The near wall physics and wall functions for turbulent natural convection

Highly accurate results of direct numerical simulations (DNS) for Grashof numbers up to 4.0 × 106 in a differentially heated infinite vertical channel are used to deduce wall functions for turbulent natural convection. These functions represent the unique time-averaged behaviour of velocity, temperature, and shear stress in the vicinity of the wall for the Grashof number range under consideration. There is a good indication that these wall function are valid as the Grashof number tends to infinity. Previous attempts to find such wall functions relied on the blending of at least two functions which are valid in adjacent regions of the flow field. In conformity with the time-averaged momentum and thermal energy equation, this study introduces a continuous description of the near wall region up to the velocity maximum.