The Naval Nuclear Laboratory is operated for the U.S. Department of Energy by Bechtel Marine Propulsion Corporation,

a wholly owned subsidiary of Bechtel National, Inc.

MC21 / CTF and VERA Multiphysics Solutions to

VERA Core Physics Benchmark Progression Problems 6 and 7

Daniel J. Kelly, Ann E. Kelly, Brian N. Aviles

Naval Nuclear Laboratory – Knolls Atomic Power Laboratory

Andrew T. Godfrey, Robert K. Salko, Benjamin S. Collins

Oak Ridge National Laboratory

Background

• Monte Carlo reactor physics plus subchannel thermal hydraulics codes becoming more common in large scale multiphysics analysis

• Complements coupled deterministic transport reactor physics / subchannel T-H codes

• Previous large-scale MC21 analyses

• BEAVRS Benchmark

• HZP: Kelly et al., M&C 2013

• Cycle 1 depletion with MC21 internal T-H feedback: Kelly et al., PHYSOR 2014

• HB Robinson isothermal depletion: Griesheimer, et al., Annals of Nuclear Energy, 2015

• Assembly Benchmarks: MC21 / COBRA-IE

• HFP Calvert Cliffs Assembly: Gill et al., PHYSOR 2014

• HFP VERA Assembly (Problem 6): Aviles et al., PHYSOR 2016

• Current work discuss explicit MC21 coupling with CTF

• Combination of VERA and in-house tools

• Evaluate complexity of integrating in-house solver with VERA

• Validate in-house tools against VERA tools

CASL VERA Core Physics Benchmark Problems

• Based on actual fuel and core geometry from

Watts Bar Nuclear 1 initial core

• Problems demonstrate increasing capabilities

for reactor physics methods and software

• Specification: Godfrey, “VERA Core Physics

Benchmark Progression Problem Specifications”,

Revision 4, CASL-U-2012-0131-004, August 29, 2014.

• Problem 6: HFP BOC Assembly

• MC21 / CTF complements previous MC21 /

COBRA-IE solution

• Problem 7: HFP ¼-Core w/ Xenon and Critical

Boron Search

• MC21 / CTF is first Monte Carlo / subchannel

T-H solution

Existing Processes

Thermal Hydraulics (VERA/CTF) Physics (MC21)

→ Reuse Features to Couple T/H (CTF) and Physics (MC21)

react2xml.pl p7.inp

p7.xml

xml2ctf –xmlfile=p7.xml

CTF

CTF Input Files

pdeck.56.x.inp,

pmaster.inp

multistate_cobra pdeck

pdeck.h5

(pin_powers)

p7.xml

VERA Input

p7.inp

CTF Results

pdeck.ctf.h5

MC21

PUMA

MC21 Input

Files

Import File

(Temp/Density)

PUMA Model

MC21.java

Job Summary file

jobSummary.h5Fission tally file

tally.h5

multistate_cobra pdeck

MC21

MC21 Input

Files

mc21_to_ctf.py

ctf_to_mc21.py

CTF Input Files

pdeck.56.x.inp,

pmaster.inp

VERA/CTF

Initialization

MC21

Initialization

pdeck.h5

(pin_powers)

VERA Input

XML (p7.xml)

CTF Results

pdeck.ctf.h5

Fission tally file

Tally.h5

Job Summary file

jobSummary.h5

Fission tally file

Tally.h5

Job Summary file

jobSummary.h5

Temp (solid, fluids), Densities (fluid)

initTempDens.h5

CTF Results

pdeck.ctf.h5

MC21

InitializationCoupled Process

PUMA Modeling - 1

Figure[] fig26 = {

g4,

f1, f1,

f1, f1, f1,

g4, f1, f1, g4,

f1, f1, f1, f1, f1,

f1, f1, f1, f1, f1, g4,

g4, f1, f1, g4, f1, f1, f1,

f1, f1, f1, f1, f1, f1, f1, f1,

f1, f1, f1, f1, f1, f1, f1, f1, f1};

Overlay lat26= VERAUtil.makeLattice("LAT26", fig26)

• MC21 model generated using the PUMA model builder

• General purpose model builder for MC21

• PUMA input based on a Java input deck

• New VERAUtil package developed

• Facilitate MC21 model building based on VERA common input format

• Enhance model QA by enabling comparison to VERA input

• VERAUtil input cards supported

• Cell, lattice, axial, assm_map

PUMA Modeling - 2

• Standard MC21 models only

requires a pin cell definition to

represent grid spacers

• For MC21 / CTF coupling require

each pin cell to be subdivided

into quadrants

• PUMA attributes are used assign

“tags” to designate specific MC21

source and sink numbering

• Numbering based on VERA / CTF

VERA Problem 6 Results

• Single PWR fuel assembly (Westinghouse

17x17-type fuel assembly)

• Conditions

• Beginning of Life (BOL)

• Hot Full Power (HFP)

• First successful demonstration of coupled

MC21 / CTF

• 2 Models (Physics, T-H) – same configuration

• Used available input/output capabilities to

couple and iterate, modifying solver

parameters as required

VERA Problem 6 Results

• Comparison to MC21 / COBRA-IE and VERA (MPACT / CTF)

• 9 coupled iterations (neutronics and T-H converged after data exchange 5)

Code SystemEigenvalue

(95% CI)

Difference

(pcm)

MC21 / COBRA-IE 1.16424 (2.6E-05) Reference

MC21 / CTF 1.16424 (2.6E-05) 0

MPACT / CTF 1.16361 -63

MC21 Eigenvalue and Number of Active Neutron

Histories during MC21 / CTF Data Exchanges

Calculated Eigenvalues for

Problem 6, ¼-Assembly0.0

0.5

1.0

1.5

2.0

1.16380

1.16385

1.16390

1.16395

1.16400

1.16405

1.16410

1.16415

1.16420

1.16425

1.16430

1.16435

1.16440

0 2 4 6 8 10

Ac

tive

His

tori

es

(B

illi

on

Neu

tro

ns)

MC

21

Eig

en

va

lue

MC21/CTF Data Exchange Index

MC21 Eigenvalue

Active Neutron Histories

VERA Problem 6 T-H Convergence Metrics

CTF Convergence Metrics for Subchannel Coolant

Temp during MC21 / CTF Data ExchangesCTF Convergence Metrics for Fuel Temp during

MC21 / CTF Data Exchanges

Neutronics and T-H Converged After Data Exchange 5

VERA Problem 6 Comparison

Axially Integrated ¼ Assembly Normalized

Pin Fission Rate Comparison,

Agree to (-0.19%, +0.17%)

RMS Difference = 0.09%

Subchannel Exit Coolant Temperature

Comparison,

Agree to ±0.1 C

RMS Difference = 0.02 C

VERA Problem 7

• Full Core (Westinghouse 17x17-type fuel assemblies in Watts Bar

Unit 1 initial cycle)

• Conditions

• Beginning of Cycle (BOC)

• Hot Full Power (HFP) with equilibrium xenon

• Nominal Power and Flow

• CASL benchmark specification: calculate critical boron concentration

• Used capabilities developed with Problem 6 for coupling of MC21

and CTF for Problem 7

• 2 Models (Physics, T-H) – same configuration

• Instrument Tubes replaced by Guide Tubes for ¼-core symmetry

VERA Problem 7 Models

H G F E D C B A

8 2.1 2.6 2.1 2.6 2.1 2.6 2.1 3.1

9 2.6 2.1 2.6 2.1 2.6 2.1 3.1 3.1

10 2.1 2.6 2.1 2.6 2.1 2.6 2.1 3.1

11 2.6 2.1 2.6 2.1 2.6 2.1 3.1 3.1

12 2.1 2.6 2.1 2.6 2.6 2.6 3.1 0

13 2.6 2.1 2.6 2.1 2.6 3.1 3.1 0

14 2.1 3.1 2.1 3.1 3.1 3.1 0 0

15 3.1 3.1 3.1 3.1 0 0 0 0

¼-Core Symmetric Model

VERA / CTF Assembly & Enrichment Layout PUMA / MC21 Model Layout

MC21 / CTF Problem 7 Results

Picard

Iter.Actions

Boron

(ppm)

Active

Histories(generation

size)

kcalc

(95% CI)

1Fixed Boron,

Isothermal,

eqXe900.0

50 million

(500,000)

1.01133

(1.8E-4)

2

Boron

Search, T/H

Feedback,

eqXe

859.7100 million

(1 million)

0.99989

(1.2E-4)

3

Boron

Search, T/H

Feedback,

eqXe

852.3100 million

(1 million)

1.00003

(1.0E-4)

4

Fixed Boron,

T/H

Feedback,

eqXe

852.3500 million

(1 million)

1.00031

(4.8E-5)

5

Fixed Boron,

T/H

Feedback,

eqXe

854.530 billion

(4 million)

0.99994

(6.8E-6)

MC21 / CTF Running Strategy

Distribution of MC21 Relative Uncertainty in

Relative Power Distribution, 30 Billion NeutronsVERA Predicted Critical Boron = 853.7 ppm

Distribution of MC21 Relative Power Uncertainties

Uncertainty >1%, 30 Billion Neutrons Uncertainty >2%, 30 Billion Neutrons

Max = 3.59%

MC21 Pin Power Distributions

MC21 Axially-Integrated Relative Pin Power Distribution.

Minimum = 0.1684, Maximum = 1.3658

MC21 Pin Power vs. VERA

• Maximum Relative Pin Power

• MC21: 1.3658 in pin (4,5) in D-12

• VERA: 1.3670 in the same pin

• Minimum Relative Pin Power

• MC21: 0.1684 in pin (17,17) in C-14

• VERA: 0.1673 in the same pin

H G F E D C B A

8

9

10

11

12

13

14

15

MC21 / CTF Local Results

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 50 100 150 200 250 300 350 400

Rela

tiv

e P

in L

inear

Heat

Rate

Axial Height (cm)

MC21/CTF: Assembly D-12, pin (5,4)

VERA: Assembly D-12, pin (5,4)

3D Octant View of CTF Subchannel

Temperature Distribution for MC21 / CTF,

RMS Difference vs. VERA = 0.08 C

Axial Relative Linear Heat Rate for Pin (5,4)

in Assembly D-12, MC21 / CTF vs. VERA

• MC21 / CTF: 1.9198 ± 0.34%

• VERA: 1.9214 (agrees w/in MC21

uncertainty)

Axial Power Results

Axially-Integrated Assembly Relative Power

MC21/CTF and VERA

RMS Difference = 0.22%

Core Relative Axial Power and Axial Offset

MC21/CTF and VERA

RMS Difference = 0.25%

-3%

-2%

-1%

0%

1%

2%

3%

0.0

0.3

0.5

0.8

1.0

1.3

1.5

0 50 100 150 200 250 300 350 400

% D

iffe

rence

: V

ER

A v

s.

MC

21

/CT

F

Re

lative

Po

we

r (-

)

Axial Height (cm)

MC21/CTF

VERA

% Difference: VERA vs. MC21/CTF

Axial Offset:

MC21/CTF = -11.06%

VERA = -11.03%

Exit Coolant Temperature Comparisons

Assembly-Averaged Exit Coolant Temperature (C)

MC21/CTF and VERA

RMS Difference = 0.13 C

Difference in Subchannel Exit Coolant

Temperature (C), VERA – (MC21/CTF),

RMS Difference = 0.13 C

Fuel Pin Temperature

Difference in Volume-Averaged Fuel Pin Temp (C) at

Axial Plane 19, VERA – (MC21/CTF)

RMS Difference = 2.1 C

• RMS difference between VERA and

MC21/CTF for all fuel pin volume-

average temperature regions in the

3D ¼-core model is 1.8 C

• Observable octant tilt resulting from

the non-symmetric MC21 solution

• Final solution based on 30B

histories (~0.5% error at this

plane)

• Previous iterations have larger

uncertainty causing stochastic

noise

Conclusions

• Successfully coupled Monte Carlo neutron transport code MC21 with

subchannel T-H code CTF

• Combination of CASL tools and in-house Python code

• Simulated VERA Benchmark Problems 6 and 7

• First published results for coupled Monte Carlo neutronics & subchannel T-H

solution for Watts Bar Unit 1 at HFP, BOC, w/ xenon and critical boron

search (Problem 7)

• Results in excellent agreement with VERA

Acknowledgements

• NNL

• MC21 Development Team

• PUMA Development Team

• ORNL

• DOE-sponsored CASL project

• ORNL supported by Office of Science of U.S. Department of Energy