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Wall-resolved and wall-modelled large-eddy simulation of plane Couette flow

Published online by Cambridge University Press:  21 January 2022

W. Cheng Open the ORCID record for W. Cheng [Opens in a new window] ,
D.I. Pullin  and
R. Samtaney Open the ORCID record for R. Samtaney [Opens in a new window]
W. Cheng*
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal23955-6900, Saudi Arabia Graduate Aerospace Laboratories, California Institute of Technology, CA91125, USA
D.I. Pullin
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, CA91125, USA
R. Samtaney
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal23955-6900, Saudi Arabia
*
†Email address for correspondence: wancheng@ustc.edu.cn
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Abstract

We describe wall-resolved and wall-modelled large-eddy simulation (LES) of plane Couette (PC) flow. Subgrid-scale (SGS) motion is represented using the stretched-spiral vortex SGS model and the virtual wall model is employed for wall-modelled LES. Cases studied include direct numerical simulation (DNS) at friction Reynolds numbers $Re_\tau = 220$, wall-resolved LES at $Re_\tau \sim 500\text {--}3600$ and wall-modelled LES at $Re_\tau \sim 3600\text {--}2.8\times 10^{5}$. All LES performed show the presence of approximately spanwise periodic sets of streamwise rolls. Averaged (including spanwise) wall-normal profiles of the mean streamwise velocity show a consistent log region across all Reynolds numbers. Two distinct measures of turbulent intensity are explored, one of which recognizes the roll structure and one that does not. The spanwise variation of turbulence flow metrics is investigated. Mean streamwise velocity profiles show substantial spanwise variation but collapse well when normalized by local skin-friction velocities. Similar collapse is found for streamwise turbulent intensities. For all present LES, the mean skin-friction variation with the plate Reynolds number is found to match a simple analytical form (Pirozzoli et al., J. Fluid Mech., vol. 758, 2014, pp. 327–343) while the scaled centre-plane, mean-velocity gradient exhibits an inverse ProductLog dependence. Both the mean-flow roll energy and circulation, scaled with outer variables, decrease monotonically for $Re_\tau \gtrsim 500$. At lower $Re_\tau$, the mean streamwise zero-velocity line follows a wavy form in the spanwise direction, while at our larger $Re_\tau$, a mushroom shape emerges which could potentially enhance local momentum transport in the spanwise direction and be responsible for the weakening of the spanwise rolls.

JFM classification

Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A19
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Avsarkisov, V., Hoyas, S., Oberlack, M. & García-Galache, J.P. 2014 Turbulent plane Couette flow at moderately high Reynolds number. J. Fluid Mech. 751, R1.CrossRefGoogle Scholar
Bae, H.J., Lozano-Durán, A., Bose, S.T. & Moin, P. 2019 Dynamic slip wall model for large-eddy simulation. J. Fluid Mech. 859, 400–432.CrossRefGoogle ScholarPubMed
Bech, K.H., Tillmark, N., Alfredsson, P.H. & Andersson, H.I. 1995 An investigation of turbulent plane Couette flow at low Reynolds numbers. J. Fluid Mech. 286, 291–325.CrossRefGoogle Scholar
Cheng, W., Pullin, D.I. & Samtaney, R. 2015 Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer. J. Fluid Mech. 785, 78–108.CrossRefGoogle Scholar
Cheng, W., Pullin, D.I. & Samtaney, R. 2020 Large-eddy simulation and modelling of Taylor–Couette flow. J. Fluid Mech. 890, A17.CrossRefGoogle Scholar
Cheng, W., Pullin, D.I., Samtaney, R., Zhang, W. & Gao, W. 2017 Large-eddy simulation of flow over a cylinder with $Re_D$ from $3.9\times 10^3$ to $8.5\times 10^5$: a skin-friction perspective. J. Fluid Mech. 820, 121–158.CrossRefGoogle Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman's estimates revisited. Phys. Fluids 24 (1), 011702.CrossRefGoogle Scholar
Chung, D. & Pullin, D.I. 2009 Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281–309.CrossRefGoogle Scholar
Gao, W., Cheng, W. & Samtaney, R. 2020 Large-eddy simulations of turbulent flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 900, A43.CrossRefGoogle Scholar
Hughes, T.J.R., Oberai, A.A. & Mazzei, L. 2001 Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys. Fluids 13 (6), 1784–1799.CrossRefGoogle Scholar
Inoue, M. & Pullin, D.I. 2011 Large-eddy simulation of the zero-pressure-gradient turbulent boundary layer up to $Re = O(10^{12})$. J. Fluid Mech. 686, 507–533.CrossRefGoogle Scholar
Kitoh, O., Nakabyashi, K. & Nishimura, F. 2005 Experimental study on mean velocity and turbulence characteristics of plane Couette flow: low-Reynolds-number effects and large longitudinal vortical structure. J. Fluid Mech. 539, 199–227.CrossRefGoogle Scholar
Kitoh, O. & Umeki, M. 2008 Experimental study on large-scale streak structure in the core region of turbulent plane Couette flow. Phys. Fluids 20 (2), 025107.CrossRefGoogle Scholar
Komminaho, J., Lundbladh, A. & Johansson, A.V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259–285.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to ${Re}_{{\tau }}\approx 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2018 Extreme-scale motions in turbulent plane Couette flows. J. Fluid Mech. 842, 128–145.CrossRefGoogle Scholar
Lundgren, T.S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193–2203.CrossRefGoogle Scholar
Misra, A. & Pullin, D.I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9, 2443–2454.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.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
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2011 Large-scale motions and inner/outer layer interactions in turbulent Couette–Poiseuille flows. J. Fluid Mech. 680, 534–563.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2014 Turbulence statistics in Couette flow at high Reynolds number. J. Fluid Mech. 758, 327–343.CrossRefGoogle Scholar
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7 (19), 1–16.CrossRefGoogle Scholar
Voelkl, T., Pullin, D.I. & Chan, D.C. 2000 A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids 228, 2426–2442.Google Scholar
Willert, C.E., Soria, J., Stanislas, M., Klinner, J., Amili, O., Eisfelder, M., Cuvier, C., Bellani, G., Fiorini, T. & Talamelli, A. 2017 Near-wall statistics of a turbulent pipe flow at shear Reynolds numbers up to 40 000. J. Fluid Mech. 826, R5.CrossRefGoogle Scholar
Yang, X.I.A., Sadique, J., Mittal, R. & Meneveau, C. 2015 Integral wall model for large eddy simulations of wall-bounded turbulent flows. Phys. Fluids 27 (2), 025112.CrossRefGoogle Scholar