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Near-wall patch representation of wall-bounded turbulence

Published online by Cambridge University Press:  28 September 2020

Sean P. Carney Open the ORCID record for Sean P. Carney [Opens in a new window] ,
Björn Engquist  and
Robert D. Moser Open the ORCID record for Robert D. Moser [Opens in a new window]
Sean P. Carney
Affiliation:
Department of Mathematics, The University of Texas at Austin, TX78712, USA
Björn Engquist
Affiliation:
Department of Mathematics, The University of Texas at Austin, TX78712, USA Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, TX78712, USA
Robert D. Moser*
Affiliation:
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, TX78712, USA Department of Mechanical Engineering, The University of Texas at Austin, TX78712, USA
*
†Email address for correspondence: rmoser@oden.utexas.edu
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Abstract

Recent experimental and computational studies indicate that near-wall turbulent flows can be characterized by universal small-scale autonomous dynamics that is modulated by large-scale structures. We formulate numerical simulations of near-wall turbulence in a small domain localized to the boundary, whose size scales in viscous units. To mimic the environment in which the near-wall turbulence evolves, the formulation accounts for the flux of mean momentum through the upper boundary of the domain. Comparisons of the model's two-dimensional energy spectra and low-order single-point statistics with the corresponding quantities computed from direct numerical simulations indicate that it successfully captures the dynamics of the small-scale near-wall turbulence.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A23
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Abdulle, A., Weinan, E., Engquist, B. & Vanden-Eijnden, E. 2012 The heterogeneous multiscale method. Acta Numerica 21, 1–87.CrossRefGoogle Scholar
Aulery, F., Dupuy, D., Toutant, A., Bataille, F. & Zhou, Y. 2017 Spectral analysis of turbulence in anisothermal channel flows. Comput. Fluids 151, 115–131.CrossRefGoogle Scholar
Berendsen, H. J. C., Postma, J. P. M., van Gunsteren, W. F., DiNola, A. & Haak, J. R. 1984 Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81 (8), 3684–3690.CrossRefGoogle Scholar
Berselli, L. C., Iliescu, T. & Layton, W. J. 2006 Mathematics of Large Eddy Simulation of Turbulent Flows. Springer.Google Scholar
Borrell, G., Sillero, J. A. & Jiménez, J. 2013 A code for direct numerical simulation of turbulent boundary layers at high Reynolds numbers in BG/P supercomputers. Comput. Fluids 80, 37–43.CrossRefGoogle Scholar
Bose, S. T. & Park, G. I. 2018 Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mech. 50 (1), 535–561.CrossRefGoogle ScholarPubMed
Botella, O. & Shariff, K. 2003 B-spline methods in fluid dynamics. Intl J. Comput. Fluid Dyn. 17 (2), 133–149.CrossRefGoogle Scholar
Chin, C., Ng, H. C. H., Blackburn, H. M., Monty, J. P. & Ooi, A. 2015 Turbulent pipe flow at $Re_{\tau }\approx 1000$: a comparison of wall-resolved large-eddy simulation, direct numerical simulation and hot-wire experiment. Comput. Fluids 122, 26–33.CrossRefGoogle Scholar
Coleman, G. N., Garbaruk, A. & Spalart, P. R. 2015 Direct numerical simulation, theories and modelling of wall turbulence with a range of pressure gradients. Flow Turbul. Combust. 95 (2), 261–276.CrossRefGoogle Scholar
Colonius, T. 2004 Modeling artificial boundary conditions for compressible flow. Annu. Rev. Fluid Mech. 36, 315–345.CrossRefGoogle Scholar
Darcy, H. 1854 Recherches expérimentales rélatives au mouvement de l'eau dans les tuyeaux. Mém. Savants Etrang. Acad. Sci. Paris 17, 1–268.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.CrossRefGoogle Scholar
Hagen, G. H. L. 1839 Über den bewegung des wassers in engen cylindrischen röhren. Poggendorfs Annal. Physik Chemie 46, 423–42.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 647–664.Google ScholarPubMed
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Khujadze, G. & Oberlack, M. 2004 DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow. Theor. Comput. Fluid Dyn. 18, 391–411.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kwok, W. Y., Moser, R. D. & Jiménez, J. 2001 A critical evaluation of the resolution properties of B-spline and compact finite difference methods. J. Comput. Phys. 174 (2), 510–551.CrossRefGoogle Scholar
Lee, M., Malaya, N. & Moser, R. D. 2013 Petascale direct numerical simulation of turbulent channel flow on up to 786 K cores. In The International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 1–11. ACM Press.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to $Re_{\tau }= 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lee, M. & Moser, R. D. 2017 Large-scale motions in turbulent Poiseuille and Couette flows. In Tenth International Symposium on Turbulence and Shear Flow Phenomena. TSFP.Google Scholar
Lee, M. & Moser, R. D. 2019 Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech. 860, 886–938.CrossRefGoogle Scholar
Lee, M., Ulerich, R., Malaya, N. & Moser, R. D. 2014 Experiences from leadership computing in simulations of turbulent fluid flows. Comput. Sci. Engng 16 (5), 24–31.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 a High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31 (3), 418–428.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 b Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.CrossRefGoogle ScholarPubMed
Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.CrossRefGoogle Scholar
Millikan, C. B. 1938 A critical discussion of turbulent flows in channels and circular tubes. In Proceedings of the Fifth International Congress for Applied Mechanics, pp. 386–392.Google Scholar
Mizuno, Y. 2015 Spectra of turbulent energy transport in channel flows. In 15th European Turbulence Conference. European Mechanics Society.Google Scholar
Mizuno, Y. 2016 Spectra of energy transport in turbulent channel flows for moderate Reynolds numbers. J. Fluid Mech. 805, 171–187.CrossRefGoogle Scholar
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429–455.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Oliver, T. A., Malaya, N., Ulerich, R. & Moser, R. D. 2014 Estimating uncertainties in statistics computed from direct numerical simulation. Phys. Fluids 26, 035101.CrossRefGoogle Scholar
Pascarelli, A., Piomelli, U. & Candler, G. V. 2000 Multi-block large-eddy simulations of turbulent boundary layers. J. Comput. Phys. 157 (1), 256–279.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34 (1), 349–374.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Reynolds, O. 1895 On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. R. Soc. Lond. A 186, 123–164.Google Scholar
Richter, D. H. 2015 Turbulence modification by inertial particles and its influence on the spectral energy budget in planar Couette flow. Phys. Fluids 27 (6), 063304.CrossRefGoogle Scholar
Sagaut, P., Deck, S. & Terracol, M. 2006 Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press.CrossRefGoogle Scholar
Samie, M., Marusic, I., Hutchins, N., Fu, M. K., Fan, Y., Hultmark, M. & Smits, A. J. 2018 Fully resolved measurements of turbulent boundary layer flows up to $Re_{\tau }=20\,000$. J. Fluid Mech. 851, 391–415.CrossRefGoogle Scholar
Sandham, N. D., Johnstone, R. & Jacobs, C. T. 2017 Surface-sampled simulations of turbulent flow at high Reynolds number. Intl J. Numer. Meth. Fluids 85 (9), 525–537.CrossRefGoogle Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to $\delta ^+\approx 2000$. Phys. Fluids 25 (10), 105102.CrossRefGoogle Scholar
Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228 (11), 4218–4231.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to $Re_{\theta }=1410$. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297–324.CrossRefGoogle Scholar
Tang, Y. & Akhavan, R. 2016 Computations of equilibrium and non-equilibrium turbulent channel flows using a nested-LES approach. J. Fluid Mech. 793, 709–748.CrossRefGoogle Scholar
Topalian, V., Oliver, T. A., Ulerich, R. & Moser, R. D. 2017 Temporal slow-growth formulation for direct numerical simulation of compressible wall-bounded flows. Phys. Rev. Fluids 2 (8), 084602.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar
Yong, X. & Zhang, L. T. 2013 Thermostats and thermostat strategies for molecular dynamics simulations of nanofluidics. J. Chem. Phys. 138 (8), 084503.CrossRefGoogle ScholarPubMed