MC21/COBRA-IE and VERA-CS multiphysics solutions to VERA core physics benchmark problem #6

Progress in Nuclear Energy 101 (2017) 338e351

Contents lists available at ScienceDirect

Progress in Nuclear Energy
journal homepage: www.elsevier.com/locate/pnucene

MC21/COBRA-IE and VERA-CS multiphysics solutions to VERA core
physics benchmark problem #6
Brian N. Aviles a, *, Daniel J. Kelly a, David L. Aumiller b, Daniel F. Gill b, Brett W. Siebert a,
Andrew T. Godfrey c, Benjamin S. Collins c, Robert K. Salko c
a
b
c

Naval Nuclear Laboratory, Knolls Atomic Power Laboratory, Schenectady, NY, USA
Naval Nuclear Laboratory, Bettis Atomic Power Laboratory, West Mifflin, PA, USA
Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN, USA

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 12 September 2016
Received in revised form
8 January 2017
Accepted 19 May 2017
Available online 1 June 2017

The Virtual Environment for Reactor Applications (VERA) core physics benchmark problem #6, 3D Hot

Full Power (HFP) assembly, from the Consortium for Advanced Simulation of Light Water Reactors (CASL)
was simulated using the MC21 continuous energy Monte Carlo code coupled with the COBRA-IE subchannel thermal-hydraulics code using the R5EXEC coupling framework. The converged MC21/COBRA-IE
solution was compared to results from CASL's VERA-CS code system, MPACT coupled to COBRA-TF (CTF).
MPACT is a three-dimensional (3D) whole core transport code, executed in a 2D/1D approach employing
planar method of characteristics (MOC) solutions with SP3 in the axial direction, and CTF is a subchannel
thermal-hydraulics code designed for Light Water Reactor analysis. Eigenvalues agreed within 63 pcm,
axially-integrated normalized radial fission distributions agreed within ±0.2% (root mean square (RMS)
difference of 0.1%), local volume-averaged fuel pin temperatures agreed within ỵ8.8/-4.3 C (RMS difference of 3.9 C), and local subchannel coolant temperatures agreed within ỵ0.8/-1.5 C (RMS difference
of 0.5 C). A sensitivity study to guide tube heat transfer indicated that a statistically-significant increase
in reactivity and shift in radial pin power distribution occurred within the assembly when guide tube
heating was enabled.
© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND
license ( />
Keywords:
Multiphysics
MC21
COBRA-IE
VERA
MPACT
CTF

1. Introduction
CASL (CASL, 2014) VERA Core Physics Benchmark Progression
Problems (Godfrey, 2014) are designed to aid multiphysics researchers with a set of single reactor physics and coupled reactor
physics/thermal-hydraulics problems of increasing complexity.
Problem #6 is a single Westinghouse 17 Â 17-type fuel assembly at
beginning-of-cycle (BOC) and hot full power (HFP) conditions
based on Watts Bar Nuclear 1 (WBN1) initial core loading. The
purpose of Problem #6 is to demonstrate that coupled reactor
physics and thermal-hydraulics can be iterated to mutuallyconsistent solutions. To date, coupled solutions for VERA Problem

#6 based on deterministic neutron transport and thermalhydraulics subchannel codes have been published (Palmtag,
2013), but a coupled Monte Carlo/thermal-hydraulics subchannel
code solution has not yet been published for this benchmark.

* Corresponding author.
E-mail address: (B.N. Aviles).

High-fidelity reactor simulations that include Monte Carlo for
pin-resolved neutron transport coupled with thermal-hydraulics
codes solving for flow and temperature distributions at the subchannel level have been reported in the literature (see text and
references in Daeubler et al., 2015; Ivanov et al., 2015; Gill et al.,
2017; Lepp€
anen et al., 2015; Bennett et al., 2016; Pecchia et al.,
2015; Ellis et al., 2017; Kotlyar and Shwageraus, 2016). At the Naval Nuclear Laboratory, MC21 (Griesheimer et al., 2015) and COBRAIE (Aumiller et al., 2015) coupling via R5EXEC (Aumiller et al., 2016)
has been described previously (Gill et al., 2014) as have running
strategies for performing coupled Monte Carlo/thermal-hydraulics
analyses (Gill et al., 2015). This research utilizes these tactics and
submits a high-fidelity MC21/COBRA-IE solution for Benchmark
Problem #6. These results are compared with results from the core
simulator being developed by CASL, VERA-CS (Sieger, 2015;
Kochunas et al., 2015), which includes the deterministic neutron
transport code, MPACT (Collins and Godfrey, 2015; MPACT Team,
2015), coupled to the subchannel thermal-hydraulics code, CTF
(Salko and Avramova, 2014). COBRA-IE and CTF share a common

/>0149-1970/© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( />

B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351

COBRA code ancestor but have undergone different development

paths over the past 15 years; COBRA-IE improvements are geared
towards analyzing Loss-of-Coolant accidents, and CTF improvements are geared towards nominal PWR and BWR operating
conditions.
2. VERA problem #6 reactor physics and thermal hydraulics
model description
Specifications for Problem #6 are provided by Godfrey (2014)
and describe a Westinghouse 17 Â 17-type fuel assembly at BOC
and HFP steady-state conditions with boron concentration at
1300 ppm. There are no burnable poison or control rod clusters in
Problem #6. Because of symmetry in the assembly, a ¼-assembly
radial model is employed. Figs. 1 and 2 present the radial and axial
assembly geometry, respectively. There are 72 fuel rods, 81 coolant
subchannels, and 9 guide tubes. All fuel pins and water subchannels
are modeled explicitly in all analysis codes, and each guide tube is
modeled as an unheated cylinder with water flowing inside. From
the specification, 9% of the total flow accounts for bypass flow. Of
this, one third is assumed to flow through the guide tubes, resulting
in 0.7085 kg/s (1.5620 lbm/s) flowing through all guide tube
channels in this ¼-assembly model. The instrument tube in the
center of the assembly in the specification is modeled as a guide
tube in MC21/COBRA-IE to be consistent with VERA-CS. Because the
guide tube inner radius and thickness (0.561 cm and 0.041 cm,
respectively) are similar to the instrument tube inner radius and
thickness (0.559 cm and 0.046 cm, respectively), this assumption is
deemed valid. In both models, heat transfer through guide tube
walls is turned off such that the water flowing in the guide tubes
remains unheated. A sensitivity to this assumption is performed
with MC21/COBRA-IE in which conduction through the guide tube
walls is allowed and the water within the guide tubes is heated.
The left plot in Fig. 1 shows the MC21 geometry at an axial

elevation with a spacer grid (75.0 cm). In order to model spacer
grids correctly and to preserve flexibility in assigning subchannels,
multiple intra-channel regions were required in the MC21 model
and appropriate axially-varying materials are assigned using the
axial material capability in MC21. Thicknesses of these intrachannel regions were determined to preserve masses of the Zircaloy (intermediate) and Inconel (top and bottom) spacer grids. In

Fig. 2. Problem #6 axial geometry (from Godfrey, 2014).

Fig. 1. ¼-assembly radial geometry showing fuel rod, guide tube, and subchannel numbering scheme.

339


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B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351

the MC21 figure, lines through the subchannels denote MC21
subchannel subdivisions. The COBRA-IE and CTF fuel rod/channel
model is shown on the right in Fig. 1 at an axial elevation with no
spacer grid.
There are 49 axial mesh in the 365.76 cm active core region,
which is the domain of the COBRA-IE and CTF models. The axial
mesh definition from VERA Problem #3 (Godfrey, 2014) is used in
both MC21/COBRA-IE and VERA-CS. The lower and upper core
plates and bottom and top nozzles are modeled in both reactor
physics codes to ensure proper axial neutronic treatment.
Cross section treatment for MC21 and MPACT is as follows:
 ENDF/B-VII.1 is used for the MC21 cross section library and
contains 55 BOC nuclides. Non-water materials have cross sections ranging from 500 K to 1600 K in 50 K increments up to

900 K and 100 K increments thereafter. Water cross sections
range from 500 K to 650 K at 10 K intervals.
 MPACT employs a 47 energy group cross section library based on
ENDF/B VII.0 data with subgroup parameters to capture selfshielding effects.

3. Coupled code execution strategy
3.1. MC21/COBRA-IE
The procedure developed by Gill et al (Gill et al., 2014 and Gill
et al., 2015) in which R5EXEC (formerly known as PVMEXEC) is
used to couple MC21 and COBRA-IE is employed in this research.
R5EXEC was created to couple and control transient codes
(Aumiller et al., 2016), but it can also be used to couple a transient
thermal-hydraulics subchannel code like COBRA-IE to a steadystate reactor physics code like MC21. The kinetics coupling option
in R5EXEC is used to transfer data on common defined regions via a
well-defined API at user-specified synchronization points. R5EXEC
allows many reactor physics and thermal-hydraulics parameters to
be passed via the API, but Problem #6 only requires region-wise
powers to be transmitted from MC21 to COBRA-IE, and regionwise solid and liquid temperatures and liquid densities to be
transferred from COBRA-IE to MC21. An R5EXEC session is launched
in which a transient COBRA-IE simulation is initiated. At each userspecified synchronization point, COBRA-IE sends local densities and
temperatures as input for MC21 material properties and cross
section interpolation, and COBRA-IE is paused while an MC21 keigenvalue solution is performed. When the MC21 calculation is
complete, it returns region-wise powers to COBRA-IE and R5EXEC
continues the COBRA-IE transient simulation.
Stability of the coupled MC21/COBRA-IE solution is achieved by
exchanging data between the reactor physics and thermalhydraulics codes at an interval smaller than the time needed for
transient COBRA-IE to achieve a steady-state solution. This is
analogous to a physics-based under-relaxation scheme in which
the change in thermal-hydraulic parameters is controlled by
timestep size rather than by an under-relaxation factor. In this

coupled analysis, parameters are exchanged between MC21 and
COBRA-IE 14 times during the COBRA-IE transient, as shown in
Table 1. The COBRA-IE transient encompassed a 55 s transient to
ensure full flow conditions were achieved (the residence time for
water in the coolant subchannels is less than 1 s). The data exchanges occur at a higher frequency during the earlier portion of
the transient as the thermal-hydraulic solution is developing. The
following metrics are inspected to assess convergence of MC21/
COBRA-IE:
 MC21 eigenvalue trajectory,

Table 1
MC21/COBRA-IE data exchange intervals during COBRA-IE transient.
Data exchange index

COBRA-IE transient simulation time point (s)

1
2
3
4
5
6
7
8
9
10
11
12
13
14

0.01
0.50
2.50
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
55.00

 MC21 Shannon entropy, and
 COBRA-IE L2 and L∞ norms of local fuel temperature and coolant
density.
As will be shown in the Results section, additional parameter
exchanges between MC21 and COBRA-IE beyond the eighth exchange do not improve convergence for Problem #6.
At each reactor physics calculation, MC21 utilizes 200 active
generations (50 discarded generations) and 10 million neutrons per
generation for a total of 2 billion active neutrons per MC21
execution. These are enough neutron histories to drive local pin
power uncertainties below 0.7% as will be demonstrated in the
Results section.
3.2. VERA-CS
As described in Sieger (2015), MPACT calls CTF at every outer
iteration, at which time MPACT passes CTF region-wise powers. The

CTF solution is run as a transient; however, it is run until the
thermal-hydraulics solution is considered steady before passing
temperatures and densities back to MPACT. All data is passed between the two codes using an API that was developed in CTF for
driving solutions from other code systems (Salko et al., 2015). Thus,
the coupling of MPACT and CTF is a direct coupling, with MPACT
directly calling procedures in CTF to initialize the code, execute the
solution, pass powers to CTF, and receive temperatures and densities from CTF. The coupled iteration strategy is done using Picard
iteration with an under-relaxation of parameters passed between
MPACT and CTF. Convergence is achieved when MPACT satisfies
eigenvalue and fission source convergence criteria. Temperature
and density changes are monitored to determine if the subgroup
calculation needs to be re-executed to obtain new shielding parameters for cross section generation. MPACT was executed using
the 2D/1D technique with transport-corrected P0 2D MOC in the
radial planes and SP3 in the axial direction.
4. Results
4.1. MC21/COBRA-IE convergence metrics
Fig. 3 presents the MC21 eigenvalue trajectory and COBRA-IE
transient progression during the 14 MC21/COBRA-IE data exchanges. The 95% confidence interval is shown with each eigenvalue, and all are less than ±3.0E-5. The eigenvalue at the first
exchange is an outlier because MC21 is being fed temperatures and
densities from an under-developed COBRA-IE transient solution.
COBRA-IE transient progression described in Table 1 is shown on


B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351

341

Fig. 3. MC21 eigenvalue convergence and COBRA-IE transient progression during MC21/COBRA-IE data exchanges.

the y2-axis, indicating that data exchanges are more frequent

during the initial stages of the developing COBRA-IE solution. Four
data exchanges occur before the COBRA-IE transient is 10% complete at 5 s of simulated time, followed by more widely-spaced data
exchanges as further physical under-relaxation is no longer needed
to achieve the mutually-consistent solution between MC21 and
COBRA-IE. Based on the MC21 eigenvalue trajectory, the reactor
physics solution is converged by the eighth data exchange. Further
data exchanges result in statistically-equivalent eigenvalues.
Batch-wise eigenvalues and Shannon entropy for MC21 during
the first and eighth data exchanges are presented in Fig. 4. Although
50 discarded batches are not sufficient to converge the fission
source in the first MC21/COBRA-IE data exchange as indicated by
Shannon entropy (also true of the second data exchange, not
shown), all subsequent data exchanges exhibit a converged source
prior to 50 discarded batches. This is because the previous fission
source, which is used as the initial source guess at the next data
exchange, approaches the converged MC21/COBRA-IE solution.
Thus, 50 discarded batches are not sufficient to converge the source
in the first two MC21 executions, but early data exchanges are used
only to start the coupled analysis on the path to convergence. After
the first few data exchanges, the fission source is converged after 50
discarded batches, at which time tallies can be accumulated.
Two billion active neutron histories are sufficient for this 3D
¼-assembly model to drive all local uncertainties in fission rate to a
target of <1%. Fig. 5 presents relative uncertainty in relative power
density (RPD) for all 3528 mesh tally regions (72 fuel pins x 49 axial
levels) in 0.1% resolution bins. At two billion active histories, all
regions have a relative uncertainty (based on a 95% confidence
interval) less than 0.7%, a majority of regions have relative uncertainties between 0.1% and 0.2%, and more than 99.5% of all regions have a relative uncertainty
0.5%. The minimum relative
uncertainty is 0.097%, and the maximum relative uncertainty is

0.695%. All 16 regions with a relative uncertainty >0.5% occur in the

bottom plane, as shown in the uncertainty distribution map on the
right in Fig. 5. MC21 requires ~6000 wall clock seconds per
execution (tracking and tallies) for 2.5 billion tracked neutrons
(active plus inactive batches) using 50 nodes containing two 12core Intel Xeon E5-2680v3 2.5 GHz (Haswell) processors (1200 total
cores). COBRA-IE execution time is a small fraction of the total
simulation time.
Figs. 6 and 7 present COBRA-IE convergence metrics for local
fuel temperature and relative change in coolant density, respectively, as measured by the L2 and L∞ norms with respect to the final
(exchange index 14) fuel temperature and coolant density distributions. The L2 norms for both the fuel temperature and relative
change in coolant density were normalized by the square root of
the number of regions (3528 fuel temperature regions and 4410
coolant density regions including guide tube water, respectively).
Thus, the following norms are used to monitor convergence in the
COBRA-IE solution (N ¼ 14 in Figs. 6 and 7):
L∞ norm of fuel temperature:



n

T f À T N
f

∞

for n ¼ 1; N À 1

(1)

L2 norm of fuel temperature:



n

T f À T N
f
2 ffi
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
# Fuel Regions

for n ¼ 1; N À 1

(2)

L∞ norm of relative change in coolant density:

n

rc À rN

c


rN
c

∞

for n ¼ 1; N À 1

L2 norm of relative change in coolant density:

(3)


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Fig. 4. MC21 batch-wise shannon entropy and eigenvalue convergence during initial and eighth data exchanges.

Fig. 5. Distribution of MC21 relative uncertainty in relative power density (RPD) for CASL problem #6 3D ¼-Assembly, 2 billion neutrons.


B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351

343

Fig. 6. COBRA-IE convergence metrics for fuel temperature.

Fig. 7. COBRA-IE convergence metrics for coolant density.



rn ÀrN

c N c

rc
2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
# Coolant Regions
where,

for n ¼ 1; N À 1

(4)

T nf ¼ vector of local fuel temperatures for data exchange index n,
TN
f ¼ vector of local fuel temperatures at the final data exchange
N,
rnc ¼ vector of local subchannel coolant densities for data exchange index n, and


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B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351
Table 2
Calculated eigenvalue for CASL P6 ¼-Assembly.
Code

Eigenvalue (95% CI)

MC21/COBRA-IE
VERA-CS

1.16424 (2.6E-05)
1.16361

rNc ¼ vector of local subchannel coolant densities at the final
data exchange N.
From Figs. 6 and 7, both L2 and L∞ norms decrease as the COBRAIE transient solution develops and data is exchanged with MC21
until data exchange eight, at which time convergence metrics do
not improve given the chosen data exchange and MC21 neutron
history schemes (a simulation was run with 20 data exchanges, and
the COBRA-IE norms decreased no further). Final COBRA-IE
convergence metrics indicate that fuel temperature is converged
to <1 K, and the relative change in coolant density is converged to
<0.01%.
4.2. MC21/COBRA-IE and VERA-CS results comparison
Table 2 compares the eigenvalue for MC21/COBRA-IE and VERACS. The difference between MC21/COBRA-IE and VERA-CS is
63 pcm.
Fig. 8 presents axially-integrated normalized radial fission rate
distributions for MC21/COBRA-IE and VERA-CS. The relative 95%
confidence interval on MC21 axially-integrated normalized pin
fission rates is between 0.018% and 0.032%, depending on pin
location. Axially-integrated normalized pin powers agree within
±0.2% between MC21/COBRA-IE and VERA-CS with an RMS difference of 0.10%. Slight 1/8-core asymmetries in MC21/COBRA-IE values
are the result of Monte Carlo uncertainties.
Comparisons of normalized fission power axial profiles for fuel

rods traversing the diagonal symmetry line in the ¼-assembly (fuel
rods 11, 21, 41, 61, 71 and 81 as identified in Fig. 1) are presented in
Figs. 9 and 10. There is a slight axial bias between MC21/COBRA-IE
and VERA-CS; MC21/COBRA-IE predicts higher power from the
bottom through the elevation of peak power, and VERA-CS predicts

slightly higher power in the upper third of the core. Differences
between the different fuel rods have similar axial shapes and are
within ±3%. The RMS difference in normalized fission rate for all
3528 fuel rod power regions is 0.053 (fission rates are normalized
such that the average fission rate is 1.0).
Fig. 11 compares MC21/COBRA-IE and VERA-CS volume-averaged fuel pin temperatures at axial level 25 (the axial plane between 177.619 cm and 185.684 cm) containing the maximum fuel
pin temperature for both code suites. MC21/COBRA-IE predicts
higher maximum fuel temperatures by up to 3.2 C compared to
VERA-CS at this axial elevation. The primary reason for the difference is MC21 computes consistently higher pin powers at this axial
elevation (see Figs. 9 and 10) resulting in higher fuel pin temperatures. Axial plots of volume-averaged fuel pin temperatures
shown in Figs. 12 and 13 for the same fuel rods identified in Figs. 9
and 10 indicate that both code suites predict similar axial temperature distributions, including the temperature reductions at the
spacer grid elevations. As was seen in the power profile plots,
MC21/COBRA-IE predicts higher temperature in the bottom twothirds of the core, and VERA-CS predicts higher fuel temperatures
in the upper one-third of the core. Again, slight 1/8-core asymmetries in COBRA-IE fuel temperatures are caused by MC21 power
asymmetries. In all 3528 fuel pin regions, MC21/COBRA-IE and
VERA-CS volume-averaged fuel temperatures agree within ỵ8.8/4.3 C, with an RMS difference of 3.9 C.
Fig. 14 compares MC21/COBRA-IE and VERA-CS exit coolant
temperatures for all 81 coolant subchannels. MC21/COBRA-IE and
VERA-CS exit coolant temperatures agree within ỵ0.8/-1.5 C.
Figs. 15e17 present axial coolant temperature proles for the subchannels along the diagonal of the ¼-assembly model (1, 11, 21, 31,

Fig. 8. Axially-integrated ¼-Assembly normalized pin fission rates, MC21/COBRA-IE and VERA-CS.


B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351

345

Fig. 9. Axial normalized pin fission rate profiles for fuel rods 11, 41, and 71: MC21/COBRA-IE and VERA-CS.

41, 51, 61, 71, and 81 as identified in Fig. 1). Differences in subchannel coolant temperature rise are <1.0 C in the selected subchannels. For all 3969 subchannel regions in the core, coolant
temperatures agree within ỵ0.8/-1.5 C (the maximum differences
are at the core exit), with an RMS difference of 0.5 C.

4.3. Guide tube heating sensitivity study
To determine the effect of heat transfer through the guide tube
walls to the water flowing inside, MC21/COBRA-IE was executed
with heat transfer through the guide tube walls enabled. The MC21

Fig. 10. Axial normalized pin fission rate profiles for fuel rods 21, 61, and 81: MC21/COBRA-IE and VERA-CS.


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Fig. 11. Volume-averaged fuel pin temperatures at axial level 25, MC21/COBRA-IE and VERA-CS.

eigenvalue of this case is 1.16431 ± 2.9E-05, a gain of 7 pcm from
the base case without guide tube heating. Fig. 18 presents MC21/
COBRA-IE exit coolant temperature results for the cases with and
without guide tube heating. Exit temperatures for MC21/COBRA-IE
in subchannels neighboring guide tubes are lower when guide tube
heating is allowed, as expected due to heat transfer through the
guide tube walls. Exit coolant temperatures are now 1.4e1.6 C
cooler in subchannels neighboring guide tubes. Axial coolant

temperature profiles for subchannels 1, 41, and guide tube 7 are
presented in Fig. 19. When heat transfer through guide tube walls is

enabled, the temperature rise within the guide tube water is ~17 C,
which is approximately 50% of the temperature rise experienced in
the subchannels.
Guide tube heating also affects pin power distributions within
the assembly. Fig. 20 presents axially-integrated normalized radial
fission rate distributions for MC21/COBRA-IE for cases with and

Fig. 12. Axial volume-averaged fuel pin temperature profile for fuel rods 11, 41, and 71: MC21/COBRA-IE and VERA-CS.


B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351

347

Fig. 13. Axial volume-averaged fuel pin temperature profile for fuel rods 21, 61, and 81: MC21/COBRA-IE and VERA-CS.

Fig. 14. Subchannel exit coolant temperature, MC21/COBRA-IE and VERA-CS.

without guide tube heating. Differences in pin fission rates that are
statistically significant (i.e., larger than the relative uncertainty in
each individual pin power, noting the relative 95% confidence interval on MC21 axially-integrated normalized pin fission rates is
between 0.018% and 0.032%) are denoted by color shading in
Fig. 20. Blue shading indicates that pin powers in the case with
guide tube heating are smaller than the case with no guide tube

heating, and orange shading indicates that pin powers in the case
with guide tube heating are larger than the case with no guide tube
heating. Power in nearly all fuel pins adjacent to guide tubes have
reduced power, and power shifts radially in the assembly to fuel
pins that are further away from the guide tubes (with total assembly power kept constant). Although reactivity (7 pcm) and

power differences (<0.1% in total pin power) are small between


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Fig. 15. Axial coolant temperature profile for subchannels 1, 11, and 51: MC21/COBRA-IE and VERA-CS.

Fig. 16. Axial coolant temperature profile for subchannels 21, 41, and 71: MC21/COBRA-IE and VERA-CS.

cases with and without guide tube heating, they are noticeable and
could be important in full-core and depletion simulations. This
suggests that guide tube heating should be enabled in future
multiphysics PWR analyses.

5. Conclusions
A coupled MC21/COBRA-IE simulation of VERA core physics
benchmark problem #6, 3D Hot Full Power (HFP) Assembly, was
performed, providing the first coupled Monte Carlo neutronics/


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349

Fig. 17. Axial coolant temperature profile for subchannels 31, 61, and 81: MC21/COBRA-IE and VERA-CS.

Fig. 18. Subchannel exit coolant temperature, MC21/COBRA-IE with and without guide tube heating.

subchannel thermal-hydraulics solution to this problem. Convergence metrics for eigenvalue, Shannon entropy, fuel pin temperature, and subchannel fluid density demonstrate that the R5EXEC
physical under-relaxation methodology iterates steady-state MC21
and transient COBRA-IE to convergence in a stable manner. MC21/
COBRA-IE results were compared to VERA-CS (MPACT/CTF), and
calculated eigenvalues agree within 63 pcm. Axially-integrated
relative fission rates and peak fuel temperatures agree well

between MC21/COBRA-IE and VERA-CS, as do axial fission rate, fuel
temperature, and coolant temperature profiles. A sensitivity study
in which guide tube heating was enabled in MC21/COBRA-IE was
performed, and temperature rises in subchannels neighboring
guide tubes decreased by ~1.5 C while coolant temperature in the
guide tubes rose by ~17 C, approximately 50% of the temperature
rise of the coolant subchannels. This resulted in a statisticallysignificant (a) increase in reactivity and (b) shift in radial pin


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Fig. 19. Axial coolant temperature profile for subchannel 1, subchannel 41, and guide tube 7, MC21/COBRA-IE with and without guide tube heating.

1.0373 1.0374
1.0369 1.0370

1.0356 1.0321
1.0351 1.0320

1.0372 1.0388
1.0369 1.0384

1.0448 1.0451
1.0443 1.0444

1.0116 0.9767 MC21/COBRA-IE no GT Hea ng
1.0117 0.9769 MC21/COBRA-IE GT Hea ng
0.004% 0.013% % diff (GT Hea ng vs. no GT Hea ng)
0.9880 0.9726
0.9882 0.9728
0.017% 0.024%
Color Key
0.9880 0.9719
GT Hea ng: Lower Power
0.9882 0.9722
GT Hea ng = no GT Hea ng (w/in sta s
GT Hea ng: Higher Power
0.022% 0.036%
1.0115 0.9741
1.0112 0.9744

-0.037% -0.042%

-0.050% -0.015%

-0.038% -0.040%

-0.047% -0.073%

-0.027% 0.036%

1.0374 1.0097 1.0098 1.0372 1.0087 1.0056 1.0261
1.0370 1.0096 1.0099 1.0368 1.0086 1.0056 1.0258
-0.042% -0.009% 0.011% -0.046% -0.013% 0.000% -0.025%

1.0373 1.0096 1.0102 1.0389 1.0110 1.0086 1.0276
1.0371 1.0098 1.0102 1.0384 1.0110 1.0085 1.0272
-0.021% 0.015%

0.000% -0.045% 0.002% -0.005% -0.033%

cs)

1.0355 1.0086 1.0111 1.0449 1.0319 1.0513 1.0361 0.9830 0.9648
1.0350 1.0087 1.0110 1.0445 1.0317 1.0507 1.0357 0.9832 0.9654
-0.045% 0.012% -0.010% -0.046% -0.024% -0.054% -0.044% 0.018%

0.061%

1.0322 1.0057 1.0086 1.0452 1.0513
1.0319 1.0056 1.0087 1.0444 1.0508

1.0173 0.9647 0.9553
1.0170 0.9649 0.9557

-0.029% -0.007% 0.015% -0.074% -0.046%

-0.029% 0.022%

0.041%

1.0264 1.0278
1.0259 1.0272

1.0361 1.0172 0.9734 0.9478 0.9462
1.0356 1.0172 0.9736 0.9485 0.9466

-0.045% -0.055%

-0.046% -0.003% 0.020%

0.069%

0.050%

1.0119 0.9882 0.9880 1.0116 0.9830 0.9646 0.9481 0.9388 0.9420
1.0118 0.9882 0.9881 1.0113 0.9832 0.9649 0.9484 0.9393 0.9430
-0.007% 0.001%

0.014% -0.029% 0.027%

0.037%

0.029%

0.055%

0.099%

0.9769 0.9726 0.9720 0.9742 0.9647 0.9554 0.9462 0.9422 0.9480
0.9771 0.9729 0.9723 0.9743 0.9653 0.9558 0.9466 0.9429 0.9488

0.027%

0.031%

0.039%

0.017%

0.061%

0.039%

0.038%

0.071%

0.090%

Fig. 20. Axially-integrated ¼-Assembly normalized pin fission rates, MC21/COBRA-IE with and without guide tube heating.

power distribution within the assembly. This suggests that guide
tube heat transfer should be included in multiphysics PWR
analyses.

Acknowledgements
The Naval Nuclear Laboratory authors would like to thank the
MC21, COBRA-IE, and R5EXEC development teams for their support
during this research.
Work for the Oak Ridge National Laboratory authors was funded
by the DOE-sponsored “Consortium for Advanced Simulation of

Light Water Reactors” (CASL) project, and ORNL research used resources of the Oak Ridge Leadership Computing Facility at the Oak
Ridge National Laboratory, which is supported by the Office of
Science of the U.S. Department of Energy under Contract No. DEAC05-00OR22725.

References
Aumiller, D.L., Swartele, G.W., Meholic, M.J., Lloyd, L.J., Buschman, F.X., 2015. COBRAIE: a new sub-channel analysis code, NURETH-16eInternational Topical
Meeting on Nuclear Reactor Thermal Hydraulics. American Nuclear Society,
Chicago, Illinois.


B.N. Aviles et al. / Progress in Nuclear Energy 101 (2017) 338e351
Aumiller, D.L., Buschman, F., Tomlinson, E., Gill, D., 2016. Development of an integrated code system using R5EXEC and RELAP5-3D. Nucl. Technol. 193 (1),
183e199. />Bennett, A., Avramova, M., Ivanov, K., 2016. Coupled MCNP/CTF code: development,
testing, and application. Ann. Nucl. Energy 96, 1e11. />j.anucene.2016.05.008.
CASL, 2014. Consortium for Advanced Simulation of Light water reactors (CASL).
.
Collins, B.S., Godfrey, A.T., 2015. Analysis of the BEAVRS benchmark using VERA-CS,
ANS MC2015eJoint International Conference Mathematics and Computation
(M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo
(MC) Method. American Nuclear Society, Nashville, Tennessee.
Daeubler, M., Ivanov, A., Sjenitzer, B.L., Sanchez, V., Stieglitz, R., Macian-Juan, R.,
2015. High-fidelity coupled Monte Carlo neutron transport and thermalhydraulic simulations using Serpent 2/SUBCHANFLOW. Ann. Nucl. Energy 83,
352e375. />Ellis, M., Gaston, D., Forget, B., Smith, K., 2017. Preliminary coupling of the Monte
Carlo code OpenMC and the multiphysics object-oriented simulation environment for analyzing doppler feedback in Monte Carlo simulations. Nucl. Sci. Eng.
185 />Gill, D.F., Aumiller, D.L., Griesheimer, D.P., 2014. Monte Carlo and thermal-hydraulic
coupling via PVMEXEC, PHYSOR 2014ethe Role of Reactor Physics toward a
Sustainable Future. American Nuclear Society, Kyoto, Japan.
Gill, D.F., Griesheimer, D.P., Aumiller, D.L., 2015. Numerical methods in coupled
Monte Carlo and thermal-hydraulic calculations, ANS MC2015eJoint International Conference Mathematics and Computation (M&C), Supercomputing in

Nuclear Applications (SNA) and the Monte Carlo (MC) Method. American Nuclear Society, Nashville, Tennessee.
Gill, D.F., Griesheimer, D.P., Aumiller, D.L., 2017. Numerical methods in coupled
Monte Carlo and thermal-hydraulic calculations. Nucl. Sci. Eng. 185 http://
dx.doi.org/10.13182/NSE16-3.
Godfrey, A.T., 2014. VERA core physics benchmark progression problem

351

specifications. Revision 4, CASL Technical Report: CASL-U-2012-0131-004.
Griesheimer, D.P., Gill, D.F., Nease, B.R., Sutton, T.M., Stedry, M.H., Dobreff, P.S.,
Carpenter, D.C., Trumbull, T.H., Caro, E., Joo, H., Millman, D.L., 2015. MC21
v.6.0ea continuous-energy Monte Carlo particle transport code with integrated
reactor feedback capabilities. Ann. Nucl. Energy 82, 29e40. />10.1016/j.anucene.2014.08.020.
Ivanov, A., Sanchez, V., Stieglitz, R., Ivanov, K., 2015. Large-scale Monte Carlo
neutron transport calculations with thermal-hydraulic feedback. Ann. Nucl.
Energy 84, 204e219. />Kochunas, B., Jabaay, D., Stimpson, S., Graham, A., Downar, T., Collins, B., Kim, K.S.,
Wieselquist, W., Clarno, K., Gehin, J., 2015. VERA core simulator methodology
for PWR cycle depletion. CASL Technical Report: CASL-U-2015-0155-000.
Kotlyar, D., Shwageraus, E., 2016. Sub-step methodology for coupled Monte Carlo
depletion and thermal hydraulic codes. Ann. Nucl. Energy 96, 61e75. http://
dx.doi.org/10.1016/j.anucene.2016.05.032.
Lepp€
anen, J., Hovi, V., Ikonen, T., Kurki, J., Pusa, M., Valtavirta, V., Viitanen, T., 2015.
The numerical multi-physics project (NUMPS) at VTT Technical Research Centre
of Finland. Ann. Nucl. Energy 84, 55e62. />j.anucene.2014.10.014.
MPACT Team, 2015. MPACT theory manual. Version 2.0.0, CASL Technical Report:
CASL-U-2015-0078-000.
Palmtag, S., 2013. Coupled single assembly solution with VERA (Problem 6). Revision 1, CASL Technical Report: CASL-U-2013-0150-001.
Pecchia, M., Parisi, C., D'Auria, F., Mazzantini, O., 2015. Application of MCNP for
predicting power excursion during LOCA in Atucha-2 PHWR. Ann. Nucl. Energy

85, 271e278. />Salko, R.K., Avramova, M.N., 2014. CTF theory manual, Reactor Dynamics and Fuel
Management Group. Pennsylvania State University.
Salko, R.K., Lange, T., Kucukboyaci, V., Sung, Y., Palmtag, S., Gehin, J., Avramova, M.,
2015. Development of COBRA-TF for modeling full-core reactor operating cycles, ANFM 2015eAdvances in Nuclear Fuel Management V, Hilton Head, SC.
Sieger, M., 2015. VERA 3.3 release notes. CASL-U-2015-0042-000.