Similarity laws for transpired turbulent flows subjected to pressure gradients, separation and wall heat transfer

Abstract

New scaling laws for transpired turbulent flows with non-zero pressure gradients and wall heat transfer are derived. The new wall laws are the first presented in literature that consider flow transpiration and separation. It emerges from the proposed scaling that mean velocity and temperature profiles are self-similar with respect to the transpiration rate in the whole near wall region of the flow. The domains of validity of the wall laws are extended, to include the outer region of the boundary layer, using the intermittent character of the flow in that region. It is found that the intermittency factor used in the model is a universal function of the wall normal direction scaled by the boundary layer thickness. The new theory is compared to over 200 experimental and DNS mean velocity and temperature profiles from several turbulence databases and with other turbulence models as well showing that, for most of the profiles analyzed, the new formulation gives a better fit to the data.