Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-24T02:20:14.743Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  25 November 2008

S. DONG
S. DONG*
Affiliation:
Center for Computational and Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 615 , 25 November 2008 , pp. 371 - 399
Copyright
Copyright © Cambridge University Press 2008

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

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
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, 155–183.CrossRefGoogle Scholar
Antonijoan, J., Marques, F. & Sanchez, J. 1998 Non-linear spirals in the Taylor–Couette problem. Phys. Fluids 10, 829–838.CrossRefGoogle Scholar
Barcilon, A. & Brindley, J. 1984 Organized structures in turbulent Taylor–Couette flow. J. Fluid Mech. 143, 429–449.CrossRefGoogle Scholar
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, 453–463.CrossRefGoogle Scholar
Bech, K. H. & Andersson, H. I. 1997 Turbulent plane Couette flow subject to strong system rotation. J. Fluid Mech. 347, 289–314.CrossRefGoogle Scholar
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, 291–325.CrossRefGoogle Scholar
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.Google ScholarPubMed
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, 122–126.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Colovas, P. W. & Andereck, C. D. 1997 Turbulent bursting and spatiotemporal intermittency in the counterrotating Taylor–Couette system. Phys. Rev. E 55, 2736–2741.Google Scholar
Coughlin, K. & Marcus, P. S. 1996 Turbulent bursts in Couette–Taylor flow. Phys. Rev. Lett. 77, 2214–2217.CrossRefGoogle ScholarPubMed
Dong, S. 2007 Direct numerical simulation of turbulent Taylor–Couette flow. J. Fluid Mech. 587, 373–393.CrossRefGoogle Scholar
Dong, S. 2008 Herringbone streaks in Taylor–Couette turbulence. Phys. Rev. E 77, 035301.Google ScholarPubMed
Dong, S. & Karniadakis, G. E. 2004 Dual-level parallelism for high-order CFD methods. Parallel Comput. 30, 1–20.CrossRefGoogle Scholar
Dong, S. & Karniadakis, G. E. 2005 DNS of flow past a stationary and oscillating cylinder at Re = 10000. J. Fluids Struct. 20, 519–531.CrossRefGoogle Scholar
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, 185–207.CrossRefGoogle Scholar
Dong, S., Triantafyllou, G. S. & Karniadakis, G. E. 2008 Elimination of vortex streets in bluff-body flows. Phys. Rev. Lett. 100, 204501.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Eckhardt, B., Grossman, S. & Lohse, D. 2000 Scaling of global momentum transport in Taylor–Couette and pipe flow. Eur. Phys. J. B 18, 541–544.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.CrossRefGoogle Scholar
Esser, A. & Grossman, S. 1996 Analytic expression for Taylor–Couette stability boundary. Phys. Fluids 8, 1814–1819.CrossRefGoogle Scholar
Goharzadeh, A. & Mutabazi, I. 2001 Experimental characterization of intermittency regimes in the Couette–Taylor system. Eur. Phys. J. B 19, 157–162.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Hegseth, J. J., Andereck, C. D., Hayot, F. & Pomeau, Y. 1989 Spiral turbulence and phase dynamics. Phy. Rev. Lett. 62, 257–260.CrossRefGoogle ScholarPubMed
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.Google ScholarPubMed
Hoffmann, C., Lucke, M. & Pinter, A. 2005 Spiral vortices traveling between two rotating defects in Taylor–Couette system. Phys. Rev. E 72, 056311.Google ScholarPubMed
Hristova, H., Roch, S., Schmid, P. J. & Tuckerman, L. S. 2002 Transient growth in Taylor–Couette flow. Phys. Fluids 14, 3475–3484.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Karniadakis, G. E. & Sherwin, S. J. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn.Oxford University Press.CrossRefGoogle Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle 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.Google ScholarPubMed
Litschke, H. & Roesner, K. G. 1998 New experimental methods for turbulent spots and turbulent spirals in the Taylor–Couette flow. Exps. Fluids 24, 201–209.CrossRefGoogle Scholar
Panton, R. L. 2005 Incompressible Flow. John Wiley.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Racina, A. & Kind, M. 2006 Specific power and local micromixing times in turbulenct Taylor–Couette flow. Exps. Fluids 41, 513–522.CrossRefGoogle Scholar
Rayleigh, Lord 1916 On the dynamics of revolving fluids. Scientific Papers, vol. 6, pp. 447–453.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601.CrossRefGoogle Scholar
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409.CrossRefGoogle Scholar
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, 27–54.CrossRefGoogle Scholar
Smith, G. P. & Townsend, A. A. 1982 Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mech. 123, 187–217.CrossRefGoogle Scholar
Tritton, D. J. 1988 Physical Fluid Dynamics. Oxford University Press.Google Scholar
Vaezi, V., Oh, E. S. & Aldredge, R. C. 1997 High-intensity turbulence measurements in a Taylor–Couette flow reactor. Expl Thermal Fluid Sci. 15, 424–431.CrossRefGoogle Scholar
Van Atta, C. 1966 Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.CrossRefGoogle Scholar
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, 47–68.CrossRefGoogle Scholar
Wendt, F. 1933 Turbulente stromungen zwischen zwei eorierenden konaxialen zylindem. Ing. Arch. 4, 577–595.CrossRefGoogle Scholar