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Artificial-neural-network-based nonlinear algebraic models for large-eddy simulation of compressible wall-bounded turbulence

Published online by Cambridge University Press:  29 March 2023

Dehao Xu Open the ORCID record for Dehao Xu [Opens in a new window] ,
Jianchun Wang Open the ORCID record for Jianchun Wang [Opens in a new window] ,
Changping Yu Open the ORCID record for Changping Yu [Opens in a new window]  and
Shiyi Chen
Dehao Xu
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China
Jianchun Wang*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Changping Yu
Affiliation:
Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Shiyi Chen*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Eastern Institute for Advanced Study, Ningbo 315200, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

In this paper, we propose artificial-neural-network-based (ANN-based) nonlinear algebraic models for the large-eddy simulation (LES) of compressible wall-bounded turbulence. An innovative modification is applied to the invariants and the tensor bases of the nonlinear algebraic models through using the local grid widths along each direction to normalise the corresponding gradients of the flow variables. Furthermore, the dimensionless model coefficients are determined by the ANN method. The modified ANN-based nonlinear algebraic model (MANA model) has much higher correlation coefficients and much lower relative errors than the dynamic Smagorinsky model (DSM), Vreman model and wall-adapting local eddy-viscosity model in the a priori test. The significantly more accurate estimations of the mean subgrid-scale (SGS) fluxes of the kinetic energy and temperature variance are also obtained by the MANA models in the a priori test. Furthermore, in the a posteriori test, the MANA model can give much more accurate predictions of the flow statistics and the mean SGS fluxes of the kinetic energy and the temperature variance than other traditional eddy-viscosity models in compressible turbulent channel flows with untrained Reynolds numbers, Mach numbers and grid resolutions. The MANA model has a better performance in predicting the flow statistics in supersonic turbulent boundary layer. The MANA model can well predict both direct and inverse transfer of the kinetic energy and temperature variance, which overcomes the inherent shortcoming that the traditional eddy-viscosity models cannot predict the inverse energy transfer. Moreover, the MANA model is computationally more efficient than the DSM.

JFM classification

Mathematical Foundations: Machine learning Turbulent Flows: Turbulence modelling
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 960 , 10 April 2023 , A4
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© The Author(s), 2023. Published by Cambridge University Press

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