Multi-Source Thermal Model for Electrical Harness Design

The challenges of improving wiring harness design are safety, ecology, weight and cost. To achieve this, a better prediction of the temperature in the wiring harnesses is necessary. In terms, this involves considering a lot of compact thermal sources with an uncontrolled layout. Up to now, the main methods dedicated to resolution are based on finite elements given that temperature’s evolution according to several thermal sources, Joule effect, without controlled wire layout is complicated to evaluate. This paper deals with an alternative and faster method. An analytic equation : Infinite Line Source (ILS), is used to create a nodal network. This method coming from geothermal heat exchangers relies on a fully-connected node network which is called here full-graph method. It will be shown that, for compact heat sources, this method can be improved with a reduced model. A reduced model is a pruned node network: only the wires corresponding to the adjoining wires are selected. The bundle is a complex system which has a variable environment and an uncontrolled wire layout. The adaptation required by the models requires many assumptions. This case study focuses on a 10 wire configuration with the following assumptions: stationary state, identical wires, axial heat fluxes and neglected heat convection. Comparative studies between the two nodal methods and a Finite Volumes Method (FVM) are also presented and discussed. From a physical point of view, the results are more interesting. Further investigations, depending on the different parameters, should lead us to make more realistic nodal methods.

Pin to pin neutron flux reconstruction in a PWR reactor using support vector regression (SVR) technique

Coarse mesh nodal methods are widely used in the analysis of nuclear reactors. However, these methods provide only average values of the neutron fluxes. From a safety point of view, it is important to have an accurate analysis of the pin to pin flux distribution that nodal methods are not able to provide. Many articles have been published that make use of mathematical techniques to determine flux distributions. Most of these techniques use expansion functions to estimate these distributions. The expansion coefficients of these works are determined by conditions that take into account the average values of certain fluxes supplied by the nodal methods. There are also methods that employ analytical solutions of the neutron diffusion equation. This article presents a different approach for calculating the pin to pin neutron flux distribution for a PWR reactor. The developed method uses support vector regression (SVR) technique to determine this pin to pin neutron flux. The SVR technique uses average data computed with the Nodal Expansion Method (NEM) for learning purposes. A total of 70% of the computed data were used for training and 30% for validation, using multifold-cross-validation. Two fuel elements were removed from the training and validation sets, to test the method. Less than 2% errors were found when compared to the values ​​obtained by the nodal expansion method (NEM), using a fine-mesh spatial discretization. We concluded that use of SVR to reconstruct pin to pin fluxes is another option, which will be of great value in fuel reload calculations, since the same parameters will be applied to all cycles, thus expediting calculations when compared to standard procedure calculations.

A Comparison Between Recent Advances in Cylindrical Nodal Diffusion Methods

The resurgence of high temperature reactor (HTR) technology has prompted the development and application of modern calculation methodologies, many of which are already utilized in the existing power reactor industry, to HTR designs. To this end, the use of nodal diffusion methods for full core neutronic analysis is once again considered for both their performance and accuracy advantages. Recently a number of different approaches to two-dimensional and 3D multigroup cylindrical nodal diffusion methods were proposed by various institutions for use in HTR and, specifically, pebble-bed modular reactor (PBMR) calculations. In this regard, we may mention the NEM code from the Pennsylvania State University based on the nodal expansion method and the OSCAR-4 code from NECSA, utilizing a conformal mapping approach to the analytic nodal method. In this work we will compare these two approaches in terms of accuracy and performance. Representative problems, selected to test the methods thoroughly, were devised and based on both a modified version of the PBMR 400 MW benchmark problem and a “cylindrisized” version of the IAEA two-group problem. The comparative results between OSCAR-4 and NEM are given, focusing on global reactivity estimation, as well as power and flux errors as compared with reference finite-difference solutions. These results indicate that both OSCAR-4 and NEM recover the global reference solution for the IAEA problem and show power errors, which are generally acceptable for nodal methods. For the PBMR problem the accuracy is similar, but some convergence difficulties are experienced at the outer boundaries of the system due to the very large dimensions of the reflector (when compared with typical water-moderated reactors). For both codes a significant performance increase was found, as compared with finite-difference calculations, which is the method currently employed by the PBMR (Pty) Ltd. In conclusion it seems that nodal methods have potential for use in the HTR analysis and, specifically, the PBMR calculational arena, although cylindrical geometry based nodal methods will have to develop toward maturity before becoming the industry standard.