Unsteadiness in shock-wave/boundary layer interactions

Abstract

The need for better understanding of the low-frequency unsteadiness observed in shock
wave/turbulent boundary layer interactions has been driving research in this area for
several decades. This work investigates 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 reflectedshock
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 lowfrequency
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.

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Identifiers

ORCID for N.D. Sandham: orcid.org/0000-0002-5107-0944

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