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Controlling secondary flows in Taylor–Couette flow using stress-free boundary conditions

Published online by Cambridge University Press:  09 July 2021

Vignesh Jeganathan Open the ORCID record for Vignesh Jeganathan [Opens in a new window] ,
Kamran Alba Open the ORCID record for Kamran Alba [Opens in a new window]  and
Rodolfo Ostilla-Mónico Open the ORCID record for Rodolfo Ostilla-Mónico [Opens in a new window]
Vignesh Jeganathan
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX77204, USA
Kamran Alba
Affiliation:
Department of Engineering Technology, University of Houston, Houston, TX77204, USA
Rodolfo Ostilla-Mónico*
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX77204, USA
*
†Email address for correspondence: rostilla@central.uh.edu
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Abstract

Taylor–Couette (TC) flow, the flow between two independently rotating and co-axial cylinders, is commonly used as a canonical model for shear flows. Unlike plane Couette flow, pinned secondary flows can be found in TC flow. These are known as Taylor rolls and drastically affect the flow behaviour. We study the possibility of modifying these secondary structures using patterns of stress-free and no-slip boundary conditions on the inner cylinder. For this, we perform direct numerical simulations of narrow-gap TC flow with pure inner-cylinder rotation at four different shear Reynolds numbers up to $Re_s=3\times 10^4$. We find that one-dimensional azimuthal patterns do not have a significant effect on the flow topology, and that the resulting torque is a large fraction ($\sim$80 %–90 %) of torque in the fully no-slip case. One-dimensional axial patterns decrease the torque more, and for certain pattern frequency disrupt the rolls by interfering with the existing Reynolds stresses that generate secondary structures. For $Re\geq 10^4$, this disruption leads to a smaller torque than what would be expected from simple boundary layer effects and the resulting effective slip length and slip velocity. We find that two-dimensional checkerboard patterns have similar behaviour to azimuthal patterns and do not affect the flow or the torque substantially, but two-dimensional spiral inhomogeneities can move around the pinned secondary flows as they induce persistent axial velocities. We quantify the roll's movement for various angles and the widths of the spiral pattern, and find a non-monotonic behaviour as a function of pattern angle and pattern frequency.

JFM classification

Turbulent Flows: Turbulence control Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A17
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

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
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, 316–347.CrossRefGoogle Scholar
Bakhuis, D., Ezeta, R., Berghout, P., Bullee, P.A., Tai, D., Chung, D., Verzicco, R., Lohse, D., Huisman, S.G. & Sun, C. 2020 Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness. J. Fluid Mech. 883, A15.CrossRefGoogle Scholar
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, 491–511.CrossRefGoogle Scholar
Barros, J.M. & Christensen, K.T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748, R1.CrossRefGoogle Scholar
Brauckmann, H.J. & Eckhardt, B. 2013 Direct numerical simulations of local and global torque in Taylor–Couette flow up to $Re=30000$. J. Fluid Mech. 718, 398–427.CrossRefGoogle Scholar
Brauckmann, H., Salewski, M. & Eckhardt, B. 2015 Momentum transport in Taylor–Couette flow with vanishing curvature. J. Fluid Mech. 790, 419–452.CrossRefGoogle Scholar
Cheng, Y.P., Teo, C.J. & Khoo, B.C. 2009 Microchannel flows with superhydrophobic surfaces: effects of Reynolds number and pattern width to channel height ratio. Phys. Fluids 21 (12), 122004.CrossRefGoogle Scholar
Donnelly, R.J. 1991 Taylor–Couette flow: the early days. Phys. Today 44 (11), 32–39.CrossRefGoogle Scholar
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 (9), 095103.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
Einstein, H.A. & Li, H. 1958 Secondary currents in straight channels. EOS Trans. AGU 39 (6), 1085–1088.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High–Reynolds number Taylor–Couette turbulence. Ann. Rev. Fluid Mech. 48, 53–80.CrossRefGoogle Scholar
Hasegawa, Y., Frohnapfel, B. & Kasagi, N. 2011 Effects of spatially varying slip length on friction drag reduction in wall turbulence. J. Phys.: Conf. Ser. 318, 022028.Google Scholar
Huisman, S.G., Van, D.V., Roeland, C.A., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5, 3820.CrossRefGoogle ScholarPubMed
Jelly, T.O., Jung, S.Y. & Zaki, T.A. 2014 Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26 (9), 095102.CrossRefGoogle Scholar
Lathrop, D.P., Fineberg, J. & Swinney, H.L. 1992 Turbulent flow between concentric rotating cylinders at large Reynolds number. Phys. Rev. Lett. 68 (10), 1515.CrossRefGoogle ScholarPubMed
Lauga, E. & Stone, H.A. 2003 Effective slip in pressure-driven stokes flow. J. Fluid Mech. 489, 55–77.CrossRefGoogle Scholar
Naim, M.S. & Baig, M.F. 2019 Turbulent drag reduction in Taylor–Couette flows using different super-hydrophobic surface configurations. Phys. Fluids 31 (9), 095108.CrossRefGoogle Scholar
Nugroho, B., Hutchins, N. & Monty, J.P. 2013 Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness. Intl J. Heat Fluid Flow 41, 90–102.CrossRefGoogle Scholar
Ostilla-Mónico, R., van der Poel, E.P., Verzicco, R., Grossmann, S. & Lohse, D. 2014 Exploring the phase diagram of fully turbulent Taylor–Couette flow. J. Fluid Mech. 761, 1–26.CrossRefGoogle Scholar
Ostilla-Mónico, R., Verzicco, R., Grossmann, S. & Lohse, D. 2016 The near-wall region of highly turbulent Taylor–Couette flow. J. Fluid Mech. 788, 95–117.CrossRefGoogle Scholar
Ostilla-Mónico, R., Verzicco, R. & Lohse, D. 2015 Effects of the computational domain size on direct numerical simulations of Taylor–Couette turbulence with stationary outer cylinder. Phys. Fluids 27 (2), 025110.CrossRefGoogle Scholar
Ostilla-Mónico, R., Zhu, X., Spandan, V., Verzicco, R. & Lohse, D. 2017 Life stages of wall-bounded decay of Taylor–Couette turbulence. Phys. Rev. Fluid 2 (11), 114601.CrossRefGoogle Scholar
Ou, J., Perot, B. & Rothstein, J.P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16 (12), 4635–4643.CrossRefGoogle Scholar
Philip, J.R. 1972 a Flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23 (3), 353–372.CrossRefGoogle Scholar
Philip, J.R. 1972 b Integral properties of flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23 (6), 960–968.CrossRefGoogle Scholar
van der Poel, E.P., Ostilla-Mónico, R., Donners, J. & Verzicco, R. 2015 A pencil distributed finite difference code for strongly turbulent wall-bounded flows. Comput. Fluids 116, 10–16.CrossRefGoogle Scholar
Ripesi, P., Biferale, L., Sbragaglia, M. & Wirth, A. 2014 Natural convection with mixed insulating and conducting boundary conditions: low-and high-Rayleigh-number regimes. J. Fluid Mech. 742, 636–663.CrossRefGoogle Scholar
Sacco, F., Verzicco, R. & Ostilla-Mónico, R. 2019 Dynamics and evolution of turbulent Taylor rolls. J. Fluid Mech. 870, 970–987.CrossRefGoogle Scholar
Samaha, M.A., Vahedi Tafreshi, H. & Gad-el Hak, M. 2011 Modeling drag reduction and meniscus stability of superhydrophobic surfaces comprised of random roughness. Phys. Fluids 23 (1), 012001.CrossRefGoogle Scholar
Srinivasan, S., Kleingartner, J.A., Gilbert, J.B., Cohen, R.E., Milne, A.J.B. & McKinley, G.H. 2015 Sustainable drag reduction in turbulent taylor-couette flows by depositing sprayable superhydrophobic surfaces. Phys. Rev. Lett. 114 (1), 014501.CrossRefGoogle ScholarPubMed
Taylor, G.I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. R. Soc. Lond. A 104, 213–218.Google Scholar
Türk, S., Daschiel, G., Stroh, A., Hasegawa, Y. & Frohnapfel, B. 2014 Turbulent flow over superhydrophobic surfaces with streamwise grooves. J. Fluid Mech. 747, 186–217.CrossRefGoogle Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 123 (2), 402–414.CrossRefGoogle Scholar
Wang, F., Huang, S. & Xia, K. 2017 Thermal convection with mixed thermal boundary conditions: effects of insulating lids at the top. J. Fluid Mech. 817, R1.CrossRefGoogle Scholar
Watanabe, S., Mamori, H. & Fukagata, K. 2017 Drag-reducing performance of obliquely aligned superhydrophobic surface in turbulent channel flow. Fluid Dyn. Res. 49 (2), 025501.CrossRefGoogle Scholar
Watanabe, K., Udagawa, Y. & Udagawa, H. 1999 Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall. J. Fluid Mech. 381, 225–238.CrossRefGoogle Scholar
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 (2), 025111.CrossRefGoogle Scholar
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, 746–774.CrossRefGoogle Scholar

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