Heliyon 8 (2022) e11540Contents lists available at ScienceDirect
Heliyon
journal homepage: www.cell.com/heliyonResearch articleNumerical simulation for the control rod assembly drop time evaluation in
a LFR
Emmanuel Maurice Arthur a,b,c, Chaodong Zhang a, Seth Ko Debrah b,c, Stephen Yamoah b,efi ,
Lei Wang d,*
a Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui 230031, China
b School of Nuclear and Allied Sciences, University of Ghana, Box AE 1, Kwabenya, Accra, Ghana
c Nuclear Power Institute, Ghana Atomic Energy Commission, Box LG 80, Accra, Ghana
d School of Computer Science, Hefei Normal University, Hefei, Anhui, 230601, China
e Nuclear Power Ghana, P. O. Box KA 9152, KIA-Airport-Accra, GhanaA R T I C L E I N F O
Keywords:
Lead-cooled fast reactor
Lead–Bismuth Eutectic
Control rod assembly
Drop time* Corresponding author.
E-mail address: wanglei_petro@163.com (L. Wan
https://doi.org/10.1016/j.heliyon.2022.e11540
Received 31 January 2022; Received in revised for
2405-8440/© 2022 Published by Elsevier Ltd. ThisA B S T R A C T
During scram, the Control Rod Assembly (CRA) is quickly dropped into the core and as well, if any of the
operating limits are exceeded, the CRA is dropped into the core within a stipulated time to shut down the reactor
power as soon as possible. In this study, the Computational Fluid Dynamics (CFD) approach was used to inves-
tigate the CRA drop dynamics of a lead-based research reactor. To simulate the flow field around the CRA in the
guide tube, a 3-dimensional model of the CRA in the LBE-filled guide tube was developed and discretized; and the
averaged Navier-Stokes equations coupled with the dynamic mesh method were adopted. Considering the large
mesh deformation in the LBE coolant domain while the CRA drops, the recently developed FSI method in the CFX
code, namely the rigid body approach, was adopted, which falls under the monolithic method. In this method, the
translational CRA wall, which is partially immersed in the LBE, was set as a rigid body. It has the advantage of
updating and improving the mesh quality through the mesh and re-meshing technique during the process of
computation. Compared with the results of the work done in the available literature, the CFD model proved to be
applicable and reliable. From the results, the inherent high density among the LBE flow characteristics had the
most influence on the drop time. The mass of the CRA impacts its driving force so that the drop time reduces when
the CRA mass is increased. In conclusion, the method used in this study can be applied to compute and predict
significant parameters which can serve as a reference for a suitable design of the CRA and its drive mechanism in
the case of modification for safety.1. Introduction
In the nuclear reactor, the control rod assembly (CRA) is used to
control the reactor power and as one of the internal structures for
ensuring safety, it is used for scram. During scram, the CRA is quickly
dropped into the core. Moreover, if any of the operating limits are
exceeded, the CRA is dropped into the core within a stipulated time to
shut down the reactor power as soon as possible. On receiving the scram
signal, the CRA is released to drop into the reactor core by its weight
under gravity. Thus, the drop time and falling velocity of the CRAmust be
estimated for safety evaluation. Remarkably, the safety requirements of a
nuclear power plant include strict limitations on the maximum drop time
of CRAs, which serves as a safety index for operation. For instance, ing).
m 6 May 2022; Accepted 4 Nove
is an open access article under tFebruary 1995, several CRAs of the 944 MWe nuclear reactors in Daya
Bay in China failed to comply with these requirements. The developer of
the Daya Bay nuclear reactor, Electricite' De France, as a matter of ur-
gency, undertook a research programme to better understand and solve
the problem (Hofmann et al., 2000).
The drop time of the CRA is affected by its structural design and the
coolant state as it falls (Cheng et al., 2020). The validation of the per-
formance of the drop of the CRA is an essential aspect of the safety
analysis of a nuclear power plant. Thus, developing a computer program
that is able to compute the drop of the CRA is necessary for validating and
improving the design of the CRA as well as its drive mechanism (Zhou
et al., 2013). Theoretical studies are usually simplified and easy to use.
Meanwhile, it can be very difficult and sometimes impossible to depictmber 2022
he CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
E.M. Arthur et al. Heliyon 8 (2022) e11540the real behaviour of real phenomena with the use of the theoretical
models.
These days, computers are becoming extremely powerful when it
comes to the ability to mimic real scenarios. In effect computational fluid
dynamics (CFD) is evolving with great capabilities to study fluid-
structure interaction. With this development, theoretical studies have
been useful, as models from such studies have been implemented in CFD
codes for use. It is therefore imperative to develop the models from the
available theoretical studies into CFD codes to improve the analysis. With
respect to this, CFD analysis has proven to be a useful and convenient tool
in developing innovative designs of the CRA and CRDM for reactor
shutdown dynamics. As a result, several researches have been done to
study the drop of the control rod using the CFD approach (Cheng et al.,
2020; Hofmann et al., 2000; Huang et al., 2018; Huh et al., 2010, 2011,
2013, 2018; Kim et al., 2011, 2015; Lee et al., 2016, 2017; Profir et al.,
2015, 2017; Oh et al., 2015; Rabiee and Atf, 2016; Singh et al., 2014; Son
et al., 2019; Sun et al., 2014; Yoon et al., 2007).
However, these studies are mainly for second-generation reactors,
specifically the Pressurized Water Reactors (PWRs). Although, for the
third-generation reactors (such as the AP1000), the research experience
from the second-generation reactor can be used as reference, yet the
relevant research theory still needs to be improved and developed. For
the fourth generation of nuclear reactor technology, especially the
research on the CRA drop in the lead-cooled fast reactors (LFR), there is a
lack of relevant experimental equipment as well as experience. Generally,
studies on control rod drop in the non-water coolant is limited compared
to that in water coolant. However, safety requirements of the water-
cooled reactors are not same as the generation four (Gen IV) nuclear
reactors.
Presently in this study, the dynamics of the CRA as it drops into the
guide tube of the lead-cooled fast reactor is studied using the dynamic
mesh technology of the CFX code, which can appropriately solve fluid
boundary motion problems (Ferrini et al., 2016; Peng et al., 2012; Sui
et al., 2013). This technology of CFX possess outstanding capabilities for
simulating the drop behaviour of the CRA and can effectively avoid
complicated theoretical derivation. Besides, it could analyse the transient
coolant flow domain and ascertain vital parameters including the CRA
drop time, velocity as well as coolant resistances against the CRA.
Evidently, as a Gen IV nuclear reactor, the China Lead-based fast
research reactor (CLEAR-I) has high neutron flux with complex safety
design and thus, study into the dynamics of the drop of its CRA is pro-
spective and merits attention. However, according to the available
literature, no work has been done on CLEAR-I on the use of CFD to
analyse the drop dynamics of its CRA. This paper aims at methodologi-
cally developing a general and well-founded CRA drop CFD method that
could analyse the CRA drop dynamics in varying LFR types, especially
CLEAR-I, using CFX dynamic mesh technology.
2. Materials and method
2.1. Description of the CLEAR-I CRA and LBE-filled guide tube geometry
The pool-type fast reactor, CLEAR-I is an innovative Chinese tech-
nology archetype for the LFR, which uses Lead Bismuth Eutectic (LBE) as
the primary coolant. The reactor technology spearheads the Chinese
Academy of Sciences' (CAS) Accelerator Driven Subcritical (ADS) trans-
formation system (Arthur et al., 2020; Wu et al., 2016). In terms of safety
design, the CRA of CLEAR-I comprises seven (7) individual control rods
banded in a stationary hexagonal guide tube. The instance of free fall, the
CRA drops through the guide tube into the core. The mass of the active
part (the part that is boron-enriched and absorbs the neutrons) of the
CRA is 30 kg, which is inadequate to allow for a drop into the
high-density LBE coolant. Therefore, 220 kg balanced weight (inactive
part) is put above the active part of the CRA to allow for a free fall under
gravity. At the initial stage of the fall, the active part of the CRA (800
mm) is immersed totally into the fluid (Arthur et al., 2020). The shape2
considered during the drop analysis of the CRA for simplicity, is a circular
CRA initially partially immersed in a circular guide tube.
The geometry for the study considers a 3-dimensional model of the
test section of the actual model of the CRA and guide tube (see Figure 1).
The hexagonal shape of the guide tube is considered as circular in order
to reduce the geometrical complexity and along with it, computational
demand. Moreover, reducing the hexagonal shape of the CRA to circular
will help to reduce or avoid the uncertainties in the simulation. In the
guide tube, the CRA is initially partly (halfway) immersed in the LBE
coolant. The dimensions of the guide tube and CRA is shown in Table 1.
Since the geometry for the study mimics the test section of the actual
model, the guide tube has an inlet at the bottom and an outlet at the top.
The geometry considers the active and the inactive part as one unit and
uses the sum of their weight. The mass of the active part is 30 kg and that
of the inactive part is 220 kg; and as such, gives a total rod mass of 250 kg
(see Table 1).
2.2. Analysis conditions
From the primary LBE pump through the inlet the flow rate of LBE,
flowing into the guide tube is estimated as 80.58 kg/s and the temper-
ature of the incoming LBE is 350 
C (Arthur et al., 2020). The flow rate of
LBE flowing through the inlet was assumed constant. The density and
viscosity change of LBE due to the heat generated by the fuel rod and the
impact of the drop velocity in the heating of the control rod was not
considered due to the transient nature of the study. Since the drop is a
freefall, rotation of the CRA will not occur during the fall and the moving
CRA was assumed a one-dimensional translational motion in the direc-
tion of the gravitational force. With the CRA typically falling by gravity,
the gravitational acceleration applied during the analysis is 9.81 m/s2.
Particularly for the analysis of this study, the domain requires three
specifications. Firstly, the region defining the LBE fluid flow or the
CRA/guide tube wall. The domain is formed from one or more 3D
primitives that constraints the region occupied by the LBE fluid and CRA.
Secondly, the physical nature of the LBE fluid flow determines the
modelling of specific features such as buoyancy. Lastly, the properties of
the materials in the region.
2.3. Analysis method
To analyse the phenomenon of the CRA drop dynamics due to gravity
within the guide tube, the rigid body equations of motion was solved in
conjunction with the flow equation that accounts for the LBE flow
resistance inside the guide tube. This was done with the use of the CFX
solver, which is a code, based on finite volume method (FVM). As the
CRA drops, the generated grid is twisted and deformed continuously due
to the sliding mesh technique and the deforming mesh technique that
was used. In the model discretization, the tetrahedral mesh was gener-
ated for the analysis area that dealt with the deformation of the grid of
the flow domain due to the moving CRA. To ensure accuracy of results, a
dense grid in the expected area of deformation, the sliding surface po-
sition and the interface was constructed. It was observed that the size of
each element on the face affected the results of the analysis. Therefore, by
making the element size of the two sliding surfaces the same, and very
small, the solution is sufficiently converged at each time step and as well,
the magnitude of the error in the sliding surface is minimal.
The number of elements carefully chosen for the entire analysis
domain is about 48,805 after a sensitivity analysis conducted (see
Table 2) and Figure 2 is used to show the grid of the CRA. During
operation of the reactor, the CRA is fixed in the reactor. However, the
coolant flows at a constant rate via the bottom of the guide tube and in
the CRA flow path to the top. To simulate the turbulence effect on the
viscous term of the mass equation, the frequently used Reynolds-
averaged Navier–Stokes (RANS) turbulence model called the standard,
K-ε model was used because the model has proven useful for free-shear
layer flow (Profir et al., 2015). Moreover, the time step for the
E.M. Arthur et al. Heliyon 8 (2022) e11540
Table 1. Design parameters of the CRA and Guide tube.
Parameter Value
Mass of CRA active part (kg) 30.0
Mass of CRA inactive part (kg) 220.0
CRA diameter (mm) 100.0
CRA active height (mm) 800.0
Guide tube diameter (mm) 141.5
Figure 1. Simplified CRA geometry in 3-dimensions.
3
transient analysis was set to 0.001 s. The discretization scheme used in
the equation of motion and momentum is high-resolution advection
scheme and second order backward Euler transient scheme. For the
turbulence kinetic energy equation and dissipation rate, the upwind
advection scheme and first order backward Euler transient scheme was
used.
3. Results and discussion
3.1. Verification analysis
For verification, the CFD method being used was compared to the
drop time and velocity ascertained from the theoretical approach under
the normal operating conditions by Arthur et al. (2020).
The drop time ascertained from the theoretical approach under the
normal operating conditions of the CLEAR-I is about 576.8 m (Arthur
et al., 2020) and that ascertained from the CFD approach is about 585 m.
This shows that there is a good agreement between the two approaches
used for the study as a difference of 1.4 percent is observed between the
two drop times as shown in Table 3.
3.2. CRA drop in the LBE environment under normal condition
Under the normal operating condition of the CLEAR-1, the weight of
the CRA is about 2452.5 N as it drops under the acceleration due to
gravity. The LBE fluid with density of 10,259 kg/m3 flows at 80.58 kg/s
into the guide tube from the inlet, which is located at the bottom and
flows out from the top of the guide tube. The estimated total differential
pressure is 5.55 kPa for the required flow of 80.58 kg/s in the CRA
deposited position. To mimic exactly how the CLEAR-1 operates, the
initial velocity and time was set to 0 m/s and 0 s respectively, whereas
the initial position of the CRA was set to 800 mm. This means the CRA is
800 mm above the bottom of the guide tube where the CRA is supposed
to end its fall. Therefore, at the end of the drop the CRA position is ex-
pected to be 0 m.
3.2.1. The relationship between CRA position and time
In Figure 3(a), it can be observed that the net force is very large at the
beginning of the CRAmotion. However, it decreases as the velocity of the
CRA increases, and tends to approximately zero at the end, once the CRA
reaches the terminal velocity. Initially when the drop is initiated, the
fluid resistances are high and pushes the CRA up a bit until the CRA gains
momentum through the LBE fluid. At the start of the CRAmotion, the LBE
resistance is high, which dramatically pushes up the CRA to a height of
800.01 mm, slowing down its motion. However, the CRA begins to gain
momentum against the LBE resistances after a short time (about 8 m),
when it is pushed up to a maximum height of about 800.13 mm away
from its initial position of 800 mm. From this maximum height, it takes
the CRA about 14 m to drop to reach its initial height (800 mm) and then
continues in its drop process. By this time, the CRA has gained enough
impelling force against the resistance of the LBE fluid. From Figure 3(a),
when the CRA is dropped with the pressure difference (5.55 kPa) under
the operating condition, the CRA reaches the maximum velocity of 2.79
m/s (see Figure 3(b)) during the drop. The computed drop time is 585 m.
E.M. Arthur et al. Heliyon 8 (2022) e11540
Table 2. Mesh sensitivity. Table 3. Comparison of the theoretical and CFD approaches.
Mesh Elements Drop Time (ms) Computational Time (s) Drop Characteristics Theoretical (Arthur et al., 2020) CFD
A 25415 583.65 1015 Drop time (ms) 576.8 585
B 39904 585.00 1916 Velocity (m/s) 2.81 1.79
C 48805 585.00 4904
D 66008 585.00 15500
E 80142 585.00 41200Considerably, the pressure difference between the top and bottom ends
of the guide tube causes upward flow of LBE against the CRA. This up-
ward flow which ensures cooling also offers an amount of resistance
against the drop of the CRA.
By principle, it can be observed from Figure 3(a) that the
displacement-time curve has a changing slope. It is observed that the
displacement curve is initiated with a very small slope and begins curving
sharply (downwards) towards a large slope. The curve of changing slope
is a sign of accelerated CRA motion (that is, changing velocity) resulting
from the driving force. By applying the principle of slope, it is easy to
conclude that the CRA displacement depicted by the curve is moving
with a negative velocity (since the slope is negative) and this obeys the
coordinate frame defined in the numerical simulation code used for this
study. Furthermore, the CRA drop beginning with minimal velocity (the
slope begins small) and ending with a large one (the slope becomes large)
implies that the CRA is moving downwards with increasing speed (the
small velocity turns into a larger velocity).
3.2.2. The relationship between velocity and time
The CRA in the LBE fluid undergoes a net upward buoyant force at the
beginning of the drop process and bobs as it pushes into the LBE fluid.
The buoyant force rises when the CRA pushes down as a result of increase
in the volume of displaced coolant and the CRA experiences a net upward
force. However, when the CRA bobs, less coolant is displaced to reduce
the buoyant force to result in giving rise to a net downward force. This
phenomena is explained by Figure 3(b) where the CRA velocity curveFigure 2. Model (a) grid and (
4
falls from the time of initiating the drop until about 3 m. After this time,
the velocity begins to increase steadily. Generally speaking, the magni-
tude of the buoyant force is proportional to the LBE coolant volume
displaced by the CRA and militates against the velocity of the CRA. The
velocity contours around the CRA at height of 800 mm for varying
density are plotted in Figure 4. As expected, an area of high velocity is
observed around the surface of the CRA. This high velocity is caused by
the driving force. However, the velocity decreases with distance from the
top of the CRA in downstream.
In the drop dynamics, the CRA drops at its terminal velocity for a
constant speed because of the resistance exerted by the coolant through
which the CRA drops. Considering the impacts of the buoyancy, the drop
of the CRA (under its inherent mass) through the LBE coolant can attain a
terminal velocity if the net force acting on the CRA approaches zero.
Moreover, once the terminal velocity is achieved the CRA weight bal-
ances exactly with the upward buoyancy force and resistances of the LBE
coolant.
3.3. LBE resistance on CRA movement
Under normal operating conditions, the differential pressure and
viscous friction resistances with respect to position and time are depicted
in Figure 5(a) and (b) respectively. Both the differential pressure and
viscous friction resistances increase to militate against the driving forces
of the CRA as it drops into the LBE fluid with position and time. However,
the increase attains a maximum and reduces slightly before the drop is
ended. For this case, the initial differential pressure and viscous friction
resistances across the CRA are small at the beginning of the transient, but
gradually increase substantially as the CRA gathers speed.b) partially enlarged view.
E.M. Arthur et al. Heliyon 8 (2022) e11540
Figure 3. CRA drop in the LBE medium under normal conditions.Therefore, the effect of higher initial acceleration is neutralised by the
increased differential pressure and viscous friction resistances during the
transient phase. Notably, in the process of the CRA drop both the viscous
friction and the differential pressure resistances grow with time and at
every position, the magnitude of the viscous friction resistance in the LBE
fluid is higher than that of the differential pressure resistance. The
viscous friction resistance exerted on the weight of the CRA as it drops
typically relies on the speed of the CRA (contrary to simple friction).
Notably, experimental works have demonstrated that for laminar flow,
the viscous resistance is proportional to speed, whereas for turbulence,
viscous resistance is proportional to the square of the relative speed. For
the turbulent flow regime, the resistance increases dramatically and be-
haves with greater complexity (Rabiee and Atf, 2016). However, for the
laminar flow regime, the viscous friction resistance is proportional to the
LBE fluid viscosity, the CRA characteristic height as well as its velocity.
All of which is plausible—the more viscous the LBE coolant and the
higher the mass of CRA, the more resistance expected.
The pressure contours within the fluid domain at various time is
represented in Figure 6. It is observed that an area of high pressure in the
LBE can be detected at the bottom of the CRA. This area has a higher
pressure as the CRA velocity increases. On the other hand, an area of low
pressure at the outlet and a relatively high-pressure region can be
observed in the wake of the CRA. The velocity of the moving CRA affectsFigure 4. Velocity contour of C
5
the pressure distribution in the LBE thus, as the CRA accelerates with
time within the LBE fluid, the pressure in the LBE fluid increases until the
CRA gets to a rest position. Additionally, it is observed that the maximum
pressure distribution in the LBE fluid reduces with time as the CRA drops
into LBE fluid. This can be explained by the fact that, with constant
weight of the CRA, the pressure increases as the area of the CRA in the
fluid increases. Thus, as the CRA pushes its way towards the bottom of
the guide tube, the maximum pressure distribution which is normally
seen beneath the falling CRA reduces.
The total resistance in the LBE against the driving force of the CRA
during the drop process includes the viscous friction and differential
pressure resistances as well as the buoyancy of the LBE fluid. In
Figure 7(a), the total resistance in the LBE with position is depicted. It is
observed that, the total resistance of the LBE increases exponentially as
the CRA drops into the LBE fluid. This is anticipated because, the LBE
resistance increases with the CRA velocity relative to the LBE flow. On
the other hand, the total resistance in the LBE with time is depicted in
Figure 7(b). It is observed that, at the start of the CRA drop, the LBE
resistance increases exponentially with time and attains a maximum. The
curve begins to fall slightly until it completes its trip at about 585 m.
Remarkably, comparing the graph of the total resistance of the LBE to
the graph of viscous friction and differential pressure resistance (see
Figures 5 and 7), it is observed that the magnitude of the total resistanceRA and LBE flow domains.
E.M. Arthur et al. Heliyon 8 (2022) e11540
Figure 5. LBE Differential Pressure and viscous friction resistances against CRA drop.
Figure 6. Pressure contour of the LBE flow domains.is far higher than that of the viscous friction and the differential pressure
resistances. This vast hike in the magnitude of the total LBE resistance is
as a result of the inclusion of the resistance due to buoyancy of the LBE
fluid which is also due to its extremely high density (about 10,258 kg/
m3). The magnitude of the resistance due to buoyancy of the LBE fluid
against the driving force of the CRA alone is about 1264.7 N (see
Figure 8) and the average values of the viscous friction and differential
pressure resistances are 46.4 N and 32.8 N respectively. Clearly, the value
of the buoyancy resistance is constant in time and will increase when the
LBE density increases. Furthermore, the differential pressure and viscousFigure 7. Total resistance of L
6
friction resistances are transient terms which tend to zero once the mo-
tion of the CRA becomes steady. It is also clear that the differential
pressure resistance is small, accounting for about 2.4 percent effect on
the driving force and this is followed by the viscous friction resistance
which also account for about 3.5 percent effect on the driving force of the
CRA. However, the buoyancy of the LBE has larger contribution to the
LBE resistance and accounts for about 94.4 percent effect on the driving
force of the CRA, particularly in the accelerating phase of the motion. As
expected the resistance force against the driving force of the CRA also
increases as the velocity of the CRA increases. Moreover, it can be seenBE against the CRA drop.
E.M. Arthur et al. Heliyon 8 (2022) e11540
Figure 8. LBE resistances during the CRA drop.that the value of the resistance due to buoyancy remains constant
(Figure 8(a) and (b)) throughout the LBE in the CRA drop process.3.4. LBE mass flow rate variation on CRA drop
In the simplified model for the study, the guide tube has no bends and
so form loss were not considered in the losses of the frictional model. In
view of this, the mass flow rate in the guide tube is almost the same
everywhere in the guide tube. Generally, knowing the effect of the mass
flow rate on the drop time is very important because the direction of flow
of the LBE from the down comer into the guide tube is against the di-
rection of the CRA while it drops. A noteworthy relation is that the
thermal power produced by a nuclear reactor directly relates the coolant
flow rate as well as the temperature difference across the core. In terms of
thermodynamic, the heat generation as well relates to the temperature
difference of the coolant across the core and the flow rate of the coolant
through the core. Therefore, reactor core size depends on and is limited
by the mass of coolant that flows through the core.
3.4.1. The profiles of CRA position with time
In Figure 9(a), the CRA position with time for varying the LBE mass
flow rate is presented. It can be seen that the various position curves for
the given variation start at the same point and flattens for a distance of
about 795 mm and detach after that time. As expected, the drop time isFigure 9. LBE mass flow rate var
7
worsened for increasing magnitude of the LBE flow rate and the meaning
to this as a result of the increasing mass flow rate can be found in the
behaviour of the fluid resistance.
3.4.2. The profiles of CRA velocity with time
In Figure 9(b), the CRA velocity with time for varying mass flow rate
of the LBE fluid is presented. It can be observed as the mass flow rate of
the LBE increases, the velocity of the CRA reduces. In the CLEAR-I, the
flow of the LBE into the guide tube is against the direction of the control
rod, which means that as the CRA drops downward, the LBE fluid flows
upward. This flow configuration increases the fluid resistance to reduce
the terminal velocity and hence, increases the drop time.
3.4.3. The profiles of differential pressure resistance
The differential pressure resistance with position for varying LBE
mass flow rate is depicted in Figure 10(a). It can be seen that as the LBE
flow rate increases; the CRA does not get to enter the fluid easily as it
bobs for a while before entering the fluid. This is a safety concern as a bit
of delay is found at the initially stages when the drop is initiated, and this
is part of what leads to a drop time increase for increasing mass flow rate.
Moreover, with higher flow rates, the driving force of the CRA is resisted
even halfway before getting close to the inlet where the resistance is also
more. The resistance of the fluid due to differential pressure has effect on
the CRA driving force and as has been seen, increases when the drop isiation on the CRA drop time.
E.M. Arthur et al. Heliyon 8 (2022) e11540
Figure 10. Differential pressure resistance with for varying mass flow rate.initiated. The magnitude of the increase depends on the mass flow rate
and the velocity of the CRA. At the initiating of the CRA drop, the
magnitude of the differential pressure is what decides how high the CRA
is pushed up before gaining momentum to drop into the LBE domain.
Moreover, halfway of even before (depending on the magnitude of the
mass flow rate) the CRA reaches the bottom, there is some decrease in
resistance that is perhaps, caused by the flow of the fluid from the inlet.
Thus, as the CRA gets to the end of the trip, the resistance due to dif-
ferential pressure keeps reducing as the CRA velocity reduces. This
eventually causes a high drop time of the CRA.
3.4.4. The profiles of viscous friction resistance
In Figure 11(a), the viscous friction resistance with position as the
CRA drops the guide tube for varying mass flow rate is presented. The
delays in the drop time from the viscous resistance due to increasingmass
flow rate is obvious as the delay starts from the beginning of the drop and
somewhere during the drop where the resistance has reached its
maximum. At high mass flow rate, the viscous friction resistance is high
immediately the drop is initiated and that contributes to the bob of the
CRA. Therefore, there is some time spent by the CRA to gather mo-
mentum to drop down into the LBE fluid. Moreover, when the CRA had
entered the LBE fluid domain with the driving force while accelerating,
the viscous friction resistance increases rapidly until it gets to a
maximum to slow down the CRA. For a low flow rate, this happens at the
point where the CRA approaches the end of the trip. However, as theFigure 11. Viscous friction resistan
8
mass flow rate increases further, the maximum viscous friction resistance
is seen halfway or less, in the CRA drop.
A notable result from the increase in the LBE viscous friction resis-
tance against the CRA speed is that, in dropping through the LBE coolant,
the CRA will not continue to indefinitely accelerate (as this is possible if
the LBE resistance is neglected). Rather, viscous friction resistance rises
to slow the CRA acceleration until it approaches zero and a terminal
speed (also called the critical speed) is reached. As soon as this occurs, the
CRA continues to fall at constant speed (the terminal speed). There is a
viscous friction resistance on the CRA that depends on the viscosity of the
fluid and the differential pressure resistance as well as the size of the
CRA. Nevertheless, also a buoyant force is dependent on the density of
the CRA relative to the LBE coolant. However, the terminal velocity will
be maximum for low-viscosity fluids and high density CRA with small
base area.
The mass flow rate has direct effect on the differential pressure
resistance and the viscous friction resistance than on the buoyancy
resistance. In that case, the variation in the total resistance in the LBE
with position and time when the mass flow rate is varied comes because
of the variation in the resistance due to differential pressure and viscous
resistance. When the mass flow rate is increased, the initial observation is
the buoyancy that pushes the CRA up for a while and thereafter, it is
released to drop, the pressure difference and viscous friction resistances
coming into play. However, at high mass flow rate, the total resistance at
the start of the drop is high and its effects contributes to the delay of thece for varying mass flow rate.
E.M. Arthur et al. Heliyon 8 (2022) e11540CRA drop by pushing it to a significant height before starting to drop.
Moreover, while dropping, because the mass flow rate is high, the
maximum resistance of LBE is also high and slows the CRA before getting
to the end of the drop. The effect is an increase in the drop time of the
CRA, which is a safety concern. The behaviour of the LBE resistance due
to the mass flow rate variation is very necessary in the nuclear reactor
operation. This is because the heat transfer at the core of the reactor is
dependent on the mass flow rate of the coolant, among other factors. A
considerable magnitude of the flow rate of the coolant is needed to take
away the heat accumulated in the primary loop. However, the flow rate is
also directly proportional to the resistance that militates against the
driving force of the CRA. Therefore, choosing the appropriate mass flow
rate of the coolant is a gamble between heat transfer and CRA drop time
quality.
3.5. CRA mass variation on the CRA drop in the LBE medium
3.5.1. The profiles of CRA position with time
The position of the CRA with time for varying the CRA mass during
the drop process is shown in Figure 12(a). It is observed that the increase
in the mass of the CRA has some influence on the drop time, as it is a
contributing factor that drives the CRA. In other words, the weight of the
CRA is the product of the mass of the CRA and the gravitational accel-
eration. Thus, the driving force is a function of the mass of the CRA. In
that case, as the mass of the CRA increases, although the CRA bobs to
height, the waiting time there is minimal as well as the maximum height
at which the CRA is pushed up. Consequently, the more the mass of the
CRA the less time it takes the CRA to drop into the core and the converse
is true.
3.5.2. The profiles of velocity with time
It has been gathered that when the mass of the CRA increases the
driving force increases and the velocity of the CRA increases signifi-
cantly. Remarkably, when the CRA mass was 125 kg and 250 kg, the
LBE resistance reduces the maximum velocity but at a mass of 375 kg
and 500 kg, the maximum velocity is maintained until the end of the
drop (see Figure 12(b)). Nevertheless, the increase in the driving force
of the CRA as a result of the increased mass of the CRA leads to the
increase in the terminal velocity and hence, a decrease in the drop time
of the CRA. In the CLEAR-1 architecture, the diameter of the CRA is
about 70.7 percent of the guide tube diameter and this means the CRA
can enter the guide tube with leaving some annular region at the sides
after displacing the fluid. The CRA diameter is not large enough to
achieve certain mass that can still help in an easy drop, thus for the
CLEAR-1 a counterweight is added on top of the active part of the CRA
to make the drop possible.Figure 12. CRA mass varia
9
3.5.3. The profiles of differential pressure resistance
In Figure 13(a), the LBE differential pressure resistance with position
for varying CRA mass is depicted. It is observed that the differential
pressure resistance is related to the velocity of the CRA, and the differ-
ential pressure has adverse effect on the CRA as it accelerates. As the CRA
mass is increased, the velocity of the CRA increases which increases the
differential pressure resistance but unfortunately, the driving forces in-
crease more than proportionately as compared with the LBE resistance.
Therefore, the resistance due to differential pressure is not able to slow
the CRA down significantly during the drop and gains a higher magni-
tude rather at the end of the drop. When the weight of the CRA is more,
say 375 kg or more, the drop does not face any disturbances arising from
the differential pressure resistance and this enables the CRA to keep an
increasing velocity until the end of the drop. In effect, the drop time can
be kept well within an acceptable range to ensure the safety of the nu-
clear reactor operation.
Figure 13(b) shows the differential pressure resistance with time as the
CRA mass varies. The distribution of the differential pressure resistance
with time and position in the drop process of the CRA is not constant but
rather depends on the magnitude of the CRA mass. When the CRA mass is
high, the differential pressure force increases due to increased weight. The
increased weight affects the driving force to increase the acceleration of
the CRA. In that case, the CRA does not take much time to get to a given
position in the LBE-filled guide tube. Although at the beginning of time,
the CRA bobs despite its increased weight, the LBE fluid is not able to hold
the CRA for far too long before dropping. Notably, the differential pres-
sure resistance of the 125 kg curve tends to be constant due to its speed
gradually approaching a uniform speed. However, for the 250 kg, 375 kg
and 500 kg curves, the resistance curvewill increase due to the continuous
increase in speed. The slope of the change increases continuously and this
is because the differential pressure resistance changes with the square of
the speed, but the increase in the slope also shows a decreasing trend with
the decrease in the increase in speed.
3.5.4. The profiles of viscous friction resistance
In Figure 14(a), the LBE viscous friction resistance with position for
varying CRA mass is depicted. It is seen that the viscous friction resis-
tance distribution of the CRA at a given position while the CRA drops is
observed to be affected by the mass of the CRA. The viscous friction
resistance curves over time for varying the CRA mass increase differently
based on the mass of the CRA. The CRA increases to increase its velocity
and when the velocity is increasing, the relative velocity between the
fluid increases and increases the viscous friction resistance of the LBE
fluid. When the CRA mass is below 250 kg, it is observed that getting to
the midway to the drop time or even less, the viscous friction resistance
attains a maximum and begins to reduce until the drop is ended.tion on the drop time.
E.M. Arthur et al. Heliyon 8 (2022) e11540
Figure 13. Differential pressure resistance for varying CRA mass.
Figure 14. Viscous friction resistance for varying CRA mass.However, for a CRAmass above the 250 kg, the viscous friction resistance
attains the maximum either close to the end or at the end of the drop and
reduces until the end of the drop.
The distribution of the differential pressure resistance with time and
position in the drop process of the CRA is not constant but rather depends
on the magnitude of the CRA mass. When the CRA mass is high, the
differential pressure force increases due to increased weight. The
increased weight affects the driving force to increase the acceleration of
the CRA. In that case, the CRA does not take much time to get to a given
position in the LBE-filled guide tube. Although at the beginning of time,
the CRA bobs despite its increased weight, the LBE fluid is not able to
hold the CRA for far too long before dropping. Notably, the differential
pressure resistance of the 125 kg curve tends to be constant due to its
speed gradually approaching a uniform speed. However, for the 250 kg,
375 kg and 500 kg curves, the resistance curve will increase due to the
continuous increase in speed. The slope of the change increases contin-
uously and this is because the differential pressure resistance changes
with the square of the speed, but the increase in the slope also shows a
decreasing trend with the decrease in the increase in speed.
It can be seen that the 300 kg CRA drop curve, the change trend is the
same but gentler. The disturbance of LBE flow resistance is more obvious
for low rodmass, thus, when the total mass of the CRA is 125 kg, it cannot
meet the safety requirements. However, as a comparison, it was revealed
intuitively that the resistance time curve gradually changes from a para-
bolic form with time and approaches a straight line. This is due to the
gradual increase of buoyancy, differential pressure resistance and viscous10frictional resistance. In the mid part of the drop, the force reaches equi-
librium with the mass of the CRA, the acceleration approaches 0, and the
CRAmoves at a constant speed. In addition, under normal conditions, the
increase of gravity affects the slope of displacementwith time curve and as
the CRA weight increases, the initial acceleration gradually approaches
the acceleration due to gravity the degree of the influence of the CRAmass
gradually decreases. This is because in the case of the high mass of the
CRA, the influence of the LBE resistance from the mass flow rate is rela-
tively small. When the mass of the control rod decreases, the influence of
the LBE resistance from the mass flow rate begins to manifest.
4. Conclusion
The CLEAR-I is one of the Chinese technology archetypes for the lead-
cooled fast reactors (LFR)whichmarks the leading edge of the Accelerator
Driven Subcritical (ADS) transformation system of the Chinese Academy
of Sciences (CAS). To study the CRA drop of CLEAR-I under gravity within
the guide tube, the rigid body equation of motion was coupled with the
flow equation that accounts for the LBE flow resistance inside the guide
tube. These equations were solved with the finite volume method (FVM)
based ANSYS CFX solver. Using the sliding mesh and deforming mesh
techniques, the generated grid is twisted and deformed continuously as
the control rod drops into the LBE coolant in the guide tube. From the
simulation, the relationship between time, displacement, velocity as well
as resistance against the drop of the CRA and vital safety variables
including the drop time and velocity of the CRA were found. The CFD
E.M. Arthur et al. Heliyon 8 (2022) e11540analysis done has been carefully fashioned to mimic the exact test section
for the study and the result generated is concluded as follows:
The drop time of the CRA ascertained during the normal operating
conditions is 585 m at a final velocity of 1.79 m/s. In the LBE fluid, the
difference in the pressure at the inlet and outlet of the guide tube creates
an upward flow against the CRA. The purpose of this is ensuring cooling in
the reactor core; however, this militates against the free fall of the CRA by
offering a considerable resistance in the LBE. The CFD results have shown
that the mass density contributes most to the resistance capability of the
LBE fluid. Notwithstanding, the share of the resistance from viscous fric-
tion and differential pressure cannot be underestimated. In the drop
process of the CRA in LBE domain, the fluid solid interaction capability of
the CFX software can show the actual characteristics of the CRA drop in
response to the LBE resistance. It has been shown that at the beginning of
the drop, the LBE resistance increases and the CRA bobs and this causes a
delay, which is a safety concern. For the controlling parameters from the
LBE fluid, increasing the density and mass flow rate causes a corre-
sponding increase in the drop time as these parameters contribute to
increasing the resistance against the driving force of the CRA.
However, the controlling parameter from the CRA is the mass and as
this mass increases, the drop time reduces. In case of the CRA drop, the
study shows that the change in the drop time is because of the variation
of the fluid resistance due to buoyancy, differential pressure and viscous
friction caused by the variation in the LBE controlling parameters.
Analysis of the hydraulic resistance is one of the most important ana-
lyses in designing a CRA and analysing the hydraulic compatibility of
mixed cores. The vertical forces are induced by upward high-velocity flow
through the reactor core. Essentially, the CRAprovides real-time control of
thefission process, ensuring that it remains active while preventing it from
accelerating out of control. In effect, control rods are an important safety
systemof nuclear reactors. Their prompt action and prompt response of the
reactor is indispensable. The behaviour of the total resistance with time is
worth studying as it shows the behaviour of the CRA because of the
resistive effect of the LBE at any point in time, during the drop process.
Finally, the numerical study on the drop dynamics of the CRA done in
this work is therefore conservative and represents the CLEAR-1 condi-
tions adequately. It is also appropriate for showing the principle behind
the control rod drop dynamics as well as contribute to the qualification of
the CLEAR-I control rod design.
Declarations
Author contribution statement
Emmanuel Maurice Arthur: Performed the experiments; Analyzed
and interpreted the data; Wrote the paper.
Chaodong Zhang: Conceived and designed the experiments; Per-
formed the experiments; Analyzed and interpreted the data; Contributed
materials, analysis tools or data; Wrote the paper.
Seth Kofi Debrah: Conceived and designed the experiments; Per-
formed the experiments; Analyzed and interpreted the data.
Stephen Yamoah: Performed the experiments; Analyzed and inter-
preted the data.
Lei Wang: Conceived and designed the experiments; Performed the
experiments; Analyzed and interpreted the data; Contributed materials,
analysis tools or data.Funding statement
This work was supported by the Strategic Priority Research Program
of Chinese Academy of Sciences (Grant No. XDA22010504).Data availability statement
Data will be made available on request.11Declaration of interests statement
The authors declare no conflict of interest.
Additional information
No additional information is available for this paper.
Acknowledgements
The authors are grateful to the reviewers for their intelligible critique
to the substance of the study.
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