DEVELOPMENT AND VALIDATION OF METHOD OF CHARACTERISTICS BASED CODE FOR SOLVING NEUTRON TRANSPORT EQUATION FOR A TWO-DIMENSIONAL PIN CELL USING DELAUNAY TRIANGULATION

Abstract

The primary objective of this work is development and validation of a code for lattice level calculations using the method of characteristics (MOC) in 2-dimensions. The code solves the characteristic neutron transport equation for a 2-dimensional pin cell to compute the neutron flux values in different spatial regions of the problem domain, and uses the distribution so obtained to determine the effective multiplication factor for the region of interest. The problem is subdivided into smaller, triangular, unstructured meshes using Delaunay triangulation and mesh refinement techniques. Qualified reactor physics codes are essential for the study of all existing and envisaged designs of nuclear reactors. Such codes estimate neutron fluxes in different regions of the problem domain as a function of space, angle, energy and time dependence. This provides a holistic description of all processes occurring in the reactor core and subsequent prediction of thermal–mechanical response and degradation of various components of the core. Thus, such codes are indispensable for thorough safety analysis and verification of economic feasibility of reactor design and operation. The solution of the transport equation or linear Boltzmann equation for most practical problems must be obtained using numerical methods. Most computational schemes are based on two fundamentally different approaches, namely the deterministic and the stochastic or Monte Carlo. Major existing deterministic techniques are the spherical harmonics or Pn method, the discrete ordinates or SN method, the collision probability (CP) or Pij method and the method of characteristics (MOC). The method of characteristics (MOC) has been chosen over other available methods due to the many advantages associated with it. The spherical harmonics or Pn method leads to complicatedly coupled linear system of equations for 2- and 3-dimensional problems. The discrete ordinates or SN method requires powerful pre-conditioners and acceleration strategies to ensure convergence. The collision probability (CP) or Pij method, although capable of handling unstructured geometries unlike the Pn and SN methods, requires vii isotropic sources in LAB and is only practically feasible for few-region problems. Monte Carlo simulations are accurate but are computationally expensive to set-up and run. MOC offers solution of neutron transport equation for unstructured geometries containing isotropic/anisotropic sources in LAB with reasonable accuracy at feasible computational costs. The MOC-based lattice level code developed has been benchmarked for many two energy-group problems and the results have been compared with reference solutions obtained from DRAGON V4. The benchmark problems have 3 to 4 regions with varying material compositions. Problems with different fuel materials like uranium metal / uranium – plutonium mixed oxide MOX with varying geometrical size has been analyzed using this code.