A multi-scale homogenization and reconstruction approach for solid material temperature calculations in prismatic high temperature reactor cores

Traditional full-core heat transfer analysis of high temperature reactors uses effective coarse mesh parameters that are typically derived from a priori analysis and/or simplified analytical models that approximate the subscale temperature response. Consequently, different assumptions are made on each spatial scale, potentially yielding inconsistent solution methods with large associated uncertainties. In contrast, homogenized cross-sections used in full-core neutronics analysis are obtained using consistent homogenization techniques applied in conjunction with unit cell calculations. This approach has been proven both efficient and accurate. It is therefore surprising that formal homogenization techniques are rarely used in heat transfer analysis of nuclear reactors. In this work we take advantage of distinct unit cells that can be identified on each spatial scale in the MHTGR reactor core with the view to develop a consistent and accurate methodology for constructing hierarchical coarse mesh models for solid heat conduction in this reactor type. Three techniques have been used: formal multi-scale expansion homogenization is applied to obtain effective unit cell thermodynamic parameters; coarse mesh temperature discontinuities are defined to ensure continuity of the fine-scale temperatures at interfaces; and reduced order models for the time-dependent temperature response of the unit cells are obtained using proper orthogonal decomposition applied to detailed unit cell simulation results. The result is an efficient method, aimed toward unstructured CFD frameworks, that accurately captures coarse mesh temperatures with the capability of fully reconstructing the fine scale solution at any hierarchical level. The advantages of this method are illustrated for a small prismatic HTGR core using a cascaded solution approach. Starting at the finest scale, the TRISO coated particles, high resolution unit cell calculations are performed in a hierarchical fashion to build up a library of homogenized coarse mesh parameters and reduced order models, which are then used for the full-core heat conduction analysis. We demonstrate the accuracy and efficiency of the method by comparing results for a typical HTR power excursion transient against detailed reference solutions. (c) 2012 Elsevier B.V. All rights reserved.