Incomplete similarity of the turbulent boundary layer over an aerofoil in the presence of synthetic jets

This study is concerned with the near-wall flow structure over a NACA 0025 aerofoil at a constant chord-based Reynolds number of 100 000 across various angles of attack, where an array of 12 circular-orifice synthetic jet actuators (SJAs) was used to reattach the flow under conditions of flow separation. The SJAs were operated in burst-mode at two distinct momentum coefficients, a 50 % duty cycle and a modulation frequency of 200 Hz, targeting the separated shear layer frequency. Particle image velocimetry was conducted using three side-by-side cameras to capture the velocity fields along the aerofoil surface at the centreline. At zero angle of attack, the velocity profiles exhibited characteristics of a turbulent boundary layer, following the law of the wall in the inner layer while deviating from the logarithmic law in the outer layer. At higher angles of attack, while some logarithmic behaviour could still be detected close to the wall, a wide region of the velocity profiles became predominantly linear, exhibiting a behaviour differing from both a canonical turbulent boundary layer and a turbulent wall jet. The entire shear flow was decomposed into three regions: the boundary layer, the jet layer and the mixing layer that extended between the two. The mixing layer was analysed by applying several scaling laws to the time-averaged velocity components, where it was revealed that the characteristic velocity of the two velocity components is different. An asymptotic solution was obtained under a low spreading rate at infinite Reynolds number, providing a theoretical basis for the experimental observations.