Numerical determination of wall functions for the turbulent natural convection boundary layer

Abstract

In an analytical way George and Capp ( Int. J. Heat Mass Transfer 22 813–826 (1979)) and Cheesewright (“The scaling of turbulent natural convection boundary layers in the asymptotic limit of infinite Grashof number”, paper presented at Euromech Colloquium 207 (1986)) have derived wall functions for the natural convection boundary layer along a heated vertical plate. These wall functions are compared here with numerical calculations for air, using a k- ε turbulence model with low-Reynolds number modifications. George and Capp's wall function for the temperature in the inner layer agrees with the calculations, but their wall function for the velocity does not. George and Capp's defect laws for the velocity and the temperature in the outer layer are also numerically found, but Cheesewright's wall function for the velocity in the (lower part of the) outer layer does not agree.