Please explain the following solution (grey part) of the problem above. Identify all the variables that lead to the answer.
7. In light water reactors, fuel rods are disposed in a square lattice and the moderator-to-fuel volume ratio is calculated using the so-called pitch-to-diameter ratio (P/D), where pitch is the distance between the center of two adjacent fuel rods, and diameter is the outer diameter of the fuel clad.
Fuel Pellet
Pitch
Cladding He gap
Using data provided below, determine:
(a) the pitch-to-diameter ratio (P/D) that makes the reactor critical;
(b) the percentage of neutrons absorbed in fuel, clad, and water, respectively
Dimensions: fuel pellet diameter 0.82 cm, helium gap thickness 0.004 cm, clad thickness 0.06 cm.
Densities: fuel (UO2 3 at% enriched) 10.4 g/cm3, water 0.7 g/cm3, clad (assume 100% Zr) 6.6 g/cm3. Cross sections: U-235 = 34.8 b, U-235 = 43.0 b, U-238 = 0.9 b, Zr = 45 mb, = 25 mb.
Assumptions: absorption in He and O is negligible, leakage probability 3%, neutron flux is uniform.
(a)
VEFUELVFUEL
Where
VCLAD = ACLADH = TrCLAD - TGAPH
D = 2rCLAD
Solve for
WATERD2
(b)
DFUELAFUEL
94%
CLAD ACLAD
= 1%
= 5%