Low-order stochastic modelling of low-frequency motions in reflected shock-wave/boundary-layer interactions

Abstract

A combined numerical and analytical approach is used to study the low-frequency
shock motions observed in shock/turbulent-boundary-layer interactions in the
particular case of a shock-reflection configuration. 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. During the derivation a similarity hypothesis is verified for the
streamwise evolution of boundary-layer thickness measures in the interaction zone. In
its simplest form, the derived governing equation is mathematically equivalent to that
postulated without proof by Plotkin (AIAA J., vol. 13, 1975, p. 1036). In the present
contribution, all the terms in the equation are modelled, leading to a closed form of
the system, which is then applied to a wide range of input parameters. The resulting
map of the most energetic low-frequency motions is presented. 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. The model is proved capable of reproducing available lowfrequency
experimental and numerical wall-pressure spectra. The coupling between
the shock and the boundary layer is found to be mathematically equivalent to a
first-order low-pass filter. It is argued that the observed low-frequency unsteadiness
in such interactions is not necessarily a property of the forcing, either from upstream
or downstream of the shock, but an intrinsic property of the coupled system, whose
response to white-noise forcing is in excellent agreement with actual spectra.

More information

Identifiers

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

Catalogue record

Export record

Altmetrics