MMN-64
Analytical solution of neutron difussion equation for a PWR typical lattice
Abstract
This paper introduces an analytical technique to obtain the two-group neutron flux distribution on a typical square cell in the symmetrical core of a pressurised water reactor, PWR. Mathematically, the flux distribution is a solution to a system of fourth order homogeneous di usion equations with irregular boundary conditions in Cartesian and polar coordinates. The formulae for the solution, obtained explicitly in terms of hypergeometric functions, are suitable for computer programming leading to temperature distribution and thermal stress analysis on fuel rod, etc. The proposed technique is capable of calculating the neutron flux at the corners of the typical cell, where neither approximated equivalent cell methods nor numerical methods succeeded. An actual condition of steady state critical reactors is studied, and numerical results by the proposed technique are compared to those of an approximated equivalent cylindrical cell technique.
Vol. 4 (2003), No. 2, pp. 135-150
DOI: 10.18514/MMN.2003.64