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

By E. Touber, Neil D. Sandham. Journal of Fluid Mechanics, 2011

190 citations recorded by the source corpus.

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 low-frequency 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.

Subfields: Computational Mechanics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/506dc2554659ad2a4fe35dc8877e6efd9cc0da35

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Citations in the corpus

Flow physics and RANS modelling of oblique shock/turbulent boundary layer interaction (2013, background): “This suggests that the shock wave may be acting as a low-pass filter on larger energetic structures (damping smaller, high-frequency fluctuations), which is a characteristic observed of the stochastic model presented by Touber & Sandham (2011).”
A scaling analysis for turbulent shock-wave/boundary-layer interactions (2013, methodology): “Initially suggested in Plotkin (1975), this approach has been recently reconsidered by Touber & Sandham (2011) in the case of a Mach 2.3 shock reflection, where the interaction is proposed to act as a low-pass filter for the upstream perturbations.”
Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number (2017, background): “Our analyses support a mechanism proposed by Touber & Sandham (2011) and Grilli et al. (2012), where the low-frequency unsteadiness is an intrinsic property of the interaction.”
Stability, Receptivity, and Sensitivity Analyses of Buffeting Transonic Flow over a Profile (2015, result): “Such a behavior is reminiscent of the results by Plotkin [48] and Touber and Sandham [49], who argued that the shock exhibits such a behavior.”
Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations (2014, methodology): “Plotkin (1975) developed a simple stochastic model that assumes a linear restoring mechanism of the shock wave to its mean location based on the stability of the mean flow from the departures imposed by velocity fluctuations of the incoming TBL. Touber & Sandham (2011) developed a model mathematical”