MCNP Example: PWR Fuel Assembly Model

Problem Description

This example models a 17×17 PWR fuel assembly using the MCNP universe and lattice system. Three universes are defined — fuel pin, guide tube, and lattice — then placed in a global assembly container with a thin water reflector.

The dimensions follow from the pin. A pin pitch of 1.26 cm repeated seventeen times gives an assembly 21.42 cm across, and a water layer 0.79 cm thick surrounds it on all four sides — half of the 1.58 cm gap that separates neighboring assemblies in a real core. Twenty-five of the 289 lattice positions hold water-filled guide tubes rather than fuel. Two tallies come out: an f4 cell flux for the assembly as a whole, and an fmesh map fine enough to resolve the flux pin by pin.

Complete Input File

Hover over any highlighted block to see how each part of the assembly model works.

c PWR 17x17 Fuel Assembly Model
c ---- Universe 1: Fuel pin ----
1    1  -10.4   -1      imp:n=1  u=1   $ UO2 fuel
2    2  -0.0001  1 -2   imp:n=1  u=1   $ Helium gap
3    3  -6.56    2 -3   imp:n=1  u=1   $ Zircaloy-4 cladding
4    4  -0.998   3      imp:n=1  u=1   $ Water (fills to lattice boundary)
 
c ---- Universe 2: Guide tube (water column) ----
11   4  -0.998  -5      imp:n=1  u=2
12   4  -0.998   5      imp:n=1  u=2   $ Water (fills to lattice boundary)
 
c ---- Universe 3: 17×17 assembly lattice ----
21   0  -21 22 -23 24  lat=1  u=3  imp:n=1
     fill=-8:8 -8:8 0:0
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 1
     1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1
     1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
c ---- Assembly container and water reflector ----
31   0          -31 32 -33 34  41 -42   fill=3  imp:n=1
32   4  -0.998  (31:-32:33:-34)
                -35 36 -37 38  41 -42   imp:n=1  $ Water reflector
33   0           35:-36:37:-38:-41:42  imp:n=0  $ Outside void
 
c ---- Surface Cards ----
c Fuel pin surfaces
1    cz  0.4096
2    cz  0.4178
3    cz  0.4750
 
c Guide tube surface
5    cz  0.6020
 
c Lattice pitch (P = 1.26 cm -> 0.63 cm half pitch)
21   px   0.630
22   px  -0.630
23   py   0.630
24   py  -0.630
 
c Assembly boundary (17 x 1.26 = 21.42 cm pitch)
31   px   10.71
32   px  -10.71
33   py   10.71
34   py  -10.71
 
c Reflector boundary
35   px   11.50
36   px  -11.50
37   py   11.50
38   py  -11.50
 
c Axial slice, reflecting (makes the model 2-D and cell volumes finite)
*41  pz   0.0
*42  pz   1.0
 
c ---- Data Cards ----
m1   92235.70c   0.045    $ 4.5% enriched UO2 (atom fractions)
     92238.70c   0.955
     8016.70c    2.0
m2   2004.70c    1.0      $ Helium fill gas
m3   40090.70c   0.5145   $ Zirconium, natural (atom fractions)
     40091.70c   0.1122
     40092.70c   0.1715
     40094.70c   0.1738
     40096.70c   0.0280
m4   1001.70c    2.0      $ Light water
     8016.70c    1.0
mt4  lwtr.10t             $ S(a,b) thermal scattering
 
c Criticality settings
kcode 10000 1.0 50 250
ksrc  0 0 0.5   2 2 0.5  -2 -2 0.5   2 -2 0.5  -2 2 0.5
 
c Tallies
f4:n  1                  $ Track-length flux, summed over all 264 fuel pins
e4    1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2
      0.1 1 2 3 4 5 6 7 8 9 10
sd4   139.15             $ 264 x pi x 0.4096^2 x 1 cm (see notes)
 
fmesh14:n geom=xyz
          origin=-10.71 -10.71 0
          imesh=10.71  jmesh=10.71  kmesh=1
          iints=17     jints=17     kints=1

What to Expect

Read the geometry before you read the answer. This is one bare assembly — 21.42 cm across, 0.79 cm of water on each face, vacuum beyond, and reflecting top and bottom so it behaves as an infinitely tall column. It is not a reactor and it will not come out near critical.

Expect k-effective somewhere around 0.5 to 0.7, and expect leakage rather than the fuel to be what puts it there. The migration length in a pressurized water reactor lattice is about 7 cm — from M² = D₁/Σ_r1 + D₂/Σ_a2 ≈ 48 + 4 cm² — so this assembly is only about three migration lengths across in each of two directions. A one-group estimate with k_∞ ≈ 1.4 gives B²M² ≈ 1.5 and lands near 0.55. Treat that as an order-of-magnitude check rather than a prediction: diffusion theory is being pushed well outside its comfort zone on a system this small, and the various two-group and Fermi-age forms disagree with each other by more than 0.2.

The single most instructive thing you can do with this deck is run it twice. Put an asterisk on surfaces 35 through 38 to make them reflective and run it again. The gap between the two numbers is the leakage, and it is much larger than most people guess. What the second run gives you is not quite the pin cell's k_∞, though. Reflecting at the outside of the water layer models an infinite array of assemblies separated by 1.58 cm water gaps, which is better moderated than a bare lattice, so expect a few percent above the 1.3 to 1.5 quoted on the pin-cell page.

The 0.79 cm water layer deserves a moment on its own. It is roughly two thermal mean free paths, so it does reflect — but nowhere near saturation, which for water takes something closer to 7 cm. It buys perhaps a centimeter of reflector savings against a 10 cm shortfall, which is why the bare assembly stays so far below critical.

Power tilts down toward the edge of the assembly, not up. Peripheral pins in a real core sit next to more water and more fuel; here they sit a centimeter from a vacuum boundary, so the mesh map should peak in the middle and fall away at the periphery. That is the opposite of the edge-peaking seen in a reflected core, and noticing which one you have is a good test of whether you understand the model in front of you.

Superimposed on that tilt, the flux spikes locally at the 25 water-filled guide tube positions, which moderate well and absorb little. Remember that the mesh scores flux rather than power: the guide tubes will be the brightest cells on the map and they produce no power at all. An fmesh with no fm card is a flux map, and an fm multiplier applied to a mesh uses one material everywhere, so it cannot convert this map into a power map either.

Model Extensions

The cheapest additions reuse the universe machinery already in the deck. A burnable poison rod is a fourth universe that replaces water in selected guide tubes; multiple enrichment zones need only more fuel universes and a different fill map; and the center position, which currently holds water, carries a steel instrument thimble in the real assembly. None of these change the structure of the input — they add universes and edit the map. Axial detail is a bigger step, because replacing the reflecting top and bottom planes with real nozzles and a plenum means the model is no longer a uniform column and the flux develops an axial shape worth tallying.

Going to a full core adds a level rather than a universe: a lattice of assemblies, each of which is itself a lattice of pins, with different enrichments assigned per assembly universe. Two things bite at that scale. Structural components like grid spacers and nozzles start to matter for the neutron balance, and tallies in the peripheral assemblies converge slowly because few source particles reach them — which is where weight windows earn their keep. The variance reduction page covers that case.