MCNP Guide
Example: Simple Criticality Calculation
Problem Description
This example demonstrates a fundamental criticality calculation using MCNP. We'll model a 3×3 array of fuel pins with water moderation and reflective boundary conditions. This simple configuration serves as an excellent introduction to criticality calculations while incorporating key physics concepts like neutron multiplication, moderation, and leakage.
System Configuration
Physical Components:
- Nine UO₂ fuel pins (5% enriched)
- Zircaloy cladding (standard PWR)
- Light water moderator
- Reflective boundaries (infinite array)
Analysis Features:
- KCODE calculation for eigenvalue
- Multiple initial source points
- Thermal neutron treatment
- Periodic boundary conditions
Complete Input File with Explanations
The following MCNP input implements our 3×3 pin array. Each section is carefully structured to model the geometry, materials, and physics requirements for accurate criticality calculations.
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 -4 u=1 imp:n=1 $ Water moderator
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
4 cz 0.6617
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.01t
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 1Detailed Input Analysis
Geometry Construction
The geometry is built using a hierarchical universe structure:
- Base Universe (u=1): Contains the individual pin cell components - fuel, cladding, and surrounding water. Each component is defined by cylindrical surfaces and appropriate material assignments.
- Lattice Universe (u=2): Creates a 3×3 array by filling a rectangular region with universe 1. The lat=1 parameter specifies a rectangular lattice structure.
- Global Universe: Contains the lattice universe and defines the overall problem boundaries with reflective conditions.
Material Definitions
The materials are defined to represent typical PWR components with appropriate nuclear data specifications:
- Fuel (m1): 5% enriched UO₂, specified using atom fractions. The .70c cross-section suffix indicates ENDF/B-VII.0 data at room temperature.
- Cladding (m2): Simplified Zircaloy composition using individual Zr isotopes with weight fractions that approximate natural abundances.
- Moderator (m3): Light water with thermal scattering treatment (lwtr.01t) to accurately model neutron thermalization.
Criticality Calculation Setup
The KCODE card parameters are chosen to ensure reliable convergence:
Parameters:
- 5000 neutrons per cycle
- Initial guess k=1.0
- 50 inactive cycles
- 300 total cycles (250 active)
Source Distribution:
Multiple source points are specified in a cross pattern to ensure good initial coverage of the fissile regions, promoting faster convergence of the fission source distribution.
Expected Results and Analysis
When running this problem, you should expect the following characteristics in the results:
Physics Behavior
- k-effective: Typically above 1.0 due to the infinite lattice approximation and fresh fuel composition
- Flux Distribution: Should show thermal peaks in the moderator and depression in the fuel due to self-shielding
- Power Distribution: Relatively flat across pins due to the reflective boundaries
Statistical Checks
- Source Convergence: Should be achieved within the 50 inactive cycles due to the simple geometry
- Statistical Error: Final k-effective error should be less than 0.001 with these cycle settings
- Tally Behavior: All statistical checks should pass due to the high number of active cycles
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)
- Pin pitch effects on moderation
- Burnable absorber patterns
- Guide tube locations
Physics Studies
Investigate reactor physics phenomena:
- Temperature coefficient studies
- Void coefficient analysis
- Doppler broadening effects
- Burnup behavior
Important Analysis Considerations
When analyzing results from this model, keep in mind these key points:
- The infinite lattice approximation will overpredict k-effective compared to a finite system
- Room temperature cross sections may not be appropriate for operational analysis
- The simplified material compositions may affect detailed reaction rates
- Additional tallies may be needed for detailed power distribution analysis