Port-Hamiltonian formulation of two-phase flow models

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Abstract

Two-phase flows are frequently modelled and simulated using the Two-Fluid Model (TFM) and the Drift Flux Model (DFM). This paper proposes Stokes–Dirac structures with respect to which port-Hamiltonian representations for such two-phase flow models can be obtained. We introduce a non-quadratic candidate Hamiltonian function and present dissipative Hamiltonian representations for both models. We then use the structure of the corresponding formally skew-adjoint operator to derive a Stokes–Dirac structure for the two variants of multi-phase flow models. Moreover, we discuss the difficulties in deriving a port-Hamiltonian formulation of the DFM with general slip conditions, and argue why this model may not be energy-consistent.

Original languageEnglish
Article number104881
Number of pages9
JournalSystems and Control Letters
Volume149
DOIs
Publication statusPublished - Mar 2021

Bibliographical note

Funding Information:
The first author has been funded by the Shell NWO/ FOM Ph.D. Programme in Computational Sciences for Energy Research. The second author is supported by the DFG, Germany Collaborative Research Center 1029, project A02. The third author has carried out this research in the HYDRA project, which has received funding from European Union's Horizon 2020 research and innovation program under grant agreement No 675731.

Funding Information:
The first author has been funded by the Shell NWO/ FOM Ph.D. Programme in Computational Sciences for Energy Research . The second author is supported by the DFG, Germany Collaborative Research Center 1029, project A02 . The third author has carried out this research in the HYDRA project, which has received funding from European Union’s Horizon 2020 research and innovation program under grant agreement No 675731 .

Publisher Copyright:
© 2021 The Author(s)

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

  • Drift Flux Model
  • Non-quadratic Hamiltonian
  • Port-Hamiltonian
  • Skew-adjoint
  • Stokes–Dirac structures
  • Two-Fluid Model

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