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Effect of the number of vortices on the torque scaling in Taylor–Couette flow

Published online by Cambridge University Press:  08 May 2014

B. Martínez-Arias ,
J. Peixinho ,
O. Crumeyrolle  and
I. Mutabazi
B. Martínez-Arias
Affiliation:
Laboratoire Ondes et Milieux Complexes, Université du Havre & CNRS UMR 6294, 53 rue de Prony, 76600 Le Havre, France
J. Peixinho*
Affiliation:
Laboratoire Ondes et Milieux Complexes, Université du Havre & CNRS UMR 6294, 53 rue de Prony, 76600 Le Havre, France
O. Crumeyrolle
Affiliation:
Laboratoire Ondes et Milieux Complexes, Université du Havre & CNRS UMR 6294, 53 rue de Prony, 76600 Le Havre, France
I. Mutabazi
Affiliation:
Laboratoire Ondes et Milieux Complexes, Université du Havre & CNRS UMR 6294, 53 rue de Prony, 76600 Le Havre, France
*
†Email address for correspondence: [email protected]
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Abstract

Torque measurements in Taylor–Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct numbers of vortices along the axis were found and the aspect ratios of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque–speed curves for different states. Before each intersection, the torque for a state with a larger number of vortices is higher. After each intersection, the torque for a state with a larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.

JFM classification

Turbulent Flows: Rotating turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , pp. 756 - 767
Copyright
© 2014 Cambridge University Press 

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References

Abshagen, J., Lopez, J. M., Marques, F. & Pfisher, G. 2005 Mode competition of rotating waves in reflection-symmetric Taylor–Couette flow. J. Fluid Mech. 540, 269–299.Google Scholar
Avila, K. & Hof, B. 2013 High-precision Taylor–Couette experiment to study subcritical transitions and the role of boundary conditions and size effects. Rev. Sci. Instrum. 84, 065106.CrossRefGoogle ScholarPubMed
Barcilon, A., Brindley, J., Lessen, M. & Mobbs, F. R. 1979 Marginal instability in Taylor–Couette flows at a very high Taylor number. J. Fluid Mech. 94, 453–463.Google Scholar
Batten, W. M. J., Bressloff, N. W. & Turnock, S. R. 2002 Transition from vortex to wall driven turbulence production in the Taylor–Couette system with a rotating inner cylinder. Intl J. Numer. Meth. Fluids 38 (3), 207–226.Google Scholar
Benjamin, T. B. & Mullin, T. 1982 Notes on the multiplicity of flows in the Taylor experiment. J. Fluid Mech. 121, 219–230.CrossRefGoogle Scholar
Bilson, M. & Bremhorst, K. 2007 Direct numerical simulation of turbulent Taylor–Couette flow. J. Fluid Mech. 579, 227–270.Google Scholar
Brauckmann, H. J. & Eckhardt, B. 2013 Direct numerical simulation of local and global torque in Taylor–Couette flow up to $Re = 30\, 000$ . J. Fluid Mech. 718, 398–427.Google Scholar
Burin, M. J., Schartman, E. & Ji, H. 2010 Local measurements of turbulent angular momentum transport in circular Couette flow. Exp. Fluids 48, 763–769.Google Scholar
Cliffe, K. A., Kobine, J. J. & Mullin, T. 1992 The role of anomalous modes in Taylor–Couette flow. Proc. R. Soc. Lond. A 439, 341–357.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Couette, M. 1890 Etudes sur le frottement des liquides. Ann. Chim. Phys. 6, 433–510.Google Scholar
Coughlin, K. & Marcus, P. S. 1996 Turbulent bursts in Couette–Taylor flow. Phys. Rev. Lett. 77, 2214–2217.Google Scholar
Czarny, O., Serre, E., Bontoux, P. & Lueptow, R. M. 2003 Interaction between Ekman pumping and centrifugal instability in Taylor–Couette flow. Phys. Fluids 15, 467–477.Google Scholar
Di Prima, R. C. & Swinney, H. L. 1981 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamics Instabilities and the Transition to Turbulence, Topics in Applied Physics, vol. 45, pp. 139–180. Springer.Google Scholar
Doering, C. R. & Constantin, P. 1992 Energy equation in shear driven turbulence. Phys. Rev. Lett. 69, 1648–1651.Google Scholar
Donnelly, R. J. & Simon, N. J. 1960 An empirical torque relation for supercritical flow between rotating cylinders. J. Fluid Mech. 7, 401–418.Google Scholar
Dubrulle, B., Dauchot, O., Daviaud, F., Longaretti, P.-Y., Richard, D. & Zahn, J.-P. 2005 Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data. Phys. Fluids 17, 95103.Google Scholar
Dutcher, C. S. & Muller, S. 2009 Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows. J. Fluid Mech. 641, 85–113.CrossRefGoogle Scholar
Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221–250.Google Scholar
Esser, A. & Grossmann, S. 1996 Analytic expression for Taylor–Couette stability boundary. Phys. Fluids 8, 1814–1819.Google Scholar
van Gils, D. P. M., Huisman, S. G., Bruggert, G.-W., Sun, C. & Lohse, D. 2011 Torque scaling in turbulent Taylor–Couette flow with co- and counterrotating cylinders. Phys. Rev. Lett. 106, 24502.Google Scholar
Gollub, J. P. & Swinney, H. L. 1975 Onset of turbulence in a rotating fluid. Phys. Rev. Lett. 35 (14), 927–930.CrossRefGoogle Scholar
Huisman, S. G., van Gils, D. P. M., Grossmann, S., Sun, C. & Lohse, D. 2012 Ultimate turbulent Taylor–Couette flow. Phys. Rev. Lett. 108, 24501.Google Scholar
Koschmieder, E. L. 1979 Turbulent Taylor vortex flow. J. Fluid Mech. 93, 515–527.Google Scholar
Lathrop, D. P., Fineberg, J. & Swinney, H. L. 1992 Transition to shear-driven turbulence in Couette–Taylor flow. Phys. Rev. A 46, 6390–6405.Google Scholar
Lewis, G. S. & Swinney, H. L. 1999 Velocity structure functions, scaling and transitions in high-Reynolds-number Couette–Taylor flow. Phys. Rev. E 59, 5457–5467.CrossRefGoogle ScholarPubMed
Lim, T. T. & Tan, K. S. 2004 A note on power-law scaling in a Taylor–Couette flow. Phys. Fluids 16, 140–144.Google Scholar
Mallock, A. 1888 Determination of the viscosity of water. Proc. R. Soc. Lond. 45, 126–132.Google Scholar
Merbold, S., Brauckmann, H. J. & Egbers, C. 2013 Torque measurements and numerical determination in differentially rotating wide gap Taylor–Couette flow. Phys. Rev. E 87, 23014.Google Scholar
Mullin, T. & Benjamin, T. B. 1980 Transition to oscillatory motion in the Taylor experiment. Nature 288, 567–659.CrossRefGoogle Scholar
Nakabayashi, K., Yamada, Y. & Kishimoto, T. 1982 Viscous frictional torque in the flow between two concentric rough cylinders. J. Fluid Mech. 119, 409–422.Google Scholar
Ostilla, R., Stevens, R. J. A. M., Grossmann, S., Verzicco, R. & Lohse, D. 2013 Optimal Taylor–Couette flow: direct numerical simulation. J. Fluid Mech. 719, 14–46.Google Scholar
Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R., Grossmann, S. & Lohse, D. 2014 Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor–Couette flow. Phys. Fluids 26, 015114.CrossRefGoogle Scholar
Paoletti, M. S. & Lathrop, D. P. 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106, 24501.Google Scholar
Pirró, D. & Quadrio, M. 2008 Direct numerical simulation of turbulent Taylor–Couette flow. Eur. J. Mech. (B/Fluids) 27, 552–566.CrossRefGoogle Scholar
Racina, A. & Kind, M. 2006 Specific power input and local micro mixing times in turbulent Taylor–Couette flow. Exp. Fluids 41, 513–522.CrossRefGoogle Scholar
Ravelet, F., Delfos, R. & Westerweel, J. 2010 Influence of global rotation and Reynolds number on the large-scale features of a Taylor–Couette flow. Phys. Fluids 22, 55103.Google Scholar
Riecke, H. & Paap, H.-G. 1986 Stability and wavevector restriction of axisymmetric Taylor vortex flow. Phys. Rev. A 33 (1), 547.Google Scholar
Snyder, H. A. 1969 Wavenumber selection at finite amplitude in rotating Couette flow. J. Fluid Mech. 35 (2), 273–298.CrossRefGoogle Scholar
Stuart, J. T. 1958 On the nonlinear mechanics of hydrodynamic stability. J. Fluid Mech. 4 (1), 1–21.CrossRefGoogle Scholar
Takeda, Y. 1999 Quasi-periodic state and transition to turbulence in a rotating Couette system. J. Fluid Mech. 389, 81–99.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343.Google Scholar
Taylor, G. I. 1936 Fluid fraction between rotating cylinders. I. Torque measurements. Proc. R. Soc. Lond. A 157, 546–564.Google Scholar
Tokgoz, S., Elsinga, G. E., Delfos, R. & Westerweel, J. 2012 Spatial resolution and dissipation rate estimation in Taylor–Couette flow for tomographic PIV. Exp. Fluids 53, 561–583.Google Scholar
Wendt, F. 1933 Turbulente Strömungen zwischen zwei rotierenden konaxialen Zylindern. Ing.-Arch. 4, 577–595.Google Scholar
Xiao, Q., Lim, T. T. & Chew, Y. T. 2002 Effect of acceleration on the wavy Taylor vortex flow. Exp. Fluids 32, 639–644.CrossRefGoogle Scholar