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Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution

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, Vol. 1 (075022), pp. 1-17. DOI: 10.1088/1367-2630/12/7/075022.

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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.

Document Type:Article
Title:Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
Authors:
AuthorsInstitution or Email of Authors
Shishkina, OlgaOlga.Shishkina@dlr.de
Stevens, Richardr.j.a.m.stevens@tnw.utwente.nl
Grossmann, Siegriedgrossmann@physik.uni-marburg.de
Lohse, Detlefd.lohse@utwente.nl
Date:2010
Journal or Publication Title:New Journal of Physics
Refereed publication:Yes
In Open Access:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:Vol. 1
DOI:10.1088/1367-2630/12/7/075022
Page Range:pp. 1-17
Editors:
EditorsEmail
UNSPECIFIEDDPG / IOP
Series Name:Online
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
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Flight Physics
Location: Göttingen
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > Fluid Systems
Deposited By: PD Dr. habil. Olga Shishkina
Deposited On:09 Aug 2010 10:48
Last Modified:12 Dec 2013 20:57

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