Skip to main content Accessibility help
×
Home

Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness

  • Dennis Bakhuis (a1), Rodrigo Ezeta (a1), Pieter Berghout (a1), Pim A. Bullee (a1) (a2), Dominic Tai (a1), Daniel Chung (a3), Roberto Verzicco (a1) (a4), Detlef Lohse (a1) (a5), Sander G. Huisman (a1) and Chao Sun (a1) (a6) (a7)...

Abstract

Highly turbulent Taylor–Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations with an immersed boundary method) to determine the effects of the spacing and spanwise width $s$ of the spanwise-varying roughness on the total drag and on the flow structures. We apply sandgrain roughness, in the form of alternating rough and smooth bands to the inner cylinder. Numerically, the Taylor number is $O(10^{9})$ and the roughness width is varied in the range $0.47\leqslant \tilde{s}=s/d\leqslant 1.23$ , where $d$ is the gap width. Experimentally, we explore $Ta=O(10^{12})$ and $0.61\leqslant \tilde{s}\leqslant 3.74$ . For both approaches the radius ratio is fixed at $\unicode[STIX]{x1D702}=r_{i}/r_{o}=0.716$ , with $r_{i}$ and $r_{o}$ the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing $\tilde{s}$ . Both numerically and experimentally, we find a maximum in the angular momentum transport as a function of $\tilde{s}$ . This can be attributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness
      Available formats
      ×

Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: chaosun@tsinghua.edu.cn

References

Hide All
Anderson, W., Barros, J. M., Christensen, K. T. & Awasthi, A. 2015 Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness. J. Fluid Mech. 768, 316347.
Bakhuis, D., Ostilla Mónico, R., van der Poel, E. P., Verzicco, R. & Lohse, D. 2018 Mixed insulating and conducting thermal boundary conditions in Rayleigh–Bénard convection. J. Fluid Mech. 835, 491511.
Barros, J. M. & Christensen, K. T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748, R1.
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.
Berghout, P., Zhu, X., Chung, D., Verzicco, R., Stevens, R. J. A. M. & Lohse, D. 2019 Direct numerical simulations of Taylor–Couette turbulence: the effect of sand grain roughness. J. Fluid Mech. 873, 260286.
Bradshaw, P. 1987 Turbulent secondary flows. Annu. Rev. Fluid Mech. 19, 5374.
Brauckmann, H. J. & Eckhardt, B. 2013 Intermittent boundary layers and torque maxima in Taylor–Couette flow. Phys. Rev. E 87, 033004.
Cadot, O., Couder, Y., Daerr, A., Douady, S. & Tsinober, A. 1997 Energy injection in closed turbulent flows: stirring through boundary layers versus inertial stirring. Phys. Rev. E 56, 427433.
Chouippe, A., Climent, E., Legendre, D. & Gabillet, C. 2014 Numerical simulation of bubble dispersion in turbulent Taylor–Couette flow. Phys. Fluids 26, 043304.
Chung, D., Monty, J. P. & Hutchins, N. 2018 Similarity and structure of wall turbulence with lateral wall shear stress variations. J. Fluid Mech. 847, 591613.
Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221250.
Fadlun, E., Verzicco, R., Orlandi, P. & Mohd-Yusof, J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 3560.
Flack, K. A. & Schultz, M. P. 2010 Review of hydraulic roughness scales in the fully rough regime. Trans. ASME J. Fluids Engng 132, 041203.
van Gils, D. P., Bruggert, G.-W., Lathrop, D. P., Sun, C. & Lohse, D. 2011 The Twente turbulent Taylor–Couette (T3C) facility: strongly turbulent (multiphase) flow between independently rotating cylinders. Rev. Sci. Instrum. 82, 025105.
van Gils, D. P. M., Huisman, S. G., Grossmann, S., Sun, C. & Lohse, D. 2012 Optimal Taylor–Couette turbulence. J. Fluid Mech. 706, 118149.
Grossmann, S., Lohse, D. & Sun, C. 2014 Velocity profiles in strongly turbulent Taylor–Couette flow. Phys. Fluids 26, 025114.
Grossmann, S., Lohse, D. & Sun, C. 2016 High–Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 5380.
Gul, M., Elsinga, G. E. & Westerweel, J. 2017 Experimental investigation of torque hysteresis behaviour of Taylor–Couette flow. J. Fluid Mech. 836, 635648.
Hama, F. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Archit. Mar. Engrs 62, 333358.
Hinze, J. O. 1967 Secondary currents in wall turbulence. Phys. Fluids 10, S122.
Hinze, J. O. 1973 Experimental investigation on secondary currents in the turbulent flow through a straight conduit. Appl. Sci. Res. 28, 453465.
Huisman, S. G., van Gils, D. P. & Sun, C. 2012 Applying laser Doppler anemometry inside a Taylor–Couette geometry using a ray-tracer to correct for curvature effects. Eur. J. Mech. (B/Fluids 36, 115119.
Huisman, S. G., van der Veen, R. C., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Comm. 5, 3820.
Iaccarino, G. & Verzicco, R. 2003 Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 56, 331347.
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Koeltzsch, K., Dinkelacker, A. & Grundmann, R. 2002 Flow over convergent and divergent wall riblets. Exp. Fluids 33, 346350.
Kraichnan, R. H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5, 1374.
Lathrop, D. P., Fineberg, J. & Swinney, H. L. 1992 Turbulent flow between concentric rotating cylinders at large Reynolds number. Phys. Rev. Lett. 68, 1515.
Medjnoun, T., Vanderwel, C. & Ganapathisubramani, B. 2018 Characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. J. Fluid Mech. 838, 516543.
Mejia-Alvarez, R. & Christensen, K. T. 2013 Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness. Phys. Fluids 25, 115109.
Nikuradse, J.1933 Strömungsgesetze in rauhen rohren. VDI-Forsch. 361 (English translation: Laws of flow in rough pipes. NACA Tech. Mem. 1292 (1950)).
Nugroho, B., Hutchins, N. & Monty, J. 2013 Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness. Intl J. Heat Fluid Flow 41, 90102.
Ostilla-Mónico, R., Huisman, S. G., Jannink, T. J. G., Van Gils, D. P. M., Verzicco, R., Grossmann, S., Sun, C. & Lohse, D. 2014a Optimal Taylor–Couette flow: radius ratio dependence. J. Fluid Mech. 747, 129.
Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R., Grossmann, S. & Lohse, D. 2014b Exploring the phase diagram of fully turbulent Taylor–Couette flow. J. Fluid Mech. 761, 126.
Ostilla-Mónico, R., van der Poel, R. P., Verzicco, R., Grossmann, S. & Lohse, D. 2014c Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor–Couette flow. Phys. Fluids 26, 015114.
Ostilla-Mónico, R., Verzicco, R. & Lohse, D. 2015 Effects of the computational domain size on dns of Taylor–Couette turbulence with stationary outer cylinder. Phys. Fluids 27, 025110.
Paoletti, M. S. & Lathrop, D. P. 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106, 024501.
Ren, H. & Wu, Y. 2011 Turbulent boundary layers over smooth and rough forward-facing steps. Phys. Fluids 23, 045102.
Schultz, M. P. 2007 Effects of coating roughness and biofouling on ship resistance and powering. Biofouling 23, 331341.
Stringano, G., Pascazio, G. & Verzicco, R. 2006 Turbulent thermal convection over grooved plates. J. Fluid Mech. 557, 307336.
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Proc. R. Soc. Lond. A 102, 541542.
Townsend, A. A. R. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Vanderwel, C. & Ganapathisubramani, B. 2015 Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. J. Fluid Mech. 774, R2.
van der Veen, R. C. A., Huisman, S. G., Dung, O.-Y., Tang, H. L., Sun, C. & Lohse, D. 2016 Exploring the phase space of multiple states in highly turbulent Taylor–Couette flow. Phys. Rev. Fluids 1, 024401.
Wang, Z.-Q. & Cheng, N.-S. 2006 Time-mean structure of secondary flows in open channel with longitudinal bedforms. Adv. Water Resour. 29, 16341649.
Willingham, D., Anderson, W., Christensen, K. T. & Barros, J. M. 2014 Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization. Phys. Fluids 26, 025111.
Yang, J. & Anderson, W. 2017 Numerical study of turbulent channel flow over surfaces with variable spanwise heterogeneities: topographically-driven secondary flows affect outer-layer similarity of turbulent length scales. Flow Turbul. Combust. 100, 117.
Zhu, X., Ostilla-Mónico, R., Verzicco, R. & Lohse, D. 2016 Direct numerical simulation of Taylor–Couette flow with grooved walls: torque scaling and flow structure. J. Fluid Mech. 794, 746774.
Zhu, X., Verschoof, R. A., Bakhuis, D., Huisman, S. G., Verzicco, R., Sun, C. & Lohse, D. 2018 Wall roughness induces asymptotic ultimate turbulence. Nat. Phys. 14, 417423.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness

  • Dennis Bakhuis (a1), Rodrigo Ezeta (a1), Pieter Berghout (a1), Pim A. Bullee (a1) (a2), Dominic Tai (a1), Daniel Chung (a3), Roberto Verzicco (a1) (a4), Detlef Lohse (a1) (a5), Sander G. Huisman (a1) and Chao Sun (a1) (a6) (a7)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed