A bare cylindrical core of radius and height has the fundamental flux shape found for…
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Nuclear Physics · Temperature, heat and the macroscopic behaviour of matter
Energy from Physics, Ch Running a reactor: kinetics, heat removal, feedback, burn-up and the fuel cycle
Problem
A bare cylindrical core of radius R and height H has the fundamental flux shape found for a bare cylinder, ϕ(r,z)=ϕ0J0(j0r/R)cos(πz/H), where j0=2.405 is the first zero of the Bessel function J0 and J1(j0)=0.519. The core's average linear heat rate, set by its total thermal power divided by the total rod length, is qˉ′=15kWm−1. The fuel is UO2 with thermal conductivity kth=3Wm−1K−1, and its melting point is about 3120K. At the hottest rod, the drops across the pellet-cladding gap, the cladding and the coolant film put the pellet surface at about 800K.
((a)) Using the flux shape above, find the ratio of the peak local flux (at the core's centre, r=0, z=0) to the flux averaged over the whole core volume, and hence the peaking factor that scales the average linear heat rate up to its peak value.
((b)) Find the peak linear heat rate this core demands, and the fuel centreline temperature rise at that peak, using the result that a uniform volumetric heat source in a cylinder gives a centreline rise independent of the rod radius. Find the peak centreline temperature and state whether the core has margin against fuel melting.