Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T18:58:52.010Z Has data issue: false hasContentIssue false
  • English
  • Français

Observation of laminar–turbulent transition of a yield stress fluid in Hagen–Poiseuille flow

Published online by Cambridge University Press:  25 May 2009

B. GÜZEL ,
T. BURGHELEA ,
I. A. FRIGAARD  and
D. M. MARTINEZ
B. GÜZEL
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada
T. BURGHELEA
Affiliation:
Institute of Polymer Materials, University Erlangen-Nurnberg, Martensstrasse 7, D-91058 Erlangen, Germany
I. A. FRIGAARD*
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
D. M. MARTINEZ
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, BC V6T 1Z3, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate experimentally the transition to turbulence of a yield stress shear-thinning fluid in Hagen–Poiseuille flow. By combining direct high-speed imaging of the flow structures with Laser Doppler Velocimetry (LDV), we provide a systematic description of the different flow regimes from laminar to fully turbulent. Each flow regime is characterized by measurements of the radial velocity, velocity fluctuations and turbulence intensity profiles. In addition we estimate the autocorrelation, the probability distribution and the structure functions in an attempt to further characterize transition. For all cases tested, our results indicate that transition occurs only when the Reynolds stresses of the flow equal or exceed the yield stress of the fluid, i.e. the plug is broken before transition commences. Once in transition and when turbulent, the behaviour of the yield stress fluid is somewhat similar to a (simpler) shear-thinning fluid. Finally, we have observed the shape of slugs during transition and found their leading edges to be highly elongated and located off the central axis of the pipe, for the non-Newtonian fluids examined.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 97 - 128
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abbas, M. A. & Crowe, C. T. 1987 Experimental study of the flow properties of a homogeneous slurry near transitional Reynolds numbers. Intl J. Multiphase Flow 13 (3), 357–364.CrossRefGoogle Scholar
Balmforth, N. J. & Craster, R. V. 1999 A consistent thin-layer theory for Bingham plastics. J. Non-Newt. Fluid Mech. 84, 65–81.CrossRefGoogle Scholar
Bandyopadhyay, P. R. 1986 Aspects of the equilibrium puff in transitional pipe flow. J. Fluid Mech. 163, 439–458.CrossRefGoogle Scholar
Berman, N. S. 1978 Drag reduction by polymers. Annu. Rev. Fluid Mech. 10, 47–64.CrossRefGoogle Scholar
Bewersdorff, H. W. 1991 Turbulence structure of dilute polymer and surfactant solutions in artificially roughened pipes. In Sixth European Drag Reduction Working Meeting, Eindhoven University of Technology.Google Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics. Wiley.Google Scholar
Bogue, D. C. 1959 Entrance effects and prediction of turbulence in non-Newtonian flow. Ind. Engng Chem. 51, 874–878.CrossRefGoogle Scholar
Chapman, S. J. 2002 Subcritical transition in channel flows. J. Fluid Mech. 451, 35–97.CrossRefGoogle Scholar
Chen, R. Y. 1973 Flow in the entrance region at low Reynolds numbers. J. Fluids Engng 95, 153–158.CrossRefGoogle Scholar
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in contant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114.CrossRefGoogle Scholar
Dodge, D. W. & Metzner, A. B. 1959 Turbulent flow of non-Newtonian systems. A.I.Ch.E. J. 5, 189–204.CrossRefGoogle Scholar
Doherty, J., Ngan, P., Monty, J. & Chong, M. 2007 The development of turbulent pipe flow. In 16th Australasian Fluid Mechanics Conference, Gold Coast, Queensland, pp. 266–270.Google Scholar
Draad, A. A., Kuiken, G. D. C. & Nieuwstadt, F. T. M. 1998 Laminar-turbulent transition in pipe flow for Newtonian and non-Newtonian fluids. J. Fluid Mech. 377, 267–312.CrossRefGoogle Scholar
Draad, A. A. & Nieuwstadt, F. T. M. 1998 The Earth's rotation and laminar pipe flow. J. Fluid Mech. 361, 297–308.CrossRefGoogle Scholar
Draad, A. A. & Westerweel, J. 1996 Measurement of temporal and spatial evolution of transitional pipe flow with PIV. Presentation at the meeting of the APS, Fluid Mechanics Section, University of Buffalo, NY.Google Scholar
Durst, F., Ray, S., Unsal, B. & Bayoumi, O. A. 2005 The development lengths of laminar pipe and channel flows. J. Fluids Engng 127, 1154–1160.CrossRefGoogle Scholar
Eckhardt, B., Schneider, T., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468.CrossRefGoogle Scholar
Eliahou, S., Tumin, A. & Wygnanski, I. 1998 Laminar-turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall. J. Fluid Mech. 361, 333–349.CrossRefGoogle Scholar
Escudier, M. P., Poole, R. J., Presti, F., Dales, C., Nouar, C., Desaubry, C., Graham, L. & Pullum, L. 2005 Observations of asymmetrical flow behaviour in transitional pipe flow of yield-stress and other shear-thinning liquids. J. Non-Newt. Fluid Mech. 127, 143–155.CrossRefGoogle Scholar
Escudier, M. P. & Presti, F. 1996 Pipe flow of a thixotropic liquid. J. Non-Newt. Fluid Mech. 62, 291–306.CrossRefGoogle Scholar
Escudier, M. P., Presti, F. & Smith, F. 1999 Drag reduction in the turbulent pipe flow of polymers. J. Non-Newt. Fluid Mech. 81, 197–213.CrossRefGoogle Scholar
Esmael, A. & Nouar, C. 2008 Transitional flow of a yield stress fluid in a pipe: evidence of a robust coherent structure. Phys. Rev. E 77, 057302.Google Scholar
Faisst, H. & Eckhardt, B. 2003 Travelling waves in pipe flow. Phys. Rev. Lett. 91, 224502.CrossRefGoogle ScholarPubMed
Frigaard, I. A., Howison, S. D. & Sobey, I. J. 1994 On the stability of Poiseuille flow of a Bingham fluid. J. Fluid Mech. 263, 133–150.CrossRefGoogle Scholar
Frigaard, I. A. & Nouar, C. 2003 On three-dimensional linear stability of Poiseuille flow of Bingham fluids. Phys. Fluids 15, 2843–2851.CrossRefGoogle Scholar
Frigaard, I. A. & Ryan, D. P. 2004 Flow of a visco-plastic fluid in a channel of slowly varying width. J. Non-Newt. Fluid Mech. 123, 67–83.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Froishteter, G. B. & Vinogradov, G. V. 1980 The laminar flow of plastic disperse systems in circular tubes. Rheol. Acta. 19, 239–250.CrossRefGoogle Scholar
Govier, G. W. & Aziz, K. 1972 The Flow of Complex Mixtures in Pipes. Van Nostrand-Reinhold.Google Scholar
Guo, B., Sun, K. & Ghalambor, A. 2004 A closed-form hydraulics equation for aerated-mud drilling in inclined wells. SPE Dril. Compl. 19 (2), 72–81.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regenaration mechanism of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Han, G., Tumin, A. & Wygnanski, I. 2000 Laminar-turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall. Part 2. Late stage of transition. J. Fluid Mech. 419, 1–27.CrossRefGoogle Scholar
Hanks, R. W. & Pratt, D. R. 1967 On the flow of Bingham plastic slurries in pipes and between parallel plates. SPE Paper No. 1682.CrossRefGoogle Scholar
Hof, B., vanDoorne, C. W. H., Westerweel, J. & Nieuwstadt, F. T. M. 2005 Turbulence regeneration in pipe flow at moderate Reynolds numbers. Phys. Rev. Lett. 95, 214502.CrossRefGoogle ScholarPubMed
Hof, B., vanDoorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F. 2004 Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305, 1594–1598.CrossRefGoogle ScholarPubMed
Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502-1-4.CrossRefGoogle Scholar
Kerswell, R. R. & Tutty, O. R. 2007 Recurrence of travelling waves in transitional pipe flow. J. Fluid Mech. 584, 69–102.CrossRefGoogle Scholar
Landau, L. D. & Lifschitz, E. M. 1987 Fluid Mechanics. Pergamon Press.Google Scholar
Laufer, J. 1952 The structure of turbulence in fully developed pipe flow. National Advisory Committee of Aeronautics, USA, Report No. 1174.Google Scholar
Leite, R. J. 1959 An experimental investigation of the stability of Poiseuille flow. J. Fluid Mech. 5, 81–96.CrossRefGoogle Scholar
Lesieur, M. 1990 Turbulence in Fluids Stochastic and Numerical Modelling (Fluid Mechanics and Its Applications), 2nd rev. ed. Springer.Google Scholar
Mellibovsky, F. & Meseguer, A. 2007 Pipe flow transition threshold following localized impulsive perturbations. Phys. Fluids 19, 044102.CrossRefGoogle Scholar
Métivier, C., Nouar, C. & Brancher, J.-P. 2005 Linear stability involving the Bingham model when the yield stress approaches zero. Phys. Fluids 17, 104106.CrossRefGoogle Scholar
Metzner, A. B. & Reed, J. C. 1955 Flow of non-Newtonian fluids – correlation of the laminar, transition and turbulent-flow regions. A.I.Ch.E. J. 1, 434–440.CrossRefGoogle Scholar
Nguyen, Q. D. & Boger, D. V. 1985 Direct yield stress measurement with the vane method. J. Rheol. 29, 335–347.Google Scholar
Nikuradse, J. 1932 Gesetzmassigkeiten der turbulenten stromung in glatten rohren, Forschung auf dem Gebiet des Ingenieurwesens. Translated in NASA TT F-10, 359 (1966) 3, 1–36.Google Scholar
Nouar, C. & Frigaard, I. A. 2001 Nonlinear stability of Poiseuille flow of a Bingham fluid. J. Non-Newt. Fluid Mech. 100, 127–149.CrossRefGoogle Scholar
Nouar, C., Kabouya, N., Dusek, J. & Mamou, M. 2007 Modal and non-modal linear stability of the plane Bingham—Poiseuille flow. J. Fluid Mech. 577, 211–239.CrossRefGoogle Scholar
Park, J. T., Mannheimer, R. J., Grimley, T. A. & Morrow, T. B. 1989 Pipe flow measurements of a transparent non-Newtonian slurry. ASME J. Fluids Engng 111 (3), 331–336.CrossRefGoogle Scholar
Peixinho, J. 2004 Contribution expérimentale à l'étude de la convection thermique en régime laminaire, transitoire et turbulent pour un fluide à seuil en écoulement dans une conduite. PhD thesis, Université Henri Poincaré, Nancy, France.Google Scholar
Peixinho, J., Nouar, C., Desaubry, C. & Theron, B. 2005 Laminar transitional and turbulent flow of yield-stress fluid in a pipe. J. Non-Newt. Fluid Mech. 128, 172–184.CrossRefGoogle Scholar
Perry, A. E. & Abell, C. J. 1978 Scaling laws for pipe-flow turbulence. J. Fluid Mech. 67, 257–271.CrossRefGoogle Scholar
Poole, R. J. & Ridley, B. S. 2007 Development-length requirements for fully developed laminar pipe flow of inelastic non-newtonian liquids. J. Fluids Engng 129, 1281–1287.CrossRefGoogle Scholar
Reddy, S. C., Schmid, P. J. & Henningson, D. S. 1993 Pseudospectra of the Orr-Sommerfeld operator. SIAM J. Appl. Maths 53, 15–47.CrossRefGoogle Scholar
Reynolds, O. 1883 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. Lond. 174, 935–982.Google Scholar
Rudman, M., Blackburn, H. M., Graham, L. J. W. & Pullum, L. 2004 Turbulent pipe flow of shear-thinning fluids. J. Non-Newt. Fluid Mech. 118, 33–48.CrossRefGoogle Scholar
Shah, S. N. & Sutton, D. L. 1990 New friction correlation for cements from pipe and rotational-viscometer data. SPE Prod. Engng 5 (4), 415–424CrossRefGoogle Scholar
Shan, H., Ma, B., Zhang, Z. & Nieuwstadt, F. T. M. 1999 Direct numerical simulation of a puff and a slug in transitional cylindrical pipe flow. J. Fluid Mech. 387, 39–60.CrossRefGoogle Scholar
Slatter, P. T. 1999 The laminar-turbulent transition in large pipes. International Conference Problems in Fluid Mechanics and Hydrology, Prague, pp. 247–256.Google Scholar
Slatter, P. T. & Wasp, E. J. 2000 The laminar-turbulent transition in large pipes. Proceedings of 10th International Conference on Transport and Sedimentation of Solid Particles, Wroclaw, Poland, pp. 389–399.Google Scholar
Soto, R. J. & Shah, V. L. 1976 Entrance flow of a yield-power law fluid. Appl. Sci. Res. 32, 73–85.CrossRefGoogle Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. London, Ser. A 164, 476.CrossRefGoogle Scholar
Teitgen, R. 1980 Laminar-turbulent transition in pipe flow: development and structure of the turbulent slug. Laminar-Turbulent Transition, IUTAM Symposium, Stuttgart, Germany, vol. 1979, pp. 27–36. Springer.CrossRefGoogle Scholar
Toonder, J. M. J. & Nieuwstadt, F. T. M. 1997 Reynolds number effects in a turbulent pipe flow for low to moderate Rev. Phys. Fluids 9, 3398–3409.CrossRefGoogle Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, A. E. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.CrossRefGoogle ScholarPubMed
Turian, R. M., Ma, T. W., Hsu, F. L. G. & Sung, D. J. 1998 Experimental study of the flow properties of a homogeneous slurry near transitional Reynolds numbers. Intl J. Multiphase Flow 13 (3), 357–364.Google Scholar
Waleffe, F. 1997 On a self-sustaining mechanism in shear flows. Phys. Fluids 9, 883–900.CrossRefGoogle Scholar
Wedin, H. & Kerswell, R. R. 2004 Exact coherent solutions in pipe flow : travelling wave solutions. J. Fluid Mech. 508, 333–371.CrossRefGoogle Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.CrossRefGoogle Scholar
White, F. M. 1999 Fluid Mechanics, 4th ed. McGraw-Hill.Google Scholar
Willingham, J. D. & Shah, S. N. 2000 Friction pressures of Newtonian and non-Newtonian fluids in straight and reeled coiled tubing. SPE Paper No. 60719-MS. Proceedings of the SPE/ICoTA Coiled Tubing Roundtable, 5–6 April 2000, Houston, TX.CrossRefGoogle Scholar
Wilson, K. C. & Thomas, A. D. 1985 A new analysis of the turbulent flow of non-Newtonian fluids. Can. J. Chem. Engng 63, 539–546.CrossRefGoogle Scholar
Wilson, K.C. & Thomas, A. D. 2006 Analytic model of laminar-turbulent transition for Bingham plastics. Can. J. Chem. Engng 84 (5), 520–526.CrossRefGoogle Scholar
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281–335.CrossRefGoogle Scholar
Wygnanski, I. J., Sokolov, M. & Friedman, D. 1975 On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69, 283–304.CrossRefGoogle Scholar