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

Olga Shishkina, Richard J.A.M. Stevens, Siegfried Grossmann, Detlef Lohse

Research output: Contribution to journalArticleAcademicpeer-review

143 Citations (Scopus)
30 Downloads (Pure)

Abstract

Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Bénard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations
Original languageEnglish
Article number075022
Number of pages17
JournalNew journal of physics
Volume12
Issue number7
DOIs
Publication statusPublished - 2010

Fingerprint

boundary layer thickness
free convection
boundary layers
Prandtl number
kinetics
convection
boundary layer equations
laminar boundary layer
thermal boundary layer
turbulent boundary layer
Rayleigh number
estimates
Nusselt number
direct numerical simulation
mesh
simulation
fluids

Keywords

  • IR-79275
  • METIS-270424

Cite this

@article{dfc2841db77f425e8905045e3ee6335a,
title = "Boundary layers structure in turbulent thermal convection and its consequences for the required numerical resolution",
abstract = "Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–B{\'e}nard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations",
keywords = "IR-79275, METIS-270424",
author = "Olga Shishkina and Stevens, {Richard J.A.M.} and Siegfried Grossmann and Detlef Lohse",
note = "Open access article",
year = "2010",
doi = "10.1088/1367-2630/12/7/075022",
language = "English",
volume = "12",
journal = "New journal of physics",
issn = "1367-2630",
publisher = "IOP Publishing Ltd.",
number = "7",

}

Boundary layers structure in turbulent thermal convection and its consequences for the required numerical resolution. / Shishkina, Olga; Stevens, Richard J.A.M.; Grossmann, Siegfried; Lohse, Detlef .

In: New journal of physics, Vol. 12, No. 7, 075022, 2010.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Boundary layers structure in turbulent thermal convection and its consequences for the required numerical resolution

AU - Shishkina, Olga

AU - Stevens, Richard J.A.M.

AU - Grossmann, Siegfried

AU - Lohse, Detlef

N1 - Open access article

PY - 2010

Y1 - 2010

N2 - Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Bénard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations

AB - Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Bénard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations

KW - IR-79275

KW - METIS-270424

U2 - 10.1088/1367-2630/12/7/075022

DO - 10.1088/1367-2630/12/7/075022

M3 - Article

VL - 12

JO - New journal of physics

JF - New journal of physics

SN - 1367-2630

IS - 7

M1 - 075022

ER -