Skip to main content
Log in

Turbulent Taylor–Couette Flow at Large Reynolds Numbers*

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The problem of the steady-state turbulent flow of an incompressible fluid in the clearance between two coaxial infinite circular cylinders of radii R1 and R2, caused by the rotation of the inner cylinder of radius R1 under the conditions where the outer cylinder of radius R2 is immovable, i.e., the problem of a Taylor–Couette flow, was solved numerically within the framework of the model of a near-wall anisotropic turbulence with regard for the action of the centrifugal forces on the near-wall vortex structures determining the character of the flow between the cylinders. The profiles of the angular velocities of the fluid flowing along the radius of the clearance between the cylinders in the regime of completely developed turbulence were determined by numerical integration of the equation of motion of this fluid. The results of calculations of the flow between the cylinders at R1/R2 = 0.716 and Re = 105, 106, and 2·106 were compared with known solutions of the problem being considered and corresponding experimental data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. P. Smith and A. A. Townsend, Turbulent Couette flow between concentric cylinders at large Taylor numbers, J. Fluid Mech., 123, 187–217 (1982).

    Article  Google Scholar 

  2. A. Barcilon and J. Brindley, Organized structures in turbulent Taylor–Couette flow, J. Fluid Mech., 143, 429−449 (1984).

    Article  MATH  Google Scholar 

  3. S. Dong, Direct numerical simulation of turbulent Taylor–Couette flow, J. Fluid Mech., 587, 373–393 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Pirró and M. Quadrio, Direct numerical simulations of turbulent Taylor–Couette flow, Eur. J. Mech. B, Fluids, 27, No. 5, 552–556 (2008).

    Article  MATH  Google Scholar 

  5. D. P. M. van Gils, S. G. Huisman, S. Grossmann, C. Sun, and D. Lohse, Optimal Taylor–Couette turbulence, J. Fluid Mech., 706, 118–149 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Ostilla, R. J. A. M. Stevens, S. Grossman, R. Verzicco, and D. Lohse, Optimal Taylor–Couette flow: direct numerical simulations, J. Fluid Mech., 719, 14–46 (2013).

    Article  MATH  Google Scholar 

  7. S. Poncet, R. Da Soghe, C. Bianchini, S. Viazzo, and A. Aubert, Turbulent Couette–Taylor flows with end wall effects: A numerical benchmark, Int. J. Heat Fluid Flow, 44, 229–238 (2013).

    Article  Google Scholar 

  8. S. Grossmann, D. Lohse, and C. Sun, Velocity profiles in strongly turbulent Taylor–Couette fl ow (2013). Arxiv:1310.6196v1.

  9. A. Recktenwald, M. Lücke, and H. W. Müller, Taylor vortex formation in through flow: Linear and weakly nonlinear analysis, Phys. Rev. E, 48, 4444–4454 (1993).

    Article  Google Scholar 

  10. D. P. Lathrop, J. Fineberg, and H. L. Swinney, Turbulent flow between concentric rotating cylinders at large Reynolds number, Phys. Rev. Lett., 68, No. 10, 1515–1518 (1992).

    Article  Google Scholar 

  11. G. S. Lewis and H. L. Swinney, Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette–Taylor flow, Phys. Rev. E, 59, No. 5, 5457–5467 (1999).

    Article  Google Scholar 

  12. D. van Gils, S. G. Huisman, G.-W. Bruggert, C. Sun, and D. Lohse, Torque scaling in turbulent Taylor–Couette flow with co- and counterrotating cylinders, Phys. Rev. Lett., 106, 024502 (2011).

    Article  Google Scholar 

  13. S. A. Arsen’ev, V. A. Babkin, A. Yu. Gubar’, and V. N. Nikolaevskii, Theory of Mesoscale Turbulence. Vortices of the Atmosphere and the Ocean [in Russian], Inst. Komp. Issl. NITs “Regulyarnaya i Khaoticheskaya Dinamika,” Moscow–Izhevsk (2010).

  14. V. A. Babkin, Turbulent flow in the near-wall region as anisotropic-fluid flow, J. Eng. Phys. Thermophys., 75, No. 5, 69–73 (2002).

    Article  Google Scholar 

  15. V. A. Babkin, Fully developed turbulent Couette–Taylor flow, J. Eng. Phys. Thermophys., 87, No. 6, 1440–1447 (2014).

    Article  Google Scholar 

  16. S. G. Huisman, P. M. van Gils, S. Grossman, C. Sun, and D. Lohse, Ultimate turbulent Taylor–Couette flow, Phys. Rev. Lett., 108, 024501 (2012).

    Article  Google Scholar 

  17. A. E. Perry and M. S. Chong, On the mechanism of wall turbulence, J. Fluid Mech., 119, 173–217 (1982).

    Article  MATH  Google Scholar 

  18. B. Dubrulle and F. Hersant, Momentum transport and torque scaling in Taylor–Couette flow from analogy with turbulent convection, Eur. Phys. J. B., 26, 379–386 (2002).

    Google Scholar 

  19. S. G. Huisman, S. Scharnowski, C. Cierpka, C. Kähler, D. Lohse, and C. Sun, Logarithmic boundary layers in strong Taylor–Couette turbulence, Phys. Rev. Lett., 110, 264501 (2013).

  20. L. Labraga, B. Lagraa, A. Mazouz, and L. Keirsbulck, Propagation of shear-layer structures in the near-wall region of a turbulent boundary layer, Exp. Fluids, 33, 670–676 (2002).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Babkin.

Additional information

*The article is published as a discussion.

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 89, No. 5, pp. 1257–1264, September–October, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Babkin, V.A. Turbulent Taylor–Couette Flow at Large Reynolds Numbers* . J Eng Phys Thermophy 89, 1247–1254 (2016). https://doi.org/10.1007/s10891-016-1488-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-016-1488-3

Keywords

Navigation