NEUTRON PHYSICAL FEASIBILITY OF SMALL MODULAR DESIGN OF DUAL FLUID REACTOR

Abstract

The Dual Fluid Reactor (DFR) is a fast reactor concept proposed by the Institute of Solid-state-and Nuclear physics (IFK) in Berlin. The design of DFR aims to combine the Gen-IV Molten Salt Reactor (MSR) and the Liquid-Metal Cooled Reactor (SFR, LFR), which means that the molten-salt fuel is no more used as coolant while the heat is removed in a separate loop by liquid lead, to improve these two concepts. Without control rods, DFR is given hope to react and take steps to the change of operation conditions automatically by its inertial negative temperature feedback. Since fuel and coolant are both liquid, the circulation speed of each liquid is considered capable to adjust operational parameters for DFR. The original design of a 3000MWth (Wang, 2017) and a downscaled version of 500MWth (He, 2016) were analyzed in the aspects of reactor physics and thermal-hydraulics. For the practical purpose, this paper has proposed a small modular version of the DFR, which has power output of 2MWth. The reactor with such power level is expected in various applications. Therefore, it is necessary to perform the more explicit analysis on the design than the previous ones. The analysis focuses on the neutronic calculations with the default fuel salt of U-Pu mixture under steady state conditions.

Full text

THE NEUTRON PHYSICAL FEASIBILITY OF A SMALL MODULAR DUAL FLUID REACTOR
Xiang WANG*
Qian ZHANG
College of Nuclear Science and Technology,
Harbin Engineering University
Harbin, Heilongjiang, China
Xun HE
Science and Technology on Reactor System
Design Technology Laboratory,
Nuclear Power Institute of China
Chengdu, Sichuan, China
Zhuoqi DU
Marcus SEIDL
Rafael MACIAN-JUAN
Institute of Nuclear Engineering,
Technical University of Munich
Garching, Bayern, Germany
Konrad CZERSKI
Mariusz DABROWSKI
Faculty of Mathematics and Physics
University of Szczecin
Szczecin, Poland
Keywords: Dual Fluid Reactor; small modular reactor; reactor physics; steady state
ABSTRACT
The Dual Fluid Reactor (DFR) is a fast reactor concept
proposed by the Institute of Solid-State and Nuclear Physics
(IFK) in Berlin. The design of the DFR combines the Gen-IV
Molten Salt Reactor (MSR) and the Liquid-Metal Cooled
Reactor (SFR, LFR), which means that the molten-salt fuel is
no more used as a coolant while the heat is removed in a
separate loop by liquid lead. This improves these two concepts.
Without control rods, DFR can react and change operation
conditions automatically by its inertial negative temperature
feedback. Since the fuel and the coolant are both liquids, the
circulation speed of each liquid adjusts the operational
parameters of DFR. The original design of a 3000 MWth
reactor (Wang, 2017) and a downscaled version of 500 MWth
(He, 2016) were analyzed in the aspects of reactor physics and
thermal-hydraulics. For practical reasons, this paper has
proposed a small modular version of the DFR that has a power
output of 2 MWth. This reactor with such a power level is
expected to be needed in various applications. Therefore, it is
necessary to perform a more explicit analysis of the design
than the previous ones. This analysis focuses on the neutronic
calculations with the default fuel salt of a U-Pu mixture under
steady-state conditions.
1. INTRODUCTION
1.1 Overview
The DFR concept was originally described by A. Huke and
his group in IFK (Huke et al., 2015; Huke et al., 2017). Here,
the differences between the DFR and other liquid-salt- or
liquid-metal-cooled reactors are also discussed. The DFR uses
a chloride-based molten fuel salt to harden the neutron
spectrum. However, the DFR does not combine heat removal
and breeding into one single circuit; instead, it separates the
two functions into two independent circuits. The use of lead as
the primary means of heat removal minimizes the fuel and
breeding inventory.
This paper has proposed a small modular version of the DFR
(smDFR). The thermal power output is about 2 MW. The
reactor system and the corresponding energy transfer module
should be montaged in a standard container (Fig. 1, 2.13 m 
2.18 m  5.69 m), which is a huge challenge for the reactor
design.
Fig. 1 smDFR in the standard container
1.2 Reactor Design
The geometric restraint brings design problems like severe
neutron-leakage to the smDFR as other small-sized reactors.
Therefore, the most important issue is to make the reactor
critical with a low-level enrichment and improve or modify the
design of the original DFR. The basic concept of the DFR is
recalled here in advance for convenience (Fig. 2) (Wang et al.,
2018).
In the DFR concept, the nuclear fission reactions occur
within the numerous molten salt fuel tubes. The heat generated
by the reactions in the fuel tubes is transferred to the coolant
lead. The coolant lead also serves as a reflector. The fluids
related to the nuclear reactor during the normal operation
consist of two loops. In the primary loop, the fuel salt flows
from across the outer surface of the core region through several
cold legs meeting in the inlet distribution zone where the fuel
salt is distributed in the fuel channels of the core region
opening at the top of the inlet distribution zone. The fuel salt
flows up through the fuel tubes reaching the top of the core
region into the outlet distribution zone. The fuel salt is then re-
distributed and flows into several hot legs. Through the
primary pipes, the fuel salt can be sent to a processing unit or

storage tanks when needed. The secondary loop contains
coolant and flows in another separate circuit. The cold coolant
enters the bottom of the reactor through the inlet legs of the
coolant. The stream is distributed through the coolant tubes
located in the inlet plenum and flow through the core region.
The liquid lead flows upwards between the fuel tube arrays and
takes the fission energy within it. At the top of the core region,
the coolant is distributed once more and flows through the
coolant tubes into the outlet plenum. Finally, the coolant
arrives at the coolant outlet nozzles and is directed to the heat
exchange equipment. It cools during this process by
transferring energy to the tertiary working medium. The cold
coolant then flows back through the cold leg into the core
region.
Fig. 2 Working principle of the DFR.
Generally, the main structure remains unchanged but with a
smaller size in the smDFR. The diameter of the core decreases
to 0.80 m, and the diameter of the reactor is limited to 2.0 m
due to the limits of the container. Therefore, the total number
of hexagonally arranged fuel tubes in the center fission zone
of the core dramatically decreases from over 13,000 in the
original design to 823. The height of the core is downscaled to
1.0 m, while the total height of the reactor is also limited to 2.0
m.
The first step in the design of the smDFR is to fulfill the
requirement by using the same molten salt mixture of U-Pu
chlorides as are used in larger designs; thus, it is possible to
compare these two concepts. Next, more fuel options will be
investigated including those with a higher enrichment of
fission/fissile materials. The smDFR has less need for fuel
purification and extraction through an external flow channel
and less expectation on the breeding function because it is only
a power reactor. Therefore, the breeder zone is canceled and
replaced by a reflector: The outside fuel flow channels are
moved from outside of the reactor into the reflector zone near
to the core. The entire primary loop of the fuel is then located
in the reactor: half in the core and half in the reflector. There
are at least three advantages due to this change:
1. The bad neutron economics resulting from the small
size of the reactor have been compensated and
improved;
2. There is an increased heat exchange surface area
between the fuel salt and the coolant lead in the
reflector zone. With the same amount of transferred
heat, the velocity of the lead can be minimized—this
minimizes lead-based corrosion; and
3. The entire primary loop is embedded in the secondary
loop. This is an extra level of shielding for possible
breaks in the primary loop.
The working temperature of the smDFR also decreases
compared to the DFR. Due to the verified strong negative
temperature coefficient of the molten salt, the average
temperature of the fuel is set to ~1175 K, while the coolant
lead is about 850 K. This amount of change is expected to
criticality compensate and reduce the corrosion between the
fluids and structural material.
1.4 Application Parameters
The energy conversion of nuclear energy to electricity for
smDFR can be chosen flexibly depending on the detailed
requirements of the specific applications. Due to its small
power output, the smDFR can be coupled with thermal electric,
thermal photovoltaic, or other advanced small-sized static
energy-conversion modules. Small-sized Stirling engines or
the combined Brayton cycle are other alternatives. Due to
space constraints, this topic will be separately discussed in the
future.
1.5 Modeling
The analysis of the reactor is performed at the full core scale.
The symmetrical one-quartered model used here is shown in
Fig. 3 (horizontal arrangement); Fig. 4 shows the longitudinal
structure. The dark grey represents fuel salt, and the light grey
is the liquid coolant/reflector lead. The structural materials
including fuel tubes in the fission zone with SiC and the vessel
with high temperature/corrosion resistant alloy are white.
The smDFR reactor core has fewer fuel salt tubes (where
fission occurs) than the original DFR. This distinguishes the
fuel tubes. General information on the single fuel salt tube
includes the reaction rates, power generation, and neutron flux;
however, it is approximately obtained by the average of the
entire core results. The main parameters can be retrieved from
Tables 13. The fuel salt used here is the molten salt mixture
of the UCl3 and PuCl3.
Fig. 3 Horizontal section of the smDFR model

Fig. 4 Longitudinal section of the smDFR model
Table 1. Geometry parameters
Parameter (mm)
Tube pitch 25.5
Fission zone radius 400
Fission zone height 1000
Distribution zone height 200
Extra coolant height 300
Reflector thickness 550
Reactor vessel radius 1000
Reactor vessel total height 2000
Fuel tube inner radius (fission zone) 8
Fuel tube outer radius (fission zone) 10
Number of fuel tubes (fission zone) 823
Fuel tube inner radius (reflector) 80
Fuel tube outer radius (reflector) 100
Number of fuel tubes (reflector) 12
Table 2. Temperature parameters
Parameter (K) Parameter (K)
Fuel salt flow-in
Fuel salt mean
Fuel salt flow-out
Reflector flow-in
1150
1175
1200
700
Coolant flow-in
Coolant mean
Coolant flow-out
Reflector flow-out
750
800
850
800
Reflector mean 750
Table 3. Composition parameters
Material Nuclide (wt%)
Fuel salt 238U 52.968
238Pu 0.3076
239Pu 8.6116
240Pu 3.6907
241Pu 1.8453
242Pu 0.9227
37Cl 31.654
Coolant
Reflector
204Pb 0.0140
206Pb 0.2410
207Pb 0.2210
208Pb 0.5240
Fuel tube
12C 0.3010
28Si 0.6990
1.6 Methodology
This work used 3D Monte Carlo calculation code SERPENT
(Leppaenen, 2013) for the different objectives of the physical
feasibility analysis. The results for the neutron physics and
group-constants generation used SERPENT 2.1.30. Each
calculation used 50,000 source neutrons over 200
active/inactive cycles. The ENDF/B-VII nuclear data library
was the default data library and was selected from 238 energy
groups. However, the JEFF-3.1 and JEFF-3.11 are also used in
some calculations because they are the newest nuclear data
libraries that are implemented in the SERPENT code.
2. NEUTRON PHYSICS ANALYSIS
This section describes the stationary neutron physics analysis
including the criticality calculation, geometric design
sensitivity, and thermal sensitivity. The decay constants of the
delayed neutron precursors as well as other important
information are also provided for further studies.
2.1 Criticality Calculation
The assessment of the consistency between different data
libraries is given by the effective multiplication factor
calculation of the smDFR with U-Pu fuel salt in Fig. 5. All
errors (<4E-4) are as well plotted. In this keff calculation, the
result with ENDF7 is considered to be the reference. Based
on the given geometry and conditions, the results with the
ENDF library are smaller than those from the JEFF libraries.
The differences with both JEFF libraries can be as much as
500 pcm, which is much larger than the calculation performed
for the DFR.
The reason that the results with both JEFF are larger than
the results with ENDF has already been described (Wang et
al., 2017). To compare the fission-to-capture ratio, most
nuclides in the fuel composition are consistent over most of
the energy range of interest. Obvious discrepancies are seen
over 1 MeV or below 10 eV for 238U, 238Pu, 239Pu, and 241Pu.
The fission-to-capture ratio is more sensitive in the small
reactor than the large reactor. However, further calculations
are needed to verify this conclusion.

Fig. 5 keff assessment with data libraries.
2.2 Delayed Neutron Data
The results presented here are group constants for the delayed
neutron precursors of the DFR and the smDFR concept—both
of which are calculated with SERPENT 2.1.30. The delayed
neutron precursors (DNP) are divided into six groups
depending on their decay time. Table 4 lists the effective
fractions of the DNPs, while Table 5 shows the decay
constants of the DNPs. These results are achieved for the fuel
salt with zero flow velocity. A forthcoming paper will
describe the movement of the fuel salt to determine the
delayed neutron constants.
Table 4. Effective fraction of delayed neutron precursors
Precursors group DFR smDFR
Total 3.683×10-3 3.764×10-3
1st 8.505×10-5 7.418×10-5
2nd 7.976×10-4 7.572×10-4
3rd 5.723×10-4 5.694×10-4
4th 1.431×10-3 1.501×10-3
5th 6.212×10-4 6.808×10-4
6th 1.757×10-4 1.811×10-4
Table 5. Decay constants of delayed neutrons
Precursors group DFR (s-1) smDFR (s-1)
1st 1.285×10-2 1.276×10-2
2nd 3.002×10-2 3.007×10-2
3rd 1.121×10-1 1.125×10-1
4th 3.203×10-1 3.247×10-1
5th 1.128×10+0 1.169×10+0
6th 6.417×10+0 7.210×10+0
The DFR and the smDFR have a similar total effective
fraction of DNPs where the relative difference between them
is limited to 2%. However, the first DNP group shows a
relative difference of 13%, while other groups have relative
closer results. For the decay constants, the first groups of the
DFR and the smDFR are consistent, while other groups have
larger discrepancies.
The DFR and the smDFR treat the fuel salt stream after the
fission zone and the outlet distribution zone to be totally
different; thus, the fuel salt leaves the reactor in the DFR
while remaining in the reactor in the smDFR. The DNPs with
different lifetimes affects the reactivity depending on the flow
time and the size of the transmission pipelines.
2.3 Neutron Flux
2.3.1 Energetic Distribution
The energetic distribution of the neutron spectrum of the
entire smDFR is shown in Figs. 6 and 7, respectively. The
horizontal axis of both diagrams is labeled with the neutron
energy. Fig. 6 compares the neutron spectrum of the reactor
calculated with ENDF/B-VII, JEFF-3.1 and JEFF-3.11; the
ENDF/B-VII spectrum is the reference. The spectrum of the
smDFR is a typical fast neutron spectrum and matches for the
purpose of this design. The main body of the spectrum
spreads mostly in the energy range of 1 keV~10 MeV and its
peak is near 0.5 MeV. The relative differences with JEFF
libraries show that the spectra with different data libraries
have a good consistency of no more than ±2% in the neutron
energy range of 100 eV to 10 MeV. The relative differences
increase due to lower neutron counts at the lower energy
range.
Fig. 7 normalizes the neutron spectrum of the DFR and the
smDFR. The two spectra nearly overlap the higher energy
side of the peak with a relative difference of less than 20%.
On the lower energy side of the peak, the two spectra are
distinguished from each other. This is because of the size of
the reactor. The DFR is relatively larger, and neutrons are
moderated via collision with internal materials despite also
being a fast reactor. The smDFR is smaller, and the neutrons
have less opportunity to be scattered and moderated before
they escape from the reactor to be absorbed or participate in
nuclear reactions.
Fig. 6 Neutron spectrum of the smDFR

Fig. 7 Normalized neutron spectrum between DFR and
smDFR
2.3.2 Spatial Distribution
The spatial distribution of the neutron flux is plotted in Figs.
8 and 9, which are in the radial and axial directions,
respectively. Fig. 8 shows the radial distribution comparison
between the DFR and the smDFR with a comparable variant
smDFR’—this has no back-flow fuel tubes in the reflector.
The orientation of the fuel tube arrangement does not impact
the calculations. The horizontal axis is labeled with the
percentage of radial coordinates because the DFR and the
smDFR have different sizes; thus, they can be compared.
It is obvious that the DFR has an active zone surrounded
by the reflector and breeder—the spatial distribution of the
flux is deeply suppressed. This region is not noticeable in the
smaller smDFR. The comparison between smDFR and
smDFR’ shows the impact of the back-flow fuel tubes on the
spatial distribution of the neutron flux. This makes it more
convex with a flatter top.
The axial distribution of the flux of the DFR, the smDFR,
and the smDFR’ is shown in Fig. 8, where the horizontal axis
again presents the percentage of the axial coordinate.
The spatial distribution of the neutron flux clearly shows
the reflected shape because the DFR has a larger coolant zone
on both ends of the reactor. The flux of the smDFR shows a
relative concave shape that has the same trend as the DFR. It
is interesting that the flux of the smDFR’ is not as symmetric
as the smDFR. This can be interpreted via the asymmetrical
temperature distribution of the system. In the smDFR concept,
the inflow fuel salt has a lower temperature at the bottom
(negative axial coordinate), and the outflow fuel salt has a
higher temperature at the top (positive axial coordinate). The
asymmetry is not as clear in the smDFR because the back-
flow fuel tubes in the reflector compensate for the spatial
distribution of the flux in the shape.
Fig. 8 Normalized neutron flux in the radial direction
Fig. 9 Normalized neutron flux in the axial direction
2.4 Sensitivity Analysis
The nuclear reactor design is based on criticality and heat
transfer via a multi-x undetermined equation set. However,
this equation set has more than one single solution
mathematically; physically, there is more than one optimal
parameter set to fulfill the request of the reactor design.
Therefore, it is necessary to perform the following sensitivity
analysis.
2.4.1 Geometry Sensitivity
The change of the key parameters in the reactor design
increases the sensitivity of the system because of the smaller
size of the smDFR. This paper selects the pitch between the
fuel salt tubes including the ring radius of the back-flow fuel
tubes in the reflector and their radius (Figs. 1012). The
temperature of the fuel salt in this sensitivity analysis is the
default fuel salt mean temperature 1175 K mentioned in Table
2.
The geometry sensitivity trend is clear: The change
increases the fuel density, and the mass fraction of the reactor
brings positive reactivity. The size decrease leads to negative
reactivity. Fig. 10 shows the relationship of the change of the
fuel tube pitch in 2.522.60 cm as well as ΔReactivity. The
fitting equation suggests that the reactor is sensitive to the

change of the pitch with a coefficient of -1831 pcm/cm.
Fig. 11 shows the relationship of the change of the back-
flow tube ring radius from 54 cm to 64 cm with ΔReactivity.
The error bars are too small to be plotted. The sensitivity
coefficient is about -904 pcm/cm. Fig. 12 shows the
relationship of the change of the back-flow fuel tube radius
and ΔReactivity; the corresponding coefficient is about 2710
pcm/cm.
Fig. 10 ΔReactivity and fuel tube pitch
Fig. 11 ΔReactivity and ring radius of the back-flow fuel
tubes in the reflector
Fig. 12 ΔReactivity and radius of the back-flow fuel
tubes in the reflector
2.4.2 Thermal Sensitivity
A study related to the DFR showed that the reactor has a
significant thermal sensitivity with the given U-Pu mixture
fuel salt and the TRU fuel salt. This includes a very strong
negative temperature feedback coefficient. The calculated
temperature feedback coefficient for the DFR is about -40
pcm/K (Wang et al., 2015).
For the smDFR, the thermal sensitivity is also considered
because it is one of the most important features. This
calculation focuses on the mean fuel temperature and the
reactivity response it brings to the system. The chemical
properties of the mixture molten salt are absent, and the
relationship of the density and the temperature of pure UCl3
(Janz et al., 1975) is adopted. The mean fuel temperature in
the fission zone has a given range of [1125 K, 1225 K], which
covers the valid temperature range of the fuel salt to the
current knowledge (Janz et al., 1975). The increment step is
set to 10 K.
Fig. 13 shows the response due only to the Doppler effect
and the one caused by both the Doppler effect and the density
effect. The horizontal axis labels the fuel salt mean
temperature, and the vertical axis labels the corresponding
change of the reactivity. The trend line helps illustrate that
both effects lead to a negative temperature feedback
coefficient of -68.63 pcm/K, which is even larger than that of
the DFR. At the same time, the results with only the Doppler
effect are not so sensitive to the fuel salt mean temperature
change with a feedback coefficient of -0.13 pcm/K. Thus, the
density effect dominates the thermal sensitivity and is the
most important factor. The reason for the difference of the
temperature feedback coefficients between the DFR and the
smDFR may be the size of the reactor. In a smaller reactor,
the impact of the density change caused by fluctuation of the
temperature is more significant, though the fraction of the
reduced effective amount of the fission material from the
fission zone is the same versus larger reactors.
This key feature ensures the passive safety mechanism of
the smDFR. The system automatically becomes subcritical
when the fuel salt mean temperature rises over a certain point,
i.e., an emergency with a failing cooling system.

Fig. 13 keff and the fuel salt mean temperature
3. CONCLUSIONS
This paper proposed a small modular design, namely, the
smDFR, based on the original DFR concept. Preliminary
neutron physical steady-state calculations have been
conducted, and the fuel salt is considered with a zero flow
velocity at the moment when the snapshot was taken for the
parameters; therefore, the effects due to the effective delayed
neutrons for moving fuel salt in the reactor system are not
considered.
The keff calculation was compared to the results with
commonly used data libraries, and all of the results confirm the
criticality of the system. The effect caused by the loss of the
delayed neutron should be relatively smaller in the smDFR
considering that the fuel salt in the smDFR concept stays in the
reactor during operation (unlike the DFR where the fuel salt
leaves the reactor in the outer pipelines).
The power of the smDFR is 2 MWth, which is actually
based on the energy demand. From a very simple quantitative
estimation, the smDFR should have a better heat transfer
performance than the DFR with its increased pitch and reduced
total number of the fuel tubes. The maximal power output can
be raised to 200 MWth via heat transfer. The accurate number
and conditions must be verified in future calculations.
The energetic and spatial neutron flux describe the neutronic
features of the smDFR. Because of its small size, the smDFR
has a harder spectrum than the DFR. The leakage of neutrons
is also serious because of the small size of the smDFR. The
smDFR has sufficient neutronic stability with possible
changes in the geometry and rector temperature. The most
noticeable is the very strong negative temperature feedback
coefficient, which is about -68.63 pcm/K. We conclude that
the smDFR will be very stable during the operation, and its
response to the change of temperature will be very fast.
However, detailed transient behavior of the system needs
further study. The system will gain extra reactivity with a
smaller pitch, a smaller back-flow tube ring radius, or a larger
back-flow tube radius. However, how to achieve an even
smaller size by balancing the change of the sensitivities and
their impact on the fuel salt and structures requires further
study.
The results show that the design of the smDFR is achievable
from the perspective of neutron physics. However, many
problems remain including the following:
1. The depletion of the fuel salt needs to be calculated with
or without the on-line processing unit. Because of the
minimized size of the reactor, extra reactivity in the
DFR design is used to compensate for the neutron
economy. Therefore, the sustainability and the period
of fuel refreshment must be determined;
2. Since the negative temperature feedback coefficient has
been demonstrated here, further studies are needed to
determine the control mechanism of the system without
control rods. As mentioned in previous studies of the
DFR, this is critically important because the reactor
concept needs this kind of mechanism to change
working conditions and status including startup or shut
down;
3. There are designs of breeder and breeder coolant tubes
just outside of the core (and the reflector) in the original
DFR concept. It would be interesting to determine the
possibility of back-flow fuel tubes acting as breeder
tubes as well as the back-flow fuel salt acting as breeder
materials concurrently.
The heat balance analysis as well as other thermal-hydraulic
calculations are needed including modeling and calculations of
the entire core and the local distribution zone.
Acknowledgments
We thank LetPub (www.letpub.com) for its linguistic
assistance during the preparation of this manuscript.
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