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Near-wall numerical coherent structures and turbulence generation in wall-modelled large-eddy simulation

Published online by Cambridge University Press:  22 August 2023

Hirotaka Maeyama Open the ORCID record for Hirotaka Maeyama [Opens in a new window]  and
Soshi Kawai Open the ORCID record for Soshi Kawai [Opens in a new window]
Hirotaka Maeyama*
Affiliation:
Department of Aerospace Engineering, Tohoku University, 6-6-01, Aramaki-aza-Aoba, Aoba-ku, Sendai, Japan
Soshi Kawai
Affiliation:
Department of Aerospace Engineering, Tohoku University, 6-6-01, Aramaki-aza-Aoba, Aoba-ku, Sendai, Japan
*
†Email address for correspondence: hirotaka.maeyama.b5@tohoku.ac.jp
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Abstract

Near-wall turbulence structures and generation in the wall-modelled large-eddy simulation (WMLES) are revealed. To elucidate the turbulence structures driving a near-wall turbulence generation in the WMLES, flat-plate turbulent boundary-layer flows calculated by the WMLES and direct numerical simulation (DNS) are closely investigated. A conditional-averaging technique is applied to the instantaneous flow fields and the near-wall statistical structures of the ejection and sweep pairs, which produce the turbulence, are revealed to exist even in the WMLES although the structures are non-physically elongated compared with those obtained by the DNS. Since the near-wall turbulence structures in the WMLES are revealed not to be disordered, but to be coherent structures with low- and high-speed fluids alternating in the spanwise direction, it is suggested that the near-wall turbulence generation in the WMLES is explained by the numerically elongated coherent structures. Furthermore, the Reynolds number effects of wall-bounded turbulent flows, i.e. the appearance of the outer peak in the energy spectrum of the streamwise velocity fluctuations at increasing Reynolds numbers, is found not to be reproduced by the WMLES, and the origin of the outer peak is discussed in association with the inner–outer-layer interactions. The near-wall turbulence structures in the WMLES could depend heavily on the computational grids and the numerical methods. Therefore, additional cases varying the grid resolutions and the numerical methods (numerical schemes and sub-grid-scale models) are also conducted to confirm the consistency of the present conclusions.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 969 , 25 August 2023 , A29
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Adrian, R.J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Asada, H., Tamaki, Y., Takaki, R., Yumitori, T., Tamura, S., Hatanaka, K., Imai, K., Maeyama, H. & Kawai, S. 2023 FFVHC-ACE: fully automated Cartesian-grid-based solver for compressible large-eddy simulation. AIAA J., 61 (8), 1–19.Google 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
Bermejo-Moreno, I., Campo, L., Larsson, J., Bodart, J., Helmer, D. & Eaton, J.K. 2014 Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations. J. Fluid Mech. 758, 5–62.CrossRefGoogle Scholar
Bernardini, M. & Pirozzoli, S. 2011 Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys. Fluids 23 (6), 061701.CrossRefGoogle Scholar
Blackwelder, R.F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94 (3), 577–594.CrossRefGoogle Scholar
Blackwelder, R.F. & Kaplan, R.E. 1976 On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76 (1), 89–112.CrossRefGoogle Scholar
Bogard, D.G. & Tiederman, W.G. 1986 Burst detection with single-point velocity measurements. J. Fluid Mech. 162, 389–413.CrossRefGoogle Scholar
Bose, S.T. & Moin, P. 2014 A dynamic slip boundary condition for wall-modeled large-eddy simulation. Phys. Fluids 26 (1), 015104.CrossRefGoogle Scholar
Bose, S.T. & Park, G.I. 2018 Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mech. 50, 535.CrossRefGoogle ScholarPubMed
Brown, G.L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.CrossRefGoogle Scholar
Chapman, D.R. 1979 Computational aerodynamics development and outlook. AIAA J. 17 (12), 1293–1313.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
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.CrossRefGoogle Scholar
Chung, D. & McKeon, B.J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341–364.CrossRefGoogle Scholar
Coleman, G.N., Kim, J. & Moser, R.D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
Corino, E.R. & Brodkey, R.S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37 (1), 1–30.CrossRefGoogle Scholar
De Graaff, D.B. & Eaton, J.K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Deardorff, J.W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41 (2), 453–480.CrossRefGoogle Scholar
Fukushima, Y. & Kawai, S. 2018 Wall-modeled large-eddy simulation of transonic airfoil buffet at high Reynolds number. AIAA J. 56 (6), 2372–2388.CrossRefGoogle Scholar
Gaitonde, D.V. & Visbal, M.R. 2000 Pade-type higher-order boundary filters for the Navier–Stokes equations. AIAA J. 38 (11), 2103–2112.CrossRefGoogle Scholar
Gottlieb, S. & Shu, C.-W. 1998 Total variation diminishing Runge–Kutta schemes. Math. Comput. 67 (221), 73–85.CrossRefGoogle Scholar
Hama, F.R., Long, J.D. & Hegarty, J.C. 1957 On transition from laminar to turbulent flow. J. Appl. Phys. 28 (4), 388–394.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
Head, M.R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re_\tau =2003$. Phys. Fluids 18 (1), 011702.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hwang, Y. 2013 Near-wall turbulent fluctuations in the absence of wide outer motions. J. Fluid Mech. 723, 264–288.CrossRefGoogle Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842.CrossRefGoogle Scholar
Jiménez, J. 2022 The streaks of wall-bounded turbulence need not be long. J. Fluid Mech. 945, R3.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
Kamogawa, R., Tamaki, Y. & Kawai, S. 2023 Ordinary-differential-equation-based nonequilibrium wall modeling for large-eddy simulation. Phys. Rev. Fluids 8 (6), 064605.Google Scholar
Kawahara, G. & Kida, S. 2001 Periodic motion embedded in plane couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291–300.CrossRefGoogle Scholar
Kawai, S. 2019 Heated transcritical and unheated non-transcritical turbulent boundary layers at supercritical pressures. J. Fluid Mech. 865, 563–601.CrossRefGoogle Scholar
Kawai, S. & Larsson, J. 2012 Wall-modeling in large eddy simulation: length scales, grid resolution, and accuracy. Phys. Fluids 24 (1), 015105.CrossRefGoogle Scholar
Kawai, S. & Larsson, J. 2013 Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers. Phys. Fluids 25 (1), 015105.CrossRefGoogle Scholar
Kim, H.T., Kline, S.J. & Reynolds, W.C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50 (1), 133–160.CrossRefGoogle Scholar
Kim, J. 1985 Turbulence structures associated with the bursting event. Phys. Fluids 28 (1), 52–58.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
Kline, S.J., Reynolds, W.C., Schraub, F.A. & Runstadler, P.W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.CrossRefGoogle Scholar
Kuya, Y., Totani, K. & Kawai, S. 2018 Kinetic energy and entropy preserving schemes for compressible flows by split convective forms. J. Comput. Phys. 375, 823–853.CrossRefGoogle Scholar
Larsson, J., Kawai, S., Bodart, J. & Bermejo-Moreno, I. 2016 Large eddy simulation with modeled wall-stress: recent progress and future directions. Mech. Engng Rev. 3 (1), 15–00418.Google Scholar
Lele, S.K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.CrossRefGoogle Scholar
Lenormand, E., Sagaut, P. & Ta Phuoc, L. 2000 Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number. Int. J. Numer. Methods Fluids 32 (4), 369–406.3.0.CO;2-6>CrossRefGoogle Scholar
Lozano-Durán, A., Bose, S.T. & Moin, P. 2022 Performance of wall-modeled LES with boundary-layer-conforming grids for external aerodynamics. AIAA J. 60 (2), 747–766.CrossRefGoogle Scholar
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100–130.CrossRefGoogle Scholar
Lu, S.S. & Willmarth, W.W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60 (3), 481–511.CrossRefGoogle Scholar
Marusic, I., Baars, W.J. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner-outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.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., McKeon, B.J., Monkewitz, P.A., Nagib, H.M., Smits, A.J. & Sreenivasan, K.R. 2010 b Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.CrossRefGoogle Scholar
Marusic, I., Monty, J.P., Hultmark, M. & Smits, A.J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.CrossRefGoogle Scholar
Mäteling, E. & Schröder, W. 2022 Analysis of spatiotemporal inner-outer large-scale interactions in turbulent channel flow by multivariate empirical mode decomposition. Phys. Rev. Fluids 7 (3), 034603.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
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
Mettu, B.R. & Subbareddy, P.K. 2022 Wall-modeled large eddy simulation of high speed flows. AIAA J. 60 (7), 4302–4324.CrossRefGoogle Scholar
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429–455.CrossRefGoogle Scholar
Morgan, B., Larsson, J., Kawai, S. & Lele, S.K. 2011 Improving low-frequency characteristics of recycling/rescaling inflow turbulence generation. AIAA J. 49 (3), 582–597.CrossRefGoogle Scholar
Panton, R.L. 2001 Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37 (4), 341–383.CrossRefGoogle Scholar
Park, G.I. 2017 Wall-modeled large-eddy simulation of a high Reynolds number separating and reattaching flow. AIAA J. 55 (11), 3709–3721.CrossRefGoogle ScholarPubMed
Park, G.I. & Moin, P. 2014 An improved dynamic non-equilibrium wall-model for large eddy simulation. Phys. Fluids 26 (1), 37–48.CrossRefGoogle Scholar
Piomelli, U. 2008 Wall-layer models for large-eddy simulations. Prog. Aerosp. Sci. 44 (6), 437–446.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34 (1), 349–374.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2013 Probing high-Reynolds-number effects in numerical boundary layers. Phys. Fluids 25 (2), 021704.CrossRefGoogle Scholar
Robinson, S.K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91 (3), 99–164.2.3.CO;2>CrossRefGoogle Scholar
Smith, C.R. & Metzler, S.P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.CrossRefGoogle Scholar
Smits, A.J., McKeon, B.J. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Spalart, P.R. 1997 Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In Proceedings of First AFOSR International Conference on DNS/LES. Greyden Press.Google Scholar
Spalart, P.R. 2009 Detached-eddy simulation. Annu. Rev. Fluid Mech. 41 (1), 181–202.CrossRefGoogle Scholar
Swearingen, J.D. & Blackwelder, R.F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290.CrossRefGoogle Scholar
Tamaki, Y., Fukushima, Y., Kuya, Y. & Kawai, S. 2020 Physics and modeling of trailing-edge stall phenomena for wall-modeled large-eddy simulation. Phys. Rev. Fluids 5 (7), 074602.CrossRefGoogle Scholar
Tamaki, Y. & Kawai, S. 2021 Wall modeling for large-eddy simulation on non-body-conforming cartesian grids. Phys. Rev. Fluids 6 (11), 114603.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanisms of turbulence. In Proceedings of the 2nd Midwestern Conference on Fluid Mechanics, 1952.Google Scholar
Urbin, G. & Knight, D. 2001 Large-eddy simulation of a supersonic boundary layer using an unstructured grid. AIAA J. 39 (7), 1288–1295.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.CrossRefGoogle Scholar
Wallace, J.M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131–158.CrossRefGoogle Scholar
Wallace, J.M., Eckelmann, H. & Brodkey, R.S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54 (1), 39–48.CrossRefGoogle Scholar
Willmarth, W.W. & Lu, S.S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55 (1), 65–92.CrossRefGoogle Scholar
Yang, X.I.A. & Griffin, K.P. 2021 Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation. Phys. Fluids 33 (1), 015108.CrossRefGoogle Scholar
Yang, X.I.A., Park, G.I. & Moin, P. 2017 Log-layer mismatch and modeling of the fluctuating wall stress in wall-modeled large-eddy simulations. Phys. Rev. Fluids 2 (10), 104601.CrossRefGoogle ScholarPubMed
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
Yang, X.I.A., Urzay, J., Bose, S. & Moin, P. 2018 Aerodynamic heating in wall-modeled large-eddy simulation of high-speed flows. AIAA J. 56 (2), 731–742.CrossRefGoogle Scholar
Yang, X.I.A., Zafar, S., Wang, J.-X. & Xiao, H. 2019 Predictive large-eddy-simulation wall modeling via physics-informed neural networks. Phys. Rev. Fluids 4 (3), 034602.CrossRefGoogle Scholar
Zhou, Z., Xu, C.-X. & Jiménez, J. 2022 Interaction between near-wall streaks and large-scale motions in turbulent channel flows. J. Fluid Mech. 940, A23.CrossRefGoogle Scholar