Estimation of neutron sources driving prescribed power generations in subcritical systems using one-speed two-dimensional discrete ordinates formulations

• Published in: Annals of nuclear energy Vol. 136; p. 107053
• Main Authors: Moraes, Leonardo R.C., Alves Filho, Hermes, Barros, Ricardo C.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-02-2020
• Subjects: Adjoint response matrix method; Adjoint transport problem; ADS; Discrete ordinates; Subcritical systems; ADS; Adjoint response matrix method; Discrete ordinates; Subcritical systems; Adjoint transport problem
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2019.107053

•Estimation of uniform neutron source to drive a subcritical multiplying system at a steady prescribed power distribution.•The coarse-mesh response matrix-constant nodal method for monoenergetic adjoint Sn equations in X,Y geometry.•Adjoint Sn solution as importance function for power distribution in subcritical systems.•Reciprocity relation for neutron source estimation to sustain subcritical systems at a prescribed power level.
It is well known that any subcritical system can be driven by time-independent interior sources of neutrons. Thus, we present a methodology to determine the intensities of uniform and isotropic sources of neutrons that must be added inside a subcritical system generating a prescribed steady-state distribution of power. To accomplish this, we use the time-independent, monoenergetic, X,Y-geometry neutron transport equation for the forward transport problem and the equation which is adjoint to it for the adjoint transport problem. The well-known reciprocity relation is used to correlate these two problems, yielding an explicit relation between interior sources and the power generated by the fuel regions. The discrete ordinates (SN) formulation is applied to the forward and adjoint transport problems with the level-symmetric angular quadratures for X,Y-geometry calculations. The adjoint SN problems are solved by a new coarse-mesh method named adjoint response matrix-constant nodal (RM†-CN) method which is used with the adjoint partial one-node block inversion iterative scheme to generate numerical values for the adjoint node-edge average angular fluxes. The RM†-CN method is a companion method of the response matrix-constant nodal method used to solve forward SN transport problems. Numerical results are given to verify the offered methodology.