The Variation of k_∞ with Fuel Temperature for a Uranium Fuel Element

The change in k_∞ of a heterogeneous lattice caused by a uniform change in the temperature of the fuel has been measured, using the Physical Constants Testing Reactor (PCTR). The test lattice was moderated with graphite and fueled with concentric-tube elements of slightly enriched uranium metal. The temperature of the fuel was varied from 297 to 1241°K. The change in k_∞ with temperature was nonlinear and could be represented by the relation where T is in degrees Kelvin. The experimentally measured values of the constants were α = (−0.308 ± 0.004), β = (−0.120 ± 0.004), γ = (−0.085 ± 0.004). The unit functions, U, represent the changes in k_∞ caused by the isothermal volume expansion of the fuel element when the uranium metal undergoes transformations in its crystal structure from alpha to beta and from beta to gamma phases. The term C is a normalization factor related to the lattice under study. The reactivity techniques employed here are shown to be four times more sensitive than activation methods for determining the functional relationship between the effective resonance integral of a fuel element and the temperature of the element. The constant, α, has been experimentally separated into two components: α_v = (−0.240 ± 0.04). which is associated with the average interior temperature of the fuel, and α_s = (−0.068 ± 0.04), which is associated with the temperature of the surface of the fuel. This separation allows treatment of nonuniform temperature distribution in the fuel.