Nuclear Engineering and Design 381 (2021) 111338

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Nuclear Engineering and Design
journal homepage: www.elsevier.com/locate/nucengdes

Neutron importance based lattice-to-core projection technique and its
application for HTGR design using Monte Carlo method
Donny Hartanto a, b, Peng Hong Liem c, d, *a

Department of Mechanical and Nuclear Engineering, University of Sharjah, P.O. BOX 27272, Sharjah, United Arab Emirates
Nuclear Energy System Simulation and Safety Research Group, Research Institute for Sciences and Engineering, University of Sharjah, P.O. BOX 27272, Sharjah, United
Arab Emiratesc
Cooperative Major in Nuclear Energy, Graduate School of Engineering, Tokyo City University (TCU), 1-28-1 Tamazutsumi, Setagaya, Tokyo, Japand
Scientific Computational Division, Nippon Advanced Information Service (NAIS Co., Inc.), 416 Muramatsu, Tokaimura, Ibaraki, Japanb

A R T I C L E I N F O

A B S T R A C T

Keywords:
HTTR
Optimum fuelNeutron importance
Serpent
ENDF/B-VIII.0

In general, a nuclear core design process is divided into two subsequent phases, namely the fuel lattice designphase, and followed by the full core design phase such as for the light water reactor (LWR). The optimal design
parameters obtained from the fuel design phase can be used in a straightforward manner in the full core designphase since the neutron mean free path is much smaller than the fuel assembly dimensions. Unfortunately, theabove-mentioned favorable situation may not be applicable for a high-temperature gas-cooled reactor (HTGR)
design process. In this paper, for the HTGR design process, we propose a new technique based on the neutron
importance concept to make a projection of the optimal design parameters obtained from the fuel design phase to
the full core design phase so that the optimization works required in the full core design phase can be signifi­
cantly reduced. The proposed technique is implemented in the Japanese High-Temperature Engineering Test
Reactor to find the optimal fuel composition that can achieve an average core discharge burnup of 80 GWd/tU
using single-batch and multi-batch refueling schemes. Important core neutronics parameters, such as reactivity
coefficient and power profiles, are also discussed. Moreover, the impact of the axial shuffling scheme on the fuelcompact fuel temperature is also analyzed.

1. Introduction

geometry may require a 3-dimensional (3-D) one with large spatial di­mensions. In addition, when the burnup analysis is also conducted(which is the usual case) in the full core design phase, the core spatial
domain has to be divided into many small burnup regions to guarantee
the accuracy of the analysis results.
For a light water reactor (LWR), the optimal design parameters ob­
tained from the fuel design phase can be used in a straightforwardmanner in the full core design phase since the neutron mean free path ismuch smaller than the fuel assembly dimensions. Another design aspectthat supports this argument is the fact that an LWR core consists of only
fuel assemblies. Only in the most outer regions (both radial and axial) of
the core, an LWR designer places highly moderated reflectors to reduce
neutron leakage. This implies that the neutron spectra in the core are notsignificantly different, although they may be slightly different from one
type of fuel assembly to other types. The above-mentioned LWR design
process is well represented by, for example, the use of CASMO5 (Rhodes

In the long and iterative process of nuclear core design which de­mands substantial computational resources, a technique capable ofreducing the overall computation time is essential, especially when thecontinuous Monte Carlo method is adopted. In general, a nuclear core
design process is divided into two subsequent phases, namely the fuellattice design phase, and followed by the full core design phase. In thefuel lattice (or fuel assembly) design phase, numerous dominant design
parameters and constraints covering the fuel composition, dimension,moderation ratio, target burnup, etc. are considered, however, thecalculation geometry and domain are usually simple and small, andmostly in 2-dimensional (2-D). The main objective of the fuel latticedesign is to find narrow ranges of optimal design parameters which canbe used in the subsequent full core design phase. In the full core designphase, the free design parameters are usually fewer, but the calculation* Corresponding author at: Cooperative Major in Nuclear Energy, Graduate School of Engineering, Tokyo City University (TCU), 1-28-1 Tamazutsumi, Setagaya,
Tokyo, Japan.
E-mail address: liemph@nais.ne.jp (P.H. Liem).
https://doi.org/10.1016/j.nucengdes.2021.111338
Received 27 April 2021; Received in revised form 7 June 2021; Accepted 16 June 2021
0029-5493/© 2021 Elsevier B.V. All rights reserved.

Nuclear Engineering and Design 381 (2021) 111338

D. Hartanto and P.H. Liem

Fig. 1. Projection of optimum fuel lattice composition from lattice to core.

et al., 2015), etc. have been widely used in the design and analysis of
nuclear reactors including HTGRs. These high-fidelity codes have fea­tures that are strongly demanded by the nature of the HTGR fuel andcore, i.e. the capability to treat accurately the double-heterogeneity ef­
fect of TRISO (TRI-structural Isotropic) fuel particles (Price, 2012),
pebble or pin fuel elements. The downside of Monte Carlo code utili­zation is the resource demanded and the long computation time, espe­
cially if it is used in the full core design phase with burnup analysis. This
motivated us to develop a new technique that may reduce the number offull core Monte Carlo calculations to obtain an optimal fuel composition.
Previously a heuristic approach was used to project the core fuelcompositions based on the optimal lattice fuel compositions using anapproximation to get the “effective” NC /NHM (carbon-to-heavy metal
density ratio) between the lattice and the core (Hartanto and Liem,
2020). In this paper, for the HTGR design process, we propose a newtechnique based on the neutron importance concept to make a projec­tion of the optimal design parameters obtained from the fuel latticedesign phase to the full core design phase so that the optimization works
required in the full core design phase can be significantly reduced. The
essence of the proposed technique is to conserve the optimal neutronics
condition, in terms of graphite to fuel nuclide density ratio, in both thefuel lattice design phase and the full core design phase.
The rationale of the proposed technique is given in Chapter 2. In
Chapter 3, we will show the effectiveness of the proposed technique indesigning small HTGRs. Chapter 4 summarizes our present work anddiscusses possible future work.

Table 1
Japanese 30 MWth HTTR Main Design Parameters.
Power (MWth)30

Coolant inlet/outlet temperature (◦ C)
Primary coolant pressure (MPa)
Equivalent core diameter (m)Equivalent core height (m)Average power density (W/cm3)
Fuel
Enrichment (wt.%)
Burnup period (EFPD)
Fuel block
Coolant
Reflector thickness
Top (m)Side (m)Bottom (m)Number of fuel assemblies
Number of fuel columns
Number of pairs of control rods
In CoreIn Reflector
Number of instrumentation columns

395/950
4
2.3
2.9
2.5
UO2
3 to 10
660
C
He
1.16
0.99
1.16
150
30
7
9
3

et al., 2006) and SIMULATE5 (Bahadir and Lindahl, 2009) codes during
the fuel lattice design phase and full core design phase, respectively.
Unfortunately, the above-mentioned favorable situation may not beapplicable for a high-temperature gas-cooled reactor (HTGR) design
process for the following reasons. First, an HTGR commonly uses agraphite moderator, hence, the neutron mean free path is much longer
than the fuel lattice dimensions. As an important consequence, theneutron spectrum in one region is affected by other regions which may
not or cannot be considered during the fuel lattice design phase. Second,an HTGR core consists of not only fuel elements but also a large volumeof graphite blocks (for prismatic/block-type HTGR) or graphite(dummy) pebbles (for a pebble-bed-type HTGR). Third, for safety pur­poses, the graphite reflectors are used not only in the outer regions of thecore but also in the center of the core, namely the so-called annular core.
For this particular configuration, the core thickness becomes thinner andthe effect of inner and outer graphite reflectors becomes stronger.
Recently, continuous energy Monte Carlo codes, such as MCNP-6.2(Werner, 2017), MVP-3 (Nagaya et al., 2017), Serpent 2 (Leppänen

2. Rationale of the newly proposed technique
The newly proposed technique is performed in two steps. In the firststep, the fuel composition of the fuel lattice is optimized to have aminimum fissile content per energy generated (kg/GWd). Extensive fuelblock lattice burnup calculations with leakage-free boundary conditions
are performed using continuous energy Monte Carlo code Serpent 2 andthe latest nuclear data library ENDF/B-VIII.0 (Brown et al., 2018) byvarying two design parameters which are the fissile content (% U-235)
and the heavy metal (HM) loading per fuel block (kg HM). The HM
loading per fuel block is equivalent to the TRISO particle fuel packing
fraction (PF) and it influences the neutron spectrum and the neutron
multiplication factor k. Meanwhile, the fissile content dictates the2

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Nuclear Engineering and Design 381 (2021) 111338

Fig. 2. The radial layout of HTTR.

Fig. 3. The axial layout of HTTR.

maximum discharge burnup.
Afterward, the achievable core discharge burnup of the fuel block
lattice having a different pair of design parameters (HM loading per fuelblock and fissile content) is quantified using the non-linear reactivity
method (Driscoll et al., 1991). In this method, the reactivity of the fuelblock lattice is fitted into a polynomial equation as a function of theburnup cycle (Bc ). Similar to the previous study (Hartanto and Liem,
2020), a quartic equation is used, as shown by Eq. (1). Before calculating

the achievable discharge burnup (Bd ), the burnup cycle (Bc ) should bedetermined by taking into account the reactivity loss due to leakage inthe core (ρleakage ) and the number of the refueling batches (N), as shown
by Eq. (2). It is worth mentioning that ρleakage can be adjusted until thetargeted discharge burnup is achieved in the core calculation. Lastly, thedischarge burnup (Bd ) is computed by using Eq. (3). The optimal fuelcomposition, which has the minimum fissile mass (kg) per unit energy
generated (GWd), is then determined by taking into consideration the3

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Nuclear Engineering and Design 381 (2021) 111338

Table 2Block-type fuel lattice design parameters (Bess and Fujimoto, 2011).
Coated fuel particle(HTTR)

Fuel
Fuel density (g/cm3)
Uranium enrichment (w/o)
Burnable poison material
Type
Kernel diameter (mm)Particle diameter (mm)Coating material
Thickness (mm)Density (g/cm3)
Packing fraction (v/o)(U-235/U-238)O2
10.40363<20%
Natural Boron
TRISO
0.600
0.920
PyC/PyC/SiC/PyC
0.060/0.030/0.025/0.045
1.100/1.850/3.200/1.850
Variable < 30%

Fuel compact
Inner diameter (cm)Outer diameter (cm)Matrix density (g/cm3)
Graphite sleeve
Inner diameter (cm)Outer diameter (cm)Density (g/cm3)
Coolant annulus channel
Inner diameter (cm)Outer diameter (cm)Fuel block
Flat to flat distance (cm)
No. of fuel pin
No. of BP holes
BP channel diameter (cm)
No. of central handling socket
Handling socket depth (cm)Top and bottom graphite layer thickness (cm)Matrix density (g/cm3)(HTTR)
1.00
2.60
1.70
2.60
3.40
1.77
3.40
4.10
5.15
31 or 33
3
1.5
1
25.0
1.7
1.7512discharge burnup.

ρ(Bc ) = a0 + a1 Bc + a2 B2c + a3 B3c + a4 B4c

(1)

N
1 ∑
ρ(iBc ) = ρleakage
N i=1

(2)

Bd = NBc(3)

Fig. 4. Infinite neutron multiplication factor at 0 and 80 GWd/tU.

In the second step, the full core burnup calculation is performed. The
fissile content and HM loading per fuel block of the optimal fuelcomposition from the first step cannot be used directly in this step.
Typically, an HTGR core consists of not only fuel block but a consider­able amount of graphite blocks which will alter NC /NHM of the core.
Also, an HTGR is surrounded by a thick layer of radial and axial graphitereflectors and it also increases the NC /NHM of the core significantly
compared to that of the fuel block lattice. An equivalent NC /NHM between
lattice and core can be obtained by increasing the TRISO particle fuelpacking fraction in the core so that the optimal fuel composition fromthe lattice calculations can be adopted, i.e. projected into the core, as
illustrated in Fig. 1. One should be cautious that the “importance” ofgraphite in the graphite blocks and of the graphite reflectors is different
compared to the “importance” of graphite in the fuel blocks. Hence, a
simple volume-weighted NC /NHM relationship would not project the
optimal lattice NC /NHM into the optimal core NC /NHM . In our previous
study with a heuristic approach (Hartanto and Liem, 2020), the graphite
blocks in the core are considered using a simple volume-weighted, while
the graphite in the reflector region was not included in the NC /NHM .
A better approach is suggested in this paper by introducing the use ofneutron importance I(r), a well-known concept in the reactor physics
field. One can easily understand intuitively that the effect or contribu­
tion of a graphite reflector located far away from the core to the NC /NHM
must be lower than a graphite block located inside the core. The neutron
importance provides a quantitative as well as a systematic way to“weigh” the graphite contribution to the core equivalent NC /NHM . In theFig. 5. Fissile loading per energy generated against HM loading per fuel block
for single batch refueling scheme.

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Nuclear Engineering and Design 381 (2021) 111338

Fig. 6. NC /NHM of lattice and core.

Fig. 7. Neutron importance distribution at the center of the core.

following, we will describe the new technique by using the Serpent 2
code but the technique is not limited by the analytical tool used. Even
one can prepare the neutron importance by a deterministic code.
Serpent 2 has the capability to generate the neutron importance ofthe cell for the weight-window-based variance reduction based on the
response matrix method (Leppänen, 2019). Two importance values are
generated: 1) cellwise source important, defined as “a contribution of asingle source particle emitted in energy group g to the given global
response”, and 2) current importance, defined as “the response contri­
bution of a particle entering the cell through the boundary in energy
group g” (Leppänen, 2019). The neutron importance used in this study isthe current importance in one group energy structure and the response isdetermined as the contribution of each mesh to the fission reaction. The
mesh is defined as a hexagonal mesh with the same pitch as a fuel blockand the height is half of the fuel block.
An eigenvalue mode calculation is first performed to collect and savethe fission source distribution into a file to be used in the next step
(neutron importance calculation). A fixed source mode calculation isthen carried out to generate neutron importance using the previously

saved fission source distribution. Several iterations are typicallyrequired until the result is converged. In this study, the total number of
iterations is eight where the first three iterations are for the global
variance reduction. Later, the NC of the core can be calculated bydirectly multiplying the normalized neutron importance of each mesh by
the number of graphite atoms in each mesh, as shown in Eqs. (4) and (5).
∫̃C = 1NC (r)I(r)dr(4)
N
V Reactor∫
I(r)dV = 1.0(5)

3. Application to small-sized HTGR design
The proposed technique is implemented in the Japanese HighTemperature Engineering Test Reactor (HTTR) (Bess and Fujimoto,2011) to find the optimal fuel composition that can achieve an averagecore discharge burnup of 80 GWd/tU. HTTR is a block-type high5

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Nuclear Engineering and Design 381 (2021) 111338

Table 3Single batch core parameters.
Fissile loading per energy generated (kg/GWd)
HM loading per block (kg)
Total HM mass in core (kg)Fissile enrichment (wt%)
Fissile mass per block (kg)
Total fissile mass in core
TRISO fuel packing fraction
NC /NHM of fuel block

1.635
5.865
879.773
13.08
0.767
115.05028.29
323.917

BP content
Cycle length (years)
keff

4.0 wt% nat. B
6.42

BOC
EOC
FTC (pcm/K)
BOC
EOC
MTC (pcm/K)
BOC
EOC
Radial peak power BOC/EOC
Axial peak power BOC/EOC

1.16300 ± 7 pcm
1.01432 ± 6 pcm− 2.848 ± 0.072− 3.551 ± 0.086− 2.180 ± 0.023− 3.275 ± 0.029
1.170/1.082
1.205/1.139

Fig. 8. keff of the single-batch core using different values of latticeleakage reactivity.

Fig. 9. keff of single-batch core with burnable poison.

temperature helium-cooled graphite-moderated experimental reactor,
produces 30 MWth power, and it is operated by Japan Atomic Energy
Agency. The average and maximum core discharge burnup of HTTR isabout 22 and 33 GWd/tU, respectively (JAERI, 1994).
The main design parameters of HTTR are summarized in Table 1. The
core consists of 61 hexagonal columns surrounded by a thick permanentgraphite reflector, as shown in Fig. 2. The columns are distributed suchas 30 columns are for fuel, 16 columns for control rod, 3 columns for
instrumentation, and the remaining 12 columns are for the replaceablereflector. The core has a diameter of 425 cm and a height of 522 cm.
Each fuel column has five fuel blocks and two axial reflector blocks at
the top and bottom, as illustrated in Fig. 3. In each control rod column aswell as in the instrumentation column, three insertion holes with adiameter of 12.3 cm and a depth of 416 cm are located. The replaceablereflector column and the permanent reflector are made of graphite.
The fuel block lattice design parameters are tabulated in Table 2. The
HTTR design uses two types of fuel block which are with 31 and 33 fuelpins. The fuel pin consists of an annular fuel compact enclosed in a

Fig. 10. Normalized radial power distribution of single-batch core with burn­able poison.

6

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Nuclear Engineering and Design 381 (2021) 111338

Fig. 13. keff of a single-batch core with burnable poison.

Fig. 11. The normalized axial power distribution of single-batch core withburnable poison.

Fig. 12. keff of the 5-batch core using different values of latticeleakage reactivity.

graphite sleeve. The fuel compact has an inner and outer radius of 0.5
cm and 1.3 cm, respectively, and it contains TRISO fuel particles with aradius of 0.046 cm dispersed in the graphite matrix. Low enricheduranium fuel is used in the TRISO fuel particle. In the HTTR, twelve
different enrichments (from 3% to 10% U-235) are adopted dependingon the fuel block location, for example, a lower enrichment is locatednear the center of the core. The fuel block of HTTR also has threeburnable poison (BP) insertion holes with a radius of 0.75 cm. Anotherfeature of the HTTR fuel block is the fuel handling socket located at its
center. For the sake of simplicity, a fuel block with 33 fuel pins and a
uniform enrichment is considered in this study.
3.1. Lattice physics optimization
The depletion calculation of the fuel block lattice was accomplishedusing Serpent 2. A 3-D model was considered, and a periodic boundary
condition was applied in any direction. The TRISO fuel particles weretreated explicitly and their positions were generated randomly. The
calculation was performed with 15,000 neutron histories and 200 total

Fig. 14. The normalized radial power distribution of 5-batch core with burn­able poison.

7

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Nuclear Engineering and Design 381 (2021) 111338

with 10% porosity was applied in the calculation as well as the Doppler
broadening rejection correction (DBRC) option. The temperature used in
the calculation was 1230 K for fuel compact and 1060 K for the graphite
sleeve, graphite matrix, and helium coolant.
Fig. 4 shows the infinite multiplication factor kinf as functions of fuelenrichment and HM loading per fuel block, at the BOC (beginning ofcycle or 0 GWd/tU) and EOC (end of cycle or 80 GWd/tU). A lower HM
loading fuel block has a softer spectrum and it has a higher value of kinf
compared to the higher HM loading fuel block with the same fuelenrichment. Additionally, certain fuel enrichment is also required toachieve the desired discharge burnup value.
Using the non-linear reactivity method, the fissile loading per energy
generated is determined for several ρleakage values and a quartic function
is again used to fit the points, as depicted in Fig. 5. The optimum fuelcomposition is quantified by finding the root that gives the derivative of
the fitting function equals zero. Later, this optimum fuel composition isused in the core using the projection technique discussed previously.
3.2. Single batch core optimization design
Fig. 15. The normalized axial power distribution of 5-batch core with burn­able poison.

The first step to use the optimum fuel composition obtained from thefuel block lattice calculations is to calculate the NC /NHM of the core, andlater the NC /NHM of the optimum fuel from lattice is projected to thecore’s so they become equal. Therefore, the TRISO fuel packing fractionin the core increases, but the fissile loading per energy generated and thefissile enrichment is still the same between lattice and core. The amountof graphite in the core should be reasonably considered. In Fig. 6, several
approaches including the newly proposed technique are considered.
Approach 1 takes into account the graphite located in the center ringand the 3 rings of the fuel block, but the graphite in the axial reflectors is
not considered, similar to the previous study (Hartanto and Liem, 2020).
In approach 2, the graphite located in all hexagonal blocks is considered,but it also does not include the graphite in the axial reflectors. Approach
3 is similar to approach 2 but includes one block of the axial reflector ateach top and bottom. The final approach is the use of neutron impor­tance generated by Serpent 2 as plotted in Fig. 7 for the radial and axial
directions. It is clear that the meshes near the center of the core havehigher importance (darker color), however, the contribution of graphitereflectors is also considered. Therefore, the neutron importanceapproach is expected to produce an equivalently optimal NC /NHM , while
approaches 1 and 2 underestimate the NC /NHM noticeably.
Using the newly proposed projection technique, based on theneutron importance, the TRISO fuel packing fraction of the core can beobtained for each lattice neutron leakage reactivity. A depletion calcu­
lation is then performed to determine the optimum core fuel composi­tion that can achieve discharge burnup of 80 GWd/tU, and the excess
reactivity at this burnup step (EOC) is still about 1000 pcm to take into
account the addition of the experimental apparatus installed in the core.
The total neutron histories in the depletion calculation are 7 million
neutrons, and 2 million neutrons are discarded in the inactive cycle.
Moreover, the fuel blocks are divided into 3 radial and 5 axial burnup
regions. It is evident that the number of full core depletion calculations
can be significantly reduced since one does not need to conduct an
exhaustive parametric survey to obtain the optimal NC /NHM .
Fig. 8 shows the evolution of keff and the core can achieve theobjective by having a TRISO fuel packing fraction of 28.29% and thefissile enrichment is 13.08%. The selected core is loaded with BP rods inall fuel blocks, and in each fuel block, 3 BP rods are embedded. The BP
rod is the same used in HTTR; its radius is 0.7 cm, it consists of a naturalenriched B4C/C composite with a density of 1.8 g/cm3 and a length of
20 cm at each end joined by a 10 cm graphite. As illustrated in Fig. 9, theinsertion of BP rods reduces the excess reactivity at BOC significantly
and the boron content of 4% is selected as the reference core for thissingle batch scheme.
Other neutronics parameters of this core such as fuel temperature

Fig. 16. Fuel block shuffling schemes.

Fig. 17. keff of 5-batch core using different shuffling schemes.

cycles, resulting in a statistical uncertainty of the neutron multiplication
factor about 35–40 pcm. The latest nuclear data library ENDF/B-VIII.0
was used. Moreover, the thermal scattering law S(α, β) for graphite
8

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Nuclear Engineering and Design 381 (2021) 111338

Fig. 18. Normalized axial power distribution of 5-batch core using different shuffling schemes.

Fig. 19. Inner fuel compact temperature (◦ C) using different shuffling schemes.

reactivity coefficient (FTC) and moderator temperature reactivity coef­
ficient (MTC) are presented in Table 3. The FTC is calculated byincreasing the fuel compact temperature by 100 K, while the MTC is
calculated by increasing the graphite sleeve and graphite matrix by 300
K. Both FTC and MTC values are negative at BOC and EOC. The
normalized radial and axial power profiles are also presented in Figs. 10
and 11. The power profiles become slightly flat at EOC.

way as in the previous section. It is shown in Fig. 13 that the excess
reactivity can be suppressed significantly with 3 wt% boron in the BP
rods. Other results worth discussing are the radial and axial power
profiles at the beginning of the equilibrium cycle (BOEC) and end of theequilibrium cycle (EOEC) as depicted in Figs. 14 and 15. The radial
power profile has a similar trend to the single batch core, however, theaxial power profile has a peak value of 1.830 located in the fresh fuelregion near the boundary of graphite axial reflector at EOEC. The HTTR
design has a peak value of 1.7 for axial power. To reduce this value,
different shuffling schemes are proposed.
Two other fuel shuffling schemes are suggested, as illustrated inFig. 16. Shuffling scheme 1 is initially applied. In shuffling schemes 2
and 3, the fresh fuel block is moved to the center and it is surrounded by
the burned fuel blocks. This approach is expected to reduce the axial
power peak in the fresh fuel region. The keff at the equilibrium cycle forthe 3 shuffling schemes are compared in Fig. 17 and they achieve thetarget discharge burnup. It is also noticed that the excess reactivity
slightly reduces in the new shuffling schemes. However, as shown in
Fig. 18, the new shuffling schemes significantly decrease the peak axial
power, from 1.83 to 1.55.
To complete the study, the temperature analysis is also performed toinvestigate the impact of fuel shuffling on the fuel temperature. The
temperature calculation is carried out along the fuel columns. The he­lium coolant with a pressure of 4 MPa enters the core at a temperature of
350 ◦ C and exits at a temperature of 950 ◦ C. Serpent 2 provides thepower density, and for this purpose, the power density is tallied for each

3.3. 5-Batch core optimization design
To increase the fuel utilization and minimize fuel enrichment, a
multi-batch core is proposed, and in this case, it is a 5-batch refuelingscheme because each fuel column has 5 fuel blocks. During the refueling,
the fuel blocks are moved only along the axial direction, similar to those
applied in VHTR (Kim et al., 2007). For our first try, the new fuel blocks
are inserted from the top of the core and the discharged fuel blocks aretaken out from the bottom of the core. The radial fuel shuffling is notconsidered. It is assumed that the refueling interval takes 30 days. The
same calculation conditions and procedures are applied to get the op­
timum fuel composition for the 5-batch core.
Fig. 12 shows the keff of the equilibrium cycle and it is observed thatthe target discharge burnup is satisfactorily achieved by having a TRISO
fuel packing fraction of 33.73% and fissile enrichment of 9.43%. As
expected, a multi-batch core requires much lower enrichment compared
to a single batch core, however, the total HM mass is higher for a multibatch core. The selected core is then loaded with BP rods in the same9

Nuclear Engineering and Design 381 (2021) 111338

D. Hartanto and P.H. Liem

core.
The design objective of this study which is to achieve an average coredischarge burnup of 80 GWd/tU can be achieved by both single-batchand 5-batch refueling schemes. The FTC and MTC are also always
negative. However, 5-batch refueling scheme gives more advantages
such as lower fissile enrichment, lower fissile loading per energy
generated, and slightly longer fuel residence time.

Table 45-batch core parameters.
Fissile loading per energy generated (kg/GWd)
HM loading per block (kg)
Total HM mass in core (kg)Fissile enrichment (wt%)
Fissile mass per block (kg)
Total fissile mass in core
TRISO fuel packing fraction
NC /NHM of fuel block

1.178
6.993
1048.945
9.43
0.659
98.87433.73
323.074

BP content
Cycle length (years)
keff at BOEC/EOEC

3.0 wt% nat. B
1.53

Shuffling scheme 1
Shuffling scheme 2
Shuffling scheme 3
FTC (pcm/K) at BOEC/EOEC
Shuffling scheme 1
Shuffling scheme 2
Shuffling scheme 3
MTC (pcm/K) at BOEC/EOEC
Shuffling scheme 1
Shuffling scheme 2
Shuffling scheme 3
Radial peak power at BOEC/EOEC
Shuffling scheme 1
Shuffling scheme 2
Shuffling scheme 3
Axial peak power at BOEC/EOEC
Shuffling scheme 1
Shuffling scheme 2
Shuffling scheme 3
Max. inner compact fuel temp (◦ C)
Shuffling scheme 1
Shuffling scheme 2
Shuffling scheme 3

1.07349 ± 7 pcm/1.01330 ± 6 pcm
1.07087 ± 7 pcm/1.01065 ± 6 pcm
1.07145 ± 7 pcm/1.01205 ± 6 pcm

CRediT authorship contribution statement
Donny Hartanto: Conceptualization, Methodology, Software,
Formal analysis, Validation, Investigation, Data curation, Writing original draft, Writing - review & editing, Visualization. Peng Hong
Liem: Conceptualization, Methodology, Validation, Writing - originaldraft, Writing - review & editing, Supervision.

− 3.633 ± 0.083/− 3.528 ± 0.091− 3.519 ± 0.087/− 3.636 ± 0.092− 3.778 ± 0.081/− 3.636 ± 0.090

Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

− 2.746 ± 0.027/− 2.325 ± 0.031− 2.801 ± 0.029/− 2.443 ± 0.031− 2.996 ± 0.028/− 2.899 ± 0.031
1.136/1.119
1.135/1.118
1.135/1.119

Acknowledgments
The authors would like to thank Dr. Min-Jae Lee of the Korea Atomic
Energy Research Institute (KAERI) for his assistance in using VisIt
visualization software. D. Hartanto also acknowledge the use of the HPC
Facility at the University of Sharjah for part of the work reported in thispaper.

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fuel column and each column is divided into 50 axial zones. The equa­tions used in the calculations are taken from Maruyama et al. (1994) andInaba and Nishihara (2017). The inner fuel compact temperature issketched in Fig. 19, and the maximum fuel temperature is 1099.87 ◦ C,
1295.15 ◦ C, 1195.57 ◦ C for shuffling schemes 1, 2, and 3, respectively.
Although the peak axial power is relatively high in shuffling scheme 1,
the maximum fuel temperature is slightly lower than in the othershuffling schemes because the cold helium coolant flows into the corefrom the top where the peak axial power occurs. In shuffling scheme 2,
the maximum fuel temperature can reach up to 1295.15 ◦ C since thepeak axial power occurs at the bottom of the core near the exit coolant
path. Meanwhile, the maximum fuel temperate in shuffling scheme 3 isabout 100 ◦ C lower than shuffling scheme 2. Table 4 summarizes andcompares the performance of the 5-batch cores. The FTC and MTC are
also presented and they are always negative during the operation.
4. Conclusion and future work
A new technique based on the neutron importance concept to make aprojection of the optimal design parameters obtained from the fueldesign phase to the full core design phase of HTGR has been proposed
and applied to the HTTR operating in a single-batch and 5-batch refu­
eling schemes. In the first step, the fuel composition of the fuel lattice is
optimized to have a minimum fissile content per energy generated (kg/GWd). In the second step, the core calculation is performed. The NC /NHMof the core is calculated by considering the neutron importance of eachregion to the fission reaction and later the NC /NHM of the optimum fuelfrom lattice is projected to the core’s, so they are equal. The TRISO fuelpacking fraction in the core increases, but the fissile loading per energy
generated and the fissile enrichment is still the same between lattice and10