An Analytical Solution for the Calculation of the Transient Transport of Gaseous Species in Nuclear Fuel Pore Channels

A semianalytical nonlinear model is described for the calculation of the burst release and release rate of volatile fission product (VFP) from a fuel pellet under steady-state and transient reactor conditions as well as the radial density distribution in the open porosity. The density of the VFP in the porosity channels is assumed to be c(r, t) = φ(r)exp[—LT(r)ω(t)] + Λ^-1(t), where L is an analytical function of parameters characterizing the physics and the geometry of the pellet; φ(r) rigorously satisfies the required boundary conditions; and ω(t), the solution of a highly nonlinear differential equation, is a time function (“kinetic time”) that represents the evolution of the density profile. The constant Λ is suitably calculated with the zeroes of the Bessel function J_o(x). The density c(r, t) of the VFP in the open porosity of the pellet is used to find the pressure p(r, t) in the open pores. The integration procedure of the transport equation for different initial and boundary conditions is described. Calculation experiments are presented and discussed.