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On the role of secondary motions in turbulent square duct flow

Published online by Cambridge University Press:  24 May 2018

Davide Modesti Open the ORCID record for Davide Modesti [Opens in a new window] ,
Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window] ,
Paolo Orlandi  and
Francesco Grasso
Davide Modesti*
Affiliation:
Cnam-Laboratoire DynFluid, 151 Boulevard de L’Hopital, 75013 Paris, France
Sergio Pirozzoli
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
Paolo Orlandi
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
Francesco Grasso
Affiliation:
Cnam-Laboratoire DynFluid, 151 Boulevard de L’Hopital, 75013 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

We use a direct numerical simulations (DNS) database for turbulent flow in a square duct up to bulk Reynolds number $Re_{b}=40\,000$ to quantitatively analyse the role of secondary motions on the mean flow structure. For that purpose we derive a generalized form of the identity of Fukagata, Iwamoto and Kasagi (FIK), which allows one to quantify the effect of cross-stream convection on the mean streamwise velocity, wall shear stress and bulk friction coefficient. Secondary motions are found to contribute approximately 6 % of the total friction, and to act as a self-regulating mechanism of turbulence whereby wall shear stress non-uniformities induced by corners are equalized, and universality of the wall-normal velocity profiles is established. We also carry out numerical experiments whereby the secondary motions are artificially suppressed, in which case their equalizing role is partially taken by the turbulent stresses.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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