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Modelling high-Reynolds-number effects in fully developed channel flows using a two-scale Reynolds stress model

Published online by Cambridge University Press:  28 November 2024

François Chedevergne Open the ORCID record for François Chedevergne [Opens in a new window] ,
Stefan Coroama ,
Vincent Gleize  and
Hervé Bézard
François Chedevergne*
Affiliation:
DMPE, ONERA, Université de Toulouse, Toulouse, France
Stefan Coroama
Affiliation:
DAAA, ONERA, Institut Polytechnique de Paris, Meudon, France
Vincent Gleize
Affiliation:
DAAA, ONERA, Institut Polytechnique de Paris, Meudon, France
Hervé Bézard
Affiliation:
DMPE, ONERA, Université de Toulouse, Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

Reynolds-averaged models for solving the Navier–Stokes equations are implicitly based on Kolmogorov's theory for describing energy transfers between the different turbulent scales, which means that all the energy produced at large scales is transferred at a constant rate to the smallest turbulent scales where it is dissipated. As a result, these models use a single scale to describe the turbulence spectrum, which in cases of non-equilibrium turbulence does not provide an adequate description of the transfers actually observed. This is particularly the case for wall-bounded flows at high Reynolds numbers, such as turbulent channel flows. Taking up an approach developed by Schiestel (2007 Modeling and Simulation of Turbulent Flows, ISTE Ltd and John Wiley & Sons), which aims to define a Reynolds-averaged Navier–Stokes model transporting several scales of turbulence, a two-scale Reynolds stress model (RSM) was developed in order to take into account the interactions between the inner and outer regions of wall-bounded flows. The results obtained with the model are compared with the direct numerical simulations (DNS) of Lee & Moser (J. Fluid Mech., vol. 860, 2019, pp. 886–938) in a turbulent channel for several friction Reynolds numbers up to $Re_{\tau }=5200$, for which partial integrations in spectral space were carried out, highlighting distinct behaviours between small and large scales of turbulence. The model developed provides an accurate description of the contributions at small and large scales and thus reproduces the high-Reynolds-number effects observed in DNS data. In addition, comparisons with the DNS data served to validate a large part of the closure relations used for the various terms in the two-scale RSM.

JFM classification

Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulence modelling Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , A65
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Cadiou, A., Hanjalić, K. & Stawiarski, K. 2004 A two-scale second-moment turbulence closure based on weighted spectrum integration. Theor. Comput. Fluid Dyn. 18 (1), 1–26.CrossRefGoogle Scholar
Chaouat, B. & Schiestel, R. 2007 From single-scale turbulence models to multiple-scale and subgrid-scale models by Fourier transform. Theor. Comput. Fluid Dyn. 21 (3), 201–229.CrossRefGoogle Scholar
Daly, B.J. & Harlow, F.H. 1970 Transport equations in turbulence. Phys. Fluids 13 (11), 2634–2649.CrossRefGoogle Scholar
Durbin, P.A. 1991 Near-wall turbulence closure modeling without “damping functions”. Intl J. Theor. Comput. Fluid Dyn. 3, 1–13.CrossRefGoogle Scholar
Gleize, V., Schiestel, R. & Couaillier, V. 1996 Multiple scale modeling of turbulent nonequilibrium boundary layer flows. Phys. Fluids 8 (10), 2716–2732.CrossRefGoogle Scholar
Grégoire, O., Souffland, D., Gauthier, S. & Schiestel, R. 1999 A two-time-scale turbulence model for compressible flows: turbulence dominated by mean deformation interaction. Phys. Fluids 11 (12), 3793–3807.CrossRefGoogle Scholar
Hanjalić, K., Launder, B.E. & Schiestel, R. 1979 Multiple-time-scale concepts in turbulent transport modelling. In Second Symposium on Turbulent Shear Flows, pp. 10.31–10.36. Imperial College.Google Scholar
Harun, Z., Monty, J.P., Mathis, R. & Marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent boundary layers. J. Fluid Mech. 715, 477–498.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.Google ScholarPubMed
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Jones, W.P. & Launder, B.E. 1972 The prediction of laminarization with a two-equation model of turbulence. Intl J. Heat Mass Transfer 15, 301–314.CrossRefGoogle Scholar
Jooss, Y., Li, L., Bracchi, T. & Hearst, R.J. 2021 Spatial development of a turbulent boundary layer subjected to freestream turbulence. J. Fluid Mech. 911, A4.CrossRefGoogle Scholar
Laporta, A. & Bertoglio, J.-P. 1995 A model for inhomogeneous turbulence based on two-point correlations. In Advances in Turbulence V: Proceedings of the Fifth European Turbulence Conference, Siena, Italy, 5–8 July 1994, pp. 286–297. Springer.CrossRefGoogle Scholar
Laval, J.-P., Dubrulle, B. & Nazarenko, S. 2001 Nonlocality and intermittency in three-dimensional turbulence. Phys. Fluids 13 (7), 1995–2012.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to ${R}e_\tau 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lee, M. & Moser, R. 2019 Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech. 860, 886–938.CrossRefGoogle Scholar
Manceau, R. 2015 Recent progress in the development of the elliptic blending Reynolds-stress model. Intl J. Heat Fluid Flow 51, 195–220.CrossRefGoogle Scholar
Manceau, R. & Hanjalić, K. 2002 Elliptic blending model: a near-wall Reynolds-stress turbulence closure. Phys. Fluids 14 (2), 744–754.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., Mathis, R. & Hutchins, N. 2010 b Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.CrossRefGoogle ScholarPubMed
Monkewitz, P. 2017 Revisiting the quest for a universal log-law and the role of pressure gradient in “canonical” wall-bounded turbulent flows. Phys. Rev. Fluids 2 (9), 094602.CrossRefGoogle Scholar
Monkewitz, P. & Nagib, H. 2023 The hunt for the Kármán “constant” revisited. J. Fluid Mech. 967, A15.CrossRefGoogle Scholar
Nagib, H. & Chauhan, K. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20 (10), 101518.CrossRefGoogle Scholar
Ono, M., Furuichi, N. & Tsuji, Y. 2023 Reynolds number dependence of turbulent kinetic energy and energy balance of 3-component turbulence intensity in a pipe flow. J. Fluid Mech. 975, A9.CrossRefGoogle Scholar
Schiestel, R. 1974 Sur un nouveau modèle de turbulence appliwué aux transferts de quantité de mouvement et de chaleur. PhD thesis, University of Nancy I.Google Scholar
Schiestel, R. 1987 Multiple-time-scale modeling of turbulent flows in one-point closures. Phys. Fluids 30 (3), 722–731.CrossRefGoogle Scholar
Schiestel, R. 2007 Modeling and Simulation of Turbulent Flows. ISTE Ltd and John Wiley & Sons.Google Scholar
Sillero, J.A., Jiménez, J. & Moser, R. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to $\delta ^+ \approx 2000$. Phys. Fluids 25 (10), 105102.CrossRefGoogle Scholar
Speziale, C.G., Sarkar, S. & Gatski, T.B. 1991 Modelling the pressure–strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech. 227, 245–272.CrossRefGoogle Scholar
Vallikivi, M., Hultmark, M. & Smits, A.J. 2015 Turbulent boundary layer statistics at very high Reynolds number. J. Fluid Mech. 779, 371–389.CrossRefGoogle Scholar