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Scaling of cylinder-generated shock-wave/turbulent boundary-layer interactions

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Abstract

Scaling parameters of shock-wave/turbulent boundary-layer interactions generated by a semi-infinite standing cylinder were explored in a combined numerical and experimental effort, consisting of Reynolds-averaged Navier–Stokes simulations and high-speed schlieren imaging. The primary interaction variable, the cylinder diameter (d), and a secondary interaction variable, the boundary-layer thickness (\(\delta \)), were varied to study the effects of the parameter \(d/\delta \). This was found to be an appropriate scaling parameter for mean features. The characteristic interaction variables (the maximum separation distance, S, and the triple-point height, \(h_\mathrm{tp}\)) followed a linear trend when normalized as \(S/\delta \) and \(h_\mathrm{tp}/\delta \); however, when the boundary layer became larger than the cylinder diameter, a power law trend became more representative. The parameter \(d/\delta \) also determined the role that viscous effects have on the strength of the interaction, where a lower \(d/\delta \) was characterized by a greater interaction scale and lower surface pressure peaks. Moreover, the high surface pressure on the cylinder leading edge due to the Edney interaction was found to be reduced for \(d/\delta \le 0.45\), as the boundary layer encompassed the lambda-shock structure. Trends in the shapes or peaks of the auto-spectral density function were not observed based on \(d/\delta \), but appeared to be dominated by broadband low-frequency (\(f < 1~\hbox {kHz}\)) content. While the position and structure of the interaction may change as a result of varying \(d/\delta \), the effects on the unsteady dynamics were minimal.

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Acknowledgements

The authors would like to thank Datta Gaitonde of Ohio State University, Ryan Glasby of the University of Tennessee and Oak Ridge National Laboratory Joint Institute for Computational Sciences (JICS), and James Coder of the University of Tennessee, Knoxville, for their advice and assistance on this research. In addition, the authors would like to thank Joel Davenport, Andrew Davis, Jonathan Kolwyck, E. Lara Lash, Katherine Stamper, Autumn Douthitt, Matthew Schwartz, and Samantha Golter of UTSI for their assistance in the execution of the experiments, as well as Gary Payne and Jack LeGeune for their assistance in the fabrication of the test models. This material is based upon research supported by the US Office of Naval Research Under Award Number N00014-15-1-2269. This work was also internally funded by the University of Tennessee Space Institute.

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  1. The University of Tennessee Space Institute, 411 B.H. Goethert Parkway, Tullahoma, TN, 37388, USA

    S. A. Lindörfer, P. A. Kreth, R. B. Bond & J. D. Schmisseur

  2. The University of Texas at San Antonio, 1 UTSA Circle, San Antonio, TX, 78249, USA

    C. S. Combs

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Lindörfer, S.A., Combs, C.S., Kreth, P.A. et al. Scaling of cylinder-generated shock-wave/turbulent boundary-layer interactions. Shock Waves 30, 395–407 (2020). https://doi.org/10.1007/s00193-020-00938-z

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