  23. 23.
    Mackrodt, P.A.: Stability of Hagen-Poiseuille flow with superimposed rigid rotation. J. Fluid Mech. 73, 153–164 (1976)zbMATHCrossRefGoogle Scholar
  24. 24.
    Merkli, P., Thomann, H.: Transition to turbulence in oscillating pipe flow. J. Fluid Mech. 68, 567–575 (1975)CrossRefGoogle Scholar
  25. 25.
    Mizushina, T., Maruyama, T., Shiozaki, Y.: Pulsating turbulent flow in a tube. J. Chem. Eng. Jpn. 6, 487–494 (1973)CrossRefGoogle Scholar
  26. 26.
    Nerem, R.M., Seed, W.A., Wood, N.B.: An experimental study of the velocity distribution and transition to turbulence in the aorta. J. Fluid Mech. 52, 137–160 (1972)CrossRefGoogle Scholar
  27. 27.
    Ohmi M., et al.: Preprint of Jpn. Soc. Mech. Engrs. (in Japanese) 795-15, 106 (1979-10)Google Scholar
  28. 28.
    Ohmi, M., Iguchi, M.: Critical Reynolds number in an oscillating pipe flow. Bull. JSME 25, 165–172 (1982)CrossRefGoogle Scholar
  29. 29.
    Ohmi, M., Iguchi, M., Usui, T.: Flow pattern and frictional losses in pulsating pipe flow, Part 5: Wall shear stress and flow pattern in a laminar flow. Bull. JSME 24, 75–81 (1981)CrossRefGoogle Scholar
  30. 30.
    Ohmi, M., Iguchi, M., Kakehashi, K., Masuda, T.: Transition to turbulence and velocity distribution in an oscillating pipe flow. Bull. JSME 25, 365–371 (1982)CrossRefGoogle Scholar
  31. 31.
    Ohmi, M., Iguchi, M., Urahata, I.: Transition to turbulence in a pulsatile pipe flow. Part 1: Wave forms and distribution of pulsatile velocities near transition region. Bull. JSME 25, 182–189 (1982)CrossRefGoogle Scholar
  32. 32.
    Özahi, E.: Analysis of laminar-turbulent transition in time-dependent pipe flows. Ph.D. thesis, University of Gaziantep, Turkey (2011)Google Scholar
  33. 33.
    Özahi, E., Çarpınlıoğlu, M.Ö., Gündoğdu, M.Y.: Simple methods for low speed calibration of hot-wire anemometers. Flow Meas. Instrum. 21, 166–170 (2010)CrossRefGoogle Scholar
  34. 34.
    Peacock, J., Jones, T., Tock, C., Lutz, R.: The onset of turbulence in physiological pulsatile flow in a straight tube. Exp. Fluids 24, 1–9 (1998)CrossRefGoogle Scholar
  35. 35.
    Ramaprian, B., Tu, W.W.: An experimental study of oscillatory pipe flow at transitional Reynolds numbers. J. Fluid Mech. 100, 513–544 (1980)CrossRefGoogle Scholar
  36. 36.
    Reynolds, O.: An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels. Phil. Trans. R. Soc. 174, 935–982 (1883)zbMATHCrossRefGoogle Scholar
  37. 37.
    Salwen, H., Grosch, C.E.: Stability of Poiseuille flow in a pipe of circular cross section. J. Fluid Mech. 54, 93–112 (1972)zbMATHCrossRefGoogle Scholar
  38. 38.
    Sarpkaya, T.: Experimental determination of the critical Reynolds number for pulsating poiseuille flow. Trans. ASME D, J. Basic Eng. 88, 589–598 (1966)CrossRefGoogle Scholar
  39. 39.
    Sarpkaya, T.: A note on the stability of developing laminar pipe flow subjected to axisymmetric and non-axisymmetric disturbances. J. Fluid Mech. 68, 345–351 (1975)CrossRefGoogle Scholar
  40. 40.
    Sergeev, S.I.: Fluid oscillations in pipes at moderate Reynolds numbers. Fluid Dyn. 1, 121–122 (1966)CrossRefGoogle Scholar
  41. 41.
    Sexl, T.: On the annular effect discovered by E.G. Richardson. Z. Physik. 61, 349–362 (1930)zbMATHCrossRefGoogle Scholar
  42. 42.
    Shemer, L.: Laminar-turbulent transition in a slowly pulsating pipe flow. Phys. Fluids 28, 3506–3509 (1985)CrossRefGoogle Scholar
  43. 43.
    Stettler, J.C., Hussain, K.M.F.: On transition of the pulsatile pipe flow. J. Fluid Mech. 170, 169–197 (1986)CrossRefGoogle Scholar
  44. 44.
    Szymanski, P.: Some exact solution of the hydrodynamic equations of a viscous fluid in the case of a cylindrical. J. Math. Pure Appl. 11, 67–107 (1932)zbMATHGoogle Scholar
  45. 45.
    Ünsal, B., Durst, F.: Pulsating flows: experimental equipment and its application. JSME 49, 980–987 (2006)Google Scholar
  46. 46.
    Womersley, J.R.: Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553–563 (1955)Google Scholar
  47. 47.
    Yang, W.H., Yih, C.-S.: Stability of time-periodic flows in a circular pipe. J. Fluid Mech. 82, 497–505 (1977)zbMATHCrossRefGoogle Scholar
  48. 48.
    Yellin, E.L.: Laminar-turbulent transition process in pulsatile flow. Circ. Res. 19, 791–804 (1966)CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Faculty of Engineering, Department of Mechanical EngineeringUniversity of GaziantepGaziantepTurkey

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