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Disentangling the origins of torque enhancement through wall roughness in Taylor–Couette turbulence

Published online by Cambridge University Press:  22 December 2016

Xiaojue Zhu ,
Roberto Verzicco  and
Detlef Lohse
Xiaojue Zhu*
Affiliation:
Physics of Fluids Group, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands
Roberto Verzicco
Affiliation:
Physics of Fluids Group, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy
Detlef Lohse
Affiliation:
Physics of Fluids Group, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
*
†Email address for correspondence: xiaojue.zhu@utwente.nl
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Abstract

Direct numerical simulations (DNS) are performed to analyse the global transport properties of turbulent Taylor–Couette flow with inner rough wall up to Taylor number$Ta=10^{10}$. The dimensionless torque $Nu_{\unicode[STIX]{x1D714}}$ shows an effective scaling of $Nu_{\unicode[STIX]{x1D714}}\propto Ta^{0.42\pm 0.01}$, which is steeper than the ultimate regime effective scaling $Nu_{\unicode[STIX]{x1D714}}\propto Ta^{0.38}$ seen for smooth inner and outer walls. It is found that at the inner rough wall, the dominant contribution to the torque comes from the pressure forces on the radial faces of the rough elements; while viscous shear stresses on the rough surfaces contribute little to $Nu_{\unicode[STIX]{x1D714}}$. Thus, the log layer close to the rough wall depends on the roughness length scale, rather than on the viscous length scale. We then separate the torque contributed from the smooth inner wall and the rough outer wall. It is found that the smooth wall torque scaling follows $Nu_{s}\propto Ta_{s}^{0.38\pm 0.01}$, in excellent agreement with the case where both walls are smooth. In contrast, the rough wall torque scaling follows $Nu_{r}\propto Ta_{r}^{0.47\pm 0.03}$, very close to the pure ultimate regime scaling $Nu_{\unicode[STIX]{x1D714}}\propto Ta^{1/2}$. The energy dissipation rate at the wall of an inner rough cylinder decreases significantly as a consequence of the wall shear stress reduction caused by the flow separation at the rough elements. On the other hand, the latter shed vortices in the bulk that are transported towards the outer cylinder and dissipated. Compared to the purely smooth case, the inner wall roughness renders the system more bulk dominated and thus increases the effective scaling exponent.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 279 - 293
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Copyright
© 2016 Cambridge University Press 

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