Multiphysics analysis with CAD-based parametric breeding blanket creation for rapid design iteration

Abstract

Breeding blankets are designed to ensure tritium self-sufficiency in deuterium-tritium fusion power plants. In addition to this, breeder blankets play a vital role in shielding key components of the reactor, and provide the main source of heat which will ultimately be used to generate electricity. Blanket design is critical to the success of fusion reactors and integral to the design process. Neutronic simulations of breeder blankets are regularly performed to ascertain the performance of a particular design. An iterative process of design improvements and parametric studies are required to optimize the design and meet performance targets. Within the EU DEMO program the breeding blanket design cycle is repeated for each new baseline design. One of the key steps is to create three-dimensional models suitable primarily for use in neutronics, but could be used in other computer-aided design (CAD)-based physics and engineering analyses. This article presents a novel blanket design tool which automates the process of producing heterogeneous 3D CAD-based geometries of the helium-cooled pebble bed, water-cooled lithium lead, helium-cooled lithium lead and dual-coolant lithium lead blanket types. The paper shows a method of integrating neutronics, thermal analysis and mechanical analysis with parametric CAD to facilitate the design process. The blanket design tool described in this paper provides parametric geometry for use in neutronics and engineering simulations. This paper explains the methodology of the design tool and demonstrates use of the design tool by generating all four EU blanket designs using the EU DEMO baseline. Neutronics and heat transfer simulations using the models have been carried out. The approach described has the potential to considerably speed up the design cycle and greatly facilitate the integration of multiphysics studies.

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Multiphysics analysis with CAD-based parametric breeding blanket
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Nuclear Fusion
Multiphysics analysis with CAD-based
parametric breeding blanket creation
for rapid design iteration
JonathanShimwell1, RémiDelaporte-Mathurin2, Jean-CharlesJaboulay3,
JulienAubert3, ChrisRichardson4, ChrisBowman5, AndrewDavis1,
AndrewLahiff1, JamesBernardi6, SikanderYasin7,8 and XiaoyingTang7,9
1 Culham Centre for Fusion Energy (CCFE), Culham Science Centre, Abingdon, Oxfordshire OX14 3DB,
United Kingdom of Great Britain and Northern Ireland
2 Département Thermique-Énergétique, Polytech Nantes, Université de Nantes, Rue Christian Pauc,
CS50609, 44306 Nantes Cedex 3, France
3 Den-Département de Modélisation des Systèmes et Structures (DM2S), CEA, Université Paris-Saclay,
F-91191 Gif-sur-Yvette, France
4 BP Institute, Bullard Laboratories, Madingley Road, Cambridge CB3 0EZ, United Kingdom of Great
Britain and Northern Ireland
5 York Plasma Institute, University of York, Heslington YO10 5DD, United Kingdom of Great Britain
and Northern Ireland
6 University of Cambridge, The Old Schools, Trinity Lane, Cambridge CB2 1TN,
United Kingdom ofGreat Britain and Northern Ireland
7 University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom of Great Britain
and Northern Ireland
8 Blackpool and The Fylde College, Asheld Rd, Blackpool FY2 0HB, United Kingdom of Great Britain
and Northern Ireland
9 School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
E-mail: mail@jshimwell.com
Received 27 September 2018, revised 21 December 2018
Accepted for publication 18 January 2019
Published 8 March 2019
Abstract
Breeding blankets are designed to ensure tritium self-sufciency in deuterium–tritium
fusion power plants. In addition to this, breeder blankets play a vital role in shielding key
components of the reactor, and provide the main source of heat which will ultimately be used
to generate electricity. Blanket design is critical to the success of fusion reactors and integral
to the design process. Neutronic simulations of breeder blankets are regularly performed to
ascertain the performance of a particular design. An iterative process of design improvements
and parametric studies are required to optimize the design and meet performance targets.
Within the EU DEMO program the breeding blanket design cycle is repeated for each new
baseline design. One of the key steps is to create three-dimensional models suitable primarily
for use in neutronics, but could be used in other computer-aided design (CAD)-based physics
and engineering analyses. This article presents a novel blanket design tool which automates
the process of producing heterogeneous 3D CAD-based geometries of the helium-cooled
pebble bed, water-cooled lithium lead, helium-cooled lithium lead and dual-coolant lithium
lead blanket types. The paper shows a method of integrating neutronics, thermal analysis
J. Shimwell etal
Multiphysics analysis with CAD-based parametric breeding blanket creation for rapid design iteration
Printed in the UK
046019
NUFUAU
© EURATOM 2019
59
Nucl. Fusion
NF
10.1088/1741-4326/ab0016
Paper
4
Nuclear Fusion
IOP
Original content from this work may be used under the terms
of the Creative Commons Attribution 3.0 licence. Any further
distribution of this work must maintain attribution to the author(s) and the title
of the work, journal citation and DOI.
International Atomic Energy Agency
2019
1741-4326
1741-4326/19/046019+12$33.00
https://doi.org/10.1088/1741-4326/ab0016
Nucl. Fusion 59 (2019) 046019 (12pp)

J. Shimwell etal
2
and mechanical analysis with parametric CAD to facilitate the design process. The blanket
design tool described in this paper provides parametric geometry for use in neutronics
and engineering simulations. This paper explains the methodology of the design tool and
demonstrates use of the design tool by generating all four EU blanket designs using the EU
DEMO baseline. Neutronics and heat transfer simulations using the models have been carried
out. The approach described has the potential to considerably speed up the design cycle and
greatly facilitate the integration of multiphysics studies.
Keywords: fusion, parametric, CAD, neutronics, 3D model, breeder blanket
(Some guresmay appear in colour only in the online journal)
1. Introduction
Breeding blankets are designed to full several high-level plant
requirements, including tritium self-sufciency, shielding
non-sacricial components from the intense neutron ux and
producing heat which is ultimately used to generate elec-
tricity. Designing and engineering components for use within
fusion reactors is challenging due to the high radiation uxes
and signicant heat loads that they experience. Maintaining
an operational and safe component within the inner vessel of a
fusion reactor presents a range of difculties; however, adding
functional requirements such as tritium breeding, heat genera-
tion and heat removal further complicates the task.
Methods of design optimization such as parameter studies
and a ‘designing by analysis’ approach are possible avenues
for designing fusion reactor components that could provide
solutions to this challenge. Such methods rely on human intui-
tion and iterative analysis of models to close in on an optimal
solution. Performing analysis in an isolated discipline will
only nd the optimal solution for performance metrics that
are obtainable within that discipline. For instance neutronics
optimizations may nd the tritium breeding ratio (TBR) but
may nd unacceptable temperatures. Multiphysics analysis
is required to optimize component design. To maintain data
provenance it would be preferable to have a single model basis
when sharing data between analysis techniques.
Traditionally, models are generated for neutronics using
constructive solid geometry (CSG) and the models are suit-
able for use in parametric studies. Engineering analysis tends
to require computer-aided design (CAD) models and CSG
models are typically not compatible with engineering pro-
grams. Models for use in engineering analysis are often cre-
ated via graphical user interfaces. The process of creating new
engineering and neutronics models can be a time-consuming
exercise. This is compounded since the models must be gen-
erated with the release of a new EU DEMO baseline design,
and there are also four EU blanket designs for each iteration.
To analyze the performance of different designs within
the parameter space it would be desirable to be able to pro-
duce an accurate three-dimensional (3D) geometry rapidly.
Adopting a common geometry format would allow geometry
to be used in multiple domains. Allowing ne details (such as
cooling pipes) to be included or excluded during model gen-
eration can facilitate specic requirements of the particular
analysis. Use of open source geometry-producing software
such as FreeCAD [1] (used for this project), Salome [2] or
PythonOCC [3] can be used to quickly generate parametric
CAD geometry which can be exported into a variety of for-
mats. CAD les in STEP format [4] are an open le standard
compatible with engineering simulation software. STEP les
can be easily converted into surface faceted geometry (e.g.
h5m or STL les) for use in neutronics codes such as Serpent
2 [5] (used for this project) and DAG-MCNP5/6 [6]. Ideally
any solution to making component models would be exible
enough to work with new DEMO baseline models and also to
produce different blanket designs.
2. Method
2.1. Geometry creation
It is clear that in order for any advanced method to generate
any detailed geometry it must require the minimum human
intervention, so it was determined that a software library
should be created that allows arbitrary geometric operations
to be performed, with the end goal of creating parametrically
built blanket modules for the EU Demo program. This soft-
ware is called the ‘Breeder Blanket Model Maker’ and can be
found here [7]. Routines for the generation, modication and
serialization of blanket envelopes were created that ultimately
automatically produce detailed heterogeneous blankets for
use in DEMO modelling. Demonstration neutronic and heat
diffusion simulations were performed to illustrate the ease of
carrying out parameter studies. Parametric models of all four
EU blanket designs were generated to demonstrate the design
tool. These include the helium-cooled pebble bed blanket
(HCPB) [8–10], helium-cooled lithium lead blanket (HCLL)
[11, 12], water-cooled lithium lead blanket (WCLL) [13] and
dual-coolant lithium lead blanket (DCLL) [14]. The process
has been broken down into two parts, the rst owchart (see
gure1) summarizes the construction of all the non-breeder
zone components, this includes the rst wall, armour and rear
plates. The second owchart (see gure2) summarizes the
construction of the breeder zone structure.
The breeding blanket is segmented into different mod-
ules which have different shapes, orientations and positions
depending upon the positioning within the reactor (see stage 1
in gure1). The blanket designs share some common features
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
3
such as: lleted corners on the toroidal HCPB, HCLL and
WCLL designs or poloidal DCLL edges.
2.1.1. Structural components. The procedure for the creation
of the structural part of the blanket module is performed rst.
A number of key parameters dene the structure of the blan-
ket: rst wall armour thickness, rst wall thickness, rear plate
count and thickness, and end cap thickness. An automated
procedure regarding the automatic construction of a full
detailed blanket structure was dened, and the full implemen-
tation details can be found in [7]. Additional ne detail is also
included at the user’s discretion including the introduction of
llets and cooling channels. The overall programmatic ow
is shown in gure2, where differing blankets follow different
logical routes.
2.1.2. Breeder zone components. In order to generate the
full heterogeneous blanket description the internal detail
of the breeder zone must be generated. This is a two-stage
process: rst the cooling structure is generated starting from
the breeder zone envelope and generating the cooling struc-
ture from it then the cooling structure is subtracted from the
breeder zone envelope, leaving the non-structural breeding
material (lithium lead/lithium ceramic/neutron multiplier).
2.1.3. Cooling structure generation. The segmentation of the
cooling structure varies for each of the four breeder blanket
modules, but is almost entirely a combination of poloidal-,
toroidal- and radial-based segmentations. The cooling structure
of the HCLL advanced plus module [12] can be represented
by a series of poloidal segmentations with alternating layers of
1. Selection of example blanket
moduleenvelope from the EU
DEMO baseline [15]
2. Example blanketenvelopeshowing the
front face (green), poloidal edges (blue)
and toroidal edges (red)
3. Example blanket envelope with filleted
poloidal edges (right) and toroidal edges
(left) the fillet radius has been increased
to clearlyshow the operation
4. Example blanket envelope with
first wall armour shownin green
5. Example blanket envelope with
first wall shown in green
6.
First wall cooling
c
hannels (optional)
6. Firstwall co
oling
channels (optional)
7. Example blanket envelope with
end caps shown in green
8. Example breeder zoneenvelope
with backwall components
shown in blue and green
Figure 1. Automated workow for generating rst wall, end caps and back plates from EU DEMO baseline [15] blanket envelopes.
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
4
stiffening plates. This can be reproduced using alternate poloi-
dal segmentation with alternating poloidal extrusion lengths, as
shown in gure2 section 2. In the case of the HCPB module
there are alternating poloidal layers of lithium ceramic and neu-
tron multiplier between the stiffening plates. The poloidal seg-
mentation functions have been designed to allow any number
of layer repetitions; this is demonstrated in stage 3 of gure2).
The wedge-shaped regions at the upper and lower extremities
of the HCPB module are lled with neutron multiplier and are
therefore not considered part of the cooling structure. The soft-
ware is able to identify these wedge-shaped regions and group
them with the other neutron multiplier regions.
Radial cuts, and thereby radial segmentation, are also
implemented; these are required for both the WCLL and the
DCLL blanket designs. The WCLL cooling structure can be
generated with a combination of poloidal and toroidal seg-
mentation (see stage 6 in gure 2). Both the toroidal and
poloidal directions have alternating thicknesses for the struc-
tural plates and the lithium lead regions. Every other layer of
the poloidal structural plate has an offset from the rst wall
that allows lithium lead to ow between plates. The poloidal
segmentation for such a model can be carried out in a similar
way to the HCLL, but the WCLL has an additional complica-
tion which requires radial segmentation. The WCLL model
requires toroidal segmentation and additionally requires that
the upper and lower wedge volumes should be considered to
be entirely lithium lead. The resulting product of the toroidal
segmentation can be seen in stage 6 in gure2.
The DCLL cooling structure can be formed from a com-
bination of radial and toroidal segmentation plus some detail
to guide the ow of lithium lead. The procedure used was
to rst radially segment the blankets into three or ve parts
(depending upon the radial depth of the blanket). In general
most of the inboard blankets accommodate three radial layers
and the outboard blankets accommodate ve radial layers. The
addition of toroidal segmentation to the previously radial seg-
mented breeder zone forms the rst stage of the DCLL model
(see stage 8 of gure2). The DCLL blanket design allows the
lithium lead to ow around the structure. An additional struc-
tural component at the upper end of each blanket module is
also required by the DCLL design, the only additional compli-
cation is that a Boolean subtraction with the rst radial layer is
also required to obtain the desired structural plate shape (see
stage 10 of gure2).
Breeder zone
1. Poloidal
segmentation
4. Toroidal
segmentation
7. Radial
segmentation
6. Alternate poloidal
layers cut with
radiallayer
HCLL
HCPB
WCLL
DCLL
9. Radial plate
cut with upper
andlower offset
8. Combination of
radial and toroidal
segmentation
10.Addition o
f
upper channel
guide
3. Poloidal segmentation
with pair of repeating
layers andnoplates in
theend regions
2. Poloidal segmentation
with single repeating
layerand platesin
theend regions
5. Combination of
toroidal andpoloidal
segmentation
Figure 2. Creation of internal breeder zone structure using a combination of toroidal, poloidal and radial segmentations.
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
5
2.1.4. Breeding material. The complete description of the
breeder zone comprises the description of the cooling struc-
ture and the description of the breeding material. The nal
stage is take the original breeder zone envelope and subtract
the newly created cooling plates/stiffening plates from it,
thus dening the description of the complete breeding zone.
HCLL, WCLL and DCLL all require that the end regions are
lithium lead and HCPB requires the end regions to be neutron
multiplier.
2.1.5. Slice geometry generation. The slice geometry used in
the thermal simulation can also be generated automatically.
The procedure for generating the slice geometry of the HCLL
is outlined in gure3. The user species the blanket module
from which to extract a slice. A slice envelope is created with
a poloidal height equal to the poloidal height of a stiffening
plate plus the poloidal height of the breeder zone. The enve-
lope poloidal position is centred around the stiffening plate
so that the slice contains half a breeder zone above and half a
breeder zone bellow the stiffening plate. The cooling channel
positions were found by offsetting the rst wall towards the
rear of the blanket, with the size of the offset progressively
increasing. Surface identication for cooling surfaces was
carried out by merging the coolant volumes with the structure
volumes and searching for merged surfaces in the resulting
geometry. The identication was manually checked after this
stage to ensure a robust procedure.
2.2. Parametric geometries
As a result of the method previously described there is now an
automated procedure for obtaining semi-detailed CAD geom-
etry for the HCPB, HCLL, WCLL and DCLL blankets. The
process relies on a library of common functions which can
be mixed and matched to create particular blanket designs.
The breeder blanket design tool is released as an open source
project under the Apache 2.0 license and distributed via the
UKAEA Github repository [7]. The software is subject to a
test suite and the build status is updated automatically with
every commit. Continuous integration practices are employed
using Circle CI and Docker.
The model construction process is parametric, which
allows models required for parameter studies to be generated
rapidly. Currently the parameters that a user can input are:
• lename of blanket envelope required for segmentation
• blanket type (HCPB, HCLL, WCLL, DCLL) which also
denes the geometry layout as shown in gures1 and 2
• poloidal llet radius for the rst wall and rst wall armour
• toroidal llet radius for the rst wall and rst wall armour
• rst wall armour thickness
• rst wall thickness
• end cap thickness
• thickness of each rear plate
• thickness of each poloidal segmentation
• thickness of each toroidal segmentation
Complete HCLL
blanketmodule
Envelope reserved
for slice
Geometry commonto the blanket
module and the slice envelope
Cen
tral stiffening plate with
added cooling channels
Stiffening plate dividedinto three
sections (upper, lower and central)
Homogenized stiffening plate
extracted for further
detailing
Figure 3. Creation of the slice geometry structure used in thermal analysis.
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
6
• thickness of each radial segmentation
• rst wall coolant channel poloidal height
• rst wall coolant channel radial height
• rst wall coolant channel pitch
• rst wall coolant channel offset from the front face
• output le format (STEP or STL) and tolerance.
Not all parameters are needed for each design as some are not
applicable, for instance the breeder zone in the HCPB blanket
has no radial segmentation option and does not require
this input. Figure 4 shows each of the four blanket designs
formed from a particular module from the baseline DEMO
model [15]. Currently the tool requires that the rst wall is a
at plane to determine the location of the internal structure.
The tool would therefore need some alterations to work with
blanket envelopes with curved front surfaces (i.e. full banana-
shaped segments).
The process of building a blanket module from an enve-
lope typically takes a few seconds on a single core. Build time
depends on the input parameters, as many very small layers
would necessitate more Boolean operations than for the case
of a few large layers. The process is parallelizable, and there-
fore a model such as the EU DEMO with 26 blanket modules
typically takes less than 5 min on a quad core Intel i5 7600
CPU.
3. Results
3.1. Neutronics model creation
Once the parametric CAD models have been created, one
potential use is in neutronics simulations. There are several
routes from CAD to neutronics models, such as conversion
to CSG using conversion software such as McCad [16] or
SuperMC [17]). Alternatively the use of faceted geometry is
also possible. Previously, parameter studies for fusion blanket
optimization have converted parametric CAD models to CSG
(a) HCPB blanket (b) HCLL blanket (c) WCLL blanket (d) DCLL blanket
Figure 4. Example parametric blanket modules; parameter values have been enlarged in some cases to increase the visibility of
components.
(a) Slice of EU Demo viewed from above (b) Slice of EU Demo side view.
Figure 5. A neutronics model of EU DEMO using faceted geometry (STL) with detailed HCLL blankets, showing plasma (purple),
lithium lead (green), magnets (red), and structural steels (grey).
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
7
models using McCad and performed the simulation using
MCNP [18]. This study opted to simulate using faceted geom-
etry in the STL le format and perform the neutronics simula-
tion using Serpent 2, which natively supports STL geometry.
The process of converting from STEP to STL is quicker than
from STEP to CSG and the results are easier to visually verify.
To demonstrate practical use of the parametric geometry, a
series of tritium breeding simulations were obtained for the
HCLL. The poloidal height of the lithium lead sectionsand
the 6Li enrichment of the lithium lead were varied indepen-
dently. The thickness of the rst wall and the stiffening plates
were varied simultaneously with the poloidal height of the
lithium lead sectionsusing equations(1) and (2).
FWT
=CD+

Cp×LL2
p
4×SmD
=0.01 +9.552
×
10−2
×
LL
p
(1)
CPT =
P
s
×LL
p
1.1 ×SmD
=3.332
×
LLp
.
(2)
Here FWT is the rstwall thickness (m), CPT is the stiffening
plate thickness (m),
CD
is the radial width of the rst wall
cooling channel (0.01 m),
Cp
is the specic heat capacity
(J K–1),
Ps
is the coolant pressure (10 MPa for the helium
coolant), SmD is the stress limit criterion for EUROfer
(274 MPa) [19] in case of accident and
LLp
(m) is the poloidal
height of the lithium lead sections. These equations are
described in more detail in [11] and [20]. This HCLL study
is a demonstration of the model-making tool developed and
thermal-mechanical constraints are not taken into account.
Halton sampling [21] was used as the sampling technique to
select points within the parameter space. The parameter space
encompassed blankets with a poloidal height of lithium lead
between 0.01 m and 0.12 m and 6Li enrichment between 0%
and 100%. The requested simulation points found using the
Halton sampling method are shown as red crosses in gure6.
These requested input parameters were uploaded to a online
cloud-based database (Mongo Atlas [22]). Entries within
the database were agged with ‘in progress’, ‘completed’ or
‘requested’ to indicate their simulation status. The central-
ized accessible database allowed independent simulations to
be carried out in parallel and the results to be coordinated. A
containerized workow was implemented using Docker [23]
which held the breeder blanket model-maker software along
with all the dependences required, such as neutron interaction
data, FreeCAD, Python and MongoDB. Containers were then
launched on EGI FedCloud resources [24] and connected to
the cloud database to retrieve their simulation input param-
eters (6Li enrichment and lithium lead poloidal height) and
set the database entry for the simulation to ‘in progress’.
Once the simulation input parameters were received the CAD
models were automatically built and combined with material
Figure 6. Showing interpolated TBR values with a
5σ
condence for a range of different 6Li enrichments and poloidal lithium lead heights.
The Gaussian process software used [30] was able to t the TBR values along with their statistical errors and nd the condence values.
The reference design HCLL has 90% 6Li enrichment, 34.5 mm of poloidal lithium lead and achieves a TBR of 1.235.
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
8
properties to create the neutronics model. Upon completion
of the neutronics simulation the results (TBR and heating tal-
lies) were uploaded to the cloud-based database and the entry
ag was set to ‘completed’. At this point the container would
either continue with the next requested simulation in the data-
base or terminate and free up resources if all the requested
simulations were complete.
FENDL 3.1b [25] cross sectionswere used for neutron trans-
port. Neutronics materials denitions from the EUROfusion
material composition [26] were used in the model and a para-
metric plasma source based on [27] with plasma parameters
from [28] was used. The number of starting particles run for
each TBR simulation was
1×107
.
3.2. Neutronics simulations
The models generated are suitable for neutronics simulations
and gure 5 shows the blanket models within a Serpent 2
geometry. Figure6 shows the resulting TBR values from a
neutronics parameter study. The TBR was found to change
with the poloidal height of lithium lead. Models with a
small lithium lead poloidal height contain a relatively large
EUROfer fraction compared with models with a large lithium
lead poloidal height. This is due to the large number of stiff-
ening plates and it appears to have reduced tritium produc-
tion. However, models with a large poloidal height can also
have large quantities of EUROfer in the breeder blanket. As
the poloidal height of lithium lead increases the thickness of
the EUROfer rst wall (see equation(1)) and the thickness of
the EUROfer stiffening plates (see equation(2)) also increase.
There appears to be an optimal poloidal height which
becomes more pronounced with 6Li enrichment. Figure 5
shows the variation of TBR with 6Li atom fraction within the
lithium lead. Increasing 6Li enrichment shows an increase in
TBR as conrmed by previous studies [29]. Figure5 shows the
variation of TBR with the poloidal height of the lithium lead
regions within the breeder zone of the blanket. The poloidal
height has less of an effect on TBR but can be optimized.
The achievable increase in TBR depends upon the 6Li enrich-
ment. Figure 6 shows that each different enrichment of 6Li
has a different optimal height for the poloidal lithium lead. At
90% 6Li enrichment a TBR increase of nearly 0.1 is possible
(see gure 6). The size of the
5σ
condence regions varies
depending on the proximity and statistical error of nearby sim-
ulations. This is most noticeable towards the extremities of the
search space where there are fewer simulations and the size
of the
5σ
condence regions is larger. The variation in height
of the poloidal lithium lead also has mechanical considera-
tions as the rst wall thickness and stiffening plate thickness
are also increased when the lithium lead poloidal height is
increased (see equations(1) and (2)). This helps explain why
we observe an optimal lithium lead poloidal height for TBR
values from the neutronics model.
A maximum TBR of
1.278 ±0.010
(
5σ
condence) was
found using Gaussian process software [30] to t the simu-
lation data and statistical error (see gure 6). The highest
TBR value was found for a blanket design with a lithium lead
poloidal height of 0.061 m and a 6Li enrichment of 100%.
Additional constraints such as the capability of the thermal-
hydraulic design to cool the structure with reasonable pressure
drops must also be considered, and the maximum TBR design
may not meet such requirements. Thermal modes are devel-
oped in the next section.
3.3. Creation of the heat diffusion model
A slice of the HCLL blanket geometry was used to create
a simplied model of the temperature eld in the tungsten,
EUROfer and lithium lead. Dimensions for the rst wall
thickness and stiffening plate thickness were calculated using
equations(1) and (2) with the poloidal height of lithium lead
set at 34.5 mm. The model contains a single stiffening plate
with cooling channels and lithium lead either side, encased
with a rst wall; the material layout is shown in gure8. A
mesh with 2.3 million tetrahedra was created using Trelis [31]
complete with boundary conditions and volumetric source
terms. Heat diffusion simulations were carried out using
FEniCS [32] which was able to apply boundary conditions
to surfaces and temperature-dependent materials proper-
ties to different volumes. The heat diffusion equationused is
described by equation(3).
∇2
(λ
T
)+
Q
=
0
(3)
where T is the temperature in K,
λ
is the thermal conductivity
of the given material expressed in W m−1 K−1 and Q is the
volumetric source term in W m−3. As this equation is solved
using the nite elements method, equation (3) needs to be
brought to its weak formulation (or variational for mulation)
as follows:
λ
(
δΩ
δT
δn
vdS
−Ω
∇
v
∇
Tdx)=
Ω
vQdxΩ
∈
R
3
(4)
where
Ω
is the domain on which equation(4) is solved, n is the
normal direction on the external surface and
v
is a test func-
tion. The integration term on the boundary of
Ω
is determined
by the boundary conditions.
3.3.1. The Robin boundary condition. The Robin boundary
condition allows the assignment of a convective heat ux on
a boundary. In equations(5) and (6), it is shown that the heat
ux depends on the temperature of the uid and the convec-
tive coefcient h (W m−2 K−1). This coefcient depends on
the type of convection (natural, forced, laminar or turbulent)
and the uid in contact with the surface:
−
λ
dT
dn
=hFWCC(T
−
TFWCC)on Γ
FWCC
(5)
−
λ
dT
dn
=hHSPCC(T
−
THSPCC)on ΓHSPCC
.
(6)
ΓFWCC
and
ΓHSPCC
are surface domains and are shown
in blue and purple, respectively, in gure 7. This condi-
tion is used on the surfaces of the helium cooling channels.
The coefcients h have been calculated for the rst wall
cooling channels (FWCC) and horizontal stiffening plate
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
9
cooling channels (HSPCC). They are determined using
Gnielinski correlation (equation (7)) with the parameters in
table1 in accordance with [33].
Nu
D=
hD
h
λHe
=(ξ/
8
)(
Re
D−
1000
)
Pr
1+12.7(ξ/8)
1/2
(Pr
2/3
−1)
(7)
where NuD is the Nusselt number,
Dh
is the hydraulic diam-
eter in m,
λHe
is the thermal conductivity of the uid in W
m−1 K−1, ReD is the Reynolds number and Pr is the Prandtl
number. We consider a smooth surface, and thereby the
Darcy–Weisbach friction factor
ξ
is then given by:
ξ=(
0.790
ln
ReD−1.64
)
−2.
3.3.2. Neumann boundary conditions. By using Neumann
boundary conditions, xed heat ux can be assigned to the
front wall armour surface shown in red in gure7, as described
in equation(8):
−
λ
δT
δn
=Jon ΓFW
.
(8)
Here, J is a xed ux density in W m−2 on a boundary. This
condition is used on the surface
ΓFW
which corresponds to the
front wall (shown in red in gure7) with a ux of J = 0.5 MW
m−2 which corresponds to the heat ux emitted by the plasma.
The rest of the external surfaces are considered as insu-
lated. This assumption is valid as long as these surfaces are
part of a vacuum and are not exposed to an intense heat ux.
The values of the thermal conductivity
λ
in W m−1 K−1 in
equation(4) were found in [34].
Finally, the distribution of the volumetric source term Q in
equations(3) and (4) was taken from [35] and is inputted into
the nite element model using the following equations:
Q=7.53e−8.98rMW m−3in EUROfer
(9)
Q=23.2e−71.74rMW m−3in tungsten
(10)
Q=9.46e−6.20rMW m−3in LiPb
(11)
where r is the radial distance from the front face of the breeder
blanket in m. The resulting spatial distribution of volumetric
heating (Q) in MW m−3 is shown in gure9.
3.4. Heat diffusion simulations
Using the same CAD-generated models as in section3.2, heat
diffusion simulations have been performed. The steady state
solution of the temperature eld is shown in gure10. Thanks
to these simulations, we are able to determine the maximum
temperature reached by each material and determine if the
design allows the materials to stay within their maximum oper-
ating temperature limits (550 °C for EUROfer and 1300 °C
for tungsten [36]). Although the design limit of 550 °C is
reached in part of the stiffening plates, this design could be
rened with additional cooling channels to reduce the temper-
ature. Additional assessments involving computational uid
dynamics could be performed to check the accuracy of the
temperatures predicted and the conservatism of assumptions
made in this simulation. The maximum temperatures are
shown in table2.
Figure 7. Cut of a HCLL module slice showing the surfaces used for boundary conditions:
ΓFW
(red),
ΓFWCC
(blue) and
ΓHSPCC
(purple).
Table 1. Parameters used for the determination of the convective coefcients
hFWCC
and
hHSPCC
.
Symbol Description Value of FWCC Value of HSPCC
ReDReynolds number
1.310 ×105
3.018 ×104
Pr
Prandtl number
6.599 ×10−1
6.599 ×10−1
ξ
Darcy–Weisbach friction factor
3.000 ×10−2
2.000 ×10−2
Dh
Hydraulic diameter (m)
1.500 ×10−2
3.000 ×10−3
hConvective coefcient (W m−2 K−1)
4.531 ×103
4.848 ×103
Tcoolant
Average temperature of coolant (K)
6.230 ×102
7.160 ×102
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
10
Figure 8. HCLL module slice showing the materials: tungsten (brown), lithium lead (green) and EUROfer (grey).
Volumetricheating (×106Wm
−3)
0.21 246810 12 14 16 18 20 22 23
(a) toroidalview(b) poloidalview
Figure 9. Volumetric heating source term applied to a slice from middle of the equatorial outboard blanket module in W m−3.
(a) isometriccut
Temperature (K)
622 660 700 740 780820
863
(b) toroidal view
(d)poloidalview (c) clipped poloidalview
Figure 10. Resulting temperature eld of a slice from the middle of the equatorial outboard blanket module in K.
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
11
3.5. Discussion
The simulation results show that the materials stay within
their maximum operating temperature limits. However, one
must be aware that some assumptions have been made that
could introduce inaccuracy. The convective boundary con-
dition on
ΓHSPCC
and
ΓFWCC
are set with constant average
coolant temperatures along the channel. This assumption is
reliable in term of ux balance in the module although it may
introduce errors in the region near the inlets and the outlets of
the channels where the coolant should be, respectively, colder
and hotter than the average. One way to solve this issue would
be to allow
Tcoolant
to vary along the channel. Actual cooling
channel designs for HCLL might also differ from the one used
in this paper, leading to variation in the temperature eld. One
can also notice that the simulation has been run in steady state.
Running transient simulation could allow new hot spots to be
spotted before the module reaches steady state. The volu-
metric heat source used in this paper is a tted exponential
function mapped on a mesh using discontinuous Galerkin ele-
ments of order 0. In other words, the volumetric heat source
has been discretized. Again, this might lead to inaccuracy in
some big cells. This can be solved by rening the mesh, as
currently the model contains 2.3 million tetrahedral elements.
Finally, the lithium lead ow is not modelled in this paper for
simplication purposes. Lithium lead has been considered as
a solid. However, considering the very low velocity of lithium
lead in HCLL modules, this assumption can be made.
4. Conclusion
A design tool capable of generating parametric designs for
fusion breeder blankets has been demonstrated on single-
module blanket envelopes for HCLL, HCPB, WCLL and
DCLL. A wide range of design parameters can be changed
to generate CAD geometry for use in parameter studies. The
geometry generated is available in CAD format (STEP) and
faceted geometry (STL and h5m). Conversion to CSG for
neutronics simulation is achievable via existing software such
as McCad or MCAM. The option of faceted geometry allows
CSG geometry to be avoided in favour of more CAD-based
neutronic simulation techniques such as DAGMC or Serpent
2. The provision of CAD geometry also enables manipulation
to be performed with standard CAD software as opposed to
CSG geometry where manipulation of the shapes is less con-
venient. A demonstration neutronics parameter study was per-
formed, where poloidal lithium lead height and 6Li enrichment
were varied. This was done in order to optimize TBR for the
HCLL module. A maximum TBR of
1.278 ±0.010
(
5σ
con-
dence) was found using Gaussian processing to t the data.
The highest TBR value was found for a blanket design with a
lithium lead poloidal height of 0.061 m and a 6Li enrichment
of 100%. Currently the tool allows for a large range of specic
blanket module geometries to be made for use in simulations.
Thermal-mechanical and other constraints are not taken into
account when constructing the geometries and future research
will be required to identify allowable design parameters that
satisfy thermal-mechanical and thermal-hydraulic require-
ments. The geometry created can also be used in nite element
and nite volume software to simulate heat diffusion, tritium
diffusion and stress. A simplied heat diffusion problem was
demonstrated in this paper. The maximum temperature within
the different materials present in the midplane geometry slice
of the HCLL outboard equatorial blanket module was found to
be similar to previous research [33]. Maximum temper atures
were 774 K for tungsten, 863 K for lithium lead and 824 K
for EUROfer. The work performed here shows the value of
in silico design processes, multiphysics workows and, criti-
cally, integration with automated systems for the generation,
submission and analysis of calculations. The workow was
built using modern scalable techniques to run the simulations
(containerized cloud computing), store the output of the simu-
lations (centralised cloud databases) and analyze the results
(machine learning). The tool is open for extension and addi-
tional analysis such as thermal stress, mechanical stress and
tritium diffusion should be the next steps for development.
Acknowledgments
The authors would like to acknowledge the nancial support
of EUROfusion and EPSRC. This work has been carried out
within the framework of the EUROfusion Consortium and
has received funding from the Euratom research and training
programme 2014–2018 under grant agreement no. 633053.
The views and opinions expressed herein do not neces-
sarily reect those of the European Commission. This work
has also been part-funded by the RCUK Energy Programme
(grant number EP/I501045/1). This work beneted from ser-
vices and resources provided by the fedcloud.egi.eu Virtual
Organization, supported by the national resource providers
of the EGI Federation. The authors would also like to thank
the HCLL, HCPB, DCLL and WCLL breeder blanket design
teams, and Dr Lidija Shimwell Pasuljevic and Helen Gale.
ORCID iDs
Jonathan Shimwell https://orcid.org/0000-0001-6909-0946
Rémi Delaporte-Mathurin https://orcid.org/0000-0003-
1064-8882
Chris Richardson https://orcid.org/0000-0003-3137-1392
Andrew Davis https://orcid.org/0000-0003-4397-0712
James Bernardi https://orcid.org/0000-0001-9229-4613
Table 2. Maximum temperatures of each material.
Material
Maximum temperature
(K) (°C)
Tungsten 774 501
Lithium lead 863 590
EUROfer stiffening plates 824 550
EUROfer rst wall 767 494
Nucl. Fusion 59 (2019) 0 46019

J. Shimwell etal
12
Sikander Yasin https://orcid.org/0000-0001-8701-6205
Xiaoying Tang https://orcid.org/0000-0002-7894-6774
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