MCNP Guide

❮ Result AnalysisTutorial: Shielding Analysis ❯

Example: Simple Criticality Calculation

Problem Description

This example demonstrates a fundamental criticality calculation using MCNP. We model a 3×3 array of fuel pins with water moderation and reflective boundary conditions. This configuration serves as a concise introduction to criticality calculations while covering neutron multiplication, moderation, and the universe/lattice geometry system.

System Configuration

Physical Components:

  • Nine UO₂ fuel pins (5% enriched)
  • Zircaloy cladding (standard PWR dimensions)
  • Light water moderator with S(α,β) treatment
  • Reflective boundaries (infinite array approximation)

Analysis Features:

  • KCODE calculation for k-eigenvalue
  • Multiple initial fission source points
  • Thermal neutron treatment via lwtr.10t
  • Hierarchical universe/lattice geometry

Complete Input File

Hover over any highlighted section in the input to see what it does and why each parameter was chosen. On mobile, tap to show the explanation.

mcnp — hover sections to explore
3x3 Fuel Pin Array Criticality Problem
c Cell Cards
c Universe 1: fuel pin
10  1  -10.4  -1        u=1  imp:n=1  $ UO2 fuel
11  0          1 -2     u=1  imp:n=1  $ Gap (void)
12  2  -6.56   2 -3    u=1  imp:n=1  $ Zircaloy clad
13  3  -0.998  3        u=1  imp:n=1  $ Water moderator (fills to lattice boundary)
c Universe 2: 3x3 array
20  0  20 -21 -22 23  lat=1  u=2  imp:n=1
     fill=-1:1 -1:1 0:0
     1 1 1
     1 1 1
     1 1 1
c Global problem cell with reflective boundary
30   0          30 -31 -32 33  fill=2  imp:n=1
31   0          -30:31:32:-33          imp:n=0
c Surface Cards
1   cz  0.4095
2   cz  0.4178
3   cz  0.4750
c Lattice pitch (pin pitch = 1.26 cm → 0.63 cm half pitch)
20  px  -0.630
21  px   0.630
22  py   0.630
23  py  -0.630
c Problem boundary (array span = 3 × 1.26 cm)
*30  px  -1.89
*31  px   1.89
*32  py   1.89
*33  py  -1.89
c Data Cards
m1   92235.70c  0.05
     92238.70c  0.95
     8016.70c   2.0
m2   40090.70c -0.55
     40091.70c -0.11
     40092.70c -0.17
     40094.70c -0.15
     40096.70c -0.02
m3   1001.70c   2.0
     8016.70c   1.0
mt3  lwtr.10t
c Criticality settings
kcode  5000 1.0 50 300
ksrc   0 0 0   0.6 0 0  -0.6 0 0   0 0.6 0   0 -0.6 0
c Output control
prdmp  j 50 1 1

Annotated MCNP Input

Hover over any highlighted section in the code to see a detailed explanation. Tap on mobile.

●Pin-cell geometry (u=1)
●3×3 lattice (u=2)
●Global cells
●Fuel pin surfaces
●Lattice pitch planes
●Reflective boundaries
●UO₂ fuel material
●Zircaloy cladding
●Water + thermal scattering
●KCODE settings
●KSRC initial source
●Output control

Expected Results and Analysis

When running this problem, you should expect the following characteristics in the results:

Physics Behaviour

  • k-effective is typically above 1.0 due to the infinite lattice approximation (reflective BCs eliminate leakage) and fresh fuel composition.
  • The thermal flux peaks in the water moderator and dips in the fuel pellet due to resonance self-shielding.
  • Power distribution is nearly uniform across all nine pins because of the reflective boundaries.

Statistical Checks

  • Source convergence should be achieved within 50 inactive cycles for this simple symmetric geometry.
  • Final k-effective uncertainty should be less than 0.001 with 250 active cycles of 5000 neutrons.
  • All ten MCNP statistical tests should pass with the settings shown.

Model Extensions and Studies

This base model can be extended in several ways to study different aspects of reactor physics:

Geometry Variations

Modify the physical configuration to study:

  • Different array sizes (5×5, 7×7, 17×17)
  • Pin pitch effects on moderation ratio
  • Burnable absorber rod patterns
  • Guide tube locations

Physics Studies

Investigate reactor physics phenomena:

  • Temperature coefficient (Doppler + moderator)
  • Void coefficient analysis
  • Boron worth calculations
  • Burnup behaviour using BURN card

Important Analysis Considerations

When interpreting results from this model, keep in mind:

  • The reflective BCs produce k∞, not keff. A real finite reactor requires explicit modelling of leakage.
  • Room-temperature cross sections (.70c) are not appropriate for operational power analysis — use temperature-dependent data.
  • The simplified material compositions may affect detailed reaction rate tallies.
  • Additional tallies (F4, F7) are needed for spatial flux and power distribution analysis.

Related Topics

❮ Result AnalysisTutorial: Shielding Analysis ❯