Abstract

The multiphysics object-oriented simulation environment (moose) is a code package that couples a variety of physics modules, allowing for highly accessible multiphysics simulations. The physics modules include a finite element Navier–Stokes (N–S) module that is designed to solve laminar fluid dynamics problems. The usage of this module in multiple recent studies coupled with the growing interest in moose for usage in nonlight water reactor safety studies by the Nuclear Regulatory Commission (NRC) prompted the authors to investigate the computational fluid dynamics capabilities of moose. A two-dimensional laminar flow past a circular cylinder scenario is simulated in the moose framework to investigate the effectiveness of the N–S module. Simulations assumed an unsteady laminar flow with a Reynolds number of 200. To verify the results from moose, similar simulations were conducted using the well-utilized simulation of turbulent flow in arbitrary regions—computational continuum mechanics C++ (star-ccm+) finite volume code. Results from both codes are also compared to some results from literature. Velocity and pressure profiles of both transient simulations were compared. The numerical and input errors in moose are also visualized with contour plots to qualitatively understand the evolution of the errors across time and space. The comparisons between moose and star-ccm+ showed nearly perfect agreement between the codes for velocity and pressure, especially after the development of the vortex street in later time-steps. The force coefficients showed excellent agreement after the development of the vortex street, but demonstrated notable discrepancies prior to the vortex street development, which is likely due to how each code simulated the approach to the vortex street in earlier time-steps.

References

1.
Permann
,
C. J.
,
Gaston
,
D. R.
,
Andrš
,
D.
,
Carlsen
,
R. W.
,
Kong
,
F.
,
Lindsay
,
A. D.
,
Miller
,
J. M.
,
Peterson
,
J. W.
,
Slaughter
,
A. E.
,
Stogner
,
R. H.
, and
Martineau
,
R. C.
,
2020
, “
MOOSE: Enabling Massively Parallel Multiphysics Simulation
,”
SoftwareX
,
11
(
10
), pp.
100430
100435
.10.1016/j.softx.2020.100430
2.
Ahmed
,
K.
,
2020
,
Lecture 2
,
Texas A&M University
, College Station, TX, Report No. NUEN 689/MSEN 619.
3.
Gaston
,
D. R.
,
Permann
,
C. J.
,
Andrš
,
D.
, and
Peterson
,
J. W.
,
2013
, “
Massive Hybrid Parallelism for Fully Implicit Multiphysics
,”
International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013)
, Sun Valley, ID, May 5–9, 2013, Paper No. INL/CON-13-28872.
4.
Manes
,
J. P.
,
2014
, “
A New Coupled CFD/Neutron Kinetics System for High Fidelity Simulations of LWR Core Phenomena: Proof of Concept
,”
Sci. Technol. Nucl. Install.
,
2014
, pp.
1
13
.10.1155/2014/185950
5.
Clifford
,
C. E.
, and
Kimber
,
M. L.
,
2020
, “
Assessment of RANS-Based Turbulence Models for Buoyancy-Influenced Forced Convection on a Heated Vertical Surface
,”
ASME J. Verif. Valid. Uncertainty Quantif.
,
5
(
1
), p.
011005
.10.1115/1.4046715
6.
Idaho National Laboratory
,
2018
,
RELAP5-3D, Version 4.4.2
,
Idaho National Laboratory
,
Idaho Falls, ID
.
7.
Zachry Nuclear Engineering
,
2019
,
GOTHIC, Version 8.3
,
Zachry Nuclear Engineering
,
Richland, Washington, DC
.
8.
Sandia National Laboratories
,
1997
,
CONTAIN, Version 2.0
,
Sandia National Laboratories
,
Albuquerque, NM
.
9.
Sandia National Laboratories
,
2017
,
MELCOR, Version 2.2.9541
,
Sandia National Laboratories
,
Albuquerque, NM
.
10.
Sandia National Laboratories,
2000
,
MELCOR Computer Code Manuals
,
Sandia National Laboratories
, Albuquerque, NM, Report No. NUREG/CR-6119, v 1, Rev. 2.
11.
CD-Adapco
,
2016
,
STAR-CCM+ 11.0 User Guide
,
CD-Adapco
,
Melville, NY
.
12.
Weller
,
H. G.
,
Tabor
,
G.
,
Jasak
,
H.
, and
Fureby
,
C.
,
1998
, “
A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques
,”
Comput. Phys.
,
12
(
6
), pp.
620
631
.10.1063/1.168744
13.
Tung
,
Y.
,
Ferng
,
Y.
,
Johnson
,
R. W.
, and
Chieng
,
C.
,
2013
, “
Study of Natural Circulation in a VHTR After a LOFA Using Different Turbulence Models
,”
Nucl. Eng. Des.
,
263
, pp.
206
217
.10.1016/j.nucengdes.2013.04.009
14.
Tung
,
Y.
,
2012
, “
Modeling Strategies to Compute Natural Circulation Using CFD in a VHTR After a LOFA
,”
ASME Paper No. IMECE2012-93007.
15.
Tung
,
Y.-H.
,
Johnson
,
R. W.
,
Ferng
,
Y.-M.
, and
Chieng
,
C.-C.
,
2014
, “
Bypass Flow Computations on the LOFA Transient in a VHTR
,”
Appl. Therm. Eng.
,
62
(
2
), pp.
415
423
.10.1016/j.applthermaleng.2013.10.003
16.
Schultz
,
R. R.
,
2017
, “
Identification and Characterization of Thermal Fluid Phenomena Associated With Selected Operating/Accident Scenarios in Modular High Temperature Gas-Cooled Reactors
,” Idaho National Laboratory, Idaho Falls, ID, Report No. EXT17–43218.
17.
Oberkampf
,
W. L.
, and
Roy
,
C. J.
,
2010
,
Verification and Validation in Scientific Computing
, 1st ed.,
Cambridge University Press
,
New York
.
18.
Fischer
,
P.
,
Lottes
,
J.
,
Kerkemeier
,
S.
,
Marin
,
O.
,
Heisey
,
K.
,
Obabko
,
E.
,
Merzari
,
E.
, and
Peet
,
Y.
,
2016
, “
Nek5000 User Documentation
,” Argonne National Laboratory, Lemont, IL, Report No. ANL/MCS-TM-351.
19.
U.S. NRC
,
2019
, “
NRC Non-Light Water Reactor (Non-LWR) Vision and Strategy, Volume 1—Computer Code Suite for Non-LWR Design Basis Event Analysis
,” U.S. Nuclear Regulatory Commission, Rockville, MD.
20.
Peterson
,
J. W.
,
Lindsay
,
A. D.
, and
Kong
,
F.
,
2018
, “
Overview of the Incompressible Navier-Stokes Simulation Capabilities in the MOOSE Framework
,”
Adv. Eng. Software
,
119
, pp.
68
92
.10.1016/j.advengsoft.2018.02.004
21.
Gałek
,
R.
, and
Strzelczyk
,
P.
,
2019
, “
Velocity Profiles of an Electrohydrodynamic Flow Generator: CFD and Experiment
,”
J. Electrostat.
,
99
, pp.
19
30
.10.1016/j.elstat.2019.04.003
22.
Xia
,
Y.
,
2016
, “
Development of a Multiphysics Algorithm for Analyzing the Integrity of Nuclear Reactor Containment Vessels Subjected to Extreme Thermal and Overpressure-Loading Conditions
,” Idaho National Laboratory, Idaho Falls, ID, Poster.
23.
Andersson
,
R.
,
2015
, “
Development of a Transient Multiphysics Solver for Nuclear Fuel Assemblies Within a CFD Framework
,” Master's thesis,
Chalmers University of Technology
, Göteborg, Sweden.
24.
Kristo
,
P. J.
, and
Kimber
,
M. L.
,
2021
, “
Cylinders and Jets in Crossflow: Wake Formations as a Result of Varying Geometric Proximities
,”
Phys. Fluids
,
33
(
5
), p.
055106
.10.1063/5.0047790
25.
Clifford
,
C. E.
,
Fradeneck
,
A. D.
,
Oler
,
A. M.
,
Salkhordeh
,
S.
, and
Kimber
,
M. L.
,
2019
, “
Computational Study of Full-Scale VHTR Lower Plenum for Turbulent Mixing Assessment
,”
Ann. Nucl. Energy
,
134
, pp.
101
113
.10.1016/j.anucene.2019.05.055
26.
Tafuni
,
A.
,
Domínguez
,
J. M.
,
Vacondio
,
R.
, and
Crespo
,
A. J. C.
,
2018
, “
A Versatile Algorithm for the Treatment of Open Boundary Conditions in Smoothed Particle Hydrodynamic GPU Models
,”
Comput. Methods Appl. Mech. Eng.
,
342
, pp.
604
624
.10.1016/j.cma.2018.08.004
27.
Liu
,
C.
,
Zheng
,
X.
, and
Sung
,
C. H.
,
1998
, “
Preconditioned Multigrid Methods for Unsteady Incompressible Flows
,”
J. Comput. Phys.
,
139
(
1
), pp.
35
57
.10.1006/jcph.1997.5859
28.
Calhoun
,
D.
,
2002
, “
A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions
,”
J. Comput. Phys.
,
176
(
2
), pp.
231
275
.10.1006/jcph.2001.6970
29.
Marrone
,
S.
,
Colagrossi
,
A.
,
Antuono
,
M.
,
Colicchio
,
G.
, and
Graziani
,
G.
,
2013
, “
An Accurate SPH Modeling of Viscous Flows Around Bodies at Low and Moderate Reynolds Numbers
,”
J. Comput. Phys.
,
245
, pp.
456
475
.10.1016/j.jcp.2013.03.011
30.
Vacondio
,
R.
,
Rogers
,
B. D.
,
Stansby
,
P. K.
,
Mignosa
,
P.
, and
Feldman
,
J.
,
2013
, “
Variable Resolution for SPH: A Dynamic Particle Coalescing and Splitting Scheme
,”
Comput. Methods Appl. Mech. Eng.
,
256
, pp.
132
148
.10.1016/j.cma.2012.12.014
31.
Plesniak
,
M. W.
,
Bell
,
J. H.
, and
Mehta
,
R. D.
,
1993
, “
Effects of Small Changes in Initial Conditions on Mixing Layer Three-Dimensionality
,”
Exp. Fluids
,
14
(
4
), pp.
286
288
.10.1007/BF00194022
32.
Mishra
,
A. A.
, and
Girimaji
,
S. S.
,
2014
, “
On the Realizability of Pressure–Strain Closures
,”
J. Fluid Mech.
,
755
, pp.
535
560
.10.1017/jfm.2014.446
33.
Rao
,
V. M.
,
Delchini
,
M. G.
,
Bani Ahmad
,
M. T.
, and
Jain
,
P. K.
,
2019
, “
High-Performance Computing to Enable Next-Generation Low-Temperature Waste Heat Recovery
,” Oak Ridge National Laboratory, Oak Ridge, TN, Report No. ORNL/TM2019/1455.
34.
Rao
,
V. M.
,
Delchini
,
M. G.
,
Jain
,
P. K.
, and
Bani Ahmad
,
M. T.
,
2020
, “
High-Performance Computing to Enable Next-Generation Low-Temperature Waste Heat Recovery
,”
ASME Paper No. POWER2020-16374.
35.
Darwish
,
M.
,
Mangani
,
L.
, and
Moukalled
,
F.
,
2018
, “
Implicit Boundary Conditions for Coupled Solvers
,”
Comput. Fluids
,
168
, pp.
54
66
.10.1016/j.compfluid.2018.03.046
36.
Chen
,
Z.
, and
Przekwas
,
A.
,
2010
, “
A Coupled Pressure-Based Computational Method for Incompressible/Compressible Flows
,”
J. Comput. Phys.
,
229
(
24
), pp.
9150
9165
.10.1016/j.jcp.2010.08.029
37.
Darwish
,
M.
,
Sraj
,
I.
, and
Moukalled
,
F.
,
2009
, “
A Coupled Finite Volume Solver for the Solution of Incompressible Flows on Unstructured Grids
,”
J. Comput. Phys.
,
228
(
1
), pp.
180
201
.10.1016/j.jcp.2008.08.027
38.
Ruge
,
J. W.
, and
Stüben
,
K.
,
1987
, “
Algebraic Multigrid
,” Multigrid Methods. S. F. McCormick.
Soc. Ind. Appl. Math.
, pp.
77
130
.https://doi.org/10.1137/1.9781611971057.ch4
39.
Versteeg
,
H. K.
, and
Malalasekera
,
W.
,
2007
,
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
, 2nd ed.,
Pearson Education Limited
,
Harlow, Essex, UK
.
40.
Richardson
,
L. F.
,
1911
, “
The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, With an Application to Stresses in a Masonry Dam
,”
Philos. Trans. R. Soc. Ser. A
,
210
(
459–470
), pp.
307
357
.https://doi.org/10.1098/rsta.1911.0009
41.
Richardson
,
L. F.
, and
Gawnt
,
J. A.
,
1927
, “
The Deferred Approach to the Limit
,”
Philos. Trans. R. Soc. Ser. A
,
226
(
636–646
), pp.
299
361
.https://doi.org/10.1098/rsta.1927.0008
42.
Roache
,
P. J.
,
1997
, “
Quantification of Uncertainty in Computational Fluid Dynamics
,”
Annu. Rev. Fluid Mech.
,
29
(
1
), pp.
123
160
.10.1146/annurev.fluid.29.1.123
43.
Kimber
,
M.
,
2019
,
Lecture 3 – Solution Verification
,
Texas A&M University
, College Station, TX, Report No. NUEN 489/689.
44.
Roache
,
P. J.
,
2009
,
Fundamentals of Verification and Validation
,
Hermosa Publishers
,
Albuquerque, NM
.
45.
Kimber
,
M.
,
2019
,
Lecture 7 – Input Parameter Uncertainty
,
Texas A&M University
, College Station, TX, Report No. NUEN 489/689.
46.
Geuzaine
,
C.
, and
Remacle
,
J. F.
,
2009
, “
Gmsh: A Three-Dimensional Finite Element Mesh Generator With Built-in Pre- and Post-Processing Facilities
,”
Int. J. Numer. Methods Eng.
,
79
(
11
), pp.
1309
1331
.10.1002/nme.2579
47.
Weiss
,
A. G.
,
Abdoelatef
,
M. G.
,
Bani Ahmad
,
M. T. H.
,
Ahmed
,
K.
, and
Kimber
,
M. L.
,
2021
, “
A Preliminary Evaluation of the Computational Fluid Dynamics Capabilities in MOOSE
,”
ASME Paper No. ICONE28-64908.
48.
Boström
,
E.
,
2015
, “
Investigation of Outflow Boundary Conditions for Convection-Dominated Incompressible Fluid Flows in a Spectral Element Framework
,” Master's thesis,
KTH Royal Institute of Technology
, Stockholm, Sweden.
49.
Liu
,
G. R.
, and
Quek
,
S. S.
,
2014
,
The Finite Element Method
, 2nd ed.,
Butterworth-Heineman
,
Waltham, MA
.
50.
Lee
,
D. T.
, and
Schachter
,
B. J.
,
1980
, “
Two Algorithms for Constructing a Delaunay Triangulation
,”
Int. J. Comput. Inf. Sci.
,
9
(
3
), pp.
219
242
.10.1007/BF00977785
51.
Koko
,
J.
,
2015
, “
A Matlab Mesh Generator for the Two-Dimensional Finite Element Method
,”
Appl. Math. Comput.
,
250
, pp.
650
664
.
52.
MATLAB
,
2019
,
Version R2019b
,
The MathWorks
,
Natick, MA
.
53.
Balay
,
S.
,
Abhyankar
,
S.
,
Adams
,
M.
,
Brown
,
J.
,
Brune
,
P.
,
Buschelman
,
K.
,
Dalcin
,
L.
,
Dener
,
A.
,
Eijkhout
,
V.
,
Gropp
,
W.
,
Karpeyev
,
D.
,
Kaushik
,
D.
,
Knepley
,
M.
,
May
,
D.
,
Curfman McInnes
,
L.
,
Mills
,
R.
,
Munson
,
T.
,
Rupp
,
K.
,
Sanan
,
P.
,
Smith
,
B.
,
Zampini
,
S.
,
Zhang
,
H.
, and
Zhang
,
H.
,
2021
, “
PETSc Users' Manual
,” Argonne National Laboratory, Lemont, IL, Report No. ANL-95/11–Revision 3.15.
54.
Bijl
,
H.
,
Carpenter
,
M. H.
, and
Vatsa
,
V. N.
,
2001
, “
Time Integration Schemes for the Unsteady Navier-Stokes Equations
,”
AIAA
Paper No. 2001–2612.10.2514/6.2001-2612
55.
ANSYS
,
2017
,
CFD Tutorial Manual
,
ANSYS
, ANSYS ICEM CFD 14, Canonsburg, PA.
56.
Qu
,
L.
,
Norberg
,
C.
,
Davidson
,
L.
,
Peng
,
S.
, and
Wang
,
F.
,
2013
, “
Quantitative Numerical Analysis of Flow Past a Circular Cylinder at Reynolds Number Between 50 and 200
,”
J. Fluids Struct.
,
39
, pp.
347
370
.10.1016/j.jfluidstructs.2013.02.007
57.
Posdziech
,
O.
, and
Grundmann
,
R.
,
2007
, “
A Systematic Approach to the Numerical Calculation of Fundamental Quantities of the Two-Dimensional Flow Over a Circular Cylinder
,”
J. Fluids Struct.
,
23
(
3
), pp.
479
499
.10.1016/j.jfluidstructs.2006.09.004
58.
Relf
,
E. F.
,
1914
, “
Discussion of the Results of Measurements of the Resistance of Wires, With Some Additional Tests on the Resistance of Wires of Small Diameter
,” Advisory Committee for Aeronautics (ACA), Teddington, London, UK, Reports and Memoranda No 102.
59.
Wieselsberger
,
C.
,
1921
, “
NeuereFestellungen Über dieGesetzedesFlüssigkeits- undLuftwiderstandes
,”
Phys. Z.
,
22
(
11
), pp.
321
328
.https://hdl.handle.net/2027/mdp.39015020056829
60.
McCarty
,
R. D.
, and
Arp
,
V. D.
,
1990
, “
A New Wide Range Equation of State for Helium
,”
Adv. Cryogen. Eng.
,
35
, pp.
1465
147
.https://link.springer.com/chapter/10.1007/978-1-4613-0639-9_174
61.
Arp
,
V. D.
,
McCarty
,
R. D.
, and
Friend
,
D. G.
,
1998
, “
Thermophysical Properties of Helium-4 From 0.8 to 1500 K With Pressures to 2000 MPa
,”
National Institute of Standards and Technology
,
Boulder, CO
, Report No. 1334.
62.
Patankar
,
S. V.
, and
Spalding
,
D. B.
,
1972
, “
A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows
,”
Int. J. Heat Mass Transfer
,
15
(
10
), pp.
1787
1806
.10.1016/0017-9310(72)90054-3
63.
Issa
,
R. I.
,
1986
, “
Solution of the Implicitly Discretized Fluid Flow Equations by Operator-Splitting
,”
J. Comput. Phys.
,
62
(
1
), pp.
40
65
.10.1016/0021-9991(86)90099-9
64.
Deng
,
J.
,
Shao
,
X.
, and
Yu
,
Z.
,
2007
, “
Hydrodynamic Studies on Two Traveling Wavy Foils in Tandem Arrangement
,”
Phys. Fluids
,
19
(
11
), p.
113104
.10.1063/1.2814259
65.
Abdoelatef
,
M. G.
,
Badry
,
F.
,
Schwen
,
D.
,
Permann
,
C.
,
Zhang
,
Y.
, and
Ahmed
,
K.
,
2019
, “
Mesoscale Modeling of High Burn-Up Structure Formation and Evolution in UO2
,”
J. Miner., Met. Mater. Soc.
,
71
(
12
), pp.
4817
4828
.10.1007/s11837-019-03830-z
66.
Badry
,
F.
,
Brito
,
R.
,
Abdoelatef
,
M. G.
,
McDeavitt
,
S.
, and
Ahmed
,
K.
,
2019
, “
An Experimentally Validated Mesoscale Model of Thermal Conductivity of a UO2 and BeO Composite Nuclear Fuel
,”
J. Miner. Met. Mater. Soc.
,
71
(
12
), pp.
4829
4838
.10.1007/s11837-019-03831-y
67.
Shafi
,
I. I.
,
Kristo
,
P.
,
Weiss
,
A. G.
, and
Kimber
,
M. L.
,
2019
, “
Qualitative Approaches to Understanding Coherent Structures in Turbulence
,”
Proceedings of 72nd Annual Meeting of the APS Division of Fluid Dynamics
, Seattle, WA, Nov. 23–26, Paper No. NP05-035.
68.
Lewandowski
,
M.
,
Kristo
,
P.
,
Weiss
,
A.
, and
Kimber
,
M.
,
2021
, “
Time Resolved PIV Measurements of a Slot Lobed Jet Issuing Into a Crossflow
,”
ASME Paper No. FEDSM2021-65783.
69.
Giudicelli
,
G. L.
,
Lindsay
,
A. D.
,
Freile
,
R.
, and
Lee
,
J.
,
2021
, “
Neam-TH-Crab
,” Idaho National Laboratory, Idaho Falls, ID, Report No. INL/EXT-21-62895.
70.
Giudicelli
,
G.
,
Lindsay
,
A.
,
Balestra
,
P.
,
Carlsen
,
R.
,
Ortensi
,
J.
,
Gaston
,
D.
,
DeHart
,
M.
,
Abou-Jaoude
,
A.
, and
Novak
,
A. J.
,
2021
, “
Coupled Multiphysics Transient Simulations of the MK1-FHR Reactor Using the Finite Volume Capabilities of the MOOSE Framework
,”
Proceedings of Mathematics & Computation (M&C) 2021
, Virtual Meeting, Oct. 3–7, pp.
2251
2262
.
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