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

By Emile Touber and Neil D. Sandham


A combined numerical and analytical approach is used to study the low-frequency<br/>shock motions observed in shock/turbulent-boundary-layer interactions in the<br/>particular case of a shock-reflection configuration. Starting from an exact form<br/>of the momentum integral equation and guided by data from large-eddy simulations,<br/>a stochastic ordinary differential equation for the reflected-shock-foot low-frequency<br/>motions is derived. During the derivation a similarity hypothesis is verified for the<br/>streamwise evolution of boundary-layer thickness measures in the interaction zone. In<br/>its simplest form, the derived governing equation is mathematically equivalent to that<br/>postulated without proof by Plotkin (AIAA J., vol. 13, 1975, p. 1036). In the present<br/>contribution, all the terms in the equation are modelled, leading to a closed form of<br/>the system, which is then applied to a wide range of input parameters. The resulting<br/>map of the most energetic low-frequency motions is presented. It is found that while<br/>the mean boundary-layer properties are important in controlling the interaction size,<br/>they do not contribute significantly to the dynamics. Moreover, the frequency of the<br/>most energetic fluctuations is shown to be a robust feature, in agreement with earlier<br/>experimental observations. The model is proved capable of reproducing available lowfrequency<br/>experimental and numerical wall-pressure spectra. The coupling between<br/>the shock and the boundary layer is found to be mathematically equivalent to a<br/>first-order low-pass filter. It is argued that the observed low-frequency unsteadiness<br/>in such interactions is not necessarily a property of the forcing, either from upstream<br/>or downstream of the shock, but an intrinsic property of the coupled system, whose<br/>response to white-noise forcing is in excellent agreement with actual spectra

Topics: TL
Year: 2011
OAI identifier:
Provided by: e-Prints Soton
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