Coupled Fluid Structure Simulations for
Application to Grid-to-Rod Fretting
by
Sasha Angela Tan-Torres
B.S. Mechanical Engineering and Nuclear Engineering (2012)
Rensselaer Polytechnic Institute
Submitted to the Department of Nuclear Science and Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Nuclear Science and Engineering
at the
MASSACHUSETTS IN6TITUTE
OF TECHNOLOGY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUL 29 2014
June 2014
LIBRARIES
@ Massachusetts Institute of Technology 2014. All rights res erved.
Author ......
Signature
red acted
Sasha Angela Tan-Torres
Department of Nuclear Science and En ineering
I.-[ Ma 23, 2014
.
Certified by
.............
Assistant Professor of
Signature redacted
I
ViEmilio Baglietto
uclear Science and Engineering
L
Certified by
A
Thesis Supervisor
................... Signature redacted-...
Ja po Buongiorno
A cc~mh~d by
uclear Science nd Engineering
, ThesisReader
. . . . . . . . ...............Signature
redacted ...
.
Associate Professor of
MlujiA S.Kazimi
TEPCO Professor of Nuclear Engineering
Chair, Department Committee on Graduate Students
ARCIMVES
2
Coupled Fluid Structure Simulations for Application to
Grid-to-Rod Fretting
by
Sasha Angela Tan-Torres
Submitted to the Department of Nuclear Science and Engineering
on May 23, 2014, in partial fulfillment of the
requirements for the degree of
Master of Science in Nuclear Science and Engineering
Abstract
Grid-to-rod fretting (GTRF) has been the major cause of fuel leakage in Pressurized
Water Reactors (PWRs) for the past ten years. It is responsible for over 70% of the
fuel leaking in PWRs in the United States. The Consortium for Advanced Simulation of Light Water Reactors (CASL) has identified GTRF as one of the "Challenge
Problems" that motivates the need for development and application of a modeling
environment for predictive simulation of light water reactors. In this thesis, an initial verification of the Fluid Structure interaction (FSI) coupling algorithm for flow
inside a vibrating tube was conducted using CFD software STAR CCM+. The benchmark confirmed accurate predictions of the coupled frequencies over a wide range of
Reynolds numbers, providing good confidence on the generality of the approach. A
representative spacer model was then developed to be used to evaluate the coupling
phenomena in GTRF applications. The geometry consists of a 2 span, 3x3 spacer
grid. To create the coupled fluid-solid test geometry, a solid Zircaloy cladding was
added to the geometry. The solid cladding was added to capture fluid structure interaction effects. The spacer grid supports were altered to mimic having experienced
relaxation and allowing free movement of the fuel rod for small displacements. A desirable mesh was constructed over the geometry. Large Eddy Simulations (LES) have
been performed to accurately compute the turbulent forces acting on the spacers.
Simulations were first performed for a rigid rod, as a reference decoupled solution.
Fully coupled simulations were successively performed allowing for the evaluation of
the complexity of the fluid-structure coupling behavior. Results of the simulations
were also compared to previous Westinghouse analysis performed on a production
spacer with a decoupled approach, to confirm the prototypical performance of the geometrical configuration adopted in the present work. The ultimate goal of this thesis
was to demonstrate the practicability of a fully coupled FSI simulation for PWR fuel
simulations, and further to advance the understanding of the complex fluid structure
coupling in PWR fuel assemblies.
3
Thesis Supervisor: Emilio Baglietto
Title: Assistant Professor of Nuclear Science and Engineering
Thesis Reader: Jacopo Buongiorno
Title: Associate Professor of Nuclear Science and Engineering
4
Acknowledgments
I would first and foremost like to express my gratitude to my supervisor, Professor
Emilio Baglietto, whose considerable knowledge, guidance, and unending patience
has truly made my graduate experience an unforgettable journey. Without his encouragement and understanding, I would not be where I am today. I cannot express
my gratitude enough.
I would also like to thank my research group members, especially Giancarlo Lenci,
Lindsey Gilman, Gustavo Montoya, Rosemary Sugrue, and Etienne Demarly, for
continually offering help and advice whenever I was in critical need. You are not only
my colleagues, but also my true friends and I am so thankful for your friendships.
I must also thank my family for the support they have provided throughout my
entire life. I would like to thank my four siblings for setting the standard of achievement so high with all of their accomplishments. A special thanks goes to my mom for
always believing in me and pushing me to strive for the very best. Another special
thanks goes to my dad for always being there for me to count on during any time of
need.
5
6
Contents
1
Introduction
15
1.1
B ackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.2
M otivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
1.3
STAR CCM + ................................
21
2
Preliminary FSI Validation
23
3
Setup for the GTRF Test Cases
33
3.1
Fuel Assembly Geometry and Boundary Conditions . . . . . . . . . .
34
3.2
Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3.3
Solvers ........
39
3.4
Physics. ........
...................................
40
3.5
Test C ases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4
...................................
Results
43
4.1
Case 1: 5 m/s Fluid-only . . . . . . . . . . . . . . . . . . . . . . . . .
45
4.2
Case 2: 10 m/s Fluid-only . . . . . . . . . . . . . . . . . . . . . . . .
46
4.3
Case 3: 5 m/s Fluid-solid Coupled. . . . . . . . . . . . . . . . . . . .
47
4.4
Case 4: 10 m/s Fluid-solid Coupled . . . . . . . . . . . . . . . . . . .
51
5
Relevance of Findings
55
6
Conclusions and Future Work
61
7
A Power Spectral Density Plots: Case 1 and 2
63
A.1 Case 1: 5m/s Fluid-only . . . . . . . . . . . . . . . . . . . . . . . . .
63
A.2 Case 2: 10 m/s Fluid-only . . . . . . . . . . . . . . . . . . . . . . . .
73
8
List of Figures
1-1
PWR Assembly ..............................
1-2
Example of Split Vane Spacer [9]
1-3
Full Length Fuel Rod Model [9]
. 16
. . . . . . . . . . . . . . . . . . . .
16
. . . . . . . . . . . . . . . . . . . . .
17
1-4 VITRAN approximation of fuel rod as Euler-Bernoulli beam [11]
. .
20
2-1
Coriolis Flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2-2
Solid-Only Test Geometry and Mesh
. . . . . . . . . . . . . . . . . .
27
2-3
Mesh Selection: Grid Sensitivity for Velocity . . . . . . . . . . . . . .
28
2-4
Fast Fourier Transform Power Spectral Density Plot: 0.2 m Element .
28
2-5
Natural Frequency Comparison: Solid-Only tests . . . . . . . . . . . .
29
2-6
Coupled Solid Fluid Initial Beam Displacement: 0.6 m Element
. . .
30
2-7
Coupled Solid Fluid Transient Displacement: 0.6 m Element . . . . .
30
2-8
Fast Fourier Transform Power Spectral Density Plot: 0.6 m Element .
31
2-9
Natural Frequency Comparison: Coupled Fluid Structure tests . . . .
32
3-1
Initial Fuel Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
3-2
Grid Geometry with Periodic Boundary conditions [5] . . . . . . . . .
35
3-3
STAR CCM+ model . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
3-4
Spacer Grid and Center Rod . . . . . . . . . . . . . . . . . . . . . . .
36
3-5
Spacer with modified supports around the central rod. The left image
shows the spacer itself and the right image shows the same spacer with
3-6
an emphasis on the 0.5 mm gaps. . . . . . . . . . . . . . . . . . . . .
37
Inlet and Spacer Mesh . . . . . . . . . . . . . . . . . . . . . . . . . .
38
9
3-7
Near Wall Mesh and Spacer details: Top picture shows the solid Zircaloy
cladding in grey and the coolant in purple. The bottom picture shows
spacer details and the gap between the Zircaloy cladding and the support, which has experience wear . . . . . . . . . . . . . . . . . . . . .
39
3-8
Locations of Fluid and Solid monitors . . . . . . . . . . . . . . . . . .
41
3-9
Center Rod split into 1 inch segments, Fluid-only Case . . . . . . . .
42
4-1
Excitation force distribution along the span after the mixing vanes [5]
44
4-2
Lateral Velocity Vectors 0.67 inches above grid strap [5] . . . . . . . .
44
4-3
Lateral Velocity Vectors 1.97 inches above grid strap [5] . . . . . . . .
45
4-4
RMS Turbulence Forces for Case 1 (left) comparison to the turbulence
forces of Elmahdi et. al (right) . . . . . . . . . . . . . . . . . . . . . .
46
4-5
RMS Turbulence Forces for Case 2
. . . . . . . . . . . . . . . . . . .
47
4-6
Time Averaged Velocity for Case 3
. . . . . . . . . . . . . . . . . . .
48
4-7
Vibration Location of Point 4 over 0.06 seconds for Case 3 . . . . . .
49
4-8
Displacement Scene: Maximum displacement in the X and Z directions
for C ase 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
Instantaneous X and Z forces over Time
. . . . . . . . . . . . . . . .
50
4-10 Displacement Plots in X and Z directions for Case 3 . . . . . . . . . .
50
4-11 RMS Turbulence Forces for Case 3
. . . . . . . . . . . . . . . . . . .
51
4-12 Time Averaged Velocity for Case 4 . . . . . . . . . . . . . . . . . . .
52
4-13 Monitor Vibration Location of Point 4 over 0.035 seconds for Case 4 .
52
4-9
4-14 Displacement Scene: Maximum displacement in the X and Z directions
for C ase 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
4-15 Displacement Plots in X and Z directions for Case 4 . . . . . . . . . .
54
4-16 RMS Turbulence Forces for Case 4 . . . . . . . . . . . . . . . . . . .
54
5-1
Decay of RMS Values along the span of the rod downstream from the
grid for Cases 1 and 2
5-2
. . . . . . . . . . . . . . . . . . . . . . . . . .
56
Decay of RMS Values along the span of the rod downstream from the
grid for Cases 3 and 4
. . . . . . . . . . . . . . . . . . . . . . . . . .
10
56
Tangential Velcocity 5 m/s and Vanes . . . . . . . . . . . . . . . . . .
57
5-4
Tangential Velcocity 10 m/s and Vanes . . . . . .
57
5-5
Element 7 5 m/s X Force- Top: Fluid-only, Bottom: Fluid-Solid Coupled 58
5-6
Element 7 5 m/s Z Force- Top: Fluid-only, Bottom: Fluid-Solid Coupled 59
5-7
Element 2 10 m/s X Force- Top Fluid-only, Bottom: Fluid-Solid Coupled 59
5-8
Element 2 10 m/s Z Force- Top: Fluid-only, Bottom: Fluid-Solid Coupled 60
. . . . . . . . .
.
.
5-3
A-i 5 m/s X Force Fluid-only PSD: Element 1 . . . . . . . . . . . . . . .
64
A-2 5 m/s X Force Fluid-only PSD: Element 2 . . . . . . . . . . . . . . .
64
A-3 5 m/s X Force Fluid-only PSD: Element 3 . . . . . . . . . . . . . . .
65
A-4 5 m/s X Force Fluid-only PSD: Element 4 . . . . . . . . . . . . . . .
65
A-5 5 m/s X Force Fluid-only PSD: Element 5 . . . . . . . . . . . . . . .
66
A-6 5 m/s X Force Fluid-only PSD: Element 6 . . . . . . . . . . . . . . .
66
A-7 5 m/s X Force Fluid-only PSD: Element 7 . . . . . . . . . . . . . . .
67
A-8 5 m/s X Force Fluid-only PSD: Element 8 . . . . . . . . . . . . . . .
67
A-9 5 m/s X Force Fluid-only PSD: Element 9 . . . . . . . . . . . . . . .
68
A-10 5 m/s Z Force Fluid-only PSD: Element 1
. . . . . . . . . . . . . . .
68
A-11 5 m/s Z Force Fluid-only PSD: Element 2
. . . . . . . . . . . . . . .
69
A-12 5 m/s Z Force Fluid-only PSD: Element 3
. . . . . . . . . . . . . . .
69
A-13 5 m/s Z Force Fluid-only PSD: Element 4
. . . . . . . . . . . . . . .
70
A-14 5 m/s Z Force Fluid-only PSD: Element 5
. . . . . . . . . . . . . . .
70
A-15 5 m/s Z Force Fluid-only PSD: Element 6
. . . . . . . . . . . . . . .
71
A-16 5 m/s Z Force Fluid-only PSD: Element 7
. . . . . . . . . . . . . . .
71
A-17 5 m/s Z Force Fluid-only PSD: Element 8
. . . . . . . . . . . . . . .
72
A-18 5 m/s Z Force Fluid-only PSD: Element 9
. . . . . . . . . . . . . . .
72
A-19 10 m/s X Force Fluid-only PSD: Element 1 . . . . . . . . . . . . . . .
73
A-20 10 m/s X Force Fluid-only PSD: Element 2 . . . . . . . . . . . . . . .
73
A-21 10 m/s X Force Fluid-only PSD: Element 3 . . . . . . . . . . . . . . .
74
A-22 10 m/s X Force Fluid-only PSD: Element 4 . . . . . . . . . . . . . . .
74
A-23 10 m/s X Force Fluid-only PSD: Element 5 . . . . . . . . . . . . . . .
75
11
A-24 10 m/s X Force Fluid-only PSD: Element 6.
. . . . . . . . . . . .
75
A-25 10 m/s X Force Fluid-only PSD: Element 7.
. . . . . . . . . . . .
76
A-26 10 m/s X Force Fluid-only PSD: Element 8.
. . . . . . . . . . . .
76
A-27 10 m/s X Force Fluid-only PSD: Element 9.
. . . . . . . . . . . .
77
A-28 10 m/s Z Force Fluid-only PSD: Element 1
. . . . . . . . . . . .
77
A-29 10 m/s Z Force Fluid-only PSD: Element 2
. . . . . . . . . . . .
78
A-30 5 m/s Z Force Fluid-only PSD: Element 3
. . . . . . . . . . . .
78
A-31 10 m/s Z Force Fluid-only PSD: Element 4
. . . . . . . . . . . .
79
A-32 10 m/s Z Force Fluid-only PSD: Element 5
. . . . . . . . . . . .
79
A-33 10 m/s Z Force Fluid-only PSD: Element 6
. . . . . . . . . . . .
80
A-34 10 m/s Z Force Fluid-only PSD: Element 7
. . . . . . . . . . . .
80
A-35 10 m/s Z Force Fluid-only PSD: Element 8
. . . . . . . . . . . .
81
A-36 10 m/s Z Force Fluid-only PSD: Element 9
. . . . . . . . . . . .
81
12
List of Tables
2.1
Coriolis Flowmeter Geometry Specifications and Material Properties
24
2.2
Solid-Only Natural Frequencies
. . . . . . . . . . . . . . . . . . . . .
25
2.3
Solid Region M odels
. . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.4
Fluid Region M odels . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
5.1
Frequency Comparison . . . . . . . . . . . . . . . . . . . . . . . . . .
59
13
14
Chapter 1
Introduction
Pressurized Water Reactors constitute the majority of the one hundred currently operating nuclear power plants in the United States. In a PWR, the primary coolant is
pumped under high pressure to the reactor core, where it is then heated by the core
inside the reactor vessel. The coolant then carries the heat to the steam generator;
steam then turns a turbine generator, which then produces electricity. The coolant
flowing through the reactor core fuel assembly is the process which is the major focus
of this thesis. An example of a PWR assembly can be seen in Figure 1-1. Understanding and modeling of the Fluid Structure Interaction (FSI) is what motivates this
thesis.
In a PWR, grid-to-rod fretting wear is generated at grid-to-rod contact areas by
flow induced vibrations.[8] The internal vibrations are of three kinds: self-excited
fuel assembly vibration, self-excited spacer grid strap vibration, and excessive fuel
rod vibration. The self-excited fuel assembly vibration is caused by the asymmetric
mixing vane pattern across the spacer grid. An example of the spacer grid with mixing
vanes can be seen in Figure 1-2.
Excessive fuel rod vibration is especially increased when the gap size increases.
Fuel Rods in the PWR fuel assembly are supported by friction and normal forces
between the fuel rods and the springs and dimples. Friction is the only tangential
component of the force between the spacer and the rods. As the coolant flows through
the assembly, fluid forces generated by the flow field, both viscous and pressure forces,
15
Too Nozze
Spacer Grid Assembly
Fl Rod
Bottom Nozzle
Figure 1-1: PWR Assembly
L
10
7/
I 21
F,
Figure 1-2: Example of Split Vane Spacer [9]
16
F,
d
A
bd
e
1 13
F1el Rdod
Figre1-: FllLegt
dl9
Figure 1-3: Full Length Fuel Rod Model [9]
induce vibrations in the fuel rod. A full length fuel rod model can be seen in Figure
1-3. This is also an example of a the structural analysis model of the assembly in the
Westinghouse tool.
GTRF can be caused by faulty fuel design or fabrication, or even operating conditions, however, flow induced vibration and lack of grid-to-rod positive contact force is
the greatest cause of GTRF. The lack of grid-to-rod positive contact force is caused
by irradiation creep and growth. Under these conditions, the spring and the dimples
can lose contact with the fuel rod, which causes gap formation between the spacer
grid and the fuel rod.[5] These gaps increase the effects of flow induced vibration
and causes normal and tangential cyclic contact forces generated between the springdimple supports and fuel rod. This further enhances fretting wear. Computational
Fluid Dynamics can be used to compute the forces on the fuel rods which lead to
GTRF. The current industry solution that Westinghouse uses involves the use of
CFD Large Eddy Simulation (LES) modeling techniques in CD-adapco CFD code
STAR-CCM+ to calculate the instantaneous stress tensor on the fuel rod. The tran17
sient hydraulic forces on the fuel rod calculated by the model are then linked to the
Westinghouse VITRAN(VIbration TRansient Analysis - Nonlinear) code to produce
a comparison of the rod vibration and fretting wear work-rate.[5] This in turn determines the forcing function for vibrations. This method decouples the fluid and the
solid fuel assembly. Results from this decoupled method, show that the mixing vanes
of the fuel rod assembly are the main source of turbulence that generates the excitation forces on the fuel rod. The excitation forces also decay downstream of the mixing
vanes. This Master's project will seek to couple the fluid and the solid, such that
the vibration of the rod can affect the flow. The demonstration of the feasibility of a
coupled simulation approach is particularly desirable in order to support and validate
the current adopted decoupled approach. The coupled method can further provide a
new understanding in the FSI behavior, which could lead to advanced design concepts
with reduced GTRF susceptibility.
In this Master's thesis, Chapter 1 discusses the background of GTRF and the
motivation for this project.
Chapter 2 describes the preliminary FSI validation work.
Chapter 3 describes the setup and test cases for the spacer-grid assembly.
Chapter 4 describes the results and findings from the test cases.
Chapter 5 discusses the results, conclusions, and future work about the effects of
FSI.
1.1
Background
Grid-to-rod Fretting has been previously analyzed as a part of a comprehensive approach to predict fretting-wear risk based on the fuel assembly operating conditions.
There are several key factors affecting GTRF in fuel assemblies that are assessed
in this study.
These include wear damage sensitivity to the grid support forces,
fuel rod-to-grid gap size, assembly grids misalignment, rod structural damping and
stiffness, assembly bow shape, solid-to-solid friction coefficients and turbulence force
spectrum. VITRAN has successfully been applied to the prediction of fretting-wear
18
damage of fuel assemblies under controlled test conditions.
The results are com-
pared with endurance tests run in Westinghouse's VIPER loop located in Columbia,
South Carolina. The VIPER loop can contain two full scale fuel assemblies. Though
these results seem encouraging, there are uncertainties associated with the assembly's
mechanical properties and operating conditions which give rise to challenges.[11] A.
comprehensive approach to assess the fretting-wear based on the operating conditions of the reactor would reduce the assemblies wear risk by potentially introducing
new guidelines in the core loading pattern design. Rubiolo and Young [11] sought
to develop these guidelines by determining the dependency of the wear damage on
identified independent wear factors. These wear factors include cell size clearance,
assembly bow pattern, fuel rod stiffness, fuel rod structural damping, and turbulence
forces.
VITRAN approximates the fuel rod as an Euler-Bernoulli beam and uses modal
analysis techniques to solve for the rod motion equations. Figure 1-3 shows the fuel
model. It is a non-linear dynamic model that calculates the rod frequency response
and motion, the support impact forces, sliding and sticking distances, and the work
rates. [5] VITRAN considers the assembly grids as constraining forces that occur when
the fuel rod impacts the grid support. The normal impact force and the friction force
are calculated from the relative motion of the rod. In the linear-model simulation
of VITRAN, the normal force is calculated by approximating the the support as a
spring-damper system as seen in Figure 1-4. VITRAN models the turbulent flow
forces on the rod as external forces, which are independent of rod motion. This is
justified under normal reactor operating conditions. The friction forces are modeled
using the previously modeled Spring-Damper Friction Model(SFDM) by Antunes et
al. [1]. The SFDM model models two friction regimes during impact which include
sliding (dynamic) and sticking (static). The linear model is meant to obtain and
calibrate flow excitation force, which can then be directly applied to the nonlinear
simulation model. Simulating the VIPER loop is very challenging because of uncertain interactions of a fuel rod and its supports. To account for this uncertainty,
VITRAN uses a Monte Carlo code to generate a large number of single rod models
19
Gap
Bowed Rod
Spring
Gapped
---- +[;I
support
Damper
Preloade
support
y
Z
Figure 1-4: VITRAN approximation of fuel rod as Euler-Bernoulli beam [11]
with random support conditions. In the nonlinear model,VITRAN calculates the rod
displacement and impact forces against the supports by numerically integrating the
rod motion during a fixed transient simulation.[9] The work by Rubiolo and Young
showed that the two key factors that have the most significant effect wear risk are
grid cell clearance size and turbulence forces. It was found that assembly bow shape
has little effect on the distribution of wear. The model also showed a moderate impact from structural damping, whose uncertainties could be statistically introduced
in the model. The future work of Rubiolo and Young is to establish a functional
dependency of wear damage to grid cell size and turbulence excitation forces, such
that core loading guidelines can be modified for the better. The work of Rubiolo arid
Young show that the major focus in GTRF analysis should be on the gap size arid
turbulence force, which motivates the test cases prepared in this thesis.
The work of Elmahdi et. al was part of a large program to develop a complete
analytical methodology for prediction of GTRF in fuel assemblies [5]. The study
conducted evaluated the feasibility of the use of CFD Large Eddy Simulation (LES)
modeling techniques using STAR-CCM+ to calculate the stress tensor on the fuel rod
wall. This work is discussed further in Chapter 3 and provides the basis of comparison
20
for the test cases run in this Master's thesis.
1.2
Motivation
Though the decoupled solution from VITRAN offers a sufficient solution under controlled operating conditions, the solution may not necessarily be true under varied
operating conditions. The current solution does not consider the fluid and solid interaction, and fails to capture the fretting wear that causes gaps between the fuel and
the spacer grid. The goal here is to couple the fluid and the structure of a fuel rod
assembly. Fluid Structure Interaction (FSI) occurs when internal or external fluid
flow causes a deformation in the structure with which it interacts. The deformation
changes the boundary conditions of the fluid flow. In this thesis project, a comparable
CFD analysis was conducted to compare to the results of Elmahdi et. al. A representative spacer model was developed to be used to evaluate the coupling phenomena
in GTRF applications. The geometry consists of a 2 span, 3x3 spacer grid with a
solid Zircaloy cladding. The solid cladding was added to capture fluid structure interaction effects. The spacer grid supports were altered to mimic having experienced
relaxation and allowing free movement of the fuel rod for small displacements. An
optimal mesh was constructed for the geometry and LES (Large Eddy Simulation)
simulations, with fully coupled fluid structure interactions were performed to analyze
the FSI effects.
1.3
STAR CCM+
STAR CCM+ is a Computational Fluid Dynamics software developed by CD-adapco.
STAR CCM+ is able to solve problems involving flow, heat transfer, and stress.
The components of the package include a 3D-CAD modeler, CAD embedding, surface preparation tools, automatic meshing technology, physics modeling, turbulence
modeling, post-processing, and CAE integration. STAR CCM+ is based on objectoriented programming technology and is widely known for its ability to solve problems
21
involving multi-physics and complex geometries. [4]
22
Chapter 2
Preliminary FSI Validation
Performing accurate coupled FSI simulations for water flow in turbulent conditions
and stiff stiff solid structures is particularly demanding for the numerical coupling
algorithms.
In order to validate the robustness and in particular accuracy of the
FSI method a valuable benchmark was proposed by Bobovnik. The benchmark describes a Coriolis Flow meter describes a coupled finite-volume/finite-element numerical model of the straight-tube Coriolis flowmeter whose solution is evaluated in terms
of the fundamental natural frequency of the vibrating system and the phase difference
between the motion of the sensing points locating on the measuring tube.[3] A fluidconveying measuring tube that is maintained vibrating at its first natural frequency
is the primary sensing element of the Coriolis flowmeter. The model consists of a
straight measuring tube clamped at both ends and vibrating in the x-z plane due to
fluid flow. This model can be seen in Figure 2-1. Five different flow meter lengths
are modeled, and the frequency and phase difference recorded for each. The material properties and geometry specifications can be seen in Table 2.1. The numerical
model is then compared to the Euler beam model and the Flugge shell model. In
Euler theory for bending of a slender beam, the measuring tube deflections will be
represented by the displacement field as a function of position and time. The Flugge
shell model of a thin cylindrical shell represents the deformations of the measuring
tube by the displacements of the middle surface, i.e. the radial, circumferential, and
axial displacements. [3]. This benchmark is used as a starting point for validation of
23
L
I2-
LF
12S
inle rne2mgtL
TF(t)=F,
Fm F.
(t)uF.
Figure 2-1: Coriolis Flowmeter
L.
L0,
D
h
s
Tube (Ti)
4510
[kg/M]
Geoietry
0.2...0.6 ps
[i]
L. [ 0.4 E [GPa] 102.7
V[i] 0.4
[i] 0.02
[iM]
-
5-10-4
PF
L2
p
0.34
Fluid (H 2 0)
3
1000
1.002-10
[Pa-s
[kg/
Table 2.1: Coriolis Flowmeter Geometry Specifications and Material Properties
the CFD approach on STAR CCM+.
Before coupled Fluid Structure tests were conducted, a set of Solid-Only tests
for comparable geometry were conducted using STAR CCM+.
The results were
compared to a theoretical model. The fundamental frequencies in Hertz for a FixedFixed end beam geometry can be found using Equation 2.1 [7], in which E is the
modulus of elasticity, I is the area moment of inertia, L is the length, and p is the
.
mass density (mass/length)
=
F22.373-
22
1n.L
2 Ir
1
2
1
E
p
(2.1)
The theoretical natural frequencies for the varying beam lengths can be seen in
Table 2.2
Five simulations with varying beam lengths were run. The initial geometry and
mesh were built in STAR CCM+ and can be seen in Figures 2-2. They were built
using the same specifications as the Coriolis Flowmeter.
24
Surface boundaries were
L/d
10
15
20
25
30
Frequency (Hz)
3079.76
1368.78
769.94
492.76
342.2
Table 2.2: Solid-Only Natural Frequencies
Table 2.3: Solid Region Models
Constant Density
Gradients
Gravity
Implicit Unsteady
Linear Isotropic Elastic
Solid
Solid Stress
Three Dimensional
set for the inlet, outlet, and body. An interface was constructed between the Solid
and Fluid Regions and set with a FSI Coupling Method.The Fluid and Solid Region
Models can be see in Table 2.3 and Table 2.4.
To determine the base size for the mesh, a grid sensitivity test of velocity was
conducted. Four different base sizes were selected: 0.5, 1, 2, and 3 mm. Using the
same geometry, four meshes were created and the average velocity through the pipe
was recorded using a line probe positioned radially in the center of the pipe. The
results of the grid sensitivity test can be seen in Fig 2-3. A base size of 1 mm was
selected.
For the five Solid-Only tests, the Fluid Region was disabled and each beam was
fixed at each end. Because STAR CCM+ does not have a setting to allow for a direct
initial displacement in the beam, an increased gravity of 4000 m/s2 was applied to
create an initial deflection in the rod. When an initial deflection was achieved, gravity
was removed and each beam was allowed to vibrate transiently. For each test, a Fast
Fourier Transform (FFT) was conducted in order to find the natural frequency of
25
Table 2.4: Fluid Region Models
Gradients
Implicit Unsteady
K-Epsilon Turbulence
Liquid
Realizable K-Epsilon Two Layer
Reynolds-Averaged Navier Stokes
Segregated Flow
Three Dimensional
Turbulent
Two-Layer All y+ Wall Treatement
User Defined EOS
the vibrating beam. A Power Spectral Density (PSD) plot was created for each case.
An example plot for the 0.2 m element can be seen in Figure 2-4. The results of
the STAR CCM+ simulations were then compared to the mechanical model results
in Table 2.2, and can be seen in Figure 2-5. Error bars on the plot, derived from
a Triangular Distribution, show that the error about each STAR CCM+ result was
below 20%. Each natural frequency found from STAR CCM+ result was within a
7% error of the mechanical model result. This gave positive affirmation that STAR
CCM+ was producing accurate results.
Next in the initial FSI validation, the coupled Solid-Fluid tests were created and
run for comparison to the Coriolis Flowmeter results of Bobovnik et. al. The tests
were run using the same geometry and physics as in the Solid-Only tests, only in
these cases the Fluid Region was enabled, with an inlet velocity of 5 m/s. Like in
the Solid-Only tests, the first part of the simulation is used to achieve an initial
displacement in the beam.
Since in this first part of the simulation the intent is
to reach a steady-state solution, the physical coupling does not need to be strong.
Therefore using explicit fluid solid coupling is sufficient, providing a suitable level of
computational speed and stability. Numerical solution schemes are often referred to
as being explicit or implicit. When a direct computation of the dependent variables
can be made in terms of known quantities, the computation is said to be explicit.
When the dependent variables are defined by coupled sets of equations, and either a
26
Fully Developed
Flow, Titanium Shell
Fluid Inlet
V
ILi.
zx
YT
Figure 2-2: Solid-Only Test Geometry and Mesh
27
Fluid Outlet
VELOCITY
-. 2
I
4524
0.001
0-002
0,003
0.0104
0.005
0-005
0.0
0.009
0009
Radial Coordinlas (m)
ine-mobe
1 mm 02
mm 93 mm
0.5 mm
Figure 2-3: Mesh Selection: Grid Sensitivity for Velocity
SE-i 3
E
4E-1 3
3E-1 3
a
2E-13
-
I r-L. - I %F
a)0
A~
0
/1
10000
20000
30000
40000
50000
80000
70000
Frequency (Hz)
Figure 2-4: Fast Fourier Transform Power Spectral Density Plot: 0.2 m Element
28
80000
Natural Frequency: Solid Only Test
3500
~3000
C
2li
2500
200X0
Z. 1500
U-
1000
500
0.1
0.2
0.4
0.3
0.5
0.6
0.7
Element Length (m)
--
STAR CCM+
-W-Mechanical
Model
Figure 2-5: Natural Frequency Comparison: Solid-Only tests
matrix or iterative technique is needed to obtain the solution, the numerical method
is said to be implicit.[6] An example initial displacement plot for the 0.6 m element
can be seen in Figure 2-6.
In the transient part of the simulation, the second order Temporal discretization
provides a more accurate solution with little damping. The FSI coupling method was
set to implicit, for which the coupling between the solid and fluid is strong. Once
the initial displacement was achieved, the body load was removed and the pipe was
allowed to vibrate in real time, as can be seen in Figure 2-7. Again, the a FFT PSD
plot was constructed to find the natural frequencies for each of the pipes. An example
plot for the 0.6 m element can be seen in Figure 2-8
The comparison between the Coriolis Flowmeter results and the STAR CCM+
results for each pipe length can be seen in Figure 2-9. The error bars on the plot,
derived from a Triangular Distribution again, show less than 10% error for each STAR
CCM+ result. The STAR CCM+ results were found to be within a 2% error of the
Coriolis meter results. These results finalized the verification of the Fluid Structure
interaction coupling algorithm for flow inside a vibrating tube. The benchmark has
confirmed accurate predictions of the coupled frequencies for a titanium pipe. From
these CFD results, it can be seen that the pipe's natural frequency is reduced when
29
0r
1
P tI.
-6E- 4
E
2
-0.001
U
IfiAA~
I
RI~I\IiJ\I'I
I
"&-0.002 4
5
-0.00 3
-0.003
0
0.2
0.1
Physical Time (s)
Figure 2-6: Coupled Solid Fluid Initial Beam Displacement: 0.6 m Element
0.0018
0.0012
00%
E
6E-4
E
(U
6A
/
-0.0012
-0.0018
V
V
0
0.01
0.02
Physical Time (s)
Figure 2-7: Coupled Solid Fluid Transient Displacement: 0.6 m Element
30
0.03
I I
N
0%
_________
_________
_________
%01
2E-8
1 E-8
0
01
A
n
/
CO,
'
U
0
CL
0
100
200
300
400
500
Frequency (Hz)
Figure 2-8: Fast Fourier Transform Power Spectral Density Plot: 0.6 m Element
the solid and fluid are coupled. This is a physical expectation and is supported by
the work of Shizhong et. al. [12] Shizhong et. al deduced the equation of solid-liquid
coupling vibration of a pipe conveying fluid and show the influence of flowing velocity,
pressure, solid-liquid coupling damp and solid-liquid coupling stiffness on the natural
frequency of an aluminum pipe. Their work showed that the solid-liquid coupled
stiffness and the pipe's total stiffness are reduced with the presence or increase of
liquid velocity, which supports the CFD findings in this Master's thesis preliminary
work. [12]
31
600
Natural Frequency: Coupled Fluid-Structure
1600
1400
1200
,
1000
S800
600
400
200
0
0.1
0.2
0-4
0-3
0.5
0.6
0.7
Element Length (m)
---
Coriolis lowmeter
--
STAR CCM+
Figure 2-9: Natural Frequency Comparison: Coupled Fluid Structure tests
32
Chapter 3
Setup for the GTRF Test Cases
After the preliminary FSI validation was complete, the method of FSI coupling in
STAR CCM+ was proven to be accurate and the next set of test cases of the PWR
fuel assembly could begin. The work of Elmahdi et. al evaluated the feasibility of the
use of STAR CCM+ Large Eddy simulation (LES) modeling techniques to find the
instantaneous stress tensor on the fuel rod wall, and then use that data for mechanical
calculations.
The transient hydraulic forces from STAR CCM+ are linked to the
Westinghouse VITRAN code to predict fuel rod vibration. This CFD/mechanical
solution has provided a reasonable prediction of fuel rod vibration. However, this
method does not account for the effect of structure vibration on the flow. A geometry
for GTRF applications was created. The geometry consisted of a 2 span, 3x3 spacer
grid with a solid Zircaloy cladding. The solid cladding had been added to capture fluid
structure interaction effects. The spacer grid supports were altered to mimic having
experienced wear from Grid-to-Rod Fretting. Following the geometry generation, the
mesh was created and LES was run.
33
Figure 3-1: Initial Fuel Assembly
3.1
Fuel Assembly Geometry and Boundary Conditions
Fuel assemblies are often built from square arrays of 14x14, 15x15, 16x16, or 17x17
fuel rods. The fuel rods are typically longer than four meters and have diameters
ranging from 9.144 to 12.7 mm. The fuel rods are held in place by structural grids.
At the top of the of grid straps, there are mixing vanes which are meant to increase
flow mixing and turbulence. This increases heat transfer and the DNB (departure
from nuclear boiling) margin, but also increases vibration forces on the fuel rods. [5]
The initial geometry imported into STAR CCM+ can be seen in Figure 3-1.
Running a transient CFD computer simulation of a complete fuel assembly would
require an incredible amount of computing power, memory, and time. In order to
simplify this into a smaller model, the geometry is cut down to the following geometry
in Figure 3-2, and periodic boundaries are added. Periodic boundary conditions can
have limitations, but because only a small subdomain (3x3 array) in a very large
grid is analyzed, the periodic boundary conditions are used. This same approach was
used by Elmahdi et. al. The STAR CCM+ model can be seen in Figure 3-3. The
34
Periodic 3
Periodic 4
Periodic I
Y
X
Center fuel rod - used to
compute forces on rod
Periodic 2
Periodic 2
IPeriodic 3l
Periodic 4
Figure 3-2: Grid Geometry with Periodic Boundary conditions [5]
model with the outer rod walls hidden can be seen in Figure 3-4. This figure shows
the spacer grid and center rod of interest. The spacer grid supports were altered to
mimic having experienced wear from GTRF, and can be seen in Figure 3-5.
35
Figure 3-3: STAR CCM+ model
Figure 3-4: Spacer Grid and Center Rod
36
Figure 3-5: Spacer with modified supports around the central rod. The left image
shows the spacer itself and the right image shows the same spacer with an emphasis
on the 0.5 mm gaps.
3.2
Mesh
After the geometry is constructed, a mesh was created. The meshing models that were
used include the Extruder, Prism Layer Mesher, Surface Remesher, and Trimmer.
The Extruder was used to extrude the inlet, outlet, and center rod wall. The inlet
and outlet boundaries were extruded in the normal direction to the boundary by 0.24
m to create a one span geometry with a total length of 0.55 m. The center rod was
extruded inward to create a separate Solid region for the Zircaloy cladding, in order
to capture FSI effects. The Trimmer generated hexagonal cells. The Prism Layer
Mesher was used to generate multilayer hexagonal cells near the wall. The Surface
Remesher was required for the imported geometry.
The mesh for the one span length of the 3x3 nuclear fuel rod bundle, with Zircaloy
cladding and complex grid spacer was created using STAR CCM+. The core mesh
region is composed of uniform hexagonal cells, and a prism layer of hexagonal cells
in the near wall region. The Zircaloy cladding consists of three layers of hexagonal
cells. This meshing approach provides a sufficient number of computational points,
using a base size of 0.144 mm. This meshing procedure was adopted from the work of
Elmahdi et. al, which was based upon previous mesh convergence studies that have
37
Figure 3-6: Inlet and Spacer Mesh
demonstrated accuracy in capturing the average flow field. The total size of the mesh
is about 54.5 million cells. The inlet and the spacer mesh can be seen in Figure 3-6.
The near wall and Zircaloy cladding mesh and mesh details for the spacer can be seen
in Figure 3-7
38
Figure 3-7: Near Wall Mesh and Spacer details: Top picture shows the solid Zircaloy
cladding in grey and the coolant in purple. The bottom picture shows spacer details
and the gap between the Zircaloy cladding and the support, which has experience
wear.
3.3
Solvers
The LES solver was selected for the fluid.
The LES solver of STAR CCM+ was
previously validated on fundamental flow cases, and have demonstrated excellent
predictions in benchmark experiments [5]. This LES approach mimics the work of
Elmahdi et. al for comparison, and uses a WALE subgrid model with a bounded
central differencing scheme for spacial discretization of the momentum equations. A
second order temporal discretization scheme is selected and a time-step is chosen for
each case to provide a Courant number of close to 1. The simulations were run on a
high performance cluster running on CentOS. The cluster is comprised of 28 nodes
making for a total of 336 cores.
39
3.4
Physics
The fluid being modeled is water with a density and viscosity set for a temperature
of 250 F. The STAR CCM+ solvers that were selected were All y+ Wall Treatment,
Constant Density, Gradients, Implicit Unsteady, Large Eddy Simulation, Liquid, Segregated Flow, Three Dimensional, Turbulent, and WALE Subgrid Scale. The LES
model The solid cladding is set to Zircaloy with a density of 6550 kg/m 3, Poisson Coefficient of 0.37, and a Young's Modulus of 75 GPa. The models selected for the solid
include Constant Density, Gradients, Gravity, Implicit Unsteady, Linear Isotropic
Elastic, Solid, Solid Stress, and Three Dimensional.
3.5
Test Cases
A test matrix of cases was created. The first and second cases are Fluid-only and have
inlet velocities of 5 m/s and 10 m/s respectively. Though a flow of 10 m/s is higher
than anything encountered in the core, the value was selected to see the effects of a
high velocity. Thus, the standard 5 m/s flow was increased by a factor of two. The
Fluid-only geometry deactivates the Solid Region. The third and fourth cases are the
coupled Fluid-Solid have the same inlet velocities (5 and 10 m/s respectively), and are
the coupled Fluid-solid. Point Monitors were used in the flow and the solid in order
to monitor velocity convergence and center rod displacement. The monitor locations
can be seen in Figure 3-8. From these four cases, the RMS values and Power Spectral
Density of forces were obtained for comparison to cases that decouple the fluid and
the solid. The center rod is used for calculations of the transient forces. The fuel rod
boundary is divided into 1 inch segments, similar to the work of Elmahdi et. al, and
forces acting on the fuel rod surface are integrated at each rod segment in two lateral
directions, the X and Z directions. The Fluid-only cases have 9 segments after the
spacer, while the Fluid-solid coupled cases have 10 segments. The split rod can be
seen in Figure 3-9. For each case, the RMS (root mean square) of the turbulence force
is recorded for each segment of interest. The PSD spectrum plot was also created for
40
Monitors
C
Point 2
Point 2
point 1
Point 3
PIM
Figure 3-8: Locations of Fluid and Solid monitors
each case.
The work of Elmahdi et. al compared their CFD results to a experimental results
from small-scale experiments and has shown reasonable prediction of the fuel rod
vibration and an accurate representation of all the important physics and excitation
forces, thus can be a reliable basis for comparison of the coupled fluid-only test cases.
41
Figure 3-9: Center Rod split into 1 inch segments, Fluid-only Case
42
Chapter 4
Results
While the present work is targeted as a general demonstration of a fully coupled
FSI approach and general understanding of the coupling phenomena, in order to
confirm prototypical behavior of the modeled geometry and boundary conditions,
results are firstly compared to the results produced and validated by Elmhadi et.
al for a Westinghouse spacer. The work of Elmahdi et. al showed that the mixing
vanes were the main source which generate the excitation forces on the fuel rod. The
excitation forces also decay along the span downstream of the grid. A plot for the
RMS values of the turbulence forces for which the test matrix will be compared can
be seen in Figure 4-1. Power Spectral Density plots were also produced. They showed
that the spectrum components of turbulence excitation forces are below 200 Hz. [5]
Elmahdi et. al also examined the lateral flow field at 0.67 inches and 1.97 inches
above the grid strap. It showed that there are two vortices in the subchannel center
and the same flow direction in the gap between the rods. The figures of the lateral
flow field from Elmahdi et. al can be seen in Figures 4-2 and 4-3.
43
Turbulence Force along a Span with Mixing Vanes
0.035
0.030
0.025
" Z-Dir STD
z
" X-Dir STD
0.020
8C
0.015
0.010
0.005
0.000
1
2
3
4
5
6
8
7
9
10
11
12
Rod Segment
Figure 4-1: Excitation force distribution along the span after the mixing vanes [5]
Vonex inthe
Vortex in the
1
Voex in the rod
0Wg
7
\
Ny
FO
1
P
!0?)
1
X Weslo (am")
Figuw 5 (a) Latiral velocity vectors from PIV data
at 0.67 inch above strap
Figure 5 (b): Lateral velocity vectors from
CFD at 0.67 inch above strap
Figure 4-2: Lateral Velocity Vectors 0.67 inches above grid strap [5]
44
-05109MW
6
j0
50m.2
0.1
-5
X4ocaton(mm)
Figure 6 (a) Lateral velocity vectors from PIV
at 1.97 inch above grid strap
Figure 6 (a) Lateral velocity vectors from CFD
at 1.97 inch above grid strap
Figure 4-3: Lateral Velocity Vectors 1.97 inches above grid strap [5]
4.1
Case 1: 5 m/s Fluid-only
Using Equation 2.1, the natural frequency for the geometry is 126.94 Hz. The first
case starts with an inlet velocity of 5 m/s (massflowrate of 1.758 kg/s) and a time
step of 2.6E-5 seconds. The Reynolds number associated with this flow and geometry
is about 250,000, which is consistent with the work of Elmahdi et. al. The simulation
was run until a steady time averaged velocity was reached. This was accomplished
using Point Monitors 1 and 2. The RMS values of the turbulence forces can be seen
in the Figure 4-4, and are compared to the values of Elmahdi et. al and are found to
be on the same order of magnitude.
The RMS forces also decay downstream along the span of the center rod, which
follows the trend of Elmahdi et. al. The Power Spectral Density plots also follow the
same trend of the spectrum components of turbulence excitation forces below 200 Hz.
The plots can be seen in Appendix A.
45
Ow
X and Z RMS Forces: 5
0-04
wXforce
0.03
0.02S
-
___
--
X-Dir
_ _02
O4O
0.01
0
-
0.01s
015
5
.00
--
z
*reo_
0025
0.02
---
-
0.030
0 035
0
Turbulence Force along a Span with MixingVanes
0.0s
m/s
1
0 0
2 3
4
5
6
7
8
.
9
1
Element Number
2
3
4
5
6
7
a
9
to
11
12
Mod segoent
Figure 4-4: RMS Turbulence Forces for Case 1 (left) comparison to the turbulence
forces of Elmahdi et. al (right)
4.2
Case 2: 10 m/s Fluid-only
This case has an inlet velocity of 10 ni/s (massflowrate of 3.515 kg/s) and a time
step of 1.3E-05 seconds. The Reynolds number associated with this case was about
500,000.
This case was meant to see how an increase velocity would change the
results. The results were comparable to the results of the 5 m/s case. The trend
of the RMS values of turbulence forces match that of the 5 m/s case. The forces of
this case were about four times higher than the 5 m/s case, which is consistent with
the increased turbulence levels. Such a non-linear increase in the force is expected
because, in general, turbulent forces are expected to be proportional to turbulent
kinetic energy. The RMS values of the turbulence forces for this case can be seen
in Figure 4-5. The Power Spectral Density plots also follow the same trend of the
spectrum components of turbulence excitation forces below 200 Hz. The plots can
also be seen in Appendix A.
46
X and Z RMS Forces: 10 m/s
0.16
0.14
0-14
0 Xforc es
0.12
i Zfbrces
0.1
*0008
t
4~0-06
0-04
0.
1
2
3
4
5
6
7
8
9
Element Number
Figure 4-5: RMS Turbulence Forces for Case 2
4.3
Case 3: 5 m/s Fluid-solid Coupled
This first coupled case was meant to explore the significance of FSI. During the run,
the Solid Region is set to active and all other settings matched Case 1. The case
was run until a steady time averaged velocity was reached. The mean velocity from
variance was monitored using Point Monitors 1 and 2 located in the flow. The plot
of velocity can be seen in Figure 4-6. To check that the simulation was producing
logical and accurate results, the maximum displacement over time in the X and Z
directions were monitored over time. The spacer is fixed and does not move. The gap
between the spacer and the center rod is 0.5 mm, which is the absolute maximum
displacement that the rod should be able to traverse. A plot of the movement of
Point Monitor 4 over time is shown in Figure 4-7. The instantaneous solid stress
displacement scene for X and Z directions can be seen in Figure 4-8, in which the
displacement is magnified for visualization purposes by 800 times. The maximum
displacements are far smaller than the gap size, which provides confidence in the
results. The plots for instantaneous forces in the X and Z direction can be seen in
Figure 4-9. Using the equation for a beam fixed at both ends with a concentrated
load at the center [2], the theoretical maximum displacement can be found using the
47
PA 'I
E
E
0
Physical Time (s)
Figure 4-6: Time Averaged Velocity for Case 3
maximum instantaneous force from each plot. Equation 4.1 is the equation for the
maximum displacement, in which A is the maximum displacement, P is the force (N)
applied, 1 is the length of the beam, E is the modulus of elasticity, and I is the area
moment of inertia. The theoretical maximum displacement in the X and Z directions
are 0.027 and 0.023 mm respectively, which supports the findings and provides added
confidence in the results.
A =
P'3
3
193EI
(4.1)
The displacement over time in the X and Z directions were monitored using Point
Monitor 4. The displacement plots over time can be seen in Figure 4-10. From the
displacement plots the frequency of oscillation could be derived and was found to
be approximately 100 Hz. The RMS values of the turbulence forces can be seen in
figure 4-11. From the X and Z forces, power spectral density plots were produced for
comparison to the uncoupled case. They will be compared and discussed in Chapter
5.
48
0.04
0.03
0.02
F
CL
S-0.04
-0
03
-0.02
-0.
.03
0.04
-0.02
-0.03
-0.04
X position (mm)
Figure 4-7: Vibration Location of Point 4 over 0.06 seconds for Case 3
Sod Sfeu DXplacement*k) (m)
Said Strmn
DisplacemwtWi
Cm}
2.27c4e45
-74X2*-06
L.
-947210-06
374p45
6.662.-46
412797e.49
Figure 4-8: Displacement Scene: Maximum displacement in the X and Z directions
for Case 3
49
04
0.3
0-
0-.
L&
-04
o
o:i02
0
001
.30.400~060
0 02
0.03
004
005
006
00 7
00
006
?
Physical Time (s)
x
OA
-04
02
0.3,
0
001
002
0.03
004
,
0
Physical Time (s)
0.1
Figure 4-9: Instantaneous X and Z forces over Time
*0.01______
______
0.03
0,02
)
~1
E\
E
0
001
-0.010
______________
001
002
0.03
0.04
005
006
00
.
00
Physical Time (s)
Figure 4-10: Displacement Plots in X and Z directions for Case 3
50
7
7
X and Z RMS Forces:
5
m/s Coupled
0.04
0.035
0.03
0.025
0.02
a Xforce
0.015
3Xfcrce
0.0101
d
0
0.005
1
2
3
4
5
6
7
8
9
10
Element Number
Figure 4-11: RMS Turbulence Forces for Case 3
4.4
Case 4: 10 m/s Fluid-solid Coupled
The next coupled case differs from the first coupled case by the inlet velocity. The
inlet velocity is set to 10 m/s. The results are not shown from time at zero seconds,
but rather from a later time such that the calculations are made closer to convergence.
Again, the Solid Region was set to active at the simulation was run until a steady
time averaged velocity was reached using the same monitors. The plot of velocity
can be seen in Figure 4-12. Again, the maximum displacement over time in the X
and Z directions were monitored over time. A plot of the movement of Point 4 over
time is shown in Figure 4-13. The instantaneous solid stress displacement scene for
X and Z directions can be seen in Figure 4-14, in which the displacement is magnified
for 'visualization purposes by 800 times. The displacements are low enough to give
confidence in the results. Also for this case, Equation 4.1 gives a maximum theoretical
displacement in the X and Z directions of 0.036 and 0.31 mm respectively. Again,
these results support the findings.
The displacement plots over time for this case can be seen in Figure 4-15. The
frequency of oscillation was found to be approximately 100 Hz. The RMS values of
the turbulence forces can be seen in Figure 4-16. From the X and Z forces, power
spectral density plots were also produced for comparison to the uncoupled case, and
will be compared and discussed in Chapter 5.
51
10.9
E_
E
0
a,
0
0.01
0.04
0.03
Physical Time (s)
Figure 4-12: Time Averaged Velocity for Case 4
0.06
0.04
0.02
0
0
0.01
0. 2
0.03
0.05
0.06
0
-0.02
-0.04
-0.06
Z location (mm)
Figure 4-13: Monitor Vibration Location of Point 4 over 0.035 seconds for Case 4
52
SOW AVO D*Pt.nnf) Wi
-9, 1013&40
1.55&6 4
- 1428We-O
2746562
&13229-M
-944 18e.W
-48364
V
Figure 4-14: Displacement Scene: Maximum displacement in the X and Z directions
for Case 4
53
Physical Time
~001
(S)
0.02
E 0.02
0.0
I.-an
V
E
0-04
o0
- os-
001
O.03
0O4
Physical Time A.)
Figure 4-15: Displacement Plots in X and Z directions for Case 4
X and Z RMS Forces: Mdot 10 m/s Coupled
0.14
0.12
0.1
0.08
0.06
0.04
0-02
1 11111
2
3
4
5
6
7
8
* Xforces
mZforces
9
Element Number
Figure 4-16: RMS Turbulence Forces for Case 4
54
10
Chapter 5
Relevance of Findings
A comparison of the results of Elmahdi et. al and Cases 1 and 2, show similar trends
in the RMS values of the turbulent forces on rod. The turbulent forces decay along
the span of the rod downstream the grid. Cases 3 and 4 also show a similar trend
and order of magnitude as Cases 1 and 2. The trend lines seen in Figures 5-1 and 5-2
clearly show the trend of the RMS values of turbulent forces decaying downstream
the grid.
The RMS values of the turbulence forces in Figures 4-11 and 4-16 show a tendency
towards a higher forces in the X direction. Figures 4-7 and 4-13 also suggest that
there is greater vibration and force in the X direction, which is supported by the
geometry of the vanes that can be seen in Figure 5-3 and 5-4, in which the tangential
velocity vectors overlay the spacer and vanes. Black arrows represent the X-direction
velocity due to the spacer vane location and slant.
55
Case 1: Decoupled 5 rn/s
Case 2: 10 rn/s Decoupled
0.04
0.035
Z
0.03
-e-X
0.16
0.14
0.12
Force
ZForce
0 0.025
o 0.02
Farces
v ZForces
0.08
00.06
0.04
0.02
(U
0.015
0.01
0.005
0
0
2
8
6
0
10
0
Distance Downstream from Spacer Grid (inches)
2
4
6
10
8
Distance Downstream from Spacer Grid (inches)
Figure 5-1: Decay of RMS Values along the span of the rod downstream from the
grid for Cases 1 and 2
Case 3: Coupled 5 rn/s
0.04
0.035
Z0.03
0.025
o 0.02
Case 4: 10 rn/s Coupled
0.14
0.12
-w- X Force
-ZForce
L0.015
........
0.01
0.005
0
z
z
a X forces
Z Forces
0.1
........
0.08
P 0.06
0
...
.
0.04
0.02
0
2
6
8
0
10
0
Distance Downstream from Spacer Grid (inches)
2
4
6
8
10
Distance Downstream from Spacer Grid (inches)
Figure 5-2: Decay of RMS Values along the span of the rod downstream from the
grid for Cases 3 and 4
56
U
L L.
3.3561
2.5%
1.6M
asw3
2
aawm5
Figure 5-3: Tangential Velcocity 5 m/s and Vanes
I
L
LI
6.4781
4.8W
3.2525
1.6%
2
.6775
Figure 5-4: Tangential Velcocity 10 m/s and Vanes
The power spectral density plots of Cases 3 and 4 show noticeable differences from
Cases 1 and 2. A comparison of some of the plots can be seen in Figures 5-5, 5-6,
5-7, and 5-8. The plots for the Fluid-Only cases clearly show peak frequencies below
200 Hz. This is consistent with the work of Elmahdi et. al. The Fluid-solid coupled
cases for both 5 and 10 m/s, show peaks over 200 Hz, suggesting effects from FSI
causing a significant frequency over 200 Hz. Interestingly, the coupled solution shows,
as expected, the appearance of new coupling between the fluid turbulence excitations
and the rod vibrations. This coupling is observable as higher frequency modes, and as
an overall reduction in the magnitude of the excitations. This is an important finding
which could support the adoption of the simpler decoupled simulation approach as a
57
5E-5
4E-S
2E-5
0610
I.E-
-6
--
360
40
0
600
Frequency (Hz)
700
800
900
10 00
12E 6
1E0-4 ---- ~
1.4E-4
z
_
1*26l/
M-6.
z~
_________
_
___
---_________ -__
_--__
--__----- ---- ----
_________
______________
Frequency (Hz)
____
____
oo
T
1oo
Figure 5-5: Element 7 5 m/s X Force- Top: Fluid-only, Bottom: Fluid-Solid Coupled
conservative assumption for GTRF applications.
The natural frequency of the solid cladding alone was previously calculated using
Equation 2.1. A calculation for the cladding with stagnant fluid as an added mass
was done using Equation 5.1, in which m is the mass of the beam, ma is the added
mass of the fluid, and k is the stiffness of the beam which is 58037 N/m.
Wn
=
k
m + ma
(5.1)
The presence of fluid flow is often simplified in the analysis of the structures as
an "added mass." The presence of the added mass leads to lower frequencies for the
system as shown in Table 5.1, where a 25% reduction is shown. While these reductions
could lead to challenges under specific loads, as for example seismic events, the coupled
simulations performed in this work show that representing fluid flow as an "added
mass" in the analysis of structures is a rather inaccurate simplification. The coupled
system frequencies are considerably higher, and increase with increasing fluid velocity
showing a stiffening effect. This is an important finding, which has been evidenced
previously in simple configurations, but is shown here for the first time for a PWR
fuel configuration.
58
7E-5
6E-5
21-
___
___
_______
4E-5
3E-
-
-
-
2E-5
IE-5
0o
10
200
300
500
400
600
760
00
700
Frequency (Hz)
2E
so
900
100
6
I.-G
GE_
.E
7
2E
7
-
--- ---
V V --
300
S0
Fr
y
Soo
Frequency (Hz)
9Wo
1000
Figure 5-6: Element 7 5 m/s Z Force- Top: Fluid-only, Bottom: Fluid-Solid Coupled
4E-4I
f- 3E-4
-
-
08200
-T-
-
2I6I
tlE-4
400
600
S0010
00
Frequency (Hz)
SE
51
~6E-SI
4E -5
2E
---------
5
S '1E
100
200
3oo
400
500
Frequency (Hz)
600
700
Soo
g0
1000
Figure 5-7: Element 2 10 m/s X Force- Top: Fluid-only, Bottom: Fluid-Solid Coupled
Table 5.1: Frequency Comparison
Frequencies
(Hz)
Solid Cladding Only
Solid Cladding with Fluid Added Mass
Case 3: 5 m/s Fluid-solid coupled
Case 4: 10 m/s Fluid-solid coupled
59
126
95
100
120
4E-4
1
3E- 4
~~
2E-
4
-
4
o200
-
-
--
-
4006
Frequency (Hz)
-
-
-
1E-
1004
-0
9E
7rE
SE
4E
2E
sI
5
5
.51
--
-
- -
-__-__-
-
6E
1E
0
100
20
300
4WF
Soo eq
c (Hz
Frequency (Hz)
900
2000
Figure 5-8: Element 2 10 m/s Z Force- Top: Fluid-only, Bottom: Fluid-Solid Coupled
60
Chapter 6
Conclusions and Future Work
Grid-to-rod fretting is a complex phenomenon that has been identified by CASL as
one of the "Challenge Problems" that motivates the need for the development and
application of a modeling environment for predictive simulation of light water reactors. GTRF is currently one of the main causes of fuel leakage and causes over 70%
of the fuel leaks in PWRs in the United States. [10] GTRF includes flow excitation
force, non-linear mechanical vibration, tribology, and changing fuel assembly geometry. The turbulent flow through the assembly generates fuel rod vibrations. The
small relative motions caused between the grid supports and the fuel rod causes the
fretting wear. [10] The current approach to modeling and simulating this phenomenon
decouples the solid and the fluid. The results show a noticeable difference between
the decoupled and coupled approach. The results of this Master's thesis shows that
the simpler decoupled simulation approach could be adopted as a conservative assumption for most GTRF applications. This thesis was meant to show preliminary
investigation into the effects of Fluid Structure Interactions in a PWR fuel assembly
for the purposes of studying grid-to-rod fretting. The results have shown that there is
a noticeable effect due to coupling the fluid and structure. Future work of this thesis
would include an exploration on how these effects directly influence grid-to-rod fretting. Also, more simulations of varying velocity should be run for further validation
to show that the coupled system frequencies are considerably higher, and increase
with the increasing fluid velocity. Though the current decoupled solution, provides
61
an accurate solution under controlled conditions, the effects of FSI are present and
require further investigation.
62
Appendix A
Power Spectral Density Plots:
Case l and 2
A.1
Case 1: 5m/s Fluid-only
63
5E-51
N
4E-5
z
3E-5
2E-5
U
CL
Cn
> 1E-5
0( i
100
200
300
400
500
600
700
8o
900
1000
Frequency (Hz)
Figure A-1: 5 m/s X Force Fluid-only PSD: Element 1
5E-5 IN
4E-5
z
3E-5
0
15 2E-5
o 1E-5
b~
1
~
__
_____
ioNIW4
100
200
___________
-JiltI
300
400
500
600
Frequency (Hz)
__
700
Figure A-2: 5 m/s X Force Fluid-only PSD: Element 2
64
800
900
1000
N
U__
S4E-5
z
_____
_
_
__
_
_
_
_
_
_
-
SE-S
.4 3E-5
*U 2E-5
o 1E-5
iji~
h
0
100
200
300
400
500
600
700
800
900
1000
Frequency (Hz)
Figure A-3: 5 m/s X Force Fluid-only PSD: Element 3
5E-5
N
4E-5
z
4-
3E-5
t5 2E-5
______________
______________________________
______________
J
1E-5
01
0
IIkIOL- f.%
100
M p.
1-1
200
300
400
500
-L
4-
600
700
Frequency (Hz)
Figure A-4: 5 m/s X Force Fluid-only PSD: Element 4
65
800
L
900
1000
5E-5
N
~4E-5
z
S3E-5
U 2E-5
o E-5
00-
100
200
300
400
500
600
700
800
900
1000
800
900
1000
Frequency (Hz)
Figure A-5: 5 m/s X Force Fluid-only PSD: Element 5
N
I
4E-5
c'J
z
3E-5
4)
a
'U
4,
0~
4)
1 E-5
A
0
'
3:
0
a-
100
200
300
400
500
600
700
Frequency (Hz)
Figure A-6: 5 m/s X Force Fluid-only PSD: Element 6
66
5E-5
N
4E-5
z
3E-5
4
t 2E-5
tIE
o 1E-5
02
0
100
200
300
400
500
700
600
800
900
1000
Frequency (Hz)
Figure A-7: 5 m/s X Force Fluid-only PSD: Element 7
5E-5
N
4E-5
.
z
3E-5
CL
t~ 2E-5
iE
o
E-5
C
IkJ1~.A
U
_______________________
.1
U
2u0
J Vu
_______
'40v
WU
Frequency (Hz)
_______________
6U U
7u0
Figure A-8: 5 m/s X Force Fluid-only PSD: Element 8
67
_______
80 u
________
90uv
10I'
-I-
5E-5
4E-5
z
3E-5
441)
0L
in
1 E-5
jp
0
100
200
300
400
500
600
Frequency (Hz)
700
800
900
1000
800
900
1000
Figure A-9: 5 m/s X Force Fluid-only PSD: Element 9
7E-51
-
I-, AE-5
N
r
< SE-5
z
4E-5
3E-5
2E-5
1E-5
dl
0
100
200
300
400
500
600
700
Frequency (Hz)
Figure A-10: 5 m/s Z Force Fluid-only PSD: Element 1
68
7E-5
6E-5
N
<
z
I
5E-5
____
__
4E-5
3E-5
CL
E-5
00 1 E-5
00
100
200
300
400
500
600
700
800
900
1000
Frequency (Hz)
Figure A-11: 5 m/s Z Force Fluid-only PSD: Element 2
7E-5
6E-5
5E-5
<
z
'i4E-5
3E-5
tn
-
4,
2E-
-4
1 IE-51
0
0
_
100
200
300
400
500
600
Frequency (Hz)
Figure A-12: 5 m/s Z Force Fluid-only PSD: Element 3
69
800
900
1000
7E-5
6E-5
5E-5
<
z
4E-5
3 3E-5
a-
CL
L2E-5
lE-5
0
100
0
200
300
400
500
600
700
800
900
1000
Frequency (Hz)
Figure A-13: 5 m/s Z Force Fluid-only PSD: Element 4
7E-5
_-1
6E-5
<
5E-5
z
S4E-5
S3E-5
LL
0)
~2E-5
_________
_________
___
0
I L-5
'
A
0
100
200
300
400
500
600
700
Frequency (Hz)
Figure A-14: 5 m/s Z Force Fluid-only PSD: Element 5
70
800
900
1000
7E-5
6E-5
N
<
z
SE-5
4E-5
3E-5
.
2E-5
1E-5
I
0
;b
~
100
200
300
400
500
600
700
800
900
1000
Frequency (Hz)
Figure A-15: 5 m/s Z Force Fluid-only PSD: Element 6
7E-5
I-6E-E
5E-E p
<
____________________________________________________________________________
z
~4E-E
S3E-5
in-5
p
s.2E
____________________________________
COL 1E-5
I- P
0
___________________________
100
200
300
400
500
600
___________________________
700
Frequency (Hz)
Figure A-16: 5 m/s Z Force Fluid-only PSD: Element 7
71
800
___________________________
900
1000
7E-5
. 6E-5
<
5E-5
z
4E-5
3 3E-5
2E-5
2 1E-5
~~2JLJ
100
_
200
__
300
400
500
600
700
800
900
1000
800
900
1000
Frequency (Hz)
Figure A-17: 5 m/s Z Force Fluid-only PSD: Element 8
7E-5
N
z
5E-5
4E-5
-1'
CL
in-5
C
2E-5
1E-5
___-
0
100
200
300
400
500
600
700
Frequency (Hz)
Figure A-18: 5 m/s Z Force Fluid-only PSD: Element 9
72
Case 2: 10 rn/s Fluid-only
A.2
4E-41
3 E-4
1E-4
0:O
x,__
UId
C
0
200
_
400
600
1000
800
Frequency (Hz)
Figure A-19: 10 m/s X Force Fluid-only PSD: Element 1
4E-4
3JE-4
2E-4
1E)
,0 1E
_III_
_
J~
11 I
Ii
I ~ H,-,--,--~-,--,,
I
.111
-,-~--4+4-------
L _________________________
_________________________
0
200
400
600
Frequency (Hz)
Figure A-20: 10 m/s X Force Fluid-only PSD: Element 2
73
----
__________________________
Wt
800
1000
4E-4
U'
~ILj
2E-4
1E-4
____________________
III
~r' ~
~i'~
,JI1
0
0
200
600
400
800
1000
Frequency (Hz)
Figure A-21: 10 m/s X Force Fluid-only PSD: Element 3
4E-49
N
S3 E-A
52E-4FL
~
1E-4
F
0
________________________________
200
-
_________________________________
400
600
Frequency (Hz)
Figure A-22: 10 m/s X Force Fluid-only PSD: Element 4
74
800
1000
4E-4
J3 E- 4
-I
~2E-4
JJlJiL' i~
S1E-4
______
II
______
~ ~I!
kl-'
n0
____________
200
400
600
800
1000
Frequency (Hz)
Figure A-23: 10 m/s X Force Fluid-only PSD: Element 5
4E-4
3E-4
-1
Cl,
S1E-4
Y2LLi
____________
0
I~sj
'I~?.
f.t
II
,
.j.~
i,
200
400
600
Frequency (Hz)
Figure A-24: 10 m/s X Force Fluid-only PSD: Element 6
75
g00
1000
4E-4
N
6 3E-4
Cn
3 E- 4
~2E-4
I___I
L
0
S1E-4
___
0OI
0
200
400
___
___
600
800
1000
800
1000
Frequency (Hz)
Figure A-25: 10 m/s X Force Fluid-only PSD: Element 7
4E-4
N
3E-4
c)
72E-4
S1E-4
kI
00
200
k,
A
400
600
Frequency (Hz)
Figure A-26: 10 m/s X Force Fluid-only PSD: Element 8
76
4E-4
-
3E-4
-
2E-4
L
-
1E-4
0
200
600
400
800
1000
Frequency (Hz)
Figure A-27: 10 m/s X Force Fluid-only PSD: Element 9
4E-4
N
-
3E-4.
CL
(A
1E-4
______________________________
0
0
_______________________________
_______________________________
I
_______________________________
~?
200
400
600
Frequency (Hz)
Figure A-28: 10 m/s Z Force Fluid-only PSD: Element 1
77
800
1000
4E-4
N
S3E-4
2E-4
L
(A
S1 1K.A
12
I~~'iI ~~
111K
I
hI
C 1111
I
I
'IPIt
II
,~r ~ii
0
0
00
400
600
800
1000
800
1000
Frequency (Hz)
Figure A-29: 10 m/s Z Force Fluid-only PSD: Element 2
4E-4
r
S3E-4
4n
2E-4
L
(A
S1E-4
J
I
0
~IIj~I~
I
'II:
1
L\~
200
~
400
600
Frequency (Hz)
Figure A-30: 5 m/s Z Force Fluid-only PSD: Element 3
78
4E-41
N
~3E-4
=1
-R2E-4
_________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
_________________________________________________________________
I
S1E-4
0O
_____________
I~t~
I~
0
200
400
600
800
1000
Frequency (Hz)
Figure A-31: 10 m/s Z Force Fluid-only PSD: Element 4
4E-4
3E-4
S2 E-4
12E-4
n
iii1i' i I~~ ~r
ii
C0
O
______________
200
_______________
400
_______________
600
Frequency (Hz)
Figure A-32: 10 m/s Z Force Fluid-only PSD: Element 5
79
_______________
800
1000
4E-4
N
S3 E-4
~2E-4
S1E-4
JIi
C'
-00
1i
200
2U00
400
600
800
1000
Frequency (Hz)
Figure A-33: 10 m/s Z Force Fluid-only PSD: Element 6
4E-4
3 E-4
c2E-4
E.
I E-4
06-
200
600
400
Frequency (Hz)
Figure A-34: 10 m/s Z Force Fluid-only PSD: Element 7
80
800
1000
4E-4
r
33E-4
CL 2E-4
1E-4
0'C
[1
~i,
II
200
400
600
800
1000
800
1000
Frequency (Hz)
Figure A-35: 10 m/s Z Force Fluid-only PSD: Element 8
4E-4
N
o3E-4
2E-4
CL
0
200
400
600
Frequency (Hz)
Figure A-36: 10 m/s Z Force Fluid-only PSD: Element 9
81
82
Bibliography
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84