Transient thermal finite element analysis of CFC–Cu ITER monoblock using X-ray tomography data

Abstract

The thermal performance of a carbon fibre composite-copper monoblock, a sub-component of a fusion reactor divertor, was investigated by finite element analysis. High-accuracy simulations were created using an emerging technique, image-based finite element modelling, which converts X-ray tomography data into micro-structurally faithful models, capturing details such as manufacturing defects. For validation, a case study was performed where the thermal analysis by laser flash of a carbon fibre composite-copper disc was simulated such that computational and experimental results could be compared directly. Results showed that a high resolution image-based simulation (102 million elements of 32 μm width) provided increased accuracy over a low resolution image-based simulation (0.6 million elements of 194 μm width) and idealised computer aided design simulations. Using this technique to analyse a monoblock mock-up, it was possible to detect and quantify the effects of debonding regions at the carbon fibre composite-copper interface likely to impact both component performance and expected lifetime. These features would not have been accounted for in idealised computer aided design simulations.

Full text

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
Contents
lists
available
at
ScienceDirect
Fusion
Engineering
and
Design
jo
ur
nal
home
p
age:
www.elsevier.com/locate/fusengdes
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data
Ll.M.
Evans
a,b,∗
,
L.
Margetts
c
,
V.
Casalegno
d
,
L.M.
Lever
e
,
J.
Bushell
b
,
T.
Lowe
b
,
A.
Wallwork
b
,
P.
Young
f
,
A.
Lindemann
g
,
M.
Schmidt
h
,
P.M.
Mummery
h
a
CCFE,
Culham
Science
Centre,
Abingdon,
Oxon
OX14
3DB,
UK
b
School
of
Materials,
University
of
Manchester,
Grosvenor
Street,
Manchester
M1
7HS,
UK
c
School
of
Earth,
Atmospheric
and
Environmental
Sciences,
University
of
Manchester,
Williamson
Building,
Manchester
M13
9PL,
UK
d
Department
of
Applied
Science
and
Technology,
Politecnico
di
Torino,
Corso
Duca
degli
Abruzzi
24,
I-10129
Torino,
Italy
e
IT
Services
for
Research,
University
of
Manchester,
Devonshire
House,
Oxford
Road,
Manchester
M13
9PL,
UK
f
Simpleware
Ltd.,
Bradninch
Hall,
Castle
Street,
Exeter
EX4
3PL,
UK
g
NETZSCH-Gerätebau
GmbH,
Wittelsbacherstraße
42,
D-95100
Selb,
Bayern,
Germany
h
School
of
Mechanical,
Aerospace
and
Civil
Engineering
(MACE),
University
of
Manchester,
Manchester
M13
9PL,
UK
h
i
g
h
l
i
g
h
t
s
•
Thermal
performance
of
a
fusion
power
heat
exchange
component
was
investigated.
•
Microstructures
effecting
performance
were
determined
using
X-ray
tomography.
•
This
data
was
used
to
perform
a
microstructurally
faithful
finite
element
analysis.
•
FEA
demonstrated
that
manufacturing
defects
had
an
appreciable
effect
on
performance.
•
This
image-based
modelling
showed
which
regions
could
be
targeted
for
improvements.
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
9
December
2013
Received
in
revised
form
27
March
2015
Accepted
21
April
2015
Available
online
xxx
Keywords:
X-ray
tomography
Finite
element
analysis
Image-based
modelling
Thermal
conductivity
Laser
flash
Joining
a
b
s
t
r
a
c
t
The
thermal
performance
of
a
carbon
fibre
composite-copper
monoblock,
a
sub-component
of
a
fusion
reactor
divertor,
was
investigated
by
finite
element
analysis.
High-accuracy
simulations
were
created
using
an
emerging
technique,
image-based
finite
element
modelling,
which
converts
X-ray
tomogra-
phy
data
into
micro-structurally
faithful
models,
capturing
details
such
as
manufacturing
defects.
For
validation,
a
case
study
was
performed
where
the
thermal
analysis
by
laser
flash
of
a
carbon
fibre
composite-copper
disc
was
simulated
such
that
computational
and
experimental
results
could
be
com-
pared
directly.
Results
showed
that
a
high
resolution
image-based
simulation
(102
million
elements
of
32
␮m
width)
provided
increased
accuracy
over
a
low
resolution
image-based
simulation
(0.6
million
ele-
ments
of
194
␮m
width)
and
idealised
computer
aided
design
simulations.
Using
this
technique
to
analyse
a
monoblock
mock-up,
it
was
possible
to
detect
and
quantify
the
effects
of
debonding
regions
at
the
carbon
fibre
composite-copper
interface
likely
to
impact
both
component
performance
and
expected
lifetime.
These
features
would
not
have
been
accounted
for
in
idealised
computer
aided
design
simulations.
©
2015
The
Authors.
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY
license
(
http://creativecommons.org/licenses/by/4.0/).
1.
Introduction
ITER,
currently
under
construction,
will
be
the
world’s
largest
nuclear
fusion
reactor.
Its
aim
is
to
demonstrate
the
ability
to
produce
an
output
power
ten
times
that
required
to
initi-
ate
fusion.
Once
operational,
the
plasma
in
which
the
reactions
∗
Corresponding
author
at:
Culham
Centre
for
Fusion
Energy,
D3/1/25,
Culham
Science
Centre,
Abingdon,
Oxon
OX14
3DB,
UK.
Tel.:
+44
1235
466524.
E-mail
address:
llion.evans@ccfe.ac.uk
(Ll.M.
Evans).
happen
will
subject
the
plasma
facing
components
(PFCs)
to
around
10
MW
m
−2
of
thermal
flux
during
steady-state
opera-
tion.
This
value
could
be
surpassed
if
plasma
disruptions
which
release
large
amounts
of
energy
over
short
time
periods
are
not
mitigated
[1].
Therefore,
selection
of
materials
for
the
PFCs
is
largely
governed
by
their
ability
to
withstand
such
a
hos-
tile
environment
whilst
absorbing
neutronic
heating,
minimising
plasma
impurities
and
protecting
components
shielded
by
the
PFCs.
It
is
proposed
that
the
divertor
will
consist
of
a
series
of
flat
armour
tiles
aligned
in
rows
(see
Fig.
1)
with
one
side
being
plasma
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
0920-3796/©
2015
The
Authors.
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY
license
(http://creativecommons.org/licenses/by/4.0/).

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
2
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
Fig.
1.
Schematic
of
section
from
the
early
‘two-tier’
ITER
divertor
[4].
facing
[3].
In
order
to
remain
within
operational
temperature
limits
the
components
must
be
actively
cooled.
This
is
achieved
by
con-
necting
the
tiles
through
their
centres
to
a
copper
pipe
carrying
coolant
(coined
a
monoblock).
As
the
function
of
this
heat
sink
is
to
transfer
thermal
energy
away
from
the
armour,
it
is
imperative
that
the
method
of
joining
the
armour
to
the
pipe
must
provide
a
bond
that
retains
both
structural
integrity
and
a
high
thermal
con-
ductivity
under
large
thermal
loads.
As
this
region
will
contribute
to,
and
potentially
dominate,
performance
of
the
component,
it
is
of
utmost
importance
that
the
thermal
behaviour
at
the
armour-pipe
interface
is
well
characterised.
Until
recently
it
was
envisaged
that
the
ITER
divertor
would
include
of
two
tiers;
the
armour
for
lower
and
upper
parts
consist-
ing
of
carbon
fibre
composites
(CFC)
and
tungsten
(W),
respectively
[2].
Currently
the
ITER
specifications
are
now
for
an
all
W
divertor.
This
work
concentrates
on
developing
a
non-destructive
technique
to
predict
‘as-manufactured’
component
performance.
Although
the
case
study
in
this
report
investigated
CFC
armour,
the
technique
is
material
independent
and
could
therefore
be
implemented
on
a
wide
range
of
machine
critical
components.
Previous
work
has
been
carried
out
in
order
to
characterise
the
thermal
behaviour
of
a
series
of
joining
techniques
for
CFC–Cu
samples
[5].
The
thermal
performance
across
the
interface
has
been
investigated
by
measuring
thermal
diffusivity
experimentally
through
laser
flash
analysis
(LFA).
Imaging
by
X-ray
tomography
provided
high
resolution
images
of
the
materials’
microstructures
at
the
interface,
providing
insight
as
to
how
they
might
affect
ther-
mal
behaviour.
The
most
promising
joining
technique
was
the
one
developed
at
Politecnico
di
Torino
[6].
The
technique
involves
a
low
cost
process
that
requires
no
applied
pressure
and
can
be
performed
at
relatively
low
temperatures
(i.e.
lower
than
required
for
Cu
cast-
ing
[7]
or
CFC
modification
[8]).
The
method
uses
a
commercial
braze
(Gemco)
which
is
modified
by
applying
a
layer
of
chromium.
In
joining,
the
braze
is
applied
with
the
chromium
face
in
contact
with
the
CFC.
When
the
component
is
heated
the
chromium
reacts
with
the
carbon
to
form
chromium
carbides.
This
leads
to
a
better
join
between
the
CFC
and
the
braze
due
to
the
improved
wetting
angle
on
chromium
carbides,
which
would
otherwise
be
poor.
In
this
paper,
we
explore
the
capabilities
of
a
divertor
monoblock
mock-up
manufactured
using
the
Politecnico
di
Torino
technique
under
reactor-like
thermal
loads.
As
this
is
difficult
to
carry
out
in
the
laboratory,
we
use
Finite
Element
Analysis
(FEA)
to
make
our
predictions.
FEA
is
usually
performed
by
first
creating
a
digital
represen-
tation
of
the
component
using
a
computer
aided
design
(CAD)
package.
This
is
typically
a
geometrically-ideal
version
of
the
component
that
does
not
include
manufacturing
flaws
such
as
micro-cracking
or
porosity.
In
this
paper
we
show
that
these
imperfections
play
an
important
role
in
heat
transfer.
Creating
the
detailed
models
required
is
intractable
using
the
CAD
approach,
so
we
use
an
emerging
technique
called
image-based
finite
element
modelling
(IBFEM).
IBFEM
converts
a
three-dimensional
image
of
a
‘real’
manufactured
sample,
including
defects,
into
a
digital
geome-
try
to
be
meshed
for
FEA.
It
has
been
shown
that
the
IBFEM
approach
can
give
more
accurate
predictions
than
unit
cell
or
analytical
models
[9].
Another
benefit
of
the
IBFEM
technique
is
that
direct
comparison
to
experimental
results
can
be
made,
as
we
can
digi-
tise
for
simulation
the
sample
that
has
been
subjected
to
laboratory
tests
[10].
This
paper
presents
two
case
studies.
The
objective
of
the
first
case
study
is
to
verify
and
validate
the
technique.
It
involves
com-
paring
experimental
and
simulated
results
carried
out
on
a
simple
“disc”
shaped
sample
of
CFC
bonded
to
Cu
subjected
to
Laser
Flash
Analysis
(LFA).
There
are
three
simulations:
(i)
a
CAD
based
model,
(ii)
a
low
resolution
model
generated
from
an
X-ray
Tomography
scan
and
(iii)
a
high-resolution
model
generated
from
the
same
image.
The
CAD
and
low-resolution
simulations
can
be
carried
out
on
a
typical
high
end
workstation,
whilst
the
high
resolution
sim-
ulation
requires
access
to
supercomputing
facilities.
This
exercise
showed
that
the
high
resolution
model
provided
the
closest
match
to
the
experimental
results.
Therefore,
the
second
case
study
uses
high
resolution
IBFEM
only
to
predict
the
behaviour
of
a
CFC–Cu
divertor
monoblock
mock-up
under
reactor-like
thermal
loads.
2.
Materials
The
CFC
used
was
Sepcarb
NB31
(Snecma
Propulsion
Solid,
France).
This
is
manufactured
using
a
3D
NOVOLTEX
preform
nee-
dled
in
the
z-direction
with
ex-pitch
fibres
and
in
x
and
y
directions
with
ex-PAN
fibres.
Chemical
vapour
infiltration
(CVI)
is
used
for
densification.
The
copper
used
was
oxygen
free
high
conductivity
(OFHC)
copper
(Wesgo
Metals,
USA).
The
materials
were
joined
by
a
brazing
process
using
a
Gemco
®
foil,
87.75
wt%
Cu,
12
wt%
Ge
and
0.25
wt%
Ni,
(Wesgo
Metals,
USA).
The
foil
was
pre-coated
with
a
3
␮m
layer
of
chromium
using
radio
frequency
magnetron
sputter-
ing.
The
divertor
monoblock
was
produced
by
drilling
a
hole
in
a
CFC
tile,
inserting
the
Gemco
foil
and
finally
the
copper
pipe
before
brazing.
Joining
was
performed
at
Politecnico
di
Torino
as
detailed
by
Casalegno
et
al.
[6].
In
order
to
carry
out
the
CFC–Cu
disc
case
steady
(the
LFA
experiment),
further
sample
preparation
was
required.
This
was
undertaken
at
The
University
of
Manchester.
The
joined
and
indi-
vidual
samples,
originally
tile
shaped,
were
machined
using
a
lathe
to
produce
cylindrical
samples.
A
Struers
Accutom-5
cut-off
Table
1
Sample
dimensions.
Sample
Diameter
(mm)
Thickness
(mm)
Mass
(×10
−3
kg)
Volume
(×10
−6
m
3
)
Density
(×10
3
kg
m
−3
)
CFC
12.66
2.06
0.447
0.2593
1.72
Cu
10.10
2.06
1.421
0.1650
8.61
CFC–Cu
12.70
4.84
2.916
0.6131
4.76
CFC
(CFC–Cu)
12.70
2.74
0.631
0.3477
1.81
Cu
(CFC–Cu)
12.70
2.10
2.285
0.2654
8.61

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
3
Table
2
X-ray
tomography
parameters
used.
Sample
Target
Voltage
(kV)
Current
(␮A)
Filter
(mm)
Acquisition
time
(s)
Number
of
projections
Frames/projection
CFC
Cu
120
200
N/A
0.5
2001
1
Cu
W
220
210
Sn,
1.0
0.7
3142
1
CFC–Cu
W
210
135
Sn,
1.0
1.415
2001
2
Monoblock
W
200
190
Ag,
1.0
1.415
2001
2
Fig.
2.
Samples
used;
(a)
CFC,
(b)
Cu,
(c)
CFC–Cu
disc
and
(d)
CFC–Cu
divertor
monoblock.
machine
was
used
to
obtain
the
thickness
required
for
thermal
analysis.
The
wheel
was
made
of
aluminium
oxide
and
was
set
to
rotate
at
3000
rpm
with
a
medium
force
and
movement
of
2
×
10
−5
m
s
−1
.
To
clean
the
samples
they
were
placed
in
an
ultra-
sonic
bath
of
acetone
for
10
min.
Fig.
2
shows
the
samples
in
their
prepared
state.
Table
1
details
the
resultant
dimensions
and
properties.
The
samples’
thickness
and
diameter
were
used
to
calculate
the
cylindrical
volume,
com-
bined
with
mass
this
was
in
turn
used
to
obtain
density.
Because
these
values
included
the
porosity
present
within
the
CFC,
reported
values
are
for
the
bulk
properties.
Values
for
the
constituent
mate-
rials
in
the
CFC–Cu
disc
were
calculated
from
their
respective
thickness
fractions.
In
this
instance,
the
density
values
for
CFC
and
Cu
layers
were
obtained
from
an
average
of
four
CFC
samples
and
the
pure
Cu
sample,
respectively.
Scanning
electron
microscope
(SEM)
investigation
of
the
CFC
and
brazing
alloy
interface
(seen
in
Fig.
3)
shows
the
formation
of
chromium
carbide
between
the
two
layers.
There
is
also
infiltration
of
the
carbide
into
open
porosity
on
the
surface.
3.
Method
This
section
details
the
(i)
experimental
determination
of
ther-
mal
properties
using
LFA,
(ii)
three-dimensional
imaging
using
X-ray
computed
tomography,
(iii)
finite
element
mesh
generation,
(iv)
definition
of
simulation
boundary
conditions,
(v)
equation
solu-
tion
and
finally
(vi)
results
analysis.
3.1.
Thermal
diffusivity
The
Netzsch
457
MicroFlash
®
system
[11]
was
used
to
perform
LFA.
This
system
is
used
to
irradiate
the
surface
of
a
disc
shaped
sample
of
known
thickness
with
a
short
laser
pulse.
The
time
the
heat
pulse
takes
to
travel
through
the
sample
is
measured
by
an
Fig.
3.
SEM
image
of
CFC
and
brazing
alloy
interface.
infra-red
camera
directed
at
the
rear
face.
This
is
used
to
calculate
thermal
diffusivity.
Specific
heat
and
thermal
conductivity
can
be
calculated
by
comparing
results
with
a
calibration
sample.
To
ensure
stability
of
the
sample
and
maximum
absorption
of
energy
from
the
pulse,
measurements
were
performed
in
an
inert
atmosphere
after
the
sample
had
been
coated
with
graphite.
Results
were
collected
at
intervals
of
100
◦
C,
ranging
from
100
◦
C
to
700
◦
C.
The
average
of
5
measurements
at
each
interval
was
recorded.
3.2.
X-ray
tomography
The
Nikon
Metrology
225/320
kV
system
(using
the
225
kV
source)
at
the
Manchester
X-ray
Imaging
Facility
[12],
University
of
Manchester,
UK,
was
used
to
create
X-ray
tomography
scans
of
the
CFC–Cu
disc
and
the
divertor
monoblock.
Imaging
and
recon-
struction
settings
are
shown
in
Tables
2
and
3,
respectively.
Voxel
widths
of
9.7
␮m
and
21.8
␮m
were
achieved
for
the
CFC–Cu
disc
and
divertor
monoblock,
respectively.
However,
due
to
signal
noise,
not
all
features
at
these
scales
were
resolvable
e.g.
the
10
␮m
layer
of
chromium
on
the
braze.
Table
3
Reconstruction
settings.
Sample
Beam
hardening
Noise
reduction
Voxel
width
(×10
−6
m)
CFC
1
3
10.0
Cu
2
2
8.2
CFC–Cu
2
4
9.7
Monoblock
1
2
21.8

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
4
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
0
5
10
15
20
25
0
1000
200
0
3000 40
00
Energy (J)
Voltage (V
)
Fig.
4.
Laser
energy
for
a
given
voltage
for
the
NETZSCH
LFA
457.
3.3.
Finite
element
mesh
generation
The
CFC–Cu
disc
and
divertor
monoblock
scans
were
imported
into
the
Simpleware
[13]
suite
of
programmes,
version
6
(Simple-
ware
Ltd.,
Exeter,
Devon,
UK)
to
convert
the
3D
images
into
FE
meshes.
Image
segmentation
was
performed
using
a
range
of
tech-
niques
including
the
flood-fill,
cavity
fill,
island
removal,
manual
paint
tools
and
a
recursive
Gaussian
smoothing
filter.
Linear
4-node
tetrahedral
elements
were
selected
for
meshing.
A
low
resolution
and
high
resolution
mesh
was
created
for
the
CFC–Cu
disc
case
study.
The
low
resolution
mesh
captured
the
main
features,
such
as
surface
roughness
and
large
pores.
The
resolution
of
the
higher
fidelity
model
was
carefully
chosen,
striking
a
balance
between
capturing
fine
details
of
the
micro-structure
and
produc-
ing
a
model
that
could
be
easily
handed
on
the
various
computer
platforms
available.
Creating
a
finite
element
model
at
the
same
resolution
as
the
original
tomography
scan
is
technically
challeng-
ing
and
probably
offers
little
benefit
over
the
high
resolution
model
selected.
A
CAD
version
of
the
CFC–Cu
disc
was
created
and
meshed
in
Abaqus,
version
6.12
(Simula,
Providence,
RI,
USA).
This
model
comprised
a
cylinder
with
three
layers
of
varying
thickness
rep-
resenting
the
CFC,
Gemco
and
Cu.
Porosity
was
not
included.
The
CAD
based
mesh
had
approximately
50,000
tetrahedral
elements
(consistent
with
typical
engineering
practice).
As
the
results
presented
later
show,
the
high
resolution
model
gives
the
closest
match
to
the
LFA
experiment
carried
out
on
the
CFC–Cu
disc.
Therefore,
only
a
high
resolution
model
was
created
for
the
divertor
monoblock
case
study.
3.4.
Finite
Element
Analysis
3.4.1.
Boundary
conditions
for
CFC–Cu
disc
In
order
to
recreate
the
LFA
experiment
in
silico,
a
thermal
load
matching
the
laser’s
must
be
applied
to
one
surface
of
the
finite
ele-
ment
model
whilst
the
temperature
values
on
the
opposite
side
are
recorded
with
respect
to
time.
In
order
to
determine
the
magnitude
and
distribution
of
the
load
we
must
consider
the
laser’s
operation.
Experimental
measurements
showed
that,
at
the
operating
volt-
age
1538
V,
the
laser
delivered
6
J
over
the
duration
of
the
laser
pulse
(see
Fig.
4).
The
measurements
were
made
without
the
optics
in
place.
The
LFA
457
has
3
focusing
lenses,
which
cause
an
attenua-
tion
of
approximately
5%
per
surface
(i.e.
6
lens
surfaces).
Thus,
the
resultant
energy
incident
from
a
single
pulse
on
the
sample
over
a
15
mm
diameter
spot
size
is
5.8
J.
Fig.
5
shows
the
energy
amplitude
of
a
typical
laser
shot
for
a
given
applied
voltage.
As
no
calibration
data
was
available
to
link
applied
voltage
to
laser
energy
output,
the
energy
amplitude
is
therefore
normalised
between
minimum
and
maximum
values.
The
total
energy
output
of
the
laser
(calculated
above
to
be
5.8
J)
is
the
area
under
the
curve
in
Fig.
5.
Thermal
flux,
the
rate
of
energy
transfer
per
unit
of
area,
has
the
units
J
m
−2
s
−1
.
By
knowing
the
0
50000
10000
0
15000
0
20000
0
25000
0
0
0.2
0.4
0.6
0.8
1
00.20.40.60.8
Flux (x 10
3
J· m
-
2
· s
-1
)
Amplit
ude
Time (ms)
Fig.
5.
Typical
energy
pulse
emitted
from
NETZSCH
LFA
457
laser.
3
3
3
3
12
4
4
4
12
Fig.
6.
Projecting
flux
over
an
area
to
nodal
coordinates
due
to
discretisation
inher-
ent
in
FEA.
total
energy
emitted
over
a
certain
area,
it
is
possible
to
calculate
the
flux,
i.e.:
peak
flux
=
total
energy
(
J
)

spot
area

m
2

×
area
under
curve
(
s
)

This
can
be
used
with
the
non-dimensionalised
amplitude
curve
to
produce
a
flux
profile
with
respect
to
time
i.e.
the
curve
in
Fig.
5
using
the
secondary
axis
values.
Flux
is
a
quantity
which
applies
to
an
area,
but
due
to
the
dis-
cretisation
in
finite
element
analysis
it
must
be
applied
at
nodal
points.
Thus
the
equivalent
flux
value
for
an
area
must
be
projected
to
the
nodes
defining
that
area.
Assuming
the
discretised
area
is
sufficiently
small
the
flux
value
over
that
area
can
be
considered
uniform.
For
first
order
finite
elements,
the
projected
flux
value
at
the
node
is
calculated
by
dividing
the
total
flux
equally
between
each
of
the
nodes,
as
shown
in
Fig.
6
[14]
An
additional
consideration
for
the
LFA
scenario
is
that
the
sur-
face
onto
which
the
laser
is
incident
is
not
completely
flat.
Element
faces
describing
this
surface
will
be
oriented
at
different
angles
in
three-dimensional
space.
The
laser
path
is
considered
to
travel
purely
in
the
z-direction
and
will
not
arrive
normal
to
the
element
face.
Therefore,
it
is
important
to
calculate
the
effective
elemental
area
in
the
x–y
plane,
as
this
is
the
area
“seen”
by
the
laser.
A
simple
example
of
a
surface
consisting
of
4
triangular
elements
is
shown
in
Fig.
7.
Even
in
such
a
simple
case,
the
three
dimensional
area
is
30%
greater
than
the
effective
2D
area
in
the
x–y
plane.
The
3D
area
is
calculated
by
taking
the
cross
product
of
any
two
of
the
three
vectors
defining
the
triangle,
where
A,
B
&
C
are
the
nodes.
area
=




៝
AB ×
៝
AC
2




(1)
In
2D
this
simplifies
to
A
el
=





A
x

B
y
−
C
y

+
B
x

C
y
−
A
y

+
C
x

A
y
−
B
y

2





(2)
Therefore,
the
nodal
contribution
from
a
tetrahedral
element
as
a
fraction
of
the
whole
domain
would
be
1
3
A
el
A
tot
where
A
el
is
the
area
of
the
element
face
and
A
tot
is
the
area
of
the
surface
being
thermally
loaded.

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
5
Fig.
7.
Comparison
of
the
area
of
(a)
element
faces
and
(b)
the
effective
area
seen
by
the
laser
in
x–y
plane.
Fig.
8.
Multivariate
Gaussian
distribution
exhibited
by
laser
beam.
These
values
assume
a
uniform
distribution
of
flux
over
the
whole
sample
surface
area.
Lasers
typically
exhibit
a
Gaussian
dis-
tribution
of
their
beams,
as
shown
in
Fig.
8.
In
2D
this
is
known
as
the
multivariate
Gaussian
distribution
(MGD)
by
the
following
equation:
f
(
x,
y
)
=
1
2
x

y

1
−

2
exp

−
1
2

1
−

2


(
x
−

x
)
2

2
x
+

y
−

y

2

2
y
−
2
(
x
−

z
)

y
−

y


x

y

(3)
where

x
,

y
are
the
standard
deviation
in
x
and
y
directions,

is
the
correlation
between
x
&
y
and

x
&

y
are
the
mean
values.
For
the
case
of
the
laser
beam

x
=

y
and
,

x
&

y
are
zero.
Therefore,
(3)
simplifies
to
(4)
and
in
polar
coordinates
(5).
f
(
x,
y
)
=
1
2
2
exp

−
x
2
+
y
2
2
2

(4)
f
(
r
)
=
1
2
2
exp

−
r
2
2
2

(5)
As
the
CFC–Cu
disc
is
smaller
than
the
laser
spot
size,
calculating
the
total
energy
delivered
must
take
into
consideration
the
non-
uniform
distribution.
Additionally
the
applied
nodal
loads
must
reflect
this
spatial
variation
in
distribution.
According
to
the
LFA
457
manufacturers,
it
can
be
expected
that
the
laser
power
reduces
by
10%
of
the
peak
value
5
mm
from
the
centre.
This
is
observed
when
the
standard
deviation
is
10.892
(see
Fig.
9).
In
order
to
use
the
profile
in
Fig.
9
to
calculate
the
thermal
loads
to
be
applied,
the
peak
energy
needs
to
be
determined,
i.e.
where
r
=
0
mm.
To
do
this
it
must
be
ensured
that
the
volume
under
the
2D
MGD
(between
−7.5
and
7.5
in
x
and
y)
is
equal
to
the
volume
under
the
uniform
distribution
over
the
same
area.
That
is,
within
a
given
time-step,
the
amount
of
energy
delivered
is
equal
to
the
uniform
distribution
calculation.
This
volume
can
also
be
seen
as
‘power’
which
has
the
units
J
s
−1
.
Fig.
9.
MGD
profile
of
15
mm
diameter
spot
size
laser
where
energy
reduces
by
10%
between
centre
and
r
=
5.0
mm,
i.e.

=
10.892.
To
calculate
the
volume
under
the
MGD
we
must
integrate
the
equation
describing
the
curve
over
the
whole
region,
R,
using
polar
coordinates
as
shown
in
the
following
equation:
V
=

R
f
(
x,
y
)
dA
=

R
f
(
r
)
r
dr
d

R
f
(r)r
dr
d
=
1
−
exp
−
1
2

r


2
(6)
When
calculated
to
infinity,
the
volume
under
the
MGD
is
unity.
However,
for
this
purpose
it
is
necessary
for
the
distribution
deliv-
ered
over
the
15
mm
diameter
spot
size
to
be
unity.
Therefore,
a
normalising
factor,
F
n
,
is
required.
This
is
given
as
the
ratio
of
the
volumes
of
the
two
distributions
where
‘r’
is
infinity
and
7.5.
i.e.
V
∞
=
1,
V
7.5
=
0.211
F
n
=
V
∞
V
7.5
4.738
V
7.5
F
n
=
1
Thus,
the
flux
at
any
point
can
be
described
as
a
function
of
its
distance
from
the
origin
˚(r,
t)
=
F
n
f
(r)P
t

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
6
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
10 MW·m
-
2
T
=
150
°C
T
0
=150°C
Fig.
10.
Schematic
of
applied
loads
and
temperatures
in
monoblock
simulation.
0
50
100
150
200
0
200
400
600
800
Thermal Diffusivity
(x 10
-6
m
2
· s
-1
)
Temperature (
° C)
CFC
Cu
CFC-Cu
Avg
Fig.
11.
Thermal
diffusivity
measured
by
laser
flash
analysis.
where
P
t
is
the
power
for
a
given
time
step,
calculated
by
multiply-
ing
the
flux
for
a
given
time
step,
˚
t
,
(as
found
above,
see
Fig.
5)
by
the
spot
size
area
(P
t
=
˚
t
×
R
2
).
Combining
the
above
for
a
triangular
face
on
a
tetrahedral
ele-
ment,
the
flux
for
a
particular
node
at
any
given
time
step
is;
˚
(
r,
t
)
=
1
3
A
el
A
tot
F
n
2
2
exp

−
r
2
2
2

P
t
(7)
The
MGD
is
a
function
of
the
distance
of
the
node
from
the
cen-
tral
point
of
the
sample.
The
radial
distance,
r,
is
defined
as
(8)
where
the
nd
and
c
subscripts
denote
the
nodal
and
central
x–y
coordinates.
r
=

(
x
nd
−
x
c
)
2
+
(
y
nd
−
y
c
)
2
(8)
As
this
calculation
must
be
repeated
over
all
elements
on
the
surface
where
the
laser
is
incident,
it
is
probable
that
a
single
node
will
receive
a
contribution
from
several
adjacent
elements.
In
this
case,
the
values
are
summed
to
give
a
total
nodal
flux.
3.4.2.
Case
study
1:
CFC–Cu
disc
Once
the
method
for
specifying
the
boundary
conditions
had
been
determined,
verification
and
validation
of
the
IBFEM
technique
could
be
performed
by
comparing
experimental
and
sim-
ulated
results
of
the
LFA
for
the
CFC–Cu
disc
sample.
The
CAD-based
model,
together
with
the
low
resolution
IBFEM
and
high
resolu-
tion
IBFEM
models
were
analysed
using
ParaFEM
(revision
1796),
an
open
source
parallel
finite
element
platform
developed
by
the
authors
[14–18].
0
0.5
1
1.5
2
0
200
400 60
0
800
Specific Heat Capacity
(x
10
3
J
·kg
-1
·K
-1
)
Temperature (°C)
CFC
Cu
CFC
-
Cu
Avg
Fig.
12.
Specific
heat
capacity
calculated
by
calibration
of
diffusivity
against
Pyro-
ceram
9606.
0
100
200
300
400
500
600
0
200 40
0
600
800
Thermal Conducvity
(
W·m
-1
·K
-1
)
Temperature ( ° C)
CFC
Cu
CFC
-
Cu
Avg
Fig.
13.
Thermal
conductivity
calculated
from
diffusivity,
density
and
specific
heat
values.
Table
4
Details
of
time
step
sizes
used.
Time
step
size
(s)
Number
of
steps
Total
sum
of
time
(s)
0.000001
100
0.0001
0.000005
80
0.0005
0.00001
50
0.001
0.00005
80
0.005
0.0001
50
0.01
0.0005
80
0.05
0.001
50
0.1
0.005
80
0.5
0.01
50
1
0.05
40
3
0.1
20
5
To
ensure
an
accurate
non-oscillatory
(stable)
solution
a
time
step
of
2
×
10
−6
s
was
used
together
with
an
iterative
solver
stop-
ping
criterion
of
1
×
10
−6
.
The
Laser
Flash
experiment
was
simulated
at
a
furnace
temper-
ature
of
200
◦
C,
using
the
material
properties
measured
by
LFA
for
CFC
and
Cu.
Properties
for
Gemco
were
obtained
from
the
man-
ufacturer
[19]
and
standard
values
for
air
[20]
were
used
for
the
porosity.
Table
5
Materials
properties
of
CFC
and
Cu
as
specified
by
IMPH.
Properties
T
(
◦
C)
CFC
(z
direction)
Cu
Thermal
conductivity
(W
m
−1
K
−1
)
RT
a
304
379
250/200
240
355
800/350
145
351
1000/500
141
357
Specific
heat
(×10
3
J
kg
−1
K
−1
)
RT
0.780
0.388
800/200
1.820
0.400
1000/500
2.000
0.437
CTE
(×10
−6
K
−1
)
800/200
0.4
17.0
1000/500
0.5
18.6
Density
(×10
3
kg
m
−3
)
RT
1.90
8.90
Porosity
(%)
RT
8
N/A
a
Room
temperature.

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
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FUSION-7918;
No.
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Pages
12
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
7
Fig.
14.
3D
reconstruction
from
X-ray
tomography
data
for
the
CFC–Cu
disc
showing;
(a)
complete
sample,
(b)
rough
Cu
surface
at
interface
with
CFC,
(c)
slice
midway
through
CFC
section,
(d)
contact
area
at
CFC–Cu
surface
and
(e)
porosity
within
the
CFC
showing
preferential
alignment
with
direction
of
thermal
transport.
Fig.
15.
3D
reconstruction
from
X-ray
tomography
data
for
divertor
monoblock
showing;
(a)
complete
sample,
(b)
rough
Cu
surface
at
interface
with
CFC,
(c)
slice
through
the
midplane,
(d)
large
area
where
CFC
has
debonded
from
Cu
during
brazing
process
and
(e)
porosity
within
the
CFC
showing
preferential
alignment
with
direction
of
thermal
transport.
3.4.3.
Case
study
2:
Divertor
monoblock
In
the
second
case
study,
the
performance
of
the
divertor
monoblock
was
investigated
under
reactor-like
thermal
loads.
Sev-
eral
design
scenarios
exist
for
ITER
each
with
their
own
set
of
in-service
parameters.
Here,
the
transient
response
of
the
divertor
monoblock
going
from
initial
state
to
steady-state
operation
was
modelled.
A
thermal
flux
of
10
MW
m
−2
was
applied
to
one
outer
CFC
sur-
face
of
the
divertor
monoblock
to
simulate
the
thermal
load
from
the
plasma.
To
represent
a
coolant
running
at
150
◦
C
the
inner
Table
6
Segmentation
and
meshing
output
details
for
the
CFC–Cu
disc.
Name
Number
of
voxels
Segmented
volume
(×10
−9
m
3
)
Surface
area
(×10
−6
m
2
)
Number
of
elements
Number
of
nodes
Meshed
volume
(×10
−9
m
3
)
CFC–Cu
(Original
resolution,
9.7
×
10
−6
m
voxel
width)
Cu
289
M
264
478
CFC
326
M
298
2600
Porosity
26
M
24
1910
Gemco
6.3
M
5.78
357
Total
642
M
592
4988
CFC–Cu
(30%
resolution,
32.3
×
10
−6
m
voxel
width)
Cu
7.8
M
−0.38%
−5.65%
40
M
8.2
M
−0.16%
CFC
8.8
M
−0.34%
−17.69%
53
M
11
M
1.40%
Porosity
0.70
M
−0.83%
−18.85%
7.1
M
2.2
M
−27.68%
Gemco
0.17
M
−1.38%
−10.64%
1.8
M
0.47
M
−5.23%
Total
17
M
−0.39%
−10.59%
102
M
22
M
−0.54%
CFC–Cu
(5%
resolution,
194.0
×
10
−6
m
voxel
width)
Cu
35
k
−3.79%
−12.97%
206
k
46
k
−4.85%
CFC
38
k
−6.38%
−63.00%
307
k
63
k
−2.79%
Porosity
3
k
−1.25%
−69.79%
29
k
17
k
−90.45%
Gemco
4
k
496.89%
−13.17%
46
k
12
k
460.52%
Total
81
k
−0.10%
−54.59%
587
k
137
k
−2.74%

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
8
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
Fig.
16.
X-ray
tomography
slice
of
CFC
showing
effect
of
downsampling
from
(a)
original
resolution
to
(b)
30%
and
(c)
5%
resolutions.
Fig.
17.
Cross
section
of
temperature
within
CFC–Cu
sample
at
t
=
1.27
×
10
−2
s
cal-
culated
by
FEA.
surface
of
the
Cu
pipe
was
fixed
to
the
same
temperature
(see
Fig.
10).
The
CFC
surface
was
selected
such
that
fibre
orientation
matched
that
of
the
CFC–Cu
disc
modelled
in
the
first
case
study.
Ini-
tial
temperature
was
set
to
150
◦
C
throughout
the
domain,
to
match
that
of
the
coolant.
The
simulation
was
run
using
gradually
increas-
ing
time-step
sizes
until
steady-state
operation
was
achieved.
This
was
to
ensure
that
the
temperature
changes
at
the
start
of
the
simulation,
where
changes
are
at
their
greatest,
were
accurately
captured
whilst
computational
expense
was
reduced
as
the
simu-
lation
neared
equilibrium.
Details
for
time
step
size
can
be
found
in
Table
4
and
an
iterative
solver
stopping
criterion
of
1
×
10
−6
was
used.
The
results
of
both
case
studies
were
post-processed
using
ParaView,
version
3.14.1
64-bit
(Kitware
Inc.,
Clifton
Park,
New
York,
USA)
[21].
4.
Results
and
discussion
This
section
presents
(i)
the
thermal
diffusivity
values
deter-
mined
experimentally
for
the
constituent
materials
and
the
CFC–Cu
disc;
(ii)
micro-structural
observations
regarding
the
CFC–Cu
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.1
0.2
0.3
0.4
0.5
Temperature
((T-T
0
)/(T
max
-T
0
))
Time (s)
Experi
mental
ParaFEM, 0.6 M els
ParaFEM, 102 M els
CAD
Fig.
18.
Rear
surface
temperature
of
CFC–Cu
disc
during
LFA
experiment
and
sim-
ulation.
interface
in
both
the
CFC–Cu
disc
and
the
divertor
monoblock;
(iii)
quantitative
and
qualitative
analysis
of
the
image-based
meshing
technique
and
(iv)
results
of
the
finite
element
analyses
for
the
CFC–Cu
disc
and
the
divertor
monoblock.
4.1.
Thermal
diffusivity
Fig.
11
shows
the
thermal
diffusivity
results
measured
experi-
mentally
by
LFA.
Figs.
12
and
13
chart
the
specific
heat
and
thermal
conductivity
values
calculated
by
calibration
with
the
reference
sample.
The
figures
present
results
for
the
constituent
materials,
the
projected
values
for
the
CFC–Cu
disc
based
on
the
contributions
by
thickness
of
each
material
and
finally
the
actual
values
measured
for
the
CFC–Cu
disc.
The
results
for
the
constituent
materials
are
comparable
to
those
found
in
the
ITER
materials
property
handbook
(IMPH)
[22],
shown
in
Table
5.
Comparing
the
projected
and
actual
thermal
conductivity
for
the
CFC–Cu
disc,
it
can
be
seen
that
the
measured
conductivity
is
considerably
lower
than
expected.
The
CFC
appears
to
restrict
heat
flow,
with
the
conductivity
of
the
combined
sample
being
only
slightly
higher
than
that
of
CFC.
This
is
despite
43%
of
the
sample’s
thickness
consisting
of
the
more
highly
conducting
Cu.
Interest-
ingly,
over
the
temperature
range
of
600
◦
C
the
conductivities
of
the
CFC
and
Cu
decrease
by
45%
and
20%,
respectively.
Thus,
the
Table
7
Segmentation
and
meshing
output
details
for
the
divertor
monoblock
sample.
Name
Number
of
voxels
Segmented
volume
(×10
−9
m
3
)
Surface
area
(×10
−6
m
2
)
Number
of
elements
Number
of
nodes
Meshed
volume
(×10
−9
m
3
)
Monoblock
(Original
resolution,
21.8
×
10
−6
m
voxel
width)
Cu
42
M
434
723
CFC
163
M 1690
3380
Porosity
2.0
M
20.4
1560
Gemco
1.2
M
12
592
Total
208
M
2156.4
6255
Monoblock
(50%
resolution,
43.6
×
10
−6
m
voxel
width)
Cu
5.2
M
0.23%
−1.38%
27
M
5.5
M
−0.95%
CFC
20
M
0.00%
−10.95%
106
M
22
M
−0.83%
Porosity
0.24
M
−2.45%
−23.08%
2.5
M
0.86
M
−37.31%
Gemco
0.14
M
0.00%
−0.84%
1.7
M
0.45
M
−1.15%
Total
26
M
0.02%
−11.91%
137
M
28
M
−1.20%

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
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Pages
12
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
9
Fig.
19.
Time
series
analysis
of
the
divertor
monoblock
tile
created
from
an
X-ray
tomography
image.
average
change
would
be
a
decrease
of
34%,
which
is
very
close
to
the
actual
decrease
of
35%.
The
IMPH
specifies
that
the
thermal
conductivity
must
be
greater
than
300
W
m
−1
K
−1
at
room
temperature
and
only
decreasing
to
150
W
m
−1
K
−1
at
1000
◦
C.
This
is
partly
because
it
has
been
shown
that
plasma
erosion
decreases
in
CFCs
with
higher
thermal
conductivity
[23],
which
ensures
increased
longevity
for
component
life
cycles.
This
component
does
not
quite
meet
the
specified
criterion,
273
W
m
−1
K
−1
at
100
◦
C
(projected
to
be
288
W
m
−1
K
−1
at
room
temperature)
and
178
W
m
−1
K
−1
at
700
◦
C
(projected
to
be
162
W
m
−1
K
−1
at
100
◦
C),
but
is
relatively
close.
4.2.
X-ray
tomography
images
Fig.
14
shows
that
the
Cu
at
the
interface
of
the
CFC–Cu
disc
is
rough.
In
certain
regions
small
veins
of
Cu
rise
from
the
sur-
face.
This
shows
that
the
brazing
material
does
not
remain
in
its
initial
position
but
contorts
to
the
shape
of
the
CFC
and
even
fills
open
porosity.
This
greatly
increases
the
interface
surface
area
from
126.7
×
10
−6
m
2
if
smooth,
calculated
geometrically,
to
132.2
×
10
−6
m
2
,
measured
from
the
X-ray
tomography
image.
It
is
expected
that
this
enhances
both
bond
strength
and
thermal
transport
across
the
interface.
The
majority
of
the
Cu
at
the
surface
(80.4%)
is
in
contact
with
the
CFC,
therefore
it
can
be
assumed
that
the
bonding
will
be
successful
in
maximising
thermal
conductivity.
In
contrast,
the
X-ray
scan
for
the
divertor
monoblock
shows
debonding
on
one
side
of
the
pipe
(see
Fig.
15).
It
appears
that
this
area
is
linked
with
the
orientation
of
the
sample
during
the
brazing
process
i.e.
the
divertor
monoblock
was
on
its
side
during
join-
ing
and
the
upper
surface
is
where
the
pipe
has
pulled
away
most
probably
due
to
a
combination
of
the
effects
of
gravity
and
a
mis-
match
in
thermal
expansion
coefficient
between
the
CFC
and
Cu.
It
is
expected
that
this
region
will
act
as
a
substantial
thermal
barrier
during
operation.
Pores
within
CFCs
are
an
unavoidable
issue.
They
affect
ther-
mal
conductivity
by
behaving
as
thermal
barriers.
The
greatest
concentration
of
porosity
is
typically
found
aligned
between
fibre
layers.
Thus,
through
design
of
the
composite
layup,
it
is
possible
to
arrange
these
layers
to
give
directionally
preferential
performance.
It
can
be
seen
that
the
porosity
in
the
divertor
monoblock
is
aligned
to
promote
thermal
transport
radially
away
from
the
pipe.
4.3.
Conversion
of
tomography
data
into
finite
element
meshes
The
automatic
segmentation
tool
used
by
Simpleware
[13]
can
segment
images
into
different
phases
according
to
the
voxel
greyscale
values.
It
was
possible
to
segment
the
majority
of
the
images
automatically.
Because
of
noise
at
the
CFC–Cu
interface
and
ring
artefacts
in
the
CFC,
additional
attention
was
required.
Segmentation
was
carried
out
manually
using
paint/un–paint

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
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FUSION-7918;
No.
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Pages
12
10
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
Table
8
Material
properties
used
for
FEA.
Material
Conductivity
(W
m
−1
K
−1
)
Density
(×10
3
kg
m
−3
)
Specific
heat
(×10
3
J
kg
−1
K
−1
)
Cu
405.97
8.6098
0.555
CFC
232.43
1.7238
1.020
Gemco
24.300
8.8000
0.390
Porosity
0.0380
0.7380E−03
1.030
tools
on
a
slice
by
slice
basis.
Before
meshing,
the
images
were
downsampled,
reducing
computational
cost
whilst
retaining
micro-structural
detail
(see
Fig.
16).
Considering
the
CFC–Cu
disc,
at
30%
resolution,
there
is
little
difference
in
visible
detail
when
compared
with
the
full
resolution
achieved
in
the
scan
(100%).
A
lower
resolution
(5%),
suitable
for
analysis
using
a
workstation,
loses
many
features.
Details
characterising
the
models
are
given
in
Tables
6
and
7
for
the
CFC–Cu
disc
and
divertor
monoblock,
respectively.
As
the
image
comprises
voxels
(cuboids),
smoothing
is
applied
in
meshing
to
better
describe
the
curved
nature
of
the
geometry.
This
can
cause
quantities
derived
from
the
mesh
geometry
to
differ
from
those
derived
from
the
original
image.
Changes
in
volume
and
surface
area
for
all
meshes
are
recorded
in
Tables
6
and
7
as
a
percentage
of
those
values
at
the
original
resolution.
The
total
volumetric
changes
can
be
considered
negligible.
When
considering
volumetric
changes
within
the
constituent
materials
there
are
two
notable
changes.
First,
in
the
low
resolu-
tion
mesh,
the
Gemco
layer
is
greatly
increased
by
over
400%
in
the
CFC–Cu
disc.
The
reason
for
this
is
that
when
downsampled,
the
layer
becomes
smaller
than
one
voxel
width.
To
retain
the
feature,
it
had
to
be
artificially
dilated
(using
the
software)
to
the
thick-
ness
of
the
new
voxel
width,
resulting
in
the
increase
in
volume.
It
is
expected
that
this
will
affect
the
simulated
conductivity
at
the
interface
because
the
conductivity
of
Gemco
is
lower
than
both
CFC
and
Cu
(see
Table
8).
Second,
there
is
a
decrease
in
porosity
at
each
downsampling
level,
28%
then
90%
for
the
CFC–Cu
disc
and
81%
for
the
divertor
monoblock.
This
is
because
some
of
the
pores
are
smaller
than
the
new
voxel
widths.
This
should
cause
the
simu-
lated
sample
to
have
an
artificially
increased
conductivity
due
to
the
loss
of
thermal
barriers
in
the
form
of
porosity
(confirmed
later
in
Fig.
18).
The
surface
area
of
the
models
decreases
with
increasing
levels
of
downsampling.
This
can
be
attributed
to
a
reduction
in
surface
detail
as
the
image
resolution
decreases.
The
greatest
variation
can
be
seen
in
the
CFC
and
porosity.
A
few
additional
observations
can
be
drawn
from
the
segmented
image
statistical
data.
When
comparing
the
total
volume
of
the
CFC–Cu
disc
with
that
calculated
geometrically
(see
Table
1),
the
values
agree
to
within
3%.
The
porosity
fraction
of
the
CFC–Cu
disc
is
7.5%,
which
closely
agrees
with
the
literature
value
of
8%.
How-
ever,
this
reduces
to
1.2%
for
the
divertor
monoblock
because
of
the
lower
initial
image
resolution.
Overall,
the
high
resolution
meshes
were
acceptable.
For
the
CFC–Cu
disc,
meshes
with
0.6
million
and
102
million
elements
were
produced
for
the
low
and
high
resolution
models,
respectively.
For
the
divertor
monoblock,
the
high
resolution
mesh
comprised
137
million
elements.
These
numbers
were
within
the
target
range
for
use
on
a
laboratory
workstation
(low
resolution)
and
modern
supercomputer
(high
resolution).
4.4.
FEA
4.4.1.
Case
study
1:
CFC–Cu
disc
Fig.
17
shows
a
temperature
cross-section
of
the
CFC–Cu
disc
during
a
simulation
of
the
LFA,
where
the
thermal
pulse
has
0
100
200
300
400
500
012345
Temperature ( °C)
Time (s)
Debonding between
therm
al loads and pipe
Debon
din
g rotat
ed b
y 180
°
Fig.
20.
Temperature
of
a
node
located
centrally
between
the
surface
with
applied
thermal
load
and
the
CFC–Cu
interface
versus
time
for
both
orientations
of
the
debonded
region.
0
100
200
300
400
500
600
700
0
5
10
15
20
25
Temperature (°
C)
Distance (mm)
CFC
Cu
Gem
co
Debonding
Fig.
21.
Temperature
profile
between
the
front
and
rear
surfaces
of
the
divertor
monoblock
with
debonding
not
aligned
with
the
heat
source
and
sink.
0
100
200
300
400
500
600
700
0
5
10
15
20
25
Temperature (°C)
Distance (mm)
CFC
Cu
Gemco
Deb
ond
ing
Fig.
22.
Temperature
profile
between
the
front
and
rear
surfaces
of
the
divertor
monoblock
with
debonding
positioned
between
the
Cu
pipe
and
the
thermal
loads.
partially
propagated
through
the
sample.
Material
properties
used
are
given
in
Table
8.
Fig.
18
compares
the
results
obtained
for
the
CAD
model,
the
low
and
high
resolution
IBFEM
models
and
the
experimental
LFA.
The
results
are
normalised
with
respect
to
the
initial
and
maximum
temperatures
to
be
comparable
with
experimental
values
(which
are
not
available
in
absolute
temperatures
e.g.
◦
C).
This
graph
can
be
used
to
determine
thermal
diffusivity
through
the
half
rise
time
using
the
“Cowan
+
pulse
correction”
method
[24].
The
CAD
model
(Fig.
18)
underestimates
the
sample’s
thermal
diffusivity
by
approximately
110%.
The
low
resolution
IBFEM
model
which
includes
the
largest
pores
and
some
surface
detail
under-
estimates
the
thermal
diffusivity
by
approximately
30%.
The
high
resolution
IBFEM
provides
the
most
accurate
result,
overestimat-
ing
the
thermal
diffusivity
by
approximately
20%.
As
predicted,
the
result
shows
a
correlation
between
increasing
model
complexity
and
closeness
to
the
experimental
results.
In
the
high
resolution
analysis,
the
high
diffusivity
values
(com-
pared
with
the
experimental
results)
may
be
due
to
the
omission
of
some
underlying
thermodynamics.
It
is
expected
that
model

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
11
Fig.
23.
Example
of
localised
“hot
spot”
caused
by
porosity
within
the
CFC.
accuracy
could
be
further
improved
by
increasing
the
complexity
of
the
simulation,
achievable
by
the
addition
of
features
such
as
radiative
boundary
conditions,
heat
transfer
coefficients,
material
properties
that
are
temperature
dependent
or
take
into
consider-
ation
anisotropic
behaviour.
4.4.2.
Case
study
2:
Divertor
monoblock
Fig.
19
shows
a
plot
of
the
temperature
at
various
time
intervals
for
the
divertor
monoblock.
Monoblocks
usually
exhibit
hot
spots
at
the
corners
of
the
loaded
face
[25],
however
in
Fig.
19
there
is
a
more
even
distribution
of
temperature.
This
is
due
to
the
debond-
ing
region
causing
a
thermal
barrier
between
the
heat
source
and
sink
which
is
comparable
to
alternative
monoblock
concepts
which
include
a
thermal
barrier
by
design
[26,27].
Fig.
20
shows
temper-
ature
versus
time
in
the
CFC
at
a
node
located
midway
between
the
CFC–Cu
interface
and
the
sample
edge
where
the
thermal
load
is
applied.
Finite
element
analysis
of
the
divertor
monoblock
was
carried
out
in
two
orientations,
first
with
the
debonding
region
situ-
ated
in
line
with
the
source
(thermal
loading)
and
the
sink
(Cu
pipe)
and
second
with
the
debonding
region
rotated
by
180
◦
with
respect
to
this
direction.
When
the
debonding
region
was
in
line
with
the
source
and
sink,
temperatures
in
the
debonding
region
exhibited
a
more
extreme
range
of
maxima
and
minima
in
comparison
with
the
other
orientation.
This
observation
is
supported
by
Figs.
21
and
22
which
compare
the
temperature
profile
along
a
central
line
between
the
front
and
rear
surfaces
of
the
divertor
monoblock
at
steady-state
operation
(i.e.
t
=
5
s)
for
both
orientations.
In
Fig.
22,
the
debonding
creates
a
large
thermal
gradient
at
the
boundary
of
the
CFC
and
Cu
by
acting
as
a
thermal
barrier.
This
is
more
significant
than
the
gradient
caused
by
the
relatively
low
conductivity
of
the
Gemco
layer.
Zones
of
high
thermal
gradient
will
result
in
the
generation
of
internal
stresses.
If
aligned
unfavourably
in
service,
the
debonding
region
would
reduce
the
component’s
expected
lifetime
and
increase
the
chance
of
failure.
The
porosity
within
the
CFC
had
a
less
significant
influence
on
the
thermal
behaviour.
This
is
largely
due
to
the
favourable
porosity
alignment
discussed
earlier
(shown
in
Fig.
15).
At
the
micro-structural
level,
the
finite
element
results
in
Fig.
23
show
that
the
pores
behave
as
thermal
barriers
causing
“hot
spots”.
When
the
effect
of
these
hot-spots
is
summed
across
the
component,
their
contribution
would
be
non-negligible.
Regions
surrounding
the
small
veins
of
Cu
had
increased
cooling
opportunity
and
were
therefore
“cool
spots”.
These
results
show
that
reducing
porosity
and
increasing
Cu
surface
area
is
likely
to
improve
efficiency,
albeit
the
impact
of
this
would
be
far
outweighed
by
that
of
the
presence
of
the
debonding
region.
5.
Conclusions
In
the
first
case
study,
laser
flash
analysis
was
carried
out
for
a
CFC–Cu
disc
where
the
interface
had
been
joined
by
a
novel
brazing
process
using
a
Gemco
foil
pre-coated
with
chromium.
It
was
shown
that
the
thermal
conductivity
of
the
CFC–Cu
disc
decreased
by
35%
over
a
temperature
range
of
100
◦
C
to
700
◦
C.
This
was
in
line
with
the
average
decrease
of
thermal
conductivity
for
CFC
and
Cu.
The
thermal
conductivity
was
little
higher
than
that
for
CFC,
which
accounted
for
57%
of
the
sample’s
thickness,
and
not
quite
within
the
required
parameters
specified
in
the
IMPH.
This
demonstrates
the
influence
of
the
interface
on
thermal
conductiv-
ity,
and
thus
the
importance
of
being
able
to
predict
the
behaviour
of
the
interface.
It
was
shown
that
high
resolution
image-based
modelling
of
the
LFA
for
the
CFC–Cu
disc
provided
a
closer
match
with
the
exper-
imental
results
than
was
achieved
using
traditional
CAD
based
FEA.
This
verification
and
validation
exercise
demonstrated
the
reliability
of
the
image-based
modelling
technique,
and
therefore
confirmed
its
suitability
for
use
in
simulating
conditions
not
easily
reproduced
in
the
laboratory,
such
as
those
expected
in
the
ITER.
In
the
second
case
study,
the
CFC–Cu
divertor
monoblock,
X-ray
tomography
highlighted
difficulties
in
the
manufacturing
process
by
clearly
showing
the
debonding
of
the
CFC
from
the
Cu
pipe
on
one
side
of
the
interface.
The
image-based
modelling,
which
cap-
tured
this
defect,
showed
that
the
debonding
would
result
in
lower
thermal
conductivity
thus
leading
to
a
shorter
life-expectancy
and
a
higher
chance
of
component
failure
due
to
increased
internal
stresses.
Suggestions
were
made
regarding
improving
component
cooling
efficiency
such
as:
increasing
the
Cu
surface
area
at
the
interface;
reducing
porosity;
minimising
the
braze
foil’s
thickness
or
selection
of
an
alternative
braze
with
higher
thermal
conductiv-
ity.
In
the
future,
the
image-based
modelling
techniques
developed
here
could
be
used
to
simulate
other
scenarios
expected
in
ITER,
such
as
plasma
instabilities
or
loss
of
coolant.
Due
to
the
nature
of
the
technique
it
would
also
be
easy
to
digitally
alter
the
geometry
to
investigate
the
effect
of
varying
porosity
or
interface
properties.
The
ParaFEM
software
together
with
the
modifications
required
to
carry
out
the
research
in
this
paper
is
freely
available
for
down-
load
in
source
code
form
(see
http://www.parafem.org.uk).
Acknowledgements
The
authors
would
like
to
acknowledge
support
of
the
Engi-
neering
and
Physical
Sciences
Research
Council
for
the
Fusion
Doctoral
Training
Network
(Grant
EP/K504178/1)
and
Culham
Cen-
tre
for
Fusion
Energy
(Grant
EP/I501045).
This
work
made
use
of
HECToR
(Project
e254),
the
UK’s
national
high-performance
com-
puting
service,
which
is
provided
by
UoE
HPCx
Ltd
at
the
University
of
Edinburgh,
Cray
Inc
and
NAG
Ltd,
and
funded
by
the
Office
of
Science
and
Technology
through
EPSRC’s
High
End
Computing
Programme.
This
work
also
made
use
of
the
facilities
of
N8
HPC
pro-
vided
by
the
N8
consortium
under
EPSRC
Grant
no.
EP/K000225/1.
The
Centre
is
co-ordinated
by
the
Universities
of
Leeds
and

Please
cite
this
article
in
press
as:
Ll.M.
Evans,
et
al.,
Transient
thermal
finite
element
analysis
of
CFC–Cu
ITER
monoblock
using
X-ray
tomography
data,
Fusion
Eng.
Des.
(2015),
http://dx.doi.org/10.1016/j.fusengdes.2015.04.048
ARTICLE IN PRESS
G Model
FUSION-7918;
No.
of
Pages
12
12
Ll.M.
Evans
et
al.
/
Fusion
Engineering
and
Design
xxx
(2015)
xxx–xxx
Manchester.
Access
was
also
granted
to
the
HPC
resources
of
The
Hartree
Centre
(project
fusionFEM)
made
available
within
the
Distributed
European
Computing
Initiative
(DECI-12)
by
the
PRACE-2IP,
receiving
funding
from
the
European
Community’s
Seventh
Framework
Programme
(FP7/2007-2013)
under
grant
agreement
RI-283493.
Additionally,
the
authors
would
like
to
thank
the
Manchester
X-ray
Imaging
Facility
for
use
of
tomography
equip-
ment,
which
was
funded
in
part
by
the
EPSRC
(grants
EP/F007906/1,
EP/F001452/1
and
EP/I02249X/1)
and
the
staff
at
the
University
of
Manchester
for
guidance
in
preparing
this
work.
The
research
materials
supporting
this
publication
can
be
pub-
licly
accessed
via
the
University
of
Manchester’s
eScholar
archive
[28].
The
research
materials
are
available
under
a
Creative
Com-
mons
Attribution
(CC
BY)
licence.
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