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A novel entropy normalization scheme for characterization of highly compressible flows

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Abstract

A matrix normalization scheme based on thermodynamic entropy is derived for modal decomposition techniques applied compressible flows. It is demonstrated that this normalization scheme is consistent with the scalar form of entropy. Analysis based in this consistency is performed to demonstrate the theoretical underpinnings of the Chu energy norm, which is the industry standard for compressible modal decompositions. The entropy normalization is shown mathematically to converge to the Chu normalization in the absence of strong temperature gradients. It is then compared to the Chu normalization by analyzing transient growth calculated through a linear stability analysis of a self-similar compressible boundary layer profile. The entropy norm is shown to be more sensitive to temperature fluctuations around the boundary layer than the Chu norm. These observations are further validated in a POD implementation of the entropy normalization, contracted about the conservative and primitive variables. The trends observed in transient growth analysis are observed in full-scale POD. The potential for the entropy normalization to be applied to flows with additional relevant physics, such as as thermal and chemical nonequilibrium, is explored.

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Acknowledgements

This research was supported by the Air Force Research Laboratory (AFRL) through subcontracts with the University of Tennessee with the University of Dayton Research Institute (UDRI) on prime contract number FA8650-18-C-2553. Images were created using FieldView. This material was cleared for public release by the Air Force Research Laboratory (case number AFRL-2021-1165, 3 May 2021). The data that support the findings of this study are subject to export restrictions under prime contract number FA8650-18-C-2553 and so are not publicly available.

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  1. Ethan A. Vogel

    Present address: National Institute of Aerospace, Hampton, VA, USA

  2. James G. Coder

    Present address: Department of Aerospace Engineering, Pennsylvania State University, State College, PA, USA

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  1. Department of Mechanical Aerospace and Biomedical Engineering, The University of Tennessee Knoxville, Knoxville, TN, USA

    Ethan A. Vogel & James G. Coder

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  1. Ethan A. Vogel
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Correspondence to Ethan A. Vogel.

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Communicated by Vassilios Theofilis.

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Vogel, E.A., Coder, J.G. A novel entropy normalization scheme for characterization of highly compressible flows. Theor. Comput. Fluid Dyn. 36, 641–670 (2022). https://doi.org/10.1007/s00162-022-00617-y

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