Large eddy simulations of Rayleigh–Bénard convection using subgrid scale estimation model

Kimmel, Shari J.; Domaradzki, J. Andrzej

doi:10.1063/1.870292

Cited by 42 publications

(31 citation statements)

References 43 publications

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“…Finally, the modeling principle involved in the estimation procedure is immediately applicable to flows affected by additional physical phenomena, e.g., the density variations in convective and compressible turbulence. 9,13 In those cases the nonlinear term in the tem-perature equation is used to find an estimate of the SGS temperature and there is no need to introduce additional modeling assumptions for the SGS heat flux and the turbulent Prandtl number.…”

Section: ͑2͒mentioning

confidence: 99%

The subgrid-scale estimation model for high Reynolds number turbulence

Domaradzki

Yee

2000

Physics of Fluids

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Articles you may be interested inA constraint for the subgrid-scale stresses in the logarithmic region of high Reynolds number turbulent boundary layers: A solution to the log-layer mismatch problemWe propose a formulation of the subgrid-scale estimation model in which the effects of the estimated subgrid scales on the resolved scales are obtained through the truncated Navier-Stokes dynamics and the calculation of the subgrid-scale stress tensor is not required. For high Reynolds number isotropic turbulence the model predicts the k Ϫ5/3 spectrum with the correct value of the Kolmogoroff constant.

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Section: ͑2͒mentioning

confidence: 99%

The subgrid-scale estimation model for high Reynolds number turbulence

Domaradzki

Yee

2000

Physics of Fluids

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“…Because of the complexity of the governing equations, analytical progress in understanding convection has been slow, and laboratory experiments and numerical simulations have assumed increased importance. In regard to numerical work, large-eddy-simulation (LES) techniques have proved their value as reliable tools for investigating large-scale quantities as well as flow topology and structure [1]. In the present work, we use LES to shed light on a previously reported experimental result [2]-henceforth DE01-that the scaling of turbulent fluctuations in the geometric center of the convection cell are strongly influenced by the geometrical shape of the convection cell, and confirm its validity.…”

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“…The LES methodology has been validated against DNS in Rayleigh-Bénard convection [1] for the case of two infinite and parallel plates in the range 6.3 × 10 5 < Ra < 1 × 10 8 , obtaining an excellent agreement for the first-and second-order statistics. Further below we will compare our heat transfer results with recent DNS work.…”

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Influence of container shape on scaling of turbulent fluctuations in convection

et al. 2014

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We perform large-eddy simulations of turbulent convection in a cubic cell for Rayleigh numbers, Ra, between 10(6) and 10(10) and the molecular Prandtl number, Pr=0.7. The simulations were carried out using a second-order-accurate finite-difference method in which subgrid-scale fluxes of momentum and heat were both parametrized using a Lagrangian and dynamic Smagorinsky model. The scaling of the root-mean-square fluctuations of density (temperature) and velocity measured in the cell center are in excellent agreement with the scaling measured in the laboratory experiments of Daya and Ecke [Phys. Rev. Lett. 87, 184501 (2001)] and differ substantially from that observed in cylindrical cells. We also observe the time-averaged spatial distributions of the local heat flux and density fluctuations, and find that they are strongly inhomogeneous in the horizontal midplane, with the largest density gradients occurring at the corners at the midheight, where hot and cold plumes mix in the form of strong counter-rotating eddies.

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“…All DNS solutions satisfied standard convergence criteria [15] (with grid spacing l , the Kolmogorov scale). The subgridscale model in the LES was based on a dynamic eddy viscosity and eddy diffusivity (with l 10), as previously shown to be accurate for convection [16][17][18][19] (the detailed algorithms are found in [20,21]). The LES solutions were also validated against the DNS solutions at Ra 6 Â 10 8 and showed no significant differences (in heat transport, volume integrals and vertical profiles of energy conversion terms, and dissipation spectra).…”

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Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

2013

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A new, more complete view of the mechanical energy budget for Rayleigh-Bénard convection is developed and examined using three-dimensional numerical simulations at large Rayleigh numbers and Prandtl number of 1. The driving role of available potential energy is highlighted. The relative magnitudes of different energy conversions or pathways change significantly over the range of Rayleigh numbers Ra $ 10 7 -10 13 . At Ra < 10 7 small-scale turbulent motions are energized directly from available potential energy via turbulent buoyancy flux and kinetic energy is dissipated at comparable rates by both the largeand small-scale motions. In contrast, at Ra ! 10 10 most of the available potential energy goes into kinetic energy of the large-scale flow, which undergoes shear instabilities that sustain small-scale turbulence. The irreversible mixing is largely confined to the unstable boundary layer, its rate exactly equal to the generation of available potential energy by the boundary fluxes, and mixing efficiency is 50%. Introduction.-Flow in a horizontal layer of fluid heated uniformly from below and cooled from above-RayleighBénard convection (RBC)-is an idealized problem from which much can be learned about the nature of convective flow and heat transfer. Recent attention has focused on the relative importance of the boundary layer and interior behavior, including flow structures, at very large Rayleigh numbers [1][2][3][4][5][6]. The salient features of the flow can be usefully interpreted in terms of the energy budget, and previous work has considered the kinetic and thermal energy [2,3,7,8]. However, the existing framework is incomplete and provides limited insight into the exchange of mechanical energy among different forms or between fluid motions of different scales. In particular, the nature of the turbulent energy cascade in RBC is still not fully understood [3] and improved models are needed.Convection is caused by the generation of mechanical energy in the form of available potential energy (APE) by boundary buoyancy fluxes. APE is a subset of the total gravitational potential energy (GPE) and is the form essential for motions [9][10][11]. A complete mechanical energy framework has been recently developed for the case of horizontal convection forced by differential heating at one horizontal boundary [12,13] and recently extended to RBC [14]. In RBC there is a release of APE from thermal boundary layers adjacent to the top and bottom boundaries, driving flow at various scales, while complex feedbacks further distribute the potential and kinetic energy among the different scales or, through mixing, to the background potential energy. The role of APE in RBC was recognized in quantifying the overall rate of irreversible mixing [14]. Here we show that an account of GPE, its partition into available and background forms, and its links to kinetic energy at various scales are essential in a full understanding of the turbulent energy cascade and the relative roles of the boundary layer and the interior.

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Large eddy simulations of Rayleigh–Bénard convection using subgrid scale estimation model

Cited by 42 publications

References 43 publications

The subgrid-scale estimation model for high Reynolds number turbulence

The subgrid-scale estimation model for high Reynolds number turbulence

Influence of container shape on scaling of turbulent fluctuations in convection

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

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