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A POD-mode-augmented wall model and its applications to flows at non-equilibrium conditions

Published online by Cambridge University Press:  16 November 2023

Christoffer Hansen ,
Xiang I.A. Yang Open the ORCID record for Xiang I.A. Yang [Opens in a new window]  and
Mahdi Abkar Open the ORCID record for Mahdi Abkar [Opens in a new window]
Christoffer Hansen
Affiliation:
Department of Mechanical and Production Engineering, Aarhus University, 8200 Aarhus N, Denmark
Xiang I.A. Yang*
Affiliation:
Department of Mechanical Engineering, Pennsylvania State University, State College, PA 16802, USA
Mahdi Abkar*
Affiliation:
Department of Mechanical and Production Engineering, Aarhus University, 8200 Aarhus N, Denmark
*
†Email addresses for correspondence: xzy48@psu.edu, abkar@mpe.au.dk
†Email addresses for correspondence: xzy48@psu.edu, abkar@mpe.au.dk
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Abstract

Insights gained from modal analysis are invoked for predictive large-eddy simulation (LES) wall modelling. Specifically, we augment the law of the wall (LoW) by an additional mode based on a one-dimensional proper orthogonal decomposition (POD) applied to a two-dimensional turbulent channel. The constructed wall model contains two modes, i.e. the LoW-based mode and the POD-based mode, and the model matches with the LES at two, instead of one, off-wall locations. To show that the proposed model captures non-equilibrium effects, we perform a priori and a posteriori tests in the context of both equilibrium and non-equilibrium flows. The a priori tests show that the proposed wall model captures extreme wall-shear stress events better than the equilibrium wall model. The model also captures non-equilibrium effects due to adverse pressure gradients. The a posteriori tests show that the wall model captures the rapid decrease and the initial decrease of the streamwise wall-shear stress in channels subjected to suddenly imposed adverse and transverse pressure gradients, respectively, both of which are missed by currently available wall models. These results show promise in applying modal analysis for turbulence wall modelling. In particular, the results show that employing multiple modes helps in the modelling of non-equilibrium flows.

JFM classification

Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 975 , 25 November 2023 , A24
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Abkar, M. & Moin, P. 2017 Large-eddy simulation of thermally stratified atmospheric boundary-layer flow using a minimum dissipation model. Boundary-Layer Meteorol. 165, 405–419.10.1007/s10546-017-0288-4CrossRefGoogle ScholarPubMed
Aubry, N., Holmes, P., Lumley, J.L. & Stone, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115–173.10.1017/S0022112088001818CrossRefGoogle 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, 400–432.10.1017/jfm.2018.838CrossRefGoogle ScholarPubMed
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.10.1146/annurev.fl.25.010193.002543CrossRefGoogle Scholar
Bose, S. & Moin, P. 2014 A dynamic slip boundary condition for wall-modeled large-eddy simulation. Phys. Fluids 26, 015104.10.1063/1.4849535CrossRefGoogle Scholar
Bose, S.T. & Park, G.I. 2018 Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mech. 50, 535–561.CrossRefGoogle ScholarPubMed
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17, 025105.10.1063/1.1839152CrossRefGoogle Scholar
Chen, P.E., Lv, Y., Xu, H.H., Shi, Y. & Yang, X.I.A. 2022 LES wall modeling for heat transfer at high speeds. Phys. Rev. Fluids 7 (1), 014608.10.1103/PhysRevFluids.7.014608CrossRefGoogle Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman's estimates revisited. Phys. Fluids 24, 011702.10.1063/1.3676783CrossRefGoogle Scholar
De Vanna, F., Cogo, M., Bernardini, M., Picano, F. & Benini, E. 2021 Unified wall-resolved and wall-modeled method for large-eddy simulations of compressible wall-bounded flows. Phys. Rev. Fluids 6 (3), 034614.10.1103/PhysRevFluids.6.034614CrossRefGoogle Scholar
Fowler, M., Zaki, T.A. & Meneveau, C. 2022 A Lagrangian relaxation towards equilibrium wall model for large eddy simulation. J. Fluid Mech. 934, A44.10.1017/jfm.2021.1156CrossRefGoogle Scholar
Goc, K.A., Lehmkuhl, O., Park, G.I., Bose, S.T. & Moin, P. 2021 Large eddy simulation of aircraft at affordable cost: a milestone in computational fluid dynamics. Flow 1, E14.10.1017/flo.2021.17CrossRefGoogle Scholar
Graham, J., et al. 2016 A web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES. J. Turbul. 17 (2), 181–215.10.1080/14685248.2015.1088656CrossRefGoogle Scholar
He, S. & Seddighi, M. 2015 Transition of transient channel flow after a change in Reynolds number. J. Fluid Mech. 764, 395–427.10.1017/jfm.2014.698CrossRefGoogle Scholar
Holmes, P., Lumley, J.L., Berkooz, G. & Rowley, C.W. 2012 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.10.1017/CBO9780511919701CrossRefGoogle Scholar
Kawai, S. & Larsson, J. 2012 Wall-modeling in large eddy simulation: length scales, grid resolution, and accuracy. Phys. Fluids 24, 015105.10.1063/1.3678331CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.10.1017/S0022112087000892CrossRefGoogle 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
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to $Re_\tau \approx 5200$. J. Fluid Mech. 774, 395–415.10.1017/jfm.2015.268CrossRefGoogle Scholar
Lozano-Durán, A., Giometto, M.G., Park, G.I. & Moin, P. 2020 Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers. J. Fluid Mech. 883, A20.10.1017/jfm.2019.869CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to $Re_\tau = 4200$. Phys. Fluids 26, 011702.10.1063/1.4862918CrossRefGoogle Scholar
Lv, Y., Huang, X.L.D., Yang, X. & Yang, X.I.A. 2021 Wall-model integrated computational framework for large-eddy simulations of wall-bounded flows. Phys. Fluids 33, 125120.10.1063/5.0073506CrossRefGoogle Scholar
Moin, P. & Moser, R.D. 1989 Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200, 471–509.10.1017/S0022112089000741CrossRefGoogle Scholar
Monty, J.P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Intl J. Heat Fluid Flow 32 (3), 575–585.10.1016/j.ijheatfluidflow.2011.03.004CrossRefGoogle Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379–405.10.1017/S002211209800189XCrossRefGoogle Scholar
Park, G.I. & Moin, P. 2014 An improved dynamic non-equilibrium wall-model for large eddy simulation. Phys. Fluids 26, 015108.CrossRefGoogle Scholar
Park, G.I. & Moin, P. 2016 Numerical aspects and implementation of a two-layer zonal wall model for LES of compressible turbulent flows on unstructured meshes. J. Comput. Phys. 305, 589–603.10.1016/j.jcp.2015.11.010CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374.CrossRefGoogle Scholar
Reichardt, H. 1951 Vollständige darstellung der turbulenten geschwindigkeitsverteilung in glatten leitungen. Z. Angew. Math. Mech. 31 (7), 208–219.CrossRefGoogle Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18 (4), 376–404.10.1016/0021-9991(75)90093-5CrossRefGoogle Scholar
Spalding, D.B. 1961 A single formula for the law of the wall. J. Appl. Mech. 28 (3), 455–458.CrossRefGoogle Scholar
Taira, K., Brunton, S.L., Dawson, S.T., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. & Ukeiley, L.S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.10.2514/1.J056060CrossRefGoogle Scholar
Volino, R.J. 2020 Non-equilibrium development in turbulent boundary layers with changing pressure gradients. J. Fluid Mech. 897, A2.CrossRefGoogle Scholar
Yang, X.I.A. & Abkar, M. 2018 A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers. J. Fluid Mech. 842, 354–380.10.1017/jfm.2018.139CrossRefGoogle ScholarPubMed
Yang, X.I.A., Chen, P.E., Hu, R. & Abkar, M. 2022 Logarithmic-linear law of the streamwise velocity variance in stably stratified boundary layers. Boundary-Layer Meteorol. 183, 199–213.10.1007/s10546-021-00683-5CrossRefGoogle 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, 015108.CrossRefGoogle Scholar
Yang, X.I.A. & Lv, Y. 2018 A semi-locally scaled eddy viscosity formulation for LES wall models and flows at high speeds. Theor. Comput. Fluid Dyn. 32 (5), 617–627.10.1007/s00162-018-0471-3CrossRefGoogle 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, 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, 025112.10.1063/1.4908072CrossRefGoogle 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