History effects and wall-similarity of non-equilibrium turbulent boundary layers in varying pressure gradient over rough and smooth surfaces

Experimental investigations were conducted on non-equilibrium, turbulent boundary layers over rough and smooth surfaces. A NACA 0012 airfoil was systematically rotated to generate a family of bi-directional pressure fields on the research surface. The rough surface consisted of 2mm tall, staggered, circular cylindrical elements producing flow conditions that were in the fully rough regime. The velocity fields were measured using a custom Pitot-probe boundary layer rake and time-resolved particle image velocimetry (TR-PIV). The primary effect of the roughness was to increase the magnitude of the outer layer and skin friction parameters. Flows over both wall conditions exhibited “history effects” in the integrated boundary layer parameters, which indicates characteristic dependencies on the streamwise flow evolution. Indirect skin friction methods for non-equilibrium rough wall flows were sensitive to the regression fits of the empirical data, which were used in the absence of direct measurements. The effective sandgrain roughness parameter, ks, remained independent of pressure gradient flow history, within the uncertainty of empirical methods used for skin friction determination. Varying levels of wall-similarity were observed in the smooth and rough wall Reynolds stress profiles. Although past evaluations of wall-similarity have suggested that a sufficiently large boundary layer thickness to ks is sufficient for wall-similarity, the present results indicate a need for additional multivariable considerations including matching flow histories and considering local Reynolds numbers measurement resolution.