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Resolved and subgrid dynamics of Rayleigh-Bénard convection

Togni, Riccardo, Cimarelli, Andrea and De Angelis, Elisabetta 2019. Resolved and subgrid dynamics of Rayleigh-Bénard convection. Journal of Fluid Mechanics 867 , pp. 906-933. 10.1017/jfm.2019.119
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Abstract

In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scale-by-scale budget equations for the second-order velocity and temperature structure functions and their liming cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, luc for the velocity field and lθc for the temperature field are identified. These variables separate the space of scales into a quasi-homogeneous range, character- ized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of Large-Eddy Simulation (LES) to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh-B ́enard convection. It consists of single-point and scale-by-scale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length lF on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a Direct Numerical Simulation (DNS) are split into filtered and residual components using a spectral cutoff filter. It is found that when lF is smaller than the minimum values of the cross-over scales given by lθ∗ = lθ Nu/H = 0.8, the resolved processes correspond to the c,min c,min exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the near- wall region and the effect of the subgrid scales are more complex for filter lengths of the order of lF ≈ 3 lθc,min or larger. This study suggests that classic eddy-viscosity/diffusivity models employed in LES may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgrid- scale models.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TJ Mechanical engineering and machinery
Publisher: Cambridge University Press (CUP)
ISSN: 0022-1120
Date of First Compliant Deposit: 25 March 2019
Date of Acceptance: 18 January 2019
Last Modified: 17 Oct 2019 11:49
URI: http://orca.cf.ac.uk/id/eprint/121048

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