1. School of Mechanical and Nuclear Engineering North-West University
Assembly Discontinuity Factor calculation for use in the Nodal Expansion Method
G. Scholtz, V. Naicker, K. Ivanov
School of Mechanical and Nuclear Engineering
North-West University
Energy Postgraduate Conference 2013

2. Outline 1. Introduction 2. Homogenization
Research aims and objectives
Neutron flux calculation
2. Homogenization
Generalized Equivalence Theory (GET)
Assembly Discontinuity Factors (ADF’s)
3. Core layout and MCNP model
4. Results and Discussion
ADF
MCNP
Nodal Expansion Method (NEM)
5. Conclusion and further work

3. Introduction – Research aims & objectives
Benchmark studies for major reactor types.
Stand-alone neutronics and T- H simulations, coupled afterwards.
Develop input model for SAFARI-1 using NEM.
Calculate Assembly Discontinuity Factors using MCNP.
Perform steady state analysis to calculate flux, power, etc.

4. Neutron flux calculation
Knowledge of flux distribution required for power, criticality and fast fluence.
NEM is a deterministic, nodal diffusion neutronics code.
Nodal methods
- Reduced computational times.
- Large nodes compared to finite difference methods.
- Space averaged (homogenized) parameters.
- Modern, established method for full core calculations.
Deterministic methods
- Based on the solution of neutron transport equation.
- Discrete ordinates, integral transport, diffusion theory.
Stochastic methods (MCNP)
- Simulates particle behaviour by random sampling.
- Highly accurate but computationally expensive.

5. Homogenization Generalized equivalence theory
- Methods employed to replace heterogeneous lattice of materials with an
equivalent homogeneous mixture.
- Aim is to preserve reaction rates and multiplication factor.
- Generalized Equivalence Theory matches the heterogeneous and
homogeneous solutions by allowing for discontinuities.
- Accomplished through suitable multiplier on each side of node boundary.
Assembly Discontinuity Factors
- Reduces homogenization error.
- ADF is ratio of the surface averaged heterogeneous flux to the volume
averaged homogeneous flux.

6. Core layout & MCNP model
MCNP (3 x 3 x 3)
SAFARI-1 core

7. Results - ADF Thermal energy group Fast energy group (≤ 4eV)
x_max
0.486
0.122
x_min
0.494
0.124
y_max
0.449
0.104
y_min
0.455
0.105
z_max
0.473
z_min
0.472

8. Results - MCNP
Fuel filled core

9. Results - NEM
15 x14x12 Nodes
Homogenized cross sections (NECSA)

10. Conclusions and further work
MCNP can be used for ADF calculation.
Consistent values for ADF.
Current NEM results are sufficient for ADF implementation.
MCNP calculation provides second set of results to compare to NEM.
Further work
Complete heterogeneous model of SAFARI-1 reactor.
Determine multi-group surface and volume fluxes for ADF calculation.
Implement ADF into NEM input model.
This work is based upon research supported by the South African
Research Chairs Initiative of the Department of Science and
Technology and National Research Foundation.