Low-frequency unsteadiness in shock/turbulent-boundary-layer interactions

Shock/boundary-layer interactions are critical for the aerospace industry in that they often are associated with significant low-frequency shock oscillations which can impair the efficiency and/or the stability of devices such as turbofan blades or supersonic engine intakes. The physical mechanisms at the origin of the low-frequency
shock motions are not fully understood and a number of tentative explanations have been proposed. This presentation will focus on the
interaction between an impinging oblique shock and a supersonic turbulent boundary layer via large-eddy simulations. Special care is
taken at the inlet in order to avoid introducing artificial low-frequency modes that could affect the interaction. All simulations
cover extensive integration times to allow for a spectral analysis at the low frequencies of interest. The simulations bring clear evidence of
the existence of broadband and energetically-significant low-frequency oscillations in the vicinity of the reflected shock, thus confirming
earlier experimental findings. Furthermore, these oscillations are found to persist even if the upstream boundary layer is deprived of long
coherent structures.

Starting from an exact form of the momentum integral equation and guided by data from large-eddy simulations, a stochastic ordinary differential equation for the reflected-shock foot low-frequency motions is derived.
This model is applied to a wide range of input parameters. It is found that while the mean boundary-layer properties are important in
controlling the interaction size, they do not contribute significantly to the dynamics. Moreover, the frequency of the most energetic
fluctuations is shown to be a robust feature, in agreement with earlier experimental observations. Under some assumptions, the coupling between
the shock and the boundary layer is mathematically equivalent to a first-order low-pass filter. Therefore, it is argued that the observed low-frequency unsteadiness is not necessarily a property of the forcing,
either from upstream or downstream of the shock, but simply an intrinsic property of the coupled dynamical system.