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Asymptotic analysis of the near-wall region of turbulent natural convection flows

Published online by Cambridge University Press:  11 October 2005

M. HÖLLING  and
H. HERWIG
M. HÖLLING
Affiliation:
Hamburg University of Technology, Applied Thermodynamics, Denickestrasse 17, D-21073 Hamburg, Germany
H. HERWIG
Affiliation:
Hamburg University of Technology, Applied Thermodynamics, Denickestrasse 17, D-21073 Hamburg, Germany
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Abstract

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High-Grashof-number turbulent natural convection in the vicinity of vertical walls with heat transfer is analysed asymptotically. The near-wall boundary layer has a viscosity-influenced inner layer and a fully turbulent outer layer, similar to the structure of forced convection boundary layers. Scaling laws and wall functions are found by asymptotic matching of the temperature gradients in the overlap layer. The temperature wall function then is a simple logarithmic function of wall distance whereas the velocity profile in the overlap layer is a more complex correlation. Constants in these wall functions are deduced from high-quality data for large Grashof numbers. Experimental as well as numerical profiles as a whole are very well reproduced by the combination of wall functions and viscous sublayer profiles. Therefore these new asymptotic profiles can be used in CFD codes to avoid very fine grids close to the wall, when Grashof numbers are high.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 541 , 25 October 2005 , pp. 383 - 397
Copyright
© 2005 Cambridge University Press