Port-based modelling of mass transport phenomena

Authors

A. Baaiu, F. Couenne, D. Eberard, C. Jallut, L. Lefevre, Y. Legorrec, B. Maschke

Abstract

The goal of this article is to present an extension of the port-based modelling approach (bond graphs) which applies to systems subject to heat and mass transfer. The methodology is based on the first principle, conservation laws and constitutive closure relations. The latter are the phenomenological laws relating fluxes and thermodynamic forces. Then instantaneous power conservation appears naturally as a geometric interconnection structure called Dirac structure. The multi-level case (several macroscopic spatial scales) is investigated with the assumption that the spatial scales are separated and may be considered as two distinct phases. In this case, it is shown that both the interconnection coupling within a phase and the multi-level interconnection coupling are Dirac structures.

Citation

• Journal: Mathematical and Computer Modelling of Dynamical Systems
• Year: 2009
• Volume: 15
• Issue: 3
• Pages: 233–254
• Publisher: Informa UK Limited
• DOI: 10.1080/13873950902808578

BibTeX

@article{Baaiu_2009,
  title={{Port-based modelling of mass transport phenomena}},
  volume={15},
  ISSN={1744-5051},
  DOI={10.1080/13873950902808578},
  number={3},
  journal={Mathematical and Computer Modelling of Dynamical Systems},
  publisher={Informa UK Limited},
  author={Baaiu, A. and Couenne, F. and Eberard, D. and Jallut, C. and Lefevre, L. and Legorrec, Y. and Maschke, B.},
  year={2009},
  pages={233--254}
}

Download the bib file

References

• Karnopp D., System Dynamics: Modeling and Simulation of Mechatronic Systems (2006)
• Ingrim M., A discrete network representation of thermomechanical processes in continuous media
• Ingrim, M. E. & Masada, G. Y. The Extended Bond Graph Notation. Journal of Dynamic Systems, Measurement, and Control vol. 113 113–117 (1991) – 10.1115/1.2896334
• Yen C., Extended Bond Graphs with moving reference frames for flexible multibody dynamics (1992)
• Granda J., Proceedings of the Int. Conf. Bond Graph Modeling ICBGM, ‘93
• Granda J., Proceedings of the Int. Conf. Bond Graph Modeling ICBGM’93
• Lebrun, M. The Use of Modal Analysis Concepts in the Simulation of Pipeline Transients. Journal of the Franklin Institute vol. 319 137–156 (1985) – 10.1016/0016-0032(85)90070-5
• Samanta, B. & Mukherjee, A. Analysis of Acoustoelastic Systems Using Modal Bond Graphs. Journal of Dynamic Systems, Measurement, and Control vol. 112 108–115 (1990) – 10.1115/1.2894126
• Buyl F., Proceedings of the Int. Conf. Bond Graph Modeling ICBGM’93
• Yen, C., Masada, G. Y. & Ingrim, M. E. Model of a hyperelastic thin plate using the extended bond graph method. Journal of the Franklin Institute vol. 328 765–780 (1991) – 10.1016/0016-0032(91)90053-6
• Doblaré M., Proceedings of the Int. Conf. Bond Graph Modeling ICBGM’95
• Maschke B., Proceedings of the ASME Int. Mechanical Engineering Congress and Exposition
• van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
• Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica vol. 40 757–771 (2004) – 10.1016/j.automatica.2003.12.017
• Macchelli, A. & Melchiorri, C. Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach. SIAM Journal on Control and Optimization vol. 43 743–767 (2004) – 10.1137/s0363012903429530
• Hamroun H., Trans. Fluid Mech. (2006)
• Longoria, R. G. Wave-scattering formalisms for multiport energetic systems. Journal of the Franklin Institute vol. 333 539–564 (1996) – 10.1016/0016-0032(96)00019-1
• Marquardt, W. Trends in computer-aided process modeling. Computers & Chemical Engineering vol. 20 591–609 (1996) – 10.1016/0098-1354(95)00195-6
• Mangold, M., Motz, S. & Gilles, E. D. A network theory for the structured modelling of chemical processes. Chemical Engineering Science vol. 57 4099–4116 (2002) – 10.1016/s0009-2509(02)00372-x
• Baaiu A., Proceeding of the IFAC symposium on Advanced Control of Chemical Processes (ADCHEM’06)
• Baaiu A., Proceeding of the 5th MathMod (2006)
• Franco A. A., Proceeding of the 5th MathMod
• Golo G., Interconnection structures in port-based modelling: tools for analysis and simulation (2002)
• Lakatos, B. G. Multilevel modelling of heterogeneous catalytic reactors. Chemical Engineering Science vol. 56 659–666 (2001) – 10.1016/s0009-2509(00)00273-6
• Bird R. B., Transport Phenomena (2002)
• de Groot S. R., Non-Equilibrium Thermodynamics (1984)
• Flanders H., Differential Forms With Applications to the Physical Sciences (1989)
• Frankel T., The Geometry of Physics: An Introduction (2004)
• Dorfman I., Dirac Structures and integrability of Nonlinear Evolution Equations (1993)
• Courant, T. J. Dirac manifolds. Transactions of the American Mathematical Society vol. 319 631–661 (1990) – 10.2307/2001258
• Krishna, R. & Wesselingh, J. A. The Maxwell-Stefan approach to mass transfer. Chemical Engineering Science vol. 52 861–911 (1997) – 10.1016/s0009-2509(96)00458-7
• Ruthven D. M., Pressure Swing Adsorption (1994)
• Alonso, A. A., Ydstie, B. E. & Banga, J. R. From irreversible thermodynamics to a robust control theory for distributed process systems. Journal of Process Control vol. 12 507–517 (2002) – 10.1016/s0959-1524(01)00017-8