SERPENT Guide
Tutorial: Fuel Assembly
Constructing a heterogeneous 17x17 PWR fuel assembly with multiple pin types, lattice structures, and burnup tracking in Serpent.
Overview
Moving from a single pin cell to a full fuel assembly introduces several modeling concepts: multiple pin types arranged on a lattice, structural components such as guide tubes and instrument tubes that displace fuel positions, and spatial heterogeneity in neutron flux and power distribution. This tutorial constructs a realistic 17x17 PWR fuel assembly model in Serpent, building on the pin cell tutorial.
A standard Westinghouse 17x17 assembly contains 264 fuel rod positions, 24 guide tube locations reserved for control rod insertion, and one central instrument tube. The fuel pins are identical to those described in the pin cell tutorial, while the guide tubes and instrument tube have larger inner diameters to accommodate control rod fingers and in-core instrumentation, respectively. The assembly pitch of 21.504 cm encompasses the 17 pin positions at a 1.26 cm pitch plus the inter-assembly water gap. Reflective boundary conditions on all faces again simulate an infinite array of identical assemblies, yielding the assembly-level k-infinity.
Step 1: Pin Type Definitions
Each distinct pin type is defined as a separate universe using the pin card, which specifies a sequence of concentric radial zones from the centerline outward. The outermost material fills all remaining space within the lattice cell. Changes to a pin universe automatically propagate to every lattice position where it appears.
The fuel pin universe contains the same four radial zones as the pin cell model: UO2 fuel, helium gap, Zircaloy-4 cladding, and water moderator. The guide tube universe replaces the fuel and gap with a water-filled channel bounded by a Zircaloy tube wall, with the inner radius sized to accept a control rod finger and the outer radius matching the structural requirements. The instrument tube has a similar geometry but uses stainless steel 304 for the tube wall and has slightly different dimensions.
Pin Universe Definitions
% ========================================
% 17x17 PWR Assembly - Pin Universes
% ========================================
% Standard fuel pin universe
pin fuel_pin
fuel 0.4096 % Fuel pellet radius
gap 0.4178 % He gap outer radius
clad 0.4750 % Clad outer radius
water % Moderator
% Guide tube universe (for control rods)
pin guide_tube
water 0.5715 % Inner radius (larger than fuel)
gtclad 0.6350 % Guide tube wall
water % Moderator outside
% Instrument tube universe (central position)
pin instr_tube
water 0.5590 % Inner radius
itclad 0.6050 % Instrument tube wall
water % Moderator outside
% Water hole universe (corner positions)
pin water_hole
water % Just water (no solid structures)Each pin card defines a radial sequence of material zones from the center outward. The last material listed has no radius and fills all remaining space within the lattice cell. The guide tube inner radius of 0.5715 cm is substantially larger than the fuel pellet radius, providing clearance for control rod insertion.
Step 2: Material Definitions
Beyond the pin cell materials, the assembly introduces guide tube cladding and stainless steel instrument tube wall definitions. The guide tube cladding is the same Zircaloy-4 alloy as the fuel cladding but is defined as a distinct material (gtclad) at 574 K, since guide tubes operate at coolant temperature rather than the elevated temperature of a heat-generating fuel pin. The instrument tube uses type 304 stainless steel.
Assembly calculations typically also need a borated water material. The example below includes both unborated and 1000 ppm borated water definitions. The boron uses its natural isotopic composition of B-10 and B-11, with hydrogen and oxygen fractions adjusted to maintain the correct total mass density.
Assembly Material Definitions
% ========================================
% 17x17 PWR Assembly - Materials
% ========================================
% UO2 fuel with 4.5% enrichment
mat fuel -10.4 tmp 900 vol 50925.0
92235.09c 0.045 % 4.5 at% U-235
92238.09c 0.955 % 95.5 at% U-238
8016.09c 2.0 % Stoichiometric oxygen (2 atoms per UO2)
% Helium gap
mat gap -0.0018 tmp 600
2004.09c -1.0 % Helium-4
% Zircaloy-4 cladding
% Simplified: using single isotopes instead of natural element compositions
mat clad -6.56 tmp 600
40090.09c -0.9845 % Zirconium
50120.09c -0.0155 % Tin
% Guide tube material (Zircaloy-4)
% Simplified: using single isotopes instead of natural element compositions
mat gtclad -6.56 tmp 574
40090.09c -0.9845 % Same as fuel clad
50120.09c -0.0155 % but cooler temperature
% Instrument tube (Stainless steel 304)
mat itclad -8.0 tmp 574
26000.09c -0.6850 % Iron
24000.09c -0.1900 % Chromium
28000.09c -0.0950 % Nickel
14000.09c -0.0100 % Silicon
25055.09c -0.0200 % Manganese
% Light water moderator
mat water -0.714 tmp 574 moder lwtr 1001
1001.09c -0.111894 % Hydrogen
8016.09c -0.888106 % Oxygen
% Borated water (1000 ppm boron)
mat borated_water -0.7149 tmp 574 moder lwtr 1001
1001.09c -0.111782 % Hydrogen
8016.09c -0.887218 % Oxygen
5010.09c -0.000184 % B-10 (natural abundance)
5011.09c -0.000816 % B-11
% Thermal scattering library for H in light water
therm lwtr lwj3.22tThe vol keyword on the fuel material specifies the total volume in cubic centimeters, which Serpent uses to normalize power density and burnup calculations. For an assembly with 264 fuel pins, this volume should reflect the aggregate fuel volume across all pins.
Step 3: Assembly Lattice Definition
The lat card maps each of the 289 positions in the 17x17 grid to a pin universe. It specifies the lattice type (type 1 for square), center coordinates, dimensions, and pitch. The universe assignments are listed row by row, bottom to top.
The 24 guide tube positions follow the standard Westinghouse pattern, distributed symmetrically across the assembly to provide uniform control rod coverage. The central position (row 9, column 9) contains the instrument tube universe. All remaining positions are filled with fuel pins. This arrangement produces a characteristic power distribution with a slight depression near the guide tubes (due to the local increase in moderation and absence of fissile material) and a peak in the fuel pins adjacent to the water-filled tubes.
17x17 Lattice Layout
% ========================================
% 17x17 PWR Assembly - Lattice Structure
% ========================================
% Define 17x17 lattice with pin assignments (row 17 at top)
% 264 fuel pins, 24 guide tubes, 1 instrument tube (standard Westinghouse pattern)
lat assembly 1 0.0 0.0 17 17 1.26
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin instr_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pinThe lattice type 1 denotes a square lattice centered at the origin. Each row is read left to right, and the rows are ordered from bottom to top. Modifications to any pin universe definition automatically propagate to all lattice positions referencing that universe.
Step 4: Assembly Container and Boundaries
The lattice must be placed inside a container cell that defines the outer boundaries. The container is a rectangular parallelepiped with half-widths of 10.752 cm in x and y (half the assembly pitch of 21.504 cm) and 182.88 cm in z (half the active fuel height). Reflective boundary conditions simulate an infinite array of identical assemblies.
Container Geometry and Boundary Conditions
% 17x17 PWR Assembly - Container Geometry
% ----------------------------------------
% Assembly boundaries
surf assy_left px -10.752 % Half assembly pitch
surf assy_right px 10.752 % Half assembly pitch
surf assy_front py -10.752 % Half assembly pitch
surf assy_back py 10.752 % Half assembly pitch
surf assy_bottom pz -182.88 % Half active height
surf assy_top pz 182.88 % Half active height
% Container cells
cell 100 0 fill assembly +assy_left -assy_right +assy_front -assy_back +assy_bottom -assy_top
cell 200 0 outside
% Boundary conditions
set bc 2 % Reflective boundariesThe fill keyword in the container cell tells Serpent to populate the cell interior with the named lattice universe. Any neutron that reaches the outer boundary is specularly reflected, simulating an infinite periodic array of identical assemblies.
Step 5: Spatial Burnup Zones
Production-quality assembly calculations require spatial resolution in the burnup treatment to capture the radial and axial gradients in neutron flux and isotopic composition that develop during irradiation. Fuel pins near the assembly periphery operate at higher power than interior pins due to the increased moderation from neighboring water gaps, leading to faster depletion and a flatter power distribution over the course of the cycle. Similarly, the radial temperature and flux gradient within each fuel pellet causes the outer annulus to deplete faster than the center, building up a rim of plutonium isotopes that influences the local power distribution and reactivity.
Serpent supports spatial burnup resolution through the definition of multiple fuel materials assigned to distinct radial or axial zones within the fuel pin. Each zone is given the burnflag with a unique identifier, telling the depletion solver to track its isotopic inventory independently. A typical production calculation uses three to five radial zones per pin and five to ten axial zones per assembly.
Radial and Axial Burnup Zone Definitions
% ========================================
% Spatial Burnup Resolution
% ========================================
% Modify fuel material definition for burnup zones
% Central region (high flux)
mat fuel_center -10.4 tmp 900 vol 16975.0 burn 1
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
% Middle region
mat fuel_middle -10.4 tmp 900 vol 16975.0 burn 2
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
% Outer region (lower flux)
mat fuel_outer -10.4 tmp 900 vol 16975.0 burn 3
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
% Redefine fuel pin with burnup zones
pin fuel_pin_detailed
fuel_center 0.2048 % Inner fuel zone
fuel_middle 0.3096 % Middle fuel zone
fuel_outer 0.4096 % Outer fuel zone
gap 0.4178 % He gap
clad 0.4750 % Cladding
water % Moderator
% Alternative: Axial burnup zones
mat fuel_bottom -10.4 tmp 850 vol 54750.0 burn 4 % Cooler
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_top -10.4 tmp 950 vol 54750.0 burn 5 % Hotter
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0The vol entries should reflect the actual volume of each zone across all pins in the assembly. For three equal-area radial zones, the inner zone has a smaller geometric radius but the same cross-sectional area as each outer annulus. The burn identifier must be unique across all depleting materials in the model.
Step 6: Complete Assembly Input
The calculation settings use a larger neutron population than the pin cell (30,000 per cycle with 400 active and 100 inactive cycles) to achieve adequate pin-by-pin statistical convergence across the 264 fuel positions. Power normalization is set to 17.3 MW thermal, representative of a single assembly's contribution to a 3400 MWth core with 193 assemblies.
Complete Serpent Assembly Input
% ========================================
% 17x17 PWR Assembly Model
% Complete Serpent Input File
% ========================================
set title "17x17 PWR Assembly with Control Rod Guide Tubes"
% ========================================
% MATERIALS
% ========================================
mat fuel -10.4 tmp 900 burn 1
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat gap -0.0018 tmp 600
2004.09c -1.0
% Simplified: using single isotopes instead of natural element compositions
mat clad -6.56 tmp 600
40090.09c -0.9845
50120.09c -0.0155
% Simplified: using single isotopes instead of natural element compositions
mat gtclad -6.56 tmp 574
40090.09c -0.9845
50120.09c -0.0155
mat itclad -8.0 tmp 574
26000.09c -0.6850
24000.09c -0.1900
28000.09c -0.0950
14000.09c -0.0100
25055.09c -0.0200
mat water -0.714 tmp 574 moder lwtr 1001
1001.09c -0.111894
8016.09c -0.888106
therm lwtr lwj3.22t
% ========================================
% PIN DEFINITIONS
% ========================================
pin fuel_pin
fuel 0.4096
gap 0.4178
clad 0.4750
water
pin guide_tube
water 0.5715
gtclad 0.6350
water
pin instr_tube
water 0.5590
itclad 0.6050
water
% ========================================
% ASSEMBLY LATTICE
% ========================================
lat assembly 1 0.0 0.0 17 17 1.26
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin instr_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin guide_tube fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin fuel_pin
% ========================================
% ASSEMBLY GEOMETRY
% ========================================
surf assy_left px -10.752
surf assy_right px 10.752
surf assy_front py -10.752
surf assy_back py 10.752
surf assy_bottom pz -182.88
surf assy_top pz 182.88
cell 100 0 fill assembly +assy_left -assy_right +assy_front -assy_back +assy_bottom -assy_top
cell 200 0 outside
% ========================================
% CALCULATION SETTINGS
% ========================================
set bc 2 % Reflective boundaries
set pop 30000 400 100 % Particles, active cycles, inactive cycles
% TMS is configured per-material via the tmp keyword on the mat card
set ures 1 % Unresolved resonances
set entr 20 20 1 % Shannon entropy mesh (NX NY NZ)
% ========================================
% OUTPUT CONTROL
% ========================================
set his 1 % History output
set pcc 0 % Predictor-corrector off
set power 17.3E6 % Assembly power (17.3 MW)Step 7: Advanced Analysis Features
Burnup calculations track the time evolution of isotopic inventories and reactivity, producing the reactivity swing curve that governs cycle length and reload planning. Use finer time steps at the beginning of each cycle when xenon and samarium are building in, then coarsen during quasi-equilibrium.
Burnup Calculation Setup
% Add burnup calculation to assembly model
set power 17.3E6 % Assembly thermal power (17.3 MW)
% PWR burnup schedule (days)
dep daystep
10 20 30 50 100 200 365 365 90 % Cycle 1
10 20 30 50 100 200 365 365 90 % Cycle 2
10 20 30 50 100 200 365 365 90 % Cycle 3
% Write nuclide inventories to file
set inventory all % Track all isotopes
% Use the branch card to define parametric variations
% for generating lattice physics dataDetector cards provide spatially and energy-resolved tallies of neutron flux, reaction rates, and surface currents. A pin-by-pin power detector maps the fission power distribution across all 264 fuel positions. Energy-resolved detectors yield the neutron spectrum. Surface current detectors at the assembly boundaries quantify net neutron leakage. For production lattice physics, the set microxs and set b1 cards generate homogenized few-group cross sections and discontinuity factors suitable for input to deterministic core simulators.
Detector and Flux Mapping Definitions
% Pin-by-pin power distribution
det pin_power
dm fuel
dx -10.752 10.752 17 % 17 x-bins (one per pin row)
dy -10.752 10.752 17 % 17 y-bins (one per pin column)
% Energy grids
ene thermal_grid 1 1E-11 0.625E-6
ene fast_grid 1 0.625E-6 20.0
% Energy spectrum in different regions
det thermal_flux
dm fuel
de thermal_grid
det fast_flux
dm fuel
de fast_grid
% Surface currents at assembly boundaries
det left_current ds assy_left 1
det right_current ds assy_right 1
det front_current ds assy_front 1
det back_current ds assy_back 1
% Flux tally in guide tubes (useful for rod worth studies)
det guide_flux
dm gtcladStep 8: Results and Validation
A fresh 17x17 PWR assembly at 4.5% enrichment with reflective boundary conditions typically yields a k-infinity in the range of 1.28 to 1.32 at the beginning of life, somewhat lower than the pin cell k-infinity due to the parasitic absorption in the guide tube and instrument tube structural materials and the slightly different moderation environment. The pin-by-pin power distribution exhibits a radial peaking factor (ratio of maximum to average pin power) of approximately 1.15 to 1.25, with the hottest pins located adjacent to the water-filled guide tube positions where the local moderator-to-fuel ratio is highest. The thermal utilization factor is typically 0.88 to 0.92, reflecting the additional parasitic absorption from the structural materials. Assembly power is in the range of 15 to 20 MW thermal depending on the core rating and number of assemblies.
The pin power distribution is extracted from the detector output and reshaped into a 17x17 matrix for display as a color map. The k-infinity evolution during burnup shows the characteristic initial rise (plutonium buildup from U-238 capture) followed by a gradual decline as fissile material is consumed and fission products accumulate.
MATLAB Post-Processing Script
% Load assembly results
run('assembly_res.m');
run('assembly_det0.m');
run('assembly_dep.m');
% Pin power distribution analysis
pin_power = reshape(DETpin_power(:,11), 17, 17);
% Plot power map
figure;
imagesc(pin_power);
colorbar;
title('Pin Power Distribution');
xlabel('Pin Column');
ylabel('Pin Row');
% Calculate power peaking factors
max_power = max(pin_power(:));
avg_power = mean(pin_power(:));
peaking_factor = max_power / avg_power;
fprintf('Peak/Average Power Ratio: %.3f\n', peaking_factor);
% Assembly k-infinity evolution during burnup
burnup = BURNUP;
kinf = INF_KEFF(:,1);
figure;
plot(burnup, kinf);
xlabel('Burnup (MWd/kgU)');
ylabel('k-infinity');
title('Assembly Reactivity vs Burnup');
grid on;The peaking factor should be validated against published benchmark results for the same assembly design. Discrepancies exceeding a few percent in pin powers may indicate errors in the lattice definition or insufficient statistical convergence in the Monte Carlo tallies.