COMPUTATIONAL NEUTRONICS ANALYSIS OF TRIGA REACTORS DURING
POWER PULSING
By
Malcolm Bean
SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE
AND ENGINEERING
IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF
BACHELOR OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
MAY 2011
Malcolm Bean.
All Rights Reserved
The author hereby grants to MIT permission to reproduce and distribute publicly
Paper and electronic copies of this thesis document in whole or in part.
Signature of Author:
Malcolm Bean
Department of Nuclear Science and Engineering
23, 2011
Certified by:------------------Benoit Forget
Assistant Pro Lssor of Nuclear Science and Engineering
Thesis Supervisor
Certified by:
Eugene S fwageraus
Visiting Associate Professor of Nuclear Science and Engineering
Thesis Reader
Certified by:
-
Dennis Whyte
Professor of Nuclear Science and Engineering
Chairman, NSE Committee of Undergraduate Student
ARCHIIVE
COMPUTATIONAL NEUTRONICS ANALYSIS OF TRIGA REACTORS DURING
POWER PULSING
By
Malcolm Bean
Submitted to the Department of Nuclear Science and Engineering on May 19, 2011
In Partial Fulfillment of the Requirement for the Degree of
Bachelor of Science in Nuclear Science and Engineering
ABSTRACT
Training, Research, Isotopes, General Atomics (TRIGA) reactors have the unique
capability of generating high neutron flux environments with the removal of a transient
control rod, creating conditions observed in fast fission reactors. Recently, several
TRIGA reactors have had issues with the deformation of fuel rods nearest the transient
control rod, where the neutron flux is highest. This is a difficult problem to analyze
because the damage is not simply due to rods overheating, but rather the pressurization
of hydrogen, from the Uranium Hydride fuel, that has diffused into the spacing between
fuel and cladding. Previous neutronic analyses utilized point kinetics; a model which
assumes changes in reactivity uniformly affect the reactor's flux, resulting in no relative
spatial variation over time. Point kinetics is attractive because of its low computing
costs, however the pulse's localization, theoretically, should generate a pronounced flux
spike and radial neutron wave, which violates an assumption of point kinetics. The aim
of the research is not to explicitly describe the cause of fuel rod deformation, but rather
generate time dependent, high-resolution 3-dimensional flux maps. The Purdue Advance
Reactor Core Simulator (PARCS) was used to simulate a TRIGA pulse with both nodal
and point kinetics. Assuming our nodal kinetics models accurately simulate TRIGA
pulses, we find that point kinetics methods are ill suited to simulate TRIGA pulses. By
maintaining the steady-state flux profile, point kinetics does not capture the fact that
the power peak actually occurs in the center assembly, from which the transient control
rod is removed. In our simulations, point kinetics underestimated the normalize power in
the central assembly by as much as 46.19%.
Thesis Supervisor: Benoit Forget
Title: Assistant Professor of Nuclear Science and Engineering
2
Introduction
Training, Research, Isotopes, General Atomics (TRIGA) reactors have the capability to
generate high neutron flux pulses with the removal of a pneumatic transient control rod.
The high neutron flux pulse conditions can be used to simulate fast fission and fusion
reactors environments, therefore having this capability is critical in testing aspects of
new reactor designs, namely radiation damage and radiation effects.
Recently, the Texas A&M TRIGA reactor has had issues with the deformation of
fuel rods nearest the pneumatic transient control rod (Remlinger, 2009). During a pulse,
the fuel pins nearest the transient control rod experience the highest neutron flux. A
previous analysis estimates that component temperatures are significantly higher in that
area, but the peak temperatures are below critical values that would cause the observed
damage.
With that being said, it is theorized that neutron flux gradients are a larger factor
in fuel pin damages, most notably the diffusion and pressurization of hydrogen from the
uranium hydride fuel. The rate of hydrogen diffusion is based on the temperature and
temperature gradient within the fuel, which in turn are highly correlated to a pin's flux
magnitude and profile, respectively.
The past analyses significantly overestimate reactor power during pulsing, with the
gap between the simulation and measured data increasing as pulse reactivity worth is
increased. Because of this error in the estimated pulse magnitude, the spatial neutron
distributions are also in question.
Due to computing limitations, reactor core simulations use homogenized blocks of
various sizes as computational units, and then run secondary calculations to recreate the
flux profile within the blocks. In the case of the Texas A&M TRIGA reactor analysis
point kinetics was used to model neutron flux during a pulse. This method treats the
3
reactor as a single homogeneous block, where changes in reactivity uniformly affect the
reactor's flux, resulting in no relative spatial variation over time.
Point kinetics is attractive because of its low computing costs and accuracy for
small perturbations, however the magnitude of TRIGA pulses are significantly larger
than those for which point kinetics was derived. The pulse localization, theoretically,
should generate a pronounced radial neutron wave, which violates an assumption of
point kinetics. The possible errors from point kinetics are then compounded by the
application of generic pin flux profiles for fuel rods, which do not account for the steep
flux gradients that occur across fuel pin during a pulse.
It should be emphasized that the aim of this report is not to explain the cause of
the fuel pin damage. Rather, the report will focus on comparing the three dimensional
flux maps produced by point kinetics simulation and the more sophisticated scheme
of spatial nodal kinetics. Then by comparing the spatial fluxes produced by the two
scheme, give insight into the appropriateness of using point kinetics, or the need to use
a finer mesh simulation, when modeling a TRIGA reactor pulse.
Methods
To simulate the Texas A&M TRIGA reactor pulse, Serpent, a Monte Carlo reactor
physics burn-up calculation code(Leppanen, 2010), and the Purdue Advanced Reactor Core Simulator (PARCS), a reactor core simulator(Downar, September 2009), were
used in tandem. First, Serpent was used to generate cross sections for fuel and reflector
regions, which were then used in PARCS to calculate steady-state and pulse flux distrubtions. Further descriptions and details regarding each piece of software and specific
utilizations are provided in the following subsections.
4
PSG2/Serpent
Serpent is a three-dimensional continuous-energy Monte Carlo reactor physics burn-up
calculation code, developed at the VTT Technical Research Centre of Finland in 2004.
The code specializes in two-dimensional lattice physics calculations for cross section
generation. Serpent was used to generate macroscopic cross sectional data for both the
point kinetics and nodal kinetics simulations.
Serpent generated energy dependent (via 2 neutron groups) and first-order temperature dependent macroscopic neutron transport cross sections from the reactor microscopic materials properties and core geometries. Specifically, our simulations utilized
the nuclide cross sectional data from the Evaluated Nuclear Data (ENDF/B-VII) and
two neutron groups, thermal and fast, were delineated with all neutron energies below
0.625 eV categorized as thermal.
To incorporate temperature dependence, fuel cross sections are calculated at temperatures above, below and within the range of temperatures expected during a pulse.
Linear interpolations between cross section data are used to produce first-order temperature dependent cross sections for core modeling software. Temperature variance in
the coolant cross sections based on temperature are not incorporated because a TRIGA
pulse is essentially adiabatic.
Explicitly, the Serpent calculated cross sections used in the pulse are the principal
cross sections (transport, absorption, v-fission, n-fission), group scattering (both intra
and inter-group-scattering), fission neutron spectrum, inverse neutron velocity, delayed
neutron fractions and delay neutron precursor decay constants. Temperature dependence is only calculated for principal macroscopic cross sections and group scattering.
As seen in Figure 1, the basic assembly units of the Texas A&M TRIGA reactor are
two by two matrices containing combinations of control rods, fuel rods and water filled
5
rods. These sets of four pins are the basic neutronic sub-units (homogenized regions) of
the simulations. In the lateral plane, the fuel region is surrounded by graphite reflectors
to the "north" and "south". In the vertical plane, the fuel rods are capped by graphite
reflectors and control rods are followed by the same uranium hydride in fuel rods. The
transient control rod is unique in that it is followed by an air void. With the TRIGA
reactor being a pool type, it is immersed in a large pool of light water. Figure 2 is a
Serpent rendering of a center planar slice of the entire TRIGA core geometry.
A
adc" North
B\C
D
E
F
7
6
West
WfadRs
East
5m
e ft
0
Figure 1: The layout of the Texas A&M TRIGA reactor as specified in the Nuclear Regulatory
Commission's Safety Analysis Report (SAR)
6
Figure 2: A Serpent rendering of a center planar slice of the TRIGA core geometry. Fuel pins
are purple, control rods are beige, water is pink and graphite reflectors are green
Cross Section Generation Details
To generate cross sections for our PARCS model, six reactor sub-unit cross sections
were calculated. The sub-units were a fully loaded fuel assembly (C5), a half loaded
fuel assembly (B6), water reflector (D7), graphite reflector (E8), an assembly with a
control rod (E4) and the transient control rod assembly (D5). The coordinate system
listed after each subunit corresponds to an example of that sub-unit's location depicted
in Figure 1.
7
Each sub-unit was placed in the top right corner of a two by two box, surrounded
by three fully loaded sub-units. Reflective boundary conditions were imposed outside
boundary. This was critical for the graphite and water reflector because a source of
neutrons is required to generate cross sections. Figure 3 is an illustration of the geometry
used to generate cross sections for water reflector. Figure 4 illustrates the geometry used
to generate cross sections for an assembly with a control rod. Note that homogenized
cross sectional data was taken from the areas outlined in black.
Figure 3: Serpent geometry for calculating the water cross sectional data
Each layout has six branch cases: fuel temperature is set to 373"C, 6234C and
873"C, and at each of those temperatures two branches are generated, with the control
rod removed and inserted. In all cases, moderator temperature was set to 23'C. The unrodded 373
0C
fuel temperature branch was used as the reference. From the reference
case fuel temperature and control material effect, partial derivates were calculated.
Obviously, four of the sub-units (graphite reflector, water reflector, fully loaded fuel
8
000
Figure 4: Serpent geometry for calculating control rod containing assembly cross sectional data
assembly and half loaded fuel assembly) do not contain a control rod, therefore their
control material effect partial derivates are set to zero. This must be done for cross
section data file consistency (Downar, December 2009).
To improve cross section data accuracy, the entire reactor core geometry can be
modeled with Serpent, and each assembly and section of reflector in the reactor can be
treated as a unique sub-unit. This approach was initially attempted, but was abandoned
as it seemed to cause convergence issues in the PARCS model. In hindsight it was most
likely a faulty parameter in either the PARCS model, or a single cross section data file,
that was causing this issue. By only using six sub-units, we could individually test cross
section data file. Having each assembly and reflector section of the reactor treated as a
unique sub-unit would require checking 119 separate files.
9
Purdue Advanced Reactor Core Simulator (PARCS)
PARCS is a three-dimensional reactor core simulator which solves the steady-state
and time-dependent, multi-group neutron diffusion and low order transport equations.
PARCS has a built-in simple thermal-hydraulics system code which provides the thermal
hydraulic feedback information to PARCS during the transient calculations.
PARCS has the capability to perform nodal kinetics calculations for transients. For
our point kinetics model a use Matlab simulation is used to calculate power and reactivity. Steady-state flux profile is assumed throughout pulse. Using the homogenized
region cross section data generated by Serpent, PARCS calculates steady state and
pulse neuronic conditions. In PARCS the pneumatic removal of center control rod will
be simulated as a "control rod perturbation", the equivalent of a control rod ejection in
a power generating nuclear reactor.
In the PARCS model the horizontal division of the reactor core matches the Serpent model exactly. Each fuel assembly and graphite block is approximately 7.71cm
by 7.71cm squared. Axially, the reactor is divided into 14 regions, ten-3.81cm slices
representing the uranium-hydride rich region of the core. This region is capped by
a 5.21cm thick reflector regions, composed of a combination of water and graphite.
Finally, 20.0cm of water surrounds the solid core structure representing the pool of water in which the reactor core is submerged. The boundary conditions of no incoming
neutron flux at the edge of the water region are implemented.
To calculate thermal hydraulic effects, PARCS uses a one dimensional heat transfer
model. Heat transfer rates and material temperature are approximated by using user
inputs to reconstruct the fuel pin and coolant geometry.
10
Results
There are two components of the Results Section. The first subsection focuses on the
accuracy of the model. This is assessed by comparing the PARCS generated steady-state
reactor kinetic parameters to the NRC Safety Analysis Report (SAR) kinetic parameters
generated by Monte Carlo N-Particle 5 Transport Code (MCNP) and a diffusion theory
code, DIF3D. In particular, we investigated Beginning-of-Life (BOL) prompt negative
temperature coefficients of reactivity, control rod worth and flux profile. The second
section focuses on the TRIGA pulse characteristics, specifically discussing reactor core
neutronics during a pulse.
Comparison of Steady-State Reactor Calculations
The first comparison is of the "fully banked" (all control rods fully inserted) reactor
k-effective calculations. At the steady-state conditions with a fuel temperature of 373
'C and a moderator temperature of 23 'C, the SAR's MCNP-5 calculation reported
a k-effective of 0.94314 ± 0.00017, with one sigma uncertainty. Using Serpent cross
section with the same temperature parameters, PARCS converged to a k-effective of
0.9650, with a convergence criteria < 1.0 x 10-6 on k-effective between iterations. Note
that the same convergence criteria is applied to all simulations.
For a "fully unbanked" reactor (All four numbered control rods, as seen in Figure 1,
fully removed), the PARCS model also overestimates k-effective (1.05013), in comparison
to the MCNP-5 calculated k-effective of 1.04553 ± 0.00017.
With the NRC MCNP-5 calculated
#eff
value of 0.0070, the reactivity worth of the
four numbered control rods is $16.34. Based on the PARCS model we calculated a,#
value of 0.0069.
11
The definition of the prompt negative reactor temperature coefficient of reactivity,
a, is given as,
a =
dp
-T(1
where,
Reactivity, p =k
k
T= reactor temperature
0C
To calculate Ap from reactivity as a function of reactor core temperature, a simple
finite difference equation is used,
A
k2 -1
k2
ki-1
_
k1
k2 -ki
k1 k2
(2)
Therefore,
k2 -ki
k1 k2
1
T2 - T1
Using the diffusion theory code, DIF3D, the NRC calculated the prompt negative
temperature coefficients of reactivity, a, based on several temperature intervals ranging
from 200 to 1000 'C. The DIF3D and PARCS k-effective values are calculated with
an "unbanked" reactor core. Table 1 summarizes the negative temperature coefficients
approximated by DIF3D and Table 2 summarizes the negative temperature coefficients
approximated by PARCS.
For flux and power calculations, our PARCS model is limited in that it assumes
no neutron flux in homogenized regions containing no heavy metal mass. The size of
the homogenized regions used by PARCS also does not allow the visualization of the
localized peaks generated by DIF3D.
12
Table 1: DIF3D Prompt Negative Temperature Coefficients of Reactivity
Core Temperature "C
200
Kef f
1.03481
AKef f
********
********
Ap
a
********
280
400
700
1000
1.02896
1.01857
0.98486
0.94913
0.00585
0.01039
0.03271
0.03673
0.005494
0.009913
0.032574
0.039254
6.87x10-5
8.26 x10-5
1.09 x101.31x10-4
Table 2: PARCS Prompt Negative Temperature Coefficients of Reactivity
Core Temperature 'C
373
623
823
Kef f
1.04662
1.00623
0.95744
AP
a
*
0.03835
0.05064
1.52x10-4
2.40x 10-4
Table 2 exemplifies the linear interpolation used by PARCS to calculate temperature
dependent cross sections. Temperatures at which the Serpent cross sections were generated were 373 "C, 623'C and 873'C.
Along the x-axis (East to West) through the transient rod, the SAR's DIF3D model
has a thermal flux peak in water regions just outside the core and another near the
transient control rod. Figures 3 and 4 are the DIF3D and PARCS flux profiles along
the x-axis, respectively.
13
I.OOE+14
I
I
I
I
*
S
I
I
I
S
1.OOE+13
1
C
I
0 .00E+12
I
A
I
I
I
I
I
I
I
I
S
a
*
S
I
I
I
r Xi.
s
I
I
I
I
I
I
I
I
I
I
I
I
I
I
S
mr
a V
3 a
B S
S
I
I
S
IE
I
1ri
a:
I
C
D
S
I
S
-4-I
I
I
r
-
1.00E+11
0
20
40
60
80
100
x-Axis (cm)
Figure 5: Flux profile as calculated by DIF3D; left of section "B" and to the right of "F" are
outside the reactor core.
Along the y-axis,(North to South), through the transient rod, the SAR's DIF3D
model has two thermal flux peaks in the two water regions, each surrounded by fuel
assemblies on 3 sides. Figures 5 and 6 are the DIF3D and PARCS flux profiles along
the y-axis, respectively.
14
8
x 1012
i-
7-
6-
E
0
5-
X
4-
3-
2
0
5
10
15
20
25
Core X-Axis(cm)
30
35
40
Figure 6: The dimensions of this plot begins at section "B" and ends at section "F" of Figure
3.
From the two dimensional plots, it appears there are no commonalities between the
PARCS and DIF3D flux calculations. However looking at the PARCS three dimensional
flux map, we see the thermal flux peaks observed by DIF3D in water regions adjacent
to fuel flux peaks in the PARCS model.
15
1.OOE+14
I
*
*
*
I
I
I
I
I
I
*
I
I
I
3
I
I
I
I
I
6
I
I
I l
I
1.OOE+13
1.OOE+12
1 'a
2 1'3 , 14
i
i
1.00E+11
0
20
40
60
y-AxIs (cm)
80
100
120
Figure 7: Along the y-axis center line only regions 4, 5 and 6 contain fuel. Note that this plot
is from (South to North).
16
9
x 10"
876Em5 -x4-3-2-1 -0
0
10
20
30
Core Y-Axis(cm)
40
50
60
Figure 8: The dimensions of this plot begins at section "3" and ends at section "7" of Figure
3, (North to South).
17
50
40
V
0
30
20
60
50
40
11
30
10
20
EAST, V-Axis (cm)
00
0
NORTH, X-Axis (cm)
Figure 9: The phenomenon of thermal flux peaks observed by DIF3D in water regions adjacent
to fuel flux peaks in the PARCS model. This is the most pronounced along the y-axis
centerline.
18
Transient Calculation
We are unable to construct a PARCS simulation using the correct cross-sectional data
and thermal hydraulic parameters. While the model converges during transient analysis,
it produces unreasonable reactivity, power, and fuel temperature figures. In particular,
we find that the thermal hydraulics calculations of fuel temperatures tended toward
unrealistic values before the simulation crashed. We assumed the incorrect fuel temperatures are the cause of the reactivity and power inaccuracies.
Therefore, we removed temperature dependence from our model. However this is
not ideal, as the TRIGA reactor's strong negative power coefficient is key to pulse characteristics. Yet, we believe a model using temperature invariant cross sections will still
provide insight in the comparison of nodal and point kinetics. The fundamental differences between using nodal kinetics and point kinetics should be observable regardless.
We ran a transient models where the transient control rod is removed at a linear
rate (a 'ramp' control rod removal) such that it is completely removed in 1.0 seconds
(38.1 cm/s). Without thermal hydraulic feedback, it is near impossible to accurately
analogizes this to the Texas A&M TRIGA pulse. It is also worth noting that the core
geometry had to be slightly modified to achieve convergence in the PARCS model.
Figure 10 is a Serpent rendering of the new geometry.
Figures 11 and 12 are a comparison of the reactor power and reactivity versus time.
The similarity in these two plots give us confidence that the PARCS nodal kinetics
model and Matlab point kinetics model are simulating the same event.
For the 1.0 second transient, we compare the flux at three different times: in the
middle of the pulse (0.5243 seconds), just after the transient rod has exited the core
(1.0051 seconds), and well after the transient (10.0 seconds)
To quantify the difference between the nodal and point kinetics flux calculations, we
19
Figure 10: Control rods are brown, fuel is pink, graphite is light blue and water is purple.
define the "maximum percent difference" (MPD) as,
percent difference = nodalflux - pointflux
nodaliux
where (nodalflux - pointflux) is maximal.
20
(4)
x10
1.0 Ramp Pulse
Noda
Nodal
Point
4
3.5 -
c 2.5
21.5
1
0.5 -
u
0
1
2
3
4
5
Time (seconds)
6
7
8
9
10
Figure 11: As expected, reactor power grows exponentially without thermal feedback.
21
1.0 Ramp Pulse
= 0.4
0.3
0
1
2
3
4
5
6
7
8
9
10
Time (seconds)
Figure 12: Similar to power, reactivity peaks just before the transient control exists the reactor
core.
22
At 0.5243 seconds, we observe an expected difference between point and nodal kinetics. Figure 13 depicts the point kinetics flux map, the nodal kinetics flux map and
the difference of the two calculations. The nodal kinetics simulation indicated 178.26%
of steady-state power, while point kinetics indicated 160.03%.
8
M:6
a
'04
4
a)
2
E
F2
goA
100
100
60
80
40
60
50
Y-Axis
0
0
Y-Axis
X-Axis
0
0
X-Axis
.5
aV
0
z
a)
V
a)
0
z
Y-Axis
0
0
X-Axis
Figure 13: 0.5243 seconds into the 1.0 ramp pulse. The point kinetics (top right) maintains
the steady-state flux profile while nodal kinetics (top left) shows a relative increase
in the assembly containing the transient control rod. Below is the difference of the
flux maps. Note that the two normalized thermal flux profiles above were to scaled
based on the reactor power predicted by each method, respectively. The MPD is
40.90%.
23
From 0.5243 seconds to 1.0051 seconds, the nodal methods calculation indicates the
flux peak has moved to the transient control rod from assembly E6 .
20-,
&10
~-
....
.....
80
Y-AxIs
.... .
7I
40 '0~0
20 0 0
~ ~ 20
40
60
80
10
-0
60
..... 40
40
2820
00
X-Axis
Y-Axis
X-Axis
10 87
4 2.080
60..
0
60
00
Y-Axis
BO
4
X-Axls
Figure 14: At 1.0051 seconds the peak flux moves to the transient control rod assembly and
the MPD has increased to 47.01%
24
0
8
From 1.0051 seconds to 10.0 seconds, the changes in both flux profiles are relatively
small. The difference peak, as seen in Figure 13, is in the same location, but the MPD
slightly increases to of 46.19%. At 10 seconds the point kinetics reactor power is 401.25%
of steady-state while PARCS's nodal methods indicate a power of 393.52%.
2000
1500
1000.
S500
8
8
80
60
40
20
.....
80
20
0
Y-Ax~
0
X-Axis
1000 -
Y-Axis
-
800
600
500..
60
. ..
40
S
....
.
400
200
0
-200
-208
-
----..
....
80
0
40
2
..
0
Y-Axis
0..... 20
40
60
6
8
0
X-Axis
Figure 15: Flux maps at 10.0 seconds.
25
0
0
X-Axis
In hindsight, while not having a thermal feedback is not ideal in that we cannot
match calculated pulse power levels and fluxes, it also exaggerates the difference between
the two schemes making the fundamental differences more readily apparent.
26
Conclusion
The relative closeness of the k-effective, negative temperature coefficients and 3-effective
give us confidence that our model is reasonable and captures many essential characteristics of the Texas A&M TRIGA. However, there are clearly flaws in modeling such a
small reactor. The phenomena of the thermal peak being outside the core at steadystate is unique and our PARCS's inability to recognize this, is perhaps one of many
critical gaps limiting our model.
The discrepancy between our nodal and point kinetics would likely decrease with the
incorporation of thermal feedback. However, our analysis indicates that point kinetics
is fundamentally inappropriate for modeling TRIGA reactor pulses. By maintaining
the steady-state flux profile, point kinetics does not capture the movement of the power
peak from the E6 assembly to transient control rod assembly. This error is a cause for
concern, because the largest discrepancies occur in the region surrounding the transient
control rod; the same region where fuel rod deformation in the Texas A&M TRIGA
reactor was observed.
27
Bibliography
[1] J. Remlinger, Safety Analysis Report Nuclear Science Center, Texas Engineering
Experiment Station,Texas AM University System, July 2009.
[2] T. Downar, PARCS v3.0 User Manual, Department of Nuclear Engineering and
Radiological Sciences University of Michigan, September 2009.
[3] T. Downar, GenPMAXS- V5, Code for Generatingthe PARCS Cross Section Interface File PMAXS, Department of Nuclear Engineering and Radiological Sciences
University of Michigan, December 2009.
[4] J. Leppanen, PSG2 / Serpent a Continuous-energy Monte Carlo Reactor Physics
Burnup Calculation Code Users Manual, VTT Technical Research Centre of Finland, December 2010.
28