Features of shock wave unsteadiness in shock wave boundary layer interaction

Introduction The interactions between a shock wave and a boundary layer arise in several aeronautical applications and ha ve been studied for decades. When separation occurs, they have been shown to be strongly unsteady and the separation shock is moving at very low frequencies. These unsteadiness have a direct influence on the performances of the system and can create strong stress on the structure. Some authors, see for instance Ganapathisubramani et al. (2007), have proposed to relate the low frequency shock motions to the upstream perturbations in the incoming boundary layer. On the opposite, others authors including Robinet(2007); Dupontet al. (2008); Wu & Martin (2008); Priebe & Martin (2012), have suggested that theses perturbations are developing in the downstream part of the interaction. Finally, a recent analysis byTouber & Sandham(2011) proposed to assimilate the interaction as a low pass filter, with a very low frequency cut off frequency, as initially suggested in the experiments by Plotkin (1975). The aim of this paper is not not explain the physical mechanism leading to the low frequency shock motions, but to identify their localisations and how the separation shoc k is influenced. It will be shown that phenomena occurring within the recirculation bubble govern the whole interaction, whatever the frequency range: the shock motions appears to be the mirror of these phenomena developing in the separated zone. An equivalent inviscid scheme of the unsteady interaction is established to describe the whole unsteadiness of the shock system, as well as the downstream unsteady pressure field.