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Volume 27, Issue 1
Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

Sokratia Georgaka, Giovanni Stabile, Gianluigi Rozza & Michael J. Bluck

Commun. Comput. Phys., 27 (2020), pp. 1-32.

Published online: 2019-10

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  • Abstract

A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power reactor cooling systems. Thermal mixing of different temperature coolants in T-junction pipes leads to temperature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume regime. Two different parametric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model. The first test case results to a computational speed-up factor of 374 while the second test case to one of 211.

  • Keywords

Proper orthogonal decomposition, finite volume approximation, Poisson equation for pressure, inf-sup approximation, supremizer velocity space enrichment, Navier-Stokes equations.

  • AMS Subject Headings

78M34, 97N40, 35Q35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

s.georgaka16@imperial.ac.uk (Sokratia Georgaka)

gstabile@sissa.it (Giovanni Stabile)

grozza@sissa.it (Gianluigi Rozza)

m.bluck@imperial.ac.uk (Michael J. Bluck)

  • BibTex
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@Article{CiCP-27-1, author = {Sokratia and Georgaka and s.georgaka16@imperial.ac.uk and 5225 and Imperial College London, Department of Mechanical Engineering, London, SW7 2BX, UK. and Sokratia Georgaka and Giovanni and Stabile and gstabile@sissa.it and 5226 and SISSA, International School for Advanced Studies, Mathematics Area, mathLab, via Bonomea 265 – 34136, Trieste, Italy and Giovanni Stabile and Gianluigi and Rozza and grozza@sissa.it and 5227 and SISSA, International School for Advanced Studies, Mathematics Area, mathLab, via Bonomea 265 – 34136, Trieste, Italy. and Gianluigi Rozza and Michael and J. Bluck and m.bluck@imperial.ac.uk and 5228 and Imperial College London, Department of Mechanical Engineering, London, SW7 2BX, UK. and Michael J. Bluck}, title = {Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {1}, pages = {1--32}, abstract = {

A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power reactor cooling systems. Thermal mixing of different temperature coolants in T-junction pipes leads to temperature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume regime. Two different parametric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model. The first test case results to a computational speed-up factor of 374 while the second test case to one of 211.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0207}, url = {http://global-sci.org/intro/article_detail/cicp/13312.html} }
TY - JOUR T1 - Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems AU - Georgaka , Sokratia AU - Stabile , Giovanni AU - Rozza , Gianluigi AU - J. Bluck , Michael JO - Communications in Computational Physics VL - 1 SP - 1 EP - 32 PY - 2019 DA - 2019/10 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0207 UR - https://global-sci.org/intro/article_detail/cicp/13312.html KW - Proper orthogonal decomposition, finite volume approximation, Poisson equation for pressure, inf-sup approximation, supremizer velocity space enrichment, Navier-Stokes equations. AB -

A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power reactor cooling systems. Thermal mixing of different temperature coolants in T-junction pipes leads to temperature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume regime. Two different parametric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model. The first test case results to a computational speed-up factor of 374 while the second test case to one of 211.

Sokratia Georgaka, Giovanni Stabile, Gianluigi Rozza & Michael J. Bluck. (2019). Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems. Communications in Computational Physics. 27 (1). 1-32. doi:10.4208/cicp.OA-2018-0207
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