Spatial homogenization algorithm for bridging disparities in scale between the fire and solid domains |
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| Affiliation: | 1. School of Environmental Science and Engineering/State Key Lab of Engines, Tianjin University, Tianjin 300072, PR China;2. School of Science, Tibet University, No. 36 Jiangsu Street, Lhasa 850012, Tibet Autonomous Region, PR China;3. Tianjin Engineering Center of Biomass-derived Gas and Oil, Tianjin 300072, PR China;4. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), Ministry of Education, Tianjin 300072, PR China;5. The Second Artillery Engineering University, Xi''an 710025, PR China;1. Department of General Biology, Biotechnology Postgraduate Program, University of Montes Claros – UNIMONTES, 39401-089 Montes Claros, MG, Brazil;2. Department of Forest Sciences, University of Lavras – UFLA, 37200-000 Lavras, MG, Brazil;3. Department of Forest Engineering, University of Rio Grande do Norte – UFRN, 59078-900 Natal, RN, Brazil;1. West Department of Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation RAS, Kaliningrad 236017, Russia;2. Immanuel Kant Baltic Federal University, Alexandra Nevskogo Str., 14, Kaliningrad 236041, Russia;3. Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation RAS, Troitsk, Moscow Region 142190, Russia;4. Institute of Solar-Terrestrial Physics SB RAS, Irkutsk, Russia;5. Institute for Cosmophysical Research and Aeronomy, Yakutsk, Russia |
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| Abstract: | The analysis of structures exposed to non-uniform heating from localized fires is a challenging task due to the spatially varying boundary conditions and the differences in scale between the fire simulation and solid heat transfer model. This paper presents a spatial homogenization algorithm for capturing non-uniform boundary conditions from a high-resolution fire simulation in a low-resolution finite element heat transfer model of a structure. The homogenization algorithm uses numerical integration by the trapezoid rule to calculate the equivalent thermal flux vector in the finite element heat transfer model for a spatially varying surface flux. The proposed method is compared to other approximating techniques, including averaging, sampling, and least squares methods, for a 2D heat transfer problem. The results demonstrate that the proposed homogenization algorithm converges rapidly due to the energy-equivalent representation of the thermal boundary condition. The homogenization algorithm is then implemented in a 3D heat transfer model that uses macro-level plate elements. For an application involving a horizontal plate exposed to a localized fire, the model is shown to converge to the results obtained by a solid finite element model. The homogenization algorithm combined with the plate heat transfer element proves to be an accurate and highly efficient means for analyzing structures with spatially varying thermal boundary conditions calculated by computational fluid dynamics. |
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| Keywords: | Fire simulation Heat transfer Finite element analysis Numerical methods Structures |
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