MCNP Guide
MCNP Example: PWR Fuel Pin Model
Problem Description
In this example, we'll model a typical Pressurized Water Reactor (PWR) fuel pin cell. This fundamental component of nuclear reactor design consists of a cylindrical uranium dioxide fuel pellet, surrounded by a helium-filled gap and zirconium alloy cladding, all contained within a water moderator matrix.
The geometry represents a single pin cell wrapped in a reflective boundary, effectively modeling an infinite lattice of identical pins. This approach is commonly used for lattice-physics calculations and cell-averaged cross-section generation.
Key Dimensions
The model uses typical PWR dimensions:
Radial Dimensions:
- Fuel radius: 0.4095 cm
- Gap outer radius: 0.4178 cm
- Clad outer radius: 0.4750 cm
- Cell pitch: 1.26 cm
Material Properties:
- UO₂ density: 10.4 g/cm³
- Zircaloy-4 density: 6.56 g/cm³
- Water density: 0.998 g/cm³
Complete Input File
The following MCNP input file implements our pin cell model. We'll break down each section to understand its purpose and implementation details.
PWR Fuel Pin Cell Model
c Cell Cards
1 1 -10.4 -1 imp:n=1 $ UO2 Fuel
2 2 -0.0001 1 -2 imp:n=1 $ Helium Gap
3 3 -6.56 2 -3 imp:n=1 $ Zircaloy-4 Cladding
4 4 -0.998 3 -4 imp:n=1 $ Water Moderator (reflective boundary)
c Surface Cards
1 cz 0.4095 $ Fuel Radius
2 cz 0.4178 $ Gap Outer Radius
3 cz 0.4750 $ Clad Outer Radius
*4 cz 0.7108 $ Reflective boundary (P = 1.26 cm)
c Data Cards
c Materials
m1 92235.70c 0.04 $ 4% enriched UO2 (atom fractions)
92238.70c 0.96
8016.70c 2.0
m2 2004.70c 1.0 $ Helium fill gas
m3 40090.70c -0.5145 $ Zircaloy-4
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 $ Thermal treatment
c Criticality settings
kcode 5000 1.0 50 250
ksrc 0 0 0
c Tallies
f4:n 1 $ Flux in fuel
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
f7:n 1 $ Fission energy deposition
c Output control
prdmp j 300 1 2Detailed Input Explanation
Cell Cards
The cell cards define concentric cylindrical regions, starting from the fuel and moving outward. Each cell specifies its material, density, and geometric bounds using surface numbers. The negative signs before surface numbers indicate the "inside" of that surface.
The imp:n parameter sets the neutron importance - cells with imp:n=1 are part of the problem space, while imp:n=0 defines the external void where tracking ends.
Surface Cards
All surfaces use the cz (cylinder centered on z-axis) type. The outermost surface (*4) is marked reflective so neutrons crossing the boundary re-enter the cell, emulating an infinite lattice. Its radius (0.7108 cm) preserves the moderator-to-fuel ratio in a square lattice with 1.26 cm pitch:
R = P/√π ≈ 1.26/√π ≈ 0.7108 cm
This equivalence preserves the moderator-to-fuel ratio between the actual square pin cell and our cylindrical model.
Materials
The material cards use atom fractions (positive numbers) for stoichiometric mixtures like UO₂ and weight fractions (negative numbers) where alloy recipes are handy. Key features include:
- UO₂ Fuel (m1): 4% enriched uranium dioxide, defined by atom fractions to maintain the 1U:2O stoichiometry
- Helium Gap (m2): Pure He-4 fill gas, using a low density to represent the gas-filled gap
- Zircaloy-4 (m3): Detailed isotopic composition of the cladding alloy, including all major Zr isotopes
- Water (m4): Light water moderator with S(α,β) thermal scattering treatment (lwtr.10t) for accurate thermal neutron physics
Physics and Analysis Features
The input includes several important physics and analysis capabilities:
KCODE Calculation
The criticality calculation uses 5000 neutrons per cycle, with 50 inactive cycles (skipped for source convergence) and 250 total cycles, yielding 200 active cycles for tally accumulation.
Tallies
Two complementary tallies are implemented:
- F4: Track-length neutron flux with detailed energy bins
- F7: Fission energy deposition for power distribution
Analysis Considerations
When analyzing results from this model, consider these key aspects:
- The infinite lattice approximation may overestimate multiplication in finite systems
- Thermal scattering treatment is crucial for accurate moderator physics
- The cylindrical outer boundary is an approximation of the actual square pin cell
- Temperature effects are not explicitly modeled (room temperature cross sections)
Model Variations
This base model can be modified to study various effects in nuclear fuel design:
Design Studies
Modify these parameters to optimize fuel performance:
- Fuel enrichment for reactivity control
- Pin dimensions for thermal performance
- Moderator density for void effects
Advanced Analysis
Add these features for detailed studies:
- Burnable absorber coating on fuel
- Axial variation in materials
- Temperature-dependent cross sections