Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media
This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Average...
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MDPI AG
2021-07-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/6/8/266 |
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| author | Péter German Mauricio E. Tano Carlo Fiorina Jean C. Ragusa |
| author_facet | Péter German Mauricio E. Tano Carlo Fiorina Jean C. Ragusa |
| author_sort | Péter German |
| collection | DOAJ |
| description | This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative <i>L</i><sup>2</sup> errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state). |
| first_indexed | 2024-03-10T08:50:17Z |
| format | Article |
| id | doaj.art-fc491feab2df477c99eb96307cdd18c2 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T08:50:17Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-fc491feab2df477c99eb96307cdd18c22023-11-22T07:36:42ZengMDPI AGFluids2311-55212021-07-016826610.3390/fluids6080266Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous MediaPéter German0Mauricio E. Tano1Carlo Fiorina2Jean C. Ragusa3Department of Nuclear Engineering, Texas A&M University, 423 Spence St, College Station, TX 77843, USADepartment of Nuclear Engineering, Texas A&M University, 423 Spence St, College Station, TX 77843, USALaboratory of Reactor Physics and Systems Behaviour, École Polytechnique Fédérale de Lausanne, PH D3 465 (Batiment PH), Station 3, CH-1015 Lausanne, SwitzerlandDepartment of Nuclear Engineering, Texas A&M University, 423 Spence St, College Station, TX 77843, USAThis work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative <i>L</i><sup>2</sup> errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).https://www.mdpi.com/2311-5521/6/8/266reduced-order modelingproper orthogonal decompositiondiscrete empirical interpolation methodporous medium flowsmolten salt reactorOpenFOAM |
| spellingShingle | Péter German Mauricio E. Tano Carlo Fiorina Jean C. Ragusa Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media Fluids reduced-order modeling proper orthogonal decomposition discrete empirical interpolation method porous medium flows molten salt reactor OpenFOAM |
| title | Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media |
| title_full | Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media |
| title_fullStr | Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media |
| title_full_unstemmed | Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media |
| title_short | Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media |
| title_sort | data driven reduced order modeling of convective heat transfer in porous media |
| topic | reduced-order modeling proper orthogonal decomposition discrete empirical interpolation method porous medium flows molten salt reactor OpenFOAM |
| url | https://www.mdpi.com/2311-5521/6/8/266 |
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