Discrete Port-Hamiltonian Coupled Heat Transfer

Authors

Jens Jäschke, Matthias Ehrhardt, Michael Günther, Birgit Jacob

Abstract

Heat transfer and cooling solutions play an important role in the design of gas turbine blades. However, the underlying mathematical coupling structures have not been thoroughly investigated. In a previous work, we successfully modelled a simplified version of this problem as an infinite-dimensional system. Here, we construct a spatial discretization for the above problem and investigate its properties. We show that the discrete system is less restrictive than the original infinite-dimensional system, suggesting something like a regularization effect due to discretization.

Citation

• ISBN: 9783031118173
• Publisher: Springer International Publishing
• DOI: 10.1007/978-3-031-11818-0_57
• Note: European Consortium for Mathematics in Industry

BibTeX

@inbook{J_schke_2022,
  title={{Discrete Port-Hamiltonian Coupled Heat Transfer}},
  ISBN={9783031118180},
  ISSN={2198-3283},
  DOI={10.1007/978-3-031-11818-0_57},
  booktitle={{Progress in Industrial Mathematics at ECMI 2021}},
  publisher={Springer International Publishing},
  author={Jäschke, Jens and Ehrhardt, Matthias and Günther, Michael and Jacob, Birgit},
  year={2022},
  pages={439--445}
}

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References

• Backhaus, J. et al. GivEn—Shape Optimization for Gas Turbines in Volatile Energy Networks. Mathematics in Industry 71–106 (2021) doi:10.1007/978-3-030-62732-4_4 – 10.1007/978-3-030-62732-4_4
• Beattie, C., Mehrmann, V., Xu, H. & Zwart, H. Linear port-Hamiltonian descriptor systems. Mathematics of Control, Signals, and Systems vol. 30 (2018) – 10.1007/s00498-018-0223-3
• Jacob, B. & Zwart, H. J. Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces. (Springer Basel, 2012). doi:10.1007/978-3-0348-0399-1 – 10.1007/978-3-0348-0399-1
• Jäschke, J., Ehrhardt, M., Günther, M. & Jacob, B. A port-Hamiltonian formulation of coupled heat transfer. Mathematical and Computer Modelling of Dynamical Systems vol. 28 78–94 (2022) – 10.1080/13873954.2022.2038637
• Kotyczka, P. & Lefèvre, L. Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation. IFAC-PapersOnLine vol. 51 125–130 (2018) – 10.1016/j.ifacol.2018.06.035
• Mehrmann, V. & Morandin, R. Structure-preserving discretization for port-Hamiltonian descriptor systems. 2019 IEEE 58th Conference on Decision and Control (CDC) 6863–6868 (2019) doi:10.1109/cdc40024.2019.9030180 – 10.1109/cdc40024.2019.9030180