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Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

  • S. DONG (a1)


We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.



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Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.
Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155183.
Antonijoan, J., Marques, F. & Sanchez, J. 1998 Non-linear spirals in the Taylor–Couette problem. Phys. Fluids 10, 829838.
Barcilon, A. & Brindley, J. 1984 Organized structures in turbulent Taylor–Couette flow. J. Fluid Mech. 143, 429449.
Barcilon, A., Brindley, J., Lessen, M. & Mobbs, F. R. 1979 Marginal instability in Taylor–Couette flows at a high Taylor number. J. Fluid Mech. 94, 453463.
Bech, K. H. & Andersson, H. I. 1997 Turbulent plane Couette flow subject to strong system rotation. J. Fluid Mech. 347, 289314.
Bech, K. H., Tillmark, N., Henrikalfredsson, P. & Andersson, H. I. 1995 An investigation of turbulent plane Couette flow at low Reynolds numbers. J. Fluid Mech. 286, 291325.
van den Berg, T. H., Doering, C. R., Lohse, D. & Lathrop, D. P. 2003 Smooth and rough boundaries in turbulent Taylor–Couette flow. Phys. Rev. E 68, 036307.
Bilgen, E. & Boulos, E. 1973 Functional dependence of torque coefficient of coaxial cylinders gap width and Reynolds numbers. Trans. ASME I: J. Fluids Engng 95, 122126.
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385425.
Colovas, P. W. & Andereck, C. D. 1997 Turbulent bursting and spatiotemporal intermittency in the counterrotating Taylor–Couette system. Phys. Rev. E 55, 27362741.
Coughlin, K. & Marcus, P. S. 1996 Turbulent bursts in Couette–Taylor flow. Phys. Rev. Lett. 77, 22142217.
Dong, S. 2007 Direct numerical simulation of turbulent Taylor–Couette flow. J. Fluid Mech. 587, 373393.
Dong, S. 2008 Herringbone streaks in Taylor–Couette turbulence. Phys. Rev. E 77, 035301.
Dong, S. & Karniadakis, G. E. 2004 Dual-level parallelism for high-order CFD methods. Parallel Comput. 30, 120.
Dong, S. & Karniadakis, G. E. 2005 DNS of flow past a stationary and oscillating cylinder at Re = 10000. J. Fluids Struct. 20, 519531.
Dong, S., Karniadakis, G. E., Ekmekci, A. & Rockwell, D. 2006 A combined direct numerical simulation–particle image velocimetry study of the turbulent near wake. J. Fluid Mech. 569, 185207.
Dong, S., Triantafyllou, G. S. & Karniadakis, G. E. 2008 Elimination of vortex streets in bluff-body flows. Phys. Rev. Lett. 100, 204501.
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, 095103.
Eckhardt, B., Grossman, S. & Lohse, D. 2000 Scaling of global momentum transport in Taylor–Couette and pipe flow. Eur. Phys. J. B 18, 541544.
Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221250.
Esser, A. & Grossman, S. 1996 Analytic expression for Taylor–Couette stability boundary. Phys. Fluids 8, 18141819.
Goharzadeh, A. & Mutabazi, I. 2001 Experimental characterization of intermittency regimes in the Couette–Taylor system. Eur. Phys. J. B 19, 157162.
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 2756.
Hegseth, J. J., Andereck, C. D., Hayot, F. & Pomeau, Y. 1989 Spiral turbulence and phase dynamics. Phy. Rev. Lett. 62, 257260.
Hoffmann, C., Lucke, M. & Pinter, A. 2004 Spiral vortices and Taylor vortices in the annulus between rotating cylinders and the effect of an axial flow. Phys. Rev. E 69, 056309.
Hoffmann, C., Lucke, M. & Pinter, A. 2005 Spiral vortices traveling between two rotating defects in Taylor–Couette system. Phys. Rev. E 72, 056311.
Hristova, H., Roch, S., Schmid, P. J. & Tuckerman, L. S. 2002 Transient growth in Taylor–Couette flow. Phys. Fluids 14, 34753484.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Karniadakis, G. E. & Sherwin, S. J. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn.Oxford University Press.
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414443.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.
Lewis, G. S. & Swinney, H. L. 1999 Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette–Taylor flow. Phys. Rev. E 59, 54575467.
Litschke, H. & Roesner, K. G. 1998 New experimental methods for turbulent spots and turbulent spirals in the Taylor–Couette flow. Exps. Fluids 24, 201209.
Panton, R. L. 2005 Incompressible Flow. John Wiley.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Prigent, A., Gregoire, G., Chate, H., Dauchot, O. & van Saarloos, W. 2002 Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501.
Racina, A. & Kind, M. 2006 Specific power and local micromixing times in turbulenct Taylor–Couette flow. Exps. Fluids 41, 513522.
Rayleigh, Lord 1916 On the dynamics of revolving fluids. Scientific Papers, vol. 6, pp. 447453.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601.
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379409.
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 2754.
Smith, G. P. & Townsend, A. A. 1982 Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mech. 123, 187217.
Tritton, D. J. 1988 Physical Fluid Dynamics. Oxford University Press.
Vaezi, V., Oh, E. S. & Aldredge, R. C. 1997 High-intensity turbulence measurements in a Taylor–Couette flow reactor. Expl Thermal Fluid Sci. 15, 424431.
Van Atta, C. 1966 Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495512.
Wei, T., Kline, E. M., Lee, S. H. K. & Woodruff, S. 1992 Görtler vortex formation at the inner cylinder in Taylor–Couette flow. J. Fluid Mech. 245, 4768.
Wendt, F. 1933 Turbulente stromungen zwischen zwei eorierenden konaxialen zylindem. Ing. Arch. 4, 577595.
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