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The legacy of Windscale Pile No. 1
The core of Pile No. 1 at Windscale caught fire in the fall of 1957. The incident, rated a level 5, “Accident with Wider Consequences,” by the International Nuclear and Radiological Event Scale (INES), has since inspired nuclear safety culture, risk assessment, accident modeling, and emergency preparedness. Windscale also helped show how important communication and transparency are to gaining trust and public support.
Vincent M. Laboure, Ryan G. McClarren, Yaqi Wang
Nuclear Science and Engineering | Volume 185 | Number 2 | February 2017 | Pages 294-306
Technical Paper | doi.org/10.1080/00295639.2016.1272374
Articles are hosted by Taylor and Francis Online.
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids using the continuous finite element method. The main idea is to use the least-squares (LS) form of the transport equation in the void regions and the self-adjoint angular flux (SAAF) form elsewhere. While the SAAF formulation is globally conservative, the LS formulation needs correction in voids. The price to pay for this fix is the loss of symmetry of the bilinear form. We first derive this conservative LS (CLS) formulation in a void. Second, we combine the SAAF and CLS forms and end up with an hybrid SAAF-CLS method having the desired properties. We show that extending the theory to near-void regions is a minor complication and can be done without affecting the global conservation of the scheme. Being angular discretization-agnostic, this method can be applied to both discrete ordinates (SN) and spherical harmonics (PN) methods. However, since a globally conservative and void-compatible second-order form already exists for SN [Wang et al., Nucl. Sci. Eng., Vol. 176, p. 201 (2014)] but not for PN, we focus most of our attention on the latter angular discretization. We implement and test our method in Rattlesnake within the Multiphysics Object Oriented Simulation Environment (MOOSE) framework. The results are also compared to those of other methods.
