On an analytical formulation for the mono-energetic neutron space-kinetic equation in full cylinder symmetry

• Published in: Annals of nuclear energy Vol. 99; pp. 253 - 257
• Main Authors: Oliveira, F.R., Bodmann, B.E.J., Vilhena, M.T., Carvalho, F.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2017
• Subjects: Current density; Cylinders; Mathematical analysis; Mathematical models; Neutron flux; Projection; Scalars; Separation
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2016.08.032

•The present work presents an exact solution to neutron spatial kinetic equation.•It is an exact solution in a heterogeneous cylinder with temporal dependence.•The solution was constructed through the separation of variables method. In the present work we discuss a system of partial differential equations that model neutron space-kinetics in cylindrical geometry and are defined by two sectionally homogeneous cylinder cells, mono-energetic neutrons and one group of delayed neutron precursors. The solution is determined using the technique of variable separation. The associated complete spectra with respect to each variable separation are analysed and truncated such as to allow a parameterized global solution. For the obtained solution we present some numerical results for the scalar neutron flux and its time dependence and projection on the cylinder axis z and the radial and cylinder axis projection. As a case study we consider an insertion of an absorbing medium in the upper cylinder cell. Continuity of the scalar flux at the interface between the two cylinder elements and conserved current density is explained and related to scale invariance of the partial differential equation system together with the initial and boundary conditions. Some numerical results for the scalar angular neutron flux and associated current densities are shown.