A port-Hamiltonian formulation of coupled heat transfer

Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit

doi:10.1080/13873954.2022.2038637

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…Therefore, the entire model is also a port-Hamiltonian system. While the onedimensional model previously proposed in [13] had constraints on the physical parameters, this two-dimensional model no longer has constraints beyond those that are physically meaningful. However, the question of the existence and uniqueness of the solution is still open.…”

Section: Discussionmentioning

confidence: 99%

“…While this model is too simplified to be useful for actual engineering purposes, it is intended to represent the coupling structure between the turbine blade and a cooling channel and to allow us to study this coupling without having to deal with other engineering difficulties that might cloud the results. We extend and improve on the work conducted in [12,13], in which we had considered a one-dimensional model for heat conduction within the blade metal, which led to strange and undesirable behaviors and properties of the system. Instead, we will consider a two-dimensional heat equation and investigate whether this eliminates the problems of the one-dimensional model.…”

Section: Introductionmentioning

confidence: 99%

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A Two-Dimensional port-Hamiltonian Model for Coupled Heat Transfer

et al. 2022

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In this paper, we construct a highly simplified mathematical model for studying the problem of conjugate heat transfer in gas turbine blades and their cooling ducts. Our simple model focuses on the relevant coupling structures and aims to reduce the unrelated complexity as much as possible. Then, we apply the port-Hamiltonian formalism to this model and its subsystems and investigate the interconnections. Finally, we apply a simple spatial discretization to the system to investigate the properties of the resulting finite-dimensional Port-Hamiltonian system and to determine whether the order of coupling and discretization affect the resulting semi-discrete system.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Two-Dimensional port-Hamiltonian Model for Coupled Heat Transfer

et al. 2022

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“…We can model this as two interconnected subsystems: the heat conduction within the metal of the turbine blade and the coolant flow within the cooling channel. For more information and a discussion of a greatly simplified version of this system, see [1].…”

Section: Motivating Example: Cooled Gas Turbine Bladementioning

confidence: 99%

Mixed-Dimensional Geometric Coupling of Port-Hamiltonian Systems

Jäschke¹,

Skrepek²,

Ehrhardt³

2022

Preprint

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We propose a new interconnection relation for infinite-dimensional port-Hamiltonian systems that enables the coupling of ports with different spatial dimensions by integrating over the the surplus dimensions. To show the practical relevance, we apply this interconnection to a model system of an actively cooled gas turbine blade. We also show that this interconnection relation behaves well with respect to a discretization in finite element space, ensuring its usability for practical applications.

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