Scaling of streamwise Reynolds stress for turbulent boundary layers with pressure gradient

Turbulence behavior of non-zero pressure gradient flows departs significantly from what was known for canonical flows like flat plate zero pressure gradient turbulent boundary layers, channel or pipe flows. The paper presents experimental investigations performed for the pressure conditions representative for turbomachinery flows and for Reynolds number varying from Reθ≈2300–6200. By providing new data, scaling law characteristics can be better understood enabling the use of numerical modeling for flow prediction. The goal was to study and to evaluate available scaling laws using collected data. Particular attention was devoted to scaling of Reynolds stresses and the phenomenon of the outer peak of velocity fluctuation, which appears in the adverse pressure gradient conditions. At these conditions the self-similarity cannot be obtained using the scale, which is constant across the boundary layer thickness. In the paper we propose a modification of Alfredsson et al. (2012), expression, which is dedicated to ZPG flows. The proposed formulation, utilizing the shape factor H, allows to extend validity of Alfredsson et al. proposal to pressure gradient flows.