TRIGA (Training Research Isotopes General Atomics) is a nuclear reactor from General Atomics diffused all over the world, look at this page to know more about it. In this page i’ll focus on TRIGA mark II type.
The goal of this article is to show a simple input file regarding this reactor for Serpent and show some results as feedback coefficient, control rods calibration and neutron flux.
Geometry and Materials
TRIGA is a pool type thermal reactor, this mean that our coolant is watar. Our geometry is a circular lattice and fuel is made of Uranium Zirconium Hydride. Typically Uranium is higly enriched un U-235, about 20%wt and total Uranium mass concentration is about 8%wt , when ZrH is the remaining 92%wt. Proportion between Zirconium and Hydrogen can vary from 1 to 1 ratio to ZrH_{1.6} depending on fuel type. Also cladding have more than one configuration, it can be an Alluminium alloy or a stainless steel (AISI 304).
You can find more detailed information in: TRIGA REACTOR CHARACTERISTICS, H. Böck and M. Villa
Let’s talk about fuel geometry, in the picture below you can see the cros section of almost all the elements inside the reactor. Fuels are considered all with same geometry, even if different cladding have also some differences in radius and in Graphite reflectors dimensions, also enrichment and Uranium-Zirconium-Hydrogen percentage are the same for all fuel rods. You will see it in more detail looking at the input file. There are 3 types of control rods, the only difference (at least in this model) is the radius.
The following picture is a top view of the reactor core, as you can see the cylindrical arrangment of rods is surrounded by a Graphite reflector. inner radius is 22.85 cm and outer radius is 40 cm.
Fuel arrangement can vary for each reactor. Whire regions are vacuum channels. In result section i’ll use a slightly different fuel arrangement.
Some results
Results refere to the following configuration:
Pay attention to the right position of CR, from the top to the bottom we have in order: REG, SHIM, TRANS. However you find control rods information here: TRIGA REACTOR CHARACTERISTICS, H. Böck and M. Villa.
Now let’s look at Serpent geometry plot:
I’ll show three results: SHIM Control rod reactivity vs position, Fuel feedback coefficient and Flux energy density.
Simulation consist in k-eigenvalue method with 200 active cycles and 100 inactive cycles. Neutron number per cycle is 10000.
Flux energy dependence in loglog plot
Fuel feedback coefficient: please note that fuel density variation was not taken into account, however you can easly change it from the branches region in the input file. Also consider that the model is not validated and small population number is adopted. First point is actually unphysical.
SHIM reactivity vs position:
In the plot reactivity is defined as true reactivity minus reactivity at 10 cm.
Input file
Some lines are commented, such as plot and detectors, is up to you. This file is written above another input, so some previous comments are present.
% --- 3D TRIGA core
% --- NAME -----------------------------------------------
set title "TRIGA Reactor"
% --- LIBRARY DEFINITION ---------------------------------
set acelib "/your/cross/section/path/.xsdata"
set seed 14321
% --- MATERIALS -----------------------------------------------
%input definition
%mat <name> <dens> [<options>]
%<iso 1> <frac 1>
%<iso 2> <frac 2>
% --- Cladding
mat Cladding -5.015 rgb 150 150 150
V-nat.03c -0.1
Cr-nat.03c -0.02
Mn-55.03c -0.01
Fe-nat.03c -0.1
Al-27.03c -99.57
Cu-nat.03c -0.1
Ga-nat.03c -0.1
% --- Stainless steel cladding (have to verify composition and density!! aisi 304)
mat CladdingSS -7.93 rgb 255 255 255
C-nat.03c -0.0007
Cr-nat.03c -0.18
Mn-55.03c -0.02
Fe-nat.03c -0.6993
Si-nat.03c -0.01
Ni-nat.03c -0.09
% --- Fuel
mat Fuel -6.3 tmp 300 rgb 255 0 0 moder h_zrh 1001 moder zr_zrh 40000
Zr-nat.03c -91
H-1.03c -1
92235.03c -1.6
92238.03c -6.4
%moder mean that i'm inseting a thermal library, low energy with h_zrh for 1001 material
%40000 is Zr (40) 000 is natural
% --- Water
mat Water -0.99669 rgb 0 0 255 moder lw 1001
O-16.03c 1
H-1.03c 2
% --- Vacuum
mat Vacuum 0.001 rgb 230 230 230
O-16.03c -10
N-14.03c -90
% --- Control Rods
mat ControlRod -2.52 rgb 0 150 150
B-10.03c 15.8
B-11.03c 64.2
C-12.03c 20
% --- Graphite (density from: Final characterization of the first critical configuration for the TRIGA Mark II reactor of the University of Pavia using the Monte Carlo code MCNP)
mat Graphite -1.7 rgb 80 80 80
C-12.03c 1
% --- Thermal scattering data: ZrH, Light Water,graphite -----------------------------------
%therm h_zrh hzr.29t %hzr00.32t
therm h_zrh hzr.29t
%therm zr_zrh zrh.29t %ZrZrH.71t
therm zr_zrh zrh.29t
%therm lw 300 lwj3.00t %lwj3.01t
therm lw lwj3.00t
% --- GEOMETRY -----------------------------------------------
%input definition
%surf NAME TYPE [ PARAM1 PARAM2 ... ]
%Different surface type (cm)
% inf
% cyl x0 y0 r;
% sph x0 y0 z0 r;
% hexxc x0 y0 r;
% px z0
surf sf cyl 0.0 0.0 1.79 %Inner radius Fuel Element
surf sfc cyl 0.0 0.0 1.880 %Outer radius Fuel Cladding
surf scch cyl 0.0 0.0 1.905 %Outer radius central channel
surf sshim cyl 0.0 0.0 1.425 %inner shim radius
surf sshimc cyl 0.0 0.0 1.59 %uter shim radius
surf sreg cyl 0.0 0.0 0.965 %inner reg radius
surf sregc cyl 0.0 0.0 1.11 %uter reg radius
surf stran cyl 0.0 0.0 1.105 %inner trans radius
surf stranc cyl 0.0 0.0 1.27 %outr trans radius
surf srod pz 45.47 %control rod length from 0
surf stop pz 55.7 %top reflector
surf sbot pz 0 %reflector bottom
surf sfbot pz 10.07 %Start of the active lenght
surf sftop pz 46.63 %End of the active lenght
surf sref cyl 0.0 0.0 22.85 %inner radius reflector
surf s1 cyl 0.0 0.0 40.00 %cylindrical surface delimiting the core
surf sstop pz 85 %end of domain up
surf ssbot pz -50 %end of domain bottom
surf sinf inf %infinite sourface for group constant generation
% --- CELL -----------------------------------------------
%CELL DEFINITION FOR GROUP CONSTANT GENERATION
cell fuel_gcu 100 Fuel -sinf
% cell clad_gcu 200 Cladding -sinf
cell wat_gcu 300 Water -sinf
cell grap_gcu 400 Graphite -sinf
%Definition of fuel element in universe 1
% --- Fuel Element definition with alu cladding
cell cf1 1 fill 100 -sf sfbot -sftop %Fuel
cell cgt1 1 Graphite -sf sftop -stop %top reflector
cell cgb1 1 Graphite -sf sbot -sfbot %bottom reflector
cell cc1 1 Cladding sf -sfc sbot -stop %Cladding
cell cwi1 1 fill 300 sfc sbot -stop %Water in-core
cell cwob1 1 fill 300 -sbot %Water out-core (below)
cell cwoa1 1 fill 300 stop %Water out-core (above)
%Definition of fuel element in universe 8
% --- Fuel element with SS cladding
cell cf8 8 fill 100 -sf sfbot -sftop %Fuel
cell cgt8 8 Graphite -sf sftop -stop %top reflector
cell cgb8 8 Graphite -sf sbot -sfbot %bottom reflector
cell cc8 8 CladdingSS sf -sfc sbot -stop %Cladding
cell cwi8 8 fill 300 sfc sbot -stop %Water in-core
cell cwob8 8 fill 300 -sbot %Water out-core (below)
cell cwoa18 8 fill 300 stop %Water out-core (above)
%definition of central channel universe 2
cell ccch 2 Vacuum -sfc sbot -stop
cell cc2 2 Cladding sfc -scch -sbot stop
cell cwi2 2 fill 300 sfc sbot -stop %Water in-core
cell cwob2 2 fill 300 -sbot %Water out-core (below)
cell cwoa2 2 fill 300 stop %Water out-core (above)
%definition of SHIM cr in universe 3
cell cshim 3 ControlRod -sshim sbot -srod %inner rod
cell cshimc 3 Cladding sshim -sshimc sbot -srod %cladding
cell cwi3 3 fill 300 sshimc sbot -srod %Water in-core
cell cwob3 3 fill 300 -sbot %Water out-core (below)
cell cwoa3 3 fill 300 srod %Water out-core (above)
%definition of REG cr in universe 4
cell creg 4 ControlRod -sreg sbot -srod %inner rod
cell cregc 4 Cladding sreg -sregc sbot -srod %cladding
cell cwi4 4 fill 300 sregc sbot -srod %Water in-core
cell cwob4 4 fill 300 -sbot %Water out-core (below)
cell cwoa4 4 fill 300 srod %Water out-core (above)
%definition of TRANS cr in universe 5
cell ctran 5 ControlRod -stran sbot -srod %inner rod
cell ctranc 5 Cladding stran -stranc sbot -srod %cladding
cell cwi5 5 fill 300 stranc sbot -srod %Water in-core
cell cwob5 5 fill 300 -sbot %Water out-core (below)
cell cwoa5 5 fill 300 srod %Water out-core (above)
%definition of Graphite in universe 6
cell cgraphite 6 Graphite -sf sbot -stop %graphite rod
cell cgraphitec 6 Cladding sf -sfc sbot -stop %cladding for graphite element
cell cwi6 6 fill 300 sfc sbot -stop %Water in-core
cell cwob6 6 fill 300 -sbot %Water out-core (below)
cell cwoa6 6 fill 300 stop %Water out-core (above)
%definition of empty channel universe 7
cell cech 7 Vacuum -sfc sbot -stop
cell cechc 7 Cladding sfc -scch -sbot stop
cell cwi7 7 fill 300 sfc sbot -stop %Water in-core
cell cwob7 7 fill 300 -sbot %Water out-core (below)
cell cwoa7 7 fill 300 stop %Water out-core (above)
% --- Lattice core definitiion
%fills lattice with element in universe 1 2 3 4 5 6 7
% 1 fuel
% 6 graphite
%...
lat 10 4 0 0 6
1 0.0 0.0 2
6 4.20 30 8 8 8 8 8 8
12 8.15 0 8 3 8 8 8 8 8 8 8 8 8 8
18 12.15 30 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1
24 16.33 0 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1
30 20.34 30 8 1 6 6 7 6 6 6 8 1 8 1 8 1 7 1 8 1 8 1 8 1 8 1 8 1 8 8 8 1
% --- Cell c2 belongs to the base universe 0, is defined as an "outside" cell
% and covers everything outside surface s1
% NOTE univere 0 is peculiar for the plot
%creating final geometry including lattice and water up and down
cell core 11 fill 10 -sref
cell cref 11 Graphite sref
%cell cwatup 11 Water -sref stop -sstop
%cell cwatbot 11 Water -sref -sbot ssbot
cell ccore 0 fill 11 -s1 ssbot -sstop
cell c0 0 outside sstop
cell c1 0 outside -ssbot
cell c2 0 outside s1 ssbot -sstop
% --- CONTROL RODS MOVEMENTS -----------------------------------
%command for moving geometry is trans
%trans universe x y z
% -5 is central insertion
trans 3 0 0 0
trans 4 0 0 0
trans 5 0 0 0
% --- TESTING BRANCH AND AUTOMATIC PARAMETER CHANGE -----------------------------------
%movement definition
utrans pos0 0 0 +10
utrans pos1 0 0 +15
utrans pos2 0 0 +20
utrans pos3 0 0 +25
utrans pos4 0 0 +30
utrans pos5 0 0 +35
utrans pos6 0 0 +40
utrans pos7 0 0 +45
%branches definition
branch CR0 tra 5 pos0
branch CR1 tra 5 pos1
branch CR2 tra 5 pos2
branch CR3 tra 5 pos3
branch CR4 tra 5 pos4
branch CR5 tra 5 pos5
branch CR6 tra 5 pos6
branch CR7 tra 5 pos7
%nominal branch (do nothing)
branch nom
%branches temperature
%apparently i have to define the temperature and a library below and one above this temperature, for example if T = 450 i have to define one lib at 400 and one at 500
branch T0 stp Fuel -6.3 330 h_zrh hzr.29t hzr.39t zr_zrh zrh.29t zrh.39t
branch T1 stp Fuel -6.3 360 h_zrh hzr.29t hzr.39t zr_zrh zrh.29t zrh.39t
branch T2 stp Fuel -6.3 390 h_zrh hzr.29t hzr.39t zr_zrh zrh.29t zrh.39t
branch T3 stp Fuel -6.3 420 h_zrh hzr.39t hzr.49t zr_zrh zrh.39t zrh.49t
branch T4 stp Fuel -6.3 450 h_zrh hzr.39t hzr.49t zr_zrh zrh.39t zrh.49t
branch T5 stp Fuel -6.3 480 h_zrh hzr.39t hzr.49t zr_zrh zrh.39t zrh.49t
%call branches and define different burnup levels
%coef 1 0 tell us 1 burnup level at 0 MWd/kgU
%coef 1 0
%5 CR0 CR1 CR2 CR3 CR4
coef 1 0
%7 nom T0 T1 T2 T3 T4 T5
15 nom T0 T1 T2 T3 T4 T5 CR0 CR1 CR2 CR3 CR4 CR5 CR6 CR7
% --- NEUTRON POPULATION AND CRITICAL CYCLES --------------
%set pop <npop> <cycles> <skip> [<keff0> <int>]
%npop=# neutrons per cycle, cycles=# active cycles, skip=# inactive cycle
% --- Neutron population: 10000 neutrons per cycle, 200 active / 100 inactive cycles
set pop 10000 200 100
% --- BOUNDARY CONDITION (1 = black, 2 = reflective, 3 = periodic) -----------------------------------
%The reflective and periodic boundary conditions can only be used in geometries where
%the outer boundary surface is either a square or a hexagonal cylinder or a cube.
set bc 1
% --- GROUP CONSTANT GENERATION -----------------------------------
%set gcu <u1> <u2> ...
%set gcu 100 200 300
%universe must be inside a cell exploited in the geometry
%for example i have to fill a cell with universe 100 of i want to use it in set gcu
%set gcu 100 300
%define energy groups
%set nfg n_group E1 E2 ...
%E1: energy boundary in MeV
%set nfg 2 0.625e-6
% --- USE RESONANCES?
%use
%set ures 1
%do not use
%set ures 0
set ures 1
% --- PLOT GEOMETRY -----------------------------------
%plot direction nx_pixel ny_pixel positionInPerpDir x_range y_range
%plot 3 2000 2000 25
%plot 1 2000 2000
% --- Second plot is 1000 by 1000 pixels, from axial height z = 0.0
% and covers more than the whole geometry: -2.25 < (x,y) < 2.25
%plot 3 2000 2000 15.0 -7.5 7.5 -7.5 7.5
% --- The third plot is perpendicular to y-axis (2) i.e. an xz-plot
%plot 2 2000 2000
% --- DETECTOR ENERGY -----------------------------------
%The syntax is relatively simple: det <name> <param 1> <param 2> ... The integral in Eq. (7.1) is
%divided by detector volume, which is set to unity by default. This is because in most cases it
%is the total reaction rate, not the reaction rate density that is of interest to the user.
%The volume can be set manually using the “dv” entry.
%dr Reaction multiplier Determines the response function
%dv Detector volume Used for normalization
%dc Detector cell Defines the cell where the reactions are scored
%du Detector universe Defines the universe where the reactions are scored
%dm Detector material Defines the material where the reactions are scored
%dl Detector lattice Defines the lattice where the reactions are scored
%de Detector energy grid Defines the energy bins for the response function
%dx Detector mesh Defines the x-mesh where the reactions are scored
%dy Detector mesh Defines the y-mesh where the reactions are scored
%dz Detector mesh Defines the z-mesh where the reactions are scored
%dt Detector type Special detector types
%ds Surface current detector Defines surface for current detector
%Material total reactions 0 None
% -1 Total
% -2 Total capture
% -3 Total elastic
% -5 Total (n,2n)
% -6 Total fission
% -7 Total fission neutron production
% -8 Total fission energy deposition
% -9 Majorant
%ENDF Reaction modes 1 Total
% 2 Elastic scattering
% 16 (n,2n)
% 17 (n,3n)
% 18 Total fission
% --- Detector that calculates the radial fission distribution in the fuel:
% Name of the detector is AxialFission.
% The detector uses response number -6 (total fission cross section)
% of the material at the interaction site (keyword: void)
% Detector only scores interactions at material "fuel" ("dm fuel").
% Detector calculates the spatial distribution using a cylindrical mesh "dn 1"
% with 1 bins in the radial direction between 0.0 and 20 cm ("0.0 20 1")
% with 1 bin in the angular direction between 0 and 360 degrees ("0 360 1")
% with 20 bin in the axial direction that extends from 0 to 35.6 ("0 35.6 20")
%to do -inf +inf in axial dir put (0 0 1)
%det AxialFission dr -6 void dm Fuel dn 1 0.0 20 1 0 360 1 0 35.6 20
%square mesh
%det MultiDPlot dr -1 void du 0 dx -40 40 200 dy -40 40 200 dz 0 0 1
%det AxialTotal dr -2 void du 0 dn 1 0.0 0.0 1 0 360 1 -50 85 80
%det RadialTotal dr -2 void du 0 dn 1 0.0 40 80 0 360 1 0 0 1
%det AxialCapture dr -2 void du 0 dn 1 0.0 0.0 1 0 360 1 0 40 80
%Enery domain
%The number of energy bins is defined by the grid size.
%ene <name> 1 <E1> <E2> ... <En>
%ene <name> <type> <N> <Emin> <Emax>
%ene <name> 4 <struct>
%1. Cumulative spectrum (“dt -1”)
%2. Division by energy width (“dt -2”)
%3. Division by lethargy width (“dt -3”)
%Surface current detector det <name> ds <surf> <dir> (-1=inward,1=outward)
% --- Detector for tallying the flux energy spectrum
% The energy grid used for tallying will be defined later
%det EnergyDetector de MyEnergyGrid
% --- Define the energy grid to be used with the detector
% Grid type 3 (bins have uniform lethargy width)
% 500 bins between 1e-11 MeV and 2e1 MeV.
%ene MyEnergyGrid 3 500 1e-11 2e1
%thermal energy grid
%ene MyEnergyGrid 3 100 1e-11 1e-6
% --- DETECTOR DEFINITION AND PLOT RESULT -----------------------------------
%det elastic dr -3 void
%mesh 8 2 elastic 3 200 200
%mesh 8 2 elastic 1 2000 2000
%mesh 8 2 elastic 3 2000 2000
%det capture dr -2 void du 0
%mesh 8 2 capture 2 2000 2000
%mesh 3 2000 2000
%mesh 1 2000 2000