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Quasi-static method in neutron transport
Fabio Alcaro
Politecnico di Torino, dip. Energetica, c.s. Duca degli Abruzzi 24, 10129 Torino, Italy
fabio.alcaro@polito.it
ABSTRACT
The work represents a little but valuable contribution to the advancement of the research in the field of the neutron kinetics of innovative nuclear reactors. As modern computer frames are becoming more and more performing and because the treatment of innovative nuclear reactor systems requires high accuracy results, the neutron transport theory is currently being adopted for full-core calculations. Embracing such tendency, in the present work the quasi- static approach has been adopted and implemented for the design of computational codes capable of performing reliable transient calculations. The underlying idea has been the development of the kinetic module on top of the transport solver, in such a way that the former can be flexibly plugged into the code system, independently from the transport solver itself. In particular, two computer codes have been developed: the first has been designed coupling the standalone DRAGON transport solver to an ad hoc reactor kinetic module; the second code has been developed within the ERANOS code system. A Java object-oriented platform developed by CEA-Cadarache constitutes the framework where a kinetic package has been designed, adopting the code’s API (Application Programming Interface) for the full integration in the code system. The well-known Improved Quasi-static Method (IQM) and the innovative Predictor-Corrector Quasi-static Method (PCQM) have been implemented in both computer codes. In the present work a deep analysis of the two types of quasistatic schemes has been carried out as well as the description and validation of the aforementioned computer codes.
The work has been subdivided in the following three main sections:
In the first section a general settlement of the work is given as well as the fundamental information concerning the problem of the solution of the time-dependent neutron transport equation. The approximate techniques adopted for the deployment of the computer codes are introduced as a consequence of the problems related to the impracticability of performing the full time integration of the time-dependent neutron transport equation for the analysis of generally complicated transient conditions. The quasi-static scheme and in particular the types of quasi-static algorithms used in the present work, IQM and PCQM, are thoroughly described aiming at their implementation in the framework of the neutron transport theory keeping a modular approach, thus considering the neutron transport solver as a “black box”.
In the next section the first computer code that has been developed in collaboration with the École Polytechnique de Montréal is presented. The steady-state DRAGON transport solver has been employed in the development of an integrated code for the simulation of dynamic problems. A particular emphasis is posed on nuclear reactor systems fed by an external neutron source supply. This is because of the ease of benchmarking the code itself, the level of the reactor power being known a priori for suitable dynamic problems. Such integrated
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code represented a feasibility study for a full integration of a neutron transport solver with a quasi-static scheme for kinetic analyses. Various test results demonstrate the successful implementation of the quasi-static scheme as well as pointed out some issues related to the quasi-static algorithm itself and its full integration with the steady-state transport solver.
In the last section a second computer code is described. The software is the fruit of the collaboration between the CEA-Cadarache and the Politecnico di Torino. An innovative approach has been adopted for the design of the computational code in comparison with the classical scientific software deployment. A Java object-oriented platform has been developed by CEA-Cadarache and constitutes the framework where the kinetic module has been designed and plugged in. The enhanced features of the neutron transport solver, in particular the capability of handling angular-dependent neutron flux and source data structures allowed the possibility of implementing a consistent mathematical formulation of the quasistatic algorithms. The test presented show the improvement led by the consistent formulation of the quasi-static equations with respect to the previous computer code.