Analysis of Space-Time Correlations to Support the Development of Wall-Modeled LES

Boxho, Margaux; Rasquin, M.; Toulorge, T.; Dergham, G.; Winckelmans, G.; Hillewaert, Koen

doi:10.1007/s10494-022-00365-3

Download

Article (Scientific journals)

Analysis of Space-Time Correlations to Support the Development of Wall-Modeled LES

Boxho, Margaux; Rasquin, M.; Toulorge, T. et al.

2022 • In Flow, Turbulence and Combustion

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/295255

DOI
10.1007/s10494-022-00365-3

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

Boxho_SpaceTimeCorrelations_2022_Last_Version.pdf

Author postprint (7.34 MB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Physical and Theoretical Chemistry; General Physics and Astronomy; General Chemical Engineering

Abstract :

[en] Wall models reduce the computational cost of large eddy simulations (LES) by modeling the near-wall energetic scales and enable the application of LES to complex flow configurations of engineering interest. However, most wall models assume that the boundary layer is fully turbulent, at equilibrium, and attached. Such models have also been successfully applied to turbulent boundary layers under moderated adverse pressure gradients. When the adverse pressure gradient becomes too strong, and the boundary layer separates, equilibrium wall models are no longer applicable. In this work, the relations between the instantaneous wall shear stress, velocity field, and pressure gradients are evaluated using space-time correlations for the purpose of analyzing the near-wall physics in different flow configurations. These correlations are extracted from two wall-resolved LES: a channel flow at a friction Reynolds number Re$_\tau$ of 950 and the two-dimensional periodic hill at a bulk Reynolds number Re$_b$ of 10595. This analysis highlights that no instantaneous and local correlation is observed in the vicinity of the separation. The domain of high correlation appears to be shifted downstream. This study of the near-wall physics is a step for developing a data-driven wall model applied to separated flows and, in particular, selecting suitable input parameters for the training of neural networks.

Precision for document type :

Review article

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Boxho, Margaux ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Rasquin, M.; Cenaero

Toulorge, T.; Cenaero

Dergham, G.; Safran Tech

Winckelmans, G.; Ecole Polytechnique de Louvain > Institute of Mechanics, Materials and Civil Engineering (IMMC) > Thermodynamics and fluid mechanics

Hillewaert, Koen ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Design of Turbomachines

Language :

English

Title :

Analysis of Space-Time Correlations to Support the Development of Wall-Modeled LES

Publication date :

06 September 2022

Journal title :

Flow, Turbulence and Combustion

ISSN :

1386-6184

eISSN :

1573-1987

Publisher :

Springer Science and Business Media LLC

Peer reviewed :

Peer Reviewed verified by ORBi

Tags :

Tier-1 supercomputer

Additional URL :

https://link.springer.com/content/pdf/10.1007/s10494-022-00365-3.pdf

Funders :

Safran Tech

Available on ORBi :

since 29 September 2022

Statistics

Number of views

117 (36 by ULiège)

Number of downloads

58 (8 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Abel, M., Stojkovic, D., Breuer, M.: Nonlinear stochastic estimation of wall models for LES. Heat Fluid Flow 27(2), 267–278 (2006). 10.1016/j.ijheatfluidflow.2005.10.011 DOI: 10.1016/j.ijheatfluidflow.2005.10.011
Balaras, E., Benocci, C., Piomelli, U.: Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34(6), 1111–1119 (1996). 10.2514/3.13200 DOI: 10.2514/3.13200
Benocci, C., Pinelli, A.: The role of the forcing term in the large-eddy simulation of equilibrium channel flow. In: Rodi, W. (ed.) Engineering Turbulence Modeling and Experiments, pp. 287–296. Elsevier, Amsterdam (1990)
Bose, S.T., Park, G.I.: Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mecha. 50, 535–561 (2018). 10.1146/annurev-fluid-122316-045241 DOI: 10.1146/annurev-fluid-122316-045241
Breuer, M., Peller, N., Rapp, Ch., Manhart, M.: Flow over periodic hills - numerical and experimental study in a wide range of Reynolds numbers. Comput. Fluids 38(2), 433–457 (2009). 10.1016/j.compfluid.2008.05.002 DOI: 10.1016/j.compfluid.2008.05.002
Breuer, M., Kniazev, B., Abel, M.: Development of wall models for LES of separated flows using statistical evaluations. Comput. Fluids 36(5), 817–837 (2007). 10.1016/j.compfluid.2006.09.001 DOI: 10.1016/j.compfluid.2006.09.001
Brunton, S.L., Noack, B.R., Koumoutsakos, P.: Machine learning for fluid mechanics. Annu. Rev. Fluid Mech. 52, 477–508 (2020). 10.1146/annurev-fluid-010719-060214 DOI: 10.1146/annurev-fluid-010719-060214
Cadieux, F., Sadique, J., Yang, X. I., Meneveau, C., Mittal, R.: Wall-modeled large eddy simulation of laminar and turbulent separation bubble flows. In: 46th AIAA Fluid Dynamics Conference. AIAA 2016-3189. (2016). https://doi.org/10.2514/6.2016-3189
Carton de Wiart, C., Hillewaert, K., Bricteux, L., Winckelmans, G.: LES using a discontinuous Galerkin method: isotropic turbulence, channel flow and periodic hill flow. In: Fröhlich, J., Kuerten, H., Geurts, B., Armenio, V. (eds.) Direct and Large-Eddy Simulation IX. ERCOFTAC Series, vol. 20. Springer, Cham (2015). 10.1007/978-3-319-14448-1_13 DOI: 10.1007/978-3-319-14448-1_13
Carton de Wiart, C., Hillewaert, K., Bricteux, L., Winckelmans, G.: Implicit LES of free and wall bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method. Int. J. Numer. Methods Fluids 78(6), 335–354 (2014) DOI: 10.1002/fld.4021
Chaudhuri, A., Hu, W.: A fast algorithm for computing distance correlation. Comput. Stat. Data Anal. 135, 15–24 (2019). 10.1016/j.csda.2019.01.016 DOI: 10.1016/j.csda.2019.01.016
Cheng, C., Li, W., Lozano-Duran, A., Liu, H.: On the structure of streamwise wall-shear stress fluctuations in turbulent channel flows. J. Fluid Mech. 903, A29 (2020). 10.1017/jfm.2020.639 DOI: 10.1017/jfm.2020.639
Colella, K.J., Keith, W.L.: Measurements and scaling of wall shear stress fluctuations. Exp. Fluids 34, 253–260 (2003). 10.1007/s00348-002-0552-2 DOI: 10.1007/s00348-002-0552-2
Dawson, S.T.M., McKeon, B.J.: On the shape of resolvent modes in wall-bounded turbulence. J. Fluid Mech. 877, 682–716 (2019). 10.1017/jfm.2019.594 DOI: 10.1017/jfm.2019.594
Deardoff, J.W.: A numerical study of three-dimensional turbulence channel flow at large Reynolds numbers. J. Fluid Mech. 41(2), 453–480 (1970). 10.1017/S0022112070000691 DOI: 10.1017/S0022112070000691
Duraisamy, K., Iaccarino, G., Xiao, H.: Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51, 357–377 (2019) DOI: 10.1146/annurev-fluid-010518-040547
Edelmann, D., Mori, T.F., Székely, G.J.: On relationships between the Pearson and the distance correlation coefficients. Stat. Probab. Lett. 169, 108960 (2021). 10.1016/j.spl.2020.108960 DOI: 10.1016/j.spl.2020.108960
Frère, A.: Towards wall-modeled Large-Eddy Simulations of high Reynolds number airfoils using a Discontinuous Galerkin method (Unpublished doctoral dissertation). Université catholique de Louvain (2018)
Frère, A., Carton de Wiart, C., Hillewaert, K., Chatelain, P., Winckelmans, G.: Application of wall-models to discontinuous Galerkin LES channel flow. Phys. Fluids 9(8), 085111 (2017). 10.1063/1.4998977 DOI: 10.1063/1.4998977
Frère, A., Hillewaert, K., Chatelain, P., Winckelmans, G.: High Reynolds number airfoil: from wall-resolved to wall-modeled LES. Flow Turbul. Combust. 101, 457–476 (2018) DOI: 10.1007/s10494-018-9972-9
Fröhlich, J., Mellen, C.P., Rodi, W., Temmerman, L., Leschziner, M.A.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005). 10.1017/S0022112004002812 DOI: 10.1017/S0022112004002812
Gloerfelt X., Cinnella P.: Investigation of the flow dynamics in a channel constricted by periodic hills. In: 45th AIAA Fluid Dynamics Conference. Dallas. United States. 2015-2480 (2015). https://doi.org/10.2514/6.2015-2480
Grötzbach, G.: Encyclopedia of Fluid Mechanics, edited by N. P. Cheremisinoff (Gulf, West Orange, NJ), Vol. 6, (1987)
Hoffmann, G., Benocci, C.: Approximate wall boundary conditions for large eddy simulations. In: Benzi, R. (ed.) Advances in Turbulence V. Fluid Mechanics and Its Applications, vol. 24. Springer, Dordrecht (1995). 10.1007/978-94-011-0457-9_40 DOI: 10.1007/978-94-011-0457-9_40
Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Netw. 4(2), 251–257 (1991). 10.1016/0893-6080(91)90009-T DOI: 10.1016/0893-6080(91)90009-T
Hoyas, S., Jimenez, J.: Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511 (2008). 10.1063/1.3005862 DOI: 10.1063/1.3005862
Hillewaert, K.: Development of the Discontinuous Galerkin method for high-resolution, large scale CFD and acoustics in industrial geometries. PhD thesis. Ecole polytechnique de Louvain/iMMC (2013)
Krank, B., Kronbichler, M., Wall, W.A.: A multiscale approach to hybrid RANS/LES wall modeling within a high-order discontinuous Galerkin scheme using function enrichment. Numer. Methods Fluids 90(2), 81–113 (2019). 10.1002/fld.4712 DOI: 10.1002/fld.4712
Lozano-Durán, A., Bae, H. J.: Self-critical machine-learning wall-modeled LES for external aerodynamics. arXiv:2012.10005 [physics] (2021)
Marusic, I., Monty, J.P.: Attached Eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 49–74 (2019). 10.1146/annurev-fluid-010518-040427 DOI: 10.1146/annurev-fluid-010518-040427
Mason, P.J., Callen, N.S.: On the magnitude of the subgrid-scale eddy coefficient in large eddy simulation of turbulent channel flow. J. Fluid Mech. 162, 439–462 (1986). 10.1017/S0022112086002112 DOI: 10.1017/S0022112086002112
McKeon, B.J.: The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech. (2017). 10.1017/jfm.2017.115 DOI: 10.1017/jfm.2017.115
Nicoud, F., Baggett, J.S., Moin, P., Cabot, W.: Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation. Phys. Fluids 13, 2968 (2001). 10.1063/1.1389286 DOI: 10.1063/1.1389286
Piomelli, U., Moin, P., Ferziger, J.H., Kim, J.: New approximate boundary conditions for large-eddy simulations of wall-bounded flows. Phys. Fluids A Fluid Dyn. 1, 1061 (1989). 10.1063/1.857397 DOI: 10.1063/1.857397
Piomelli, U., Balaras, E.: Wall-layer models for large Eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374 (2002). 10.1146/annurev.fluid.34.082901.144919 DOI: 10.1146/annurev.fluid.34.082901.144919
Piomelli, U.: Wall-layer models for large-eddy simulations. Prog. Aerosp. Sci. 44(6), 437–446 (2008). 10.1016/j.paerosci.2008.06.001 DOI: 10.1016/j.paerosci.2008.06.001
Rajagopalan, S., Antonia, R.A.: Some properties of the large structure in a fully developed turbulent duct flow. Phys. Fluids 22, 614 (1979). 10.1063/1.862643 DOI: 10.1063/1.862643
Song, S., Eaton, J.: Flow structures of a separating, reattaching, and recovering boundary layer for a large range of Reynolds number. Exp. Fluids 36, 642–653 (2004). 10.1007/s00348-003-0762-2 DOI: 10.1007/s00348-003-0762-2
Spalart, P. R., Jou W. H., Strelets M., Allmaras S. R.: Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach. Advances in DNS/LES: Direct numerical simulation and large eddy simulation, 137-148 (1997)
Schumann, U.: Subgrid-scale model for finite-difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phy. 18(4), 376–404 (1975). 10.1016/0021-9991(75)90093-5 DOI: 10.1016/0021-9991(75)90093-5
Székely, G.J., Rizzo, M.L., Bakirov, N.K.: Measuring and testing dependence by correlation of distances. Ann. Statistics. 35(6), 2769–2794 (2007). 10.1214/009053607000000505 DOI: 10.1214/009053607000000505
Temmerman, L., Leschziner, M., Mellen, C., Fröhlich, J.: Investigation of subgrid-scale models and wall-function approximations in large eddy simulation of separated flow in a channel with streamwise periodic constrictions. Int. J. Heat Fluid Flow 24(2), 157–180 (2003). 10.1016/S0142-727X(02)00222-9 DOI: 10.1016/S0142-727X(02)00222-9
Townsend, A.A.: The structure of turbulent boundary layer. Math. Proc. Camb. Philos. Soc. 47, 375–95 (1951) DOI: 10.1017/S0305004100026724
Townsend, A.A.: The Structure of Turbulent Shear Flows. Cambridge University Press, CambridgeCambridge (1961)
Townsend, A.A.: The structure of turbulent shear flows, 2nd edn. Cambridge University Press, Cambridge (1976)
Wang, M.: LES with wall models for trailing-edge aeroacoustics. In: Annual Research Briefs. Center Turbulence Research. Stanford University California 355-364 (1999)
Werner, H., Wengle, H.: Large-eddy simulation of turbulent flow around a cube in a plane channel. In: Durst, F., Friedrich, R., Launder, B.E., Schumann, U., Whitelaw, J.H. (eds.) Selected Papers from the 8th Symposium on Turbulent Shear Flows, pp. 155–168. Springer, New York (1993)
Yang, X.I.A., Zafar, S., Wang, J.-X., Xiao, H.: Predictive large-eddy-simulation wall modeling via physics-informed neural networks. Phys. Rev. Fluids 4, 034602 (2019). 10.1103/PhysRevFluids.4.034602 DOI: 10.1103/PhysRevFluids.4.034602
Zhou, Z., He, G., Yang, X.: Wall model based on neural networks for LES of turbulent flows over periodic hills. Phys. Rev. Fluids 6, 054610 (2021). 10.1103/PhysRevFluids.6.054610 DOI: 10.1103/PhysRevFluids.6.054610