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Direct numerical simulation of turbulent Taylor–Couette flow

  • S. DONG (a1)
Abstract

We investigate the dynamical and statistical features of turbulent Taylor–Couette flow (for a radius ratio 0.5) through three-dimensional direct numerical simulations (DNS) at Reynolds numbers ranging from 1000 to 8000. We show that in three-dimensional space the Görtler vortices are randomly distributed in banded regions on the wall, concentrating at the outflow boundaries of Taylor vortex cells, which spread over the entirecylinder surface with increasing Reynolds number. Görtler vortices cause streaky structures that form herringbone-like patterns near the wall. For the Reynolds numbers studied here, the average axial spacing of the streaks is approximately 100 viscous wall units, and the average tilting angle ranges from 16° to 20°. Simulationresults have been compared to the experimental data in the literature, and the flow dynamics and statistics are discussed in detail.

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del Alamo, J. C., Jimenez J., Zandonade P. & Moser R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.
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.
Barenghi C. F. & Jones C. A. 1989 Modulated Taylor-Couette flow. J. Fluid Mech. 208, 127160.
Batten W. M., 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. Method Fluids. 38, 207226.
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: J. Fluids Engng. 95, 122126.
Bilson M. & Bremhorst K. 2007 Direct numerical simulation of turbulent Taylor-Couette flow. J. Fluid Mech. 579, 227270.
Brandstater A. & Swinney H. L. 1987 Strange attractors in weakly turbulent Couette-Taylor flow. Phys. Rev. A 35, 22072220.
Cliffe K. A. & Mullin T. 1985 A numerical and experimental study of anomalous modes in the Taylor experiment. J. Fluid Mech. 153, 243258.
Coles D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385425.
Coughlin K. T. & Marcus P. S. 1992 a Modulated waves in Taylor-Couette flow Part 1. analysis. J. Fluid Mech. 234, 118.
Coughlin K. T. & Marcus P. S. 1992 b Modulated waves in Taylor-Couette flow Part 2. numerical simulation. J. Fluid Mech. 234, 1946.
Coughlin K. & Marcus P. S. 1996 Turbulent bursts in Couette-Taylor flow. Phys. Rev. Lett. 77, 22142217.
Coughlin K. T., Marcus P. S., Tagg R. P. & Swinney H. L. 1991 Distinct quasiperiodic modes with like symmetry in a rotating fluid. Phys. Rev. Lett. 66, 11611164.
Czarny O., Serre E., Bontoux P. & Lueptow R. M. 2004 Interaction of wavy cylindrical Couette flow with endwalls. Phys. Fluids. 16, 11401148.
DiPrima R. C. & Swinney H. L. 1981 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. Swinney H. L. & Gollub J. P.) pp. 139180. Springer.
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.
Donnelly R. J. & Simon N. J. 1959 An empirical torque relation for supercritical flow between rotating cylinders. J. Fluid Mech. 7, 401418.
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.
Fasel H. & Booz O. 1984 Numerical investigation of supercritical Taylor-vortex flow for a wide gap. J. Fluid Mech. 138, 2152.
Fernstermatcher P. R., Swinney H. L. & Gollub J. P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103128.
Görtler H. 1954 On the three-dimensional instability of laminar boundary layers on concave walls. NACA TM 1375.
Jeong J. & Hussain F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Jeong J., Hussain F., Schoppa W. & Kim J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185214.
Jones C. A. 1981 Nonlinear Taylor vortices and their stability. J. Fluid Mech. 102, 249261.
Jones C. A. 1982 On flow between counter-rotating cylinders. J. Fluid Mech. 120, 433450.
Jones C. A. 1985 The transition to wavy Taylor vortices. J. Fluid Mech. 157, 135162.
Karniadakis G. E., Israeli M. & Orszag S. A. 1991 High-order splitting methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 97, 414443.
Karniadakis G. E. & Sherwin S. J. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press.
Kim J., Moin P. & Moser R. 1987 Turbulent staistics in fully-developed channel flow at low reynolds-number. J. Fluid Mech. 177, 133166.
King G. P., Li Y., Lee W., Swiney H. L. & Marcus P. S. 1984 Wave speeds in wavy Taylor-vortex flow. J. Fluid Mech. 141, 365390.
Kirby R. M. & Karniadakis G. E. 2003 De-aliasing on non-uniform grids: algorithms and applications. J. Comput. Phys. 91, 249264.
Kline S. J., Reynolds W.C., Schraub F. A. & Runstadler P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.
Koschmieder E. L. 1979 Turbulent Taylor vortex flow. J. Fluid Mech. 93, 515527.
Lathrop D. P., Fineberg J. & Swinney H. L. 1992 a Transition to shear-driven turbulence in Couette-Taylor flow. Phys. Rev. A 46, 63906405.
Lathrop D. P., Fineberg J. & Swinney H. L. 1992 b Turbulent flow between concentric rotating cylinders at large reynolds number. Phys. Rev. Lett. 68, 15151518.
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.
Marcus P. S. 1984 a Simulation of Taylor-Couette flow. Part 1. numerical methods and comparison with experiment. J. Fluid Mech. 146, 4564.
Marcus P. S. 1984 b Simulation of Taylor-Couette flow. Part 2. numerical results for wavy-vortex flow with one travelling wave. J. Fluid Mech. 146, 65113.
Moser R. D. & Moin P. 1987 The effects of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479510.
Moulic S. G. & Yao L. S. 1996 Taylor-Couette instability of travelling waves with a continuous spectrum. J. Fluid Mech. 324, 181198.
Mujumdar A. K. & Spalding D. B. 1977 Numerical computation of Taylor vortices. J. Fluid Mech. 81, 295304.
Parker J. & Merati P. 1996 An investigation of turbulent Taylor-Couette flow using laser Doppler velocimetry in a refractive index matched facility. Trans. ASME: J. Fluids Engng. 118, 810818.
Racina A. & Kind M. 2006 Specific power and local micromixing times in turbulenct Taylor-Couette flow. Exps. Fluids. 41, 513522.
Rashidi M. & Banerjee S. 1990 The effect of boundary conditions and shear rate on streak formation and breakdown in turbulent channel flows. Phys. Fluids A 2, 18271838.
Riechelmann D. & Nanbu K. 1997 Three-dimensional simulation of wavy Taylor vortex flow by direct simulation Monte Carlo method. Phys. Fluids. 9, 811813.
Rigopoulos J., Sheridan J. & Thompson M. C. 2003 State selection in Taylor-Couette flow reached with an accelerated inner cylinder. J. Fluid Mech. 489, 7999.
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.
She Z.-S., Ren K., Lewis G. S. & Swinney H. L. 2001 Scalings and structures in turbulent Couette-Taylor flow. Phys. Rev. E 64, 016308.
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.
von Stamm, J., Gerdts U., Buzug T. & Pfister G. 1996 Symmetry breaking and period doubling on a torus in the VLF regime in Taylor-Couette flow. Phys. Rev. E 54, 49384957.
Swearingen J. D. & Blackwelder R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255.
Takeda Y. 1999 Quasi-periodic state and transition to turbulence in a rotating Couette system. J. Fluid Mech. 389, 8199.
Tam W. Y. & Swinney H. L. 1987 Mass transport in turbulent Couette-Taylor flow. Phys. Rev. A 36, 13741381.
Taylor G.I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289.
Tong P., Goldburg W. I., Huang J. S. & Witten T. A. 1990 Anisotropy in turbulent drag reduction. Phys. Rev. Lett. 65, 27802783.
Townsend A. A. 1984 Axisymmetric Couette flow at large Taylor numbers. J. Fluid Mech. 144, 329362.
Vastano J. A. & Moser R. D. 1991 Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow. J. Fluid Mech. 233, 83118.
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.
Wild P. M., Djilali N. & Vickers G. W. 1996 Experimental and computational assessment of windage losses in rotating machinery. Trans. ASME: J. Fluids Engng. 118, 116122.
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