Shishkina, Olga and Stevens, Richard and Grossmann, Siegried and Lohse, Detlef (2010) Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New Journal of Physics, 12 (07), pp. 1-17. Institute of Physics (IOP) Publishing. doi: 10.1088/1367-2630/12/7/075022. ISSN 1367-2630.
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Official URL: http://stacks.iop.org/1367-2630/12/075022
Abstract
Results on the Prandtl-Blasius type kinetic and thermal boundary layer thicknesses in turbulent Rayleigh-Benard convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary layer equations, we calculate the ratio of the thermal and kinetic boundary layer thicknesses, which depends on the Prandtl number Pr only. It is approximated as 0.588Pr^{-1/2} for Pr<<Pran* and as 0.982Pr^{-1/3} for Pr*<<Pr, with Pr*=0.046. Comparison of the Prandtl-Blasius velocity boundary layer thickness with that evaluated in the direct numerical simulations by Stevens, Verzicco, and Lohse ( J. Fluid Mech. 643, 495 (2010)) gives very good agreement. Based on the Prandtl-Blasius type considerations, we derive a lower-bound estimate for the minimum number of the computational mesh nodes, required to conduct accurate numerical simulations of moderately high (boundary layer dominated) turbulent Rayleigh-Benard convection, in the thermal and kinetic boundary layers close to bottom and top plates. It is shown that the number of required nodes within each boundary layer depends on Nu and Pr and grows with the Rayleigh number Ra not slower than ~Ra^{0.15}. This estimate agrees excellently with empirical results, which were based on the convergence of the Nusselt number in numerical simulations.
Item URL in elib: | https://elib.dlr.de/64155/ | ||||||||||||||||||||
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Document Type: | Article | ||||||||||||||||||||
Additional Information: | Paper: 075022 | ||||||||||||||||||||
Title: | Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution | ||||||||||||||||||||
Authors: |
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Date: | 2010 | ||||||||||||||||||||
Journal or Publication Title: | New Journal of Physics | ||||||||||||||||||||
Refereed publication: | Yes | ||||||||||||||||||||
Open Access: | Yes | ||||||||||||||||||||
Gold Open Access: | Yes | ||||||||||||||||||||
In SCOPUS: | Yes | ||||||||||||||||||||
In ISI Web of Science: | Yes | ||||||||||||||||||||
Volume: | 12 | ||||||||||||||||||||
DOI: | 10.1088/1367-2630/12/7/075022 | ||||||||||||||||||||
Page Range: | pp. 1-17 | ||||||||||||||||||||
Editors: |
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Publisher: | Institute of Physics (IOP) Publishing | ||||||||||||||||||||
Series Name: | Online | ||||||||||||||||||||
ISSN: | 1367-2630 | ||||||||||||||||||||
Status: | Published | ||||||||||||||||||||
Keywords: | thermal convection, boundary layers, Prandtl-Blasius equations | ||||||||||||||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||||||||||||||
HGF - Program: | Aeronautics | ||||||||||||||||||||
HGF - Program Themes: | Aircraft Research (old) | ||||||||||||||||||||
DLR - Research area: | Aeronautics | ||||||||||||||||||||
DLR - Program: | L AR - Aircraft Research | ||||||||||||||||||||
DLR - Research theme (Project): | L - Flight Physics (old) | ||||||||||||||||||||
Location: | Göttingen | ||||||||||||||||||||
Institutes and Institutions: | Institute of Aerodynamics and Flow Technology > Fluid Systems | ||||||||||||||||||||
Deposited By: | Shishkina, PD Dr. habil. Olga | ||||||||||||||||||||
Deposited On: | 09 Aug 2010 10:48 | ||||||||||||||||||||
Last Modified: | 08 Mar 2018 18:47 |
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