The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model
We propose a new approach for the simulation of conjugate heat exchangers. First, we introduce a dimensionality-reduced mathematical model for conjugate (fluid-solid) heat transfer: in the fluid channels, we consider a mixed-mean temperature defined on one-dimensional filaments; in the solid we cons...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Society for Industrial and Applied Mathematics
2014
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| Online Access: | http://hdl.handle.net/1721.1/89466 https://orcid.org/0000-0002-2631-6463 |
| Summary: | We propose a new approach for the simulation of conjugate heat exchangers. First, we introduce a dimensionality-reduced mathematical model for conjugate (fluid-solid) heat transfer: in the fluid channels, we consider a mixed-mean temperature defined on one-dimensional filaments; in the solid we consider a detailed partial differential equation conduction representation. We then propose a Petrov--Galerkin finite element (FE) numerical approximation which provides suitable stability and accuracy for our mathematical model. We next apply the static condensation reduced basis element (scRBE) method: a domain synthesis approach with parametric model order reduction at the intradomain level to populate a Schur complement at the interdomain level. We first build a library of “components,” each corresponding to a subdomain with a simple fluid channel geometry; for each component, we prepare Petrov--Galerkin reduced basis bubble approximations (and error bounds). We then assemble the system equations by static condensation and solve for the temperature distribution in the full domain. System-level error bounds are derived from matrix perturbation arguments; we also introduce a new output error bound which is sharper than the original scRBE estimator. We present numerical results for a two-dimensional automotive radiator model which demonstrate the flexibility, accuracy, and computational efficiency of our approach. |
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