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Proceedings of the 2017 25th International Conference on Nuclear Engineering
July 2-6, 2017, Shanghai, China
N. Le Brun*
Imperial College London
London, U.K.
A. Charogiannis
Imperial College London
London, U.K.
G. F. Hewitt
Imperial College London
London, U.K.
C. N. Markides
Imperial College London
London, U.K.
(Flanagan, 2012; Serp, 2014). However, even if still very
promising, molten salt reactor can still incur in dangerous
scenarios. A particularly dangerous eventuality comes from the
solidification of the coolant inside the piping system, a problem
which is often overlooked. Indeed molten salt coolants present
melting temperatures of approximately 450 °C, which are much
higher than the ones exhibited by conventional coolants. If the
molten salt solidifies in the piping system, this might cause
serious problems by partially or entirely blocking the coolant
flow. A possible unit which is susceptible to coolant freezing is
the molten salt/air heat exchanger of the “Direct Reactor
Auxiliary Cooling System” (DRACS), which is the passive
safety system envisaged for the new generation MSR. DRACS,
whose schematic is given in Fig. 1, is the passive safety system
envisioned for the molten salt reactor and it is a critical
component of the design which can be prone to freezing (Lv,
2015). DRACS is composed of two natural-convection loops
(`primary' and `secondary') which are connected through the
DRACS heat exchanger (DHX). ) Molten salt is utilised as the
heat-transfer fluid in both the primary and secondary loop.
DRACS rejects heat from the secondary loop to the
environment through a molten salt/air heat exchanger (NDHX).
During normal operation, molten salt flow in DRACS is very
limited thanks to a fluid diode; the flow in the reactor is driven
by the pump which maintains a positive head on the lower leg
of the primary loop. Also, air shutters in the chimney are kept
closed so that no air flows through the NDHX removing heat
and decreasing efficiency.
In this study we describe an experimental system designed
to simulate the conditions of transient freezing which can occur
in abnormal behaviour of molten salt reactors (MSRs). Freezing
of coolant is indeed one of the main technical challenges
preventing the deployment of MSR. First a novel experimental
technique is presented by which it is possible to accurately
track the growth of the solidified layer of fluid near a cold
surface in an internal flow of liquid. This scenario simulates the
possible solidification of a molten salt coolant over a cold wall
inside the piping system of the MSR. Specifically, we
conducted measurements using water as a simulant for the
molten salt, and liquid nitrogen to achieve high heat removal
rate at the wall. Particle image velocimetry and planar induced
fluorescence were used as diagnostic techniques to track the
growth of the solid layer. In addition this study describes a
thermo-hydraulic model which has been used to characterise
transient freezing in internal flow and compares the said model
with the experiments. The numerical simulations were shown to
be able to capture qualitatively and quantitatively all the
essential processes involved in internal flow transient freezing.
Accurate numerical predictive tools such the one presented in
this work are essential in simulating the behaviour of MSR
under accident conditions.
One of the main features of the next generation nuclear
reactor will be safety. Molten salt reactors are under review as
feasible options for the next generation nuclear reactors for
their many advantages, primarily their inherent safety
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purpose to characterize transient freezing in internal flow under
the conditions which can be encountered in DRACS: 1) large
temperature differences between the internal fluid and the wall,
and 2) low Reynolds number (Re). Specifically, in DRACS, the
molten salt/air heat exchanger is exposed by the tube-side to the
hot molten salt around 500 °C and from the wall-side to
ambient air at 60 °C. This much higher temperature difference
has the effect to increase the importance of the heat transfer
through the ice layer and the wall heat capacity on the overall
freezing process. Previous experimental work on freezing in
internal flow revolved mainly around water at relatively low
cooling power. Usually the coolant is a mixture of water and a
low-boiling point organic fluid, such an alcohol. The
temperatures reached by the wall-side of the flow were
therefore between 10-40 °C less than the bulk temperature of
the water freezing (Zerkle, 1968; Savino, 1967; Weigand,
2008). Therefore such experiments are unsuitable to offer an
accurate validation case for DRACS thermo-hydraulic codes.
The experimental system hereby explained, and the
experimental measurements conducted, focused on tracking the
growth of the solidified layer in a channel flow of water (used
as a simulant) in contact with a copper plate cooled by liquid
nitrogen flow in order to achieve high wall heat fluxes. A novel
method has been used to track the ice/water interface precisely,
allowing for an accurate comparison with the numerical model
developed to simulate transient freezing.
Figure 1. Schematic of DRACS, showing the molten salt/air
heat exchanger NDHX.
In case of accident, such as loss of power with consequent
loss of forced circulation (LOFC), the air shutters in the
chimney are automatically opened and natural circulation is
initiated by the temperature differences in both the primary and
secondary loops. In such eventuality the sudden increase in air
flow through the NDHX could freeze the salt inside, given also
the low flow-rates of coolant present at the start of the transient.
Because the decay heat is ultimately removed through the
NDHX, freezing of the molten salt in this heat exchanger could
be catastrophic. Indeed the mass of solidified salt could
significantly decrease, if not completely stop, the circulation of
molten salt in the secondary circuit creating a strong
temperature difference between the DHX and the NDHX, and
ultimately compromising the heat removal capability of
DRACS. This eventuality of catastrophic molten salt freezing
has been demonstrated in detail by a recent work conducted by
the authors (Le Brun, 2016). In the mentioned study the
authors simulated the behaviour of DRACS under Loss of
Forced Circulation (LOFC), following an accident with
consequent interruption of power and scram. The simulation
showed that, under these conditions, the reactor core can reach
off-design temperatures of 900 °C within 4 hr due to freezing of
the salt in the NDHX. These sort of simulations can however
present large deviations depending on the assumptions made to
model the freezing process. Therefore experimental validation
is paramount for any of such models.
In this work we further seek to understand the validity of
the assumption used to model the freezing behaviour of molten
salt in the NDHX by conducting experiments with the specific
The experimental setup consists of a recirculating flow
facility which is capable of pumping water under different
conditions inside a test section, where the actual measurements
are conducted through the use of laser-based diagnostic
techniques: Particle Image Velocimetry (PIV) and Planar Laser
Induced Fluorescence (PLIF). Specifically, the experiment
consists in measuring the thickness of a solidified layer of
water during its constant growth. Freezing is accomplished by
placing a cold surface in contact with a laminar channel flow of
Flow facility. A schematic of the flow facility showing its main
components is given in Fig. 2. Tap water from the mains is used
as the test fluid and it is stored in a 25L tank which serves as a
reservoir. Glass hollow spheres (LaVision, 11.7 μm mean
diameter) and a dye (Sigma-Aldrich, Rhodamine B) are added
at low concentration (<1 g/L) to the water in order to conduct
the measurements. The water is pumped from the tank through
the circuit using a standard centrifugal pump. The water flowrate is controlled by a ball valve and measured via a rotameter
placed downstream of the test section. The rotameter was
installed in this position in order to reduce the amount of air
bubbles flowing through the test section during the
experiments. It was indeed found that the rotameter entrained
tiny air bubbles which would get released during the pump
start-up or even by changing the flow-rate. The readings of the
rotameter were manually checked. A heat exchanger is used to
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control the water temperature which was measured at the
entrance of the test section using a K-type thermocouple. The
heat exchanger was produced in-house using copper piping and
standard fittings.
the cavity formed by the plate and the thick Perspex channel
(see Fig. 3). Water is injected in the channel through three
access points in order to reduce bubble formation and largescale turbulence. Steel meshes are present at the entrance and
exit of the channel to further reduce large-scale turbulence and
achieve the appropriate flow condition. The main feature of the
channel is that it can be tilted up to 120°. The main reason
behind this arrangement is to clear the channel from air bubbles
which are inevitably present at the start and accumulate during
the experiment. A camera, part of the measurement system, is
placed on the same frame as the channel and it is tilted with it
so to decrease measurement errors after the calibration is
carried out (see next section).
Diagnostic techniques. PIV and PLIF were utilised to measure
the thickness of the solidified layer of water. The glass particles
and the dye are exited with a laser sheet and reflect light to the
camera. With PLIF the light fluoresced by the dye dispersed in
the fluid is detected and the fluid therefore appears as
uniformly coloured with respect to the solid parts. PIV takes
measurements of velocity fields by taking two images in short
sequence. The glass particles added to the fluid appear as bright
spots and it is possible to calculate the distance that each
particle covered by comparing the two images. The velocity is
then found by knowledge of the time gap between the two
images. More information on these techniques can be found in
the work of Charogiannis et al. (2015). These techniques were
employed to overcome some important problems identified in
the literature (Savino, 1967) and early stage experimental trials,
in which temperature-driven light distortions made it difficult to
locate the interface precisely. PIV was also used to measure the
velocity field, whose knowledge proved very important to
process the data and to allow for a proper comparison between
the simulations and the experiments.
Figure 2. Schematic of the experimental apparatus used to
conduct transient freezing measurements.
Procedure. The following procedure was conducted for each set
of measurements. First, the diagnostic techniques were
calibrated by using a specific target placed inside the test
section facing the camera. Then the target was carefully
removed, paying particular attention to vibrations which could
change the position of the camera relative to the test section.
The test section was then closed and the flow initiated through
the pump. The test section was then tilted 90° to a vertical
position. Almost all the air bubbles stuck in the test section
would then be removed leaving a clear view for the camera.
The heat exchanger was then turned on to provide heat or
cooling power to the circuit, and then the whole setup was left
to stabilise until the temperature and the flow-rate reached the
desired values. The temperature was maintained within 1°C for
all the duration of the experiment. The laser was then fired and
the recording started which last for up to 3 minutes. Soon after
the laser was initiated, liquid nitrogen was poured on top of the
copper plate and continuously added thereafter for all the
duration of the experiment.
Test Section. The test section, whose details are offered in Fig.
3, was specifically designed to allow for studying solidification
under high heat flux which can be present in operational units
utilising high melting-temperature salts. It comprises of a 6 mm
deep, 30 cm long Perspex channel cut out on one side to allow
for the placement of a 1 mm thick, 20 mm long copper plate
which serves as a cold surface for the solidification of the
water. The dimensions of the channel were chosen so that the
fluid flow and the heat transfer through the solidified layer
were 2-dimensional where the measurements were taken. The
heat removal is accomplished by placing the other surface of
the plate in contact with boiling liquid nitrogen (-197 °C). The
dimensions of the copper plate are less than the channel so that
the plate does not touch the side-walls of the channel. This
arrangement was decided in order to avoid higher solidification
rates along the side walls where the velocity and therefore the
heat transfer coefficient is less. A thicker ice-layer close to the
wall would obstruct the field of view of the camera making
measurements impossible. Liquid nitrogen is poured directly in
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ℎ(melt −)
Here, the variables P and A are respectively the perimeter and
the cross sectional area of the pipe which is in contact with the
liquid phase (thus taking into account the layer of solidified
salt); ℎ is the heat transfer coefficient;  and p are the density
and specific heat capacity of the molten salt;  is the
temperature of the salt and  the mass flow-rate. Similarly, an
energy balance can be conducted over a pipe wall section,
which is assumed to have an uniform temperature w ; The
equation was derived under the assumption of quasi-steadystate condition for the temperature profile inside the solidified
w w ,w
Figure 3. Schematic of the test section used to conduct
transient freezing measurements.

+ (s )

= −ℎext (w − ext )ext − sw w .
Here the subscript “w” and “ext” refers respectively to the
wall and the external side of the pipe; sw is the heat flux to the
wall from the layer of solidified salt and (s ) is a function of
the solidified mass of salt. The function (s ) accounts for
the energy lost or gained in the solidified salt during the
transition between different steady-states caused by a change in
w ; its value is calculated from the steady state temperature
profiles in the salt:
The measurements were taken towards the end of the copper
plate where the layer thickness achieved an uniform profile.
Indeed towards the start of the copper plate, where the thermal
boundary layer is not fully developed, the layer is progressively
thinner. Particular care was taken to avoid water moisture to
flow in front of the camera and the laser apparatus. This water
moisture was produced by the drop in temperature caused by
the cold boiling liquid nitrogen. Acquired data were reduced to
compute the thickness of the layer versus time as well as all the
other important quantities needed for an accurate comparison of
the experiments with the model. By far the most difficult task
was to track the solid/liquid interface. This was achieved by
taking the signal refracted from the interface and scattered by
the glass particles stuck at the solid/liquid interface.
(s ) = p  (
(s )2 −02
(s )
+ 02 ),
where 0 is the pipe radius and (s ) is the radius of the
liquid cross section in a pipe in which a layer of solidified salt
is present with a mass per unit of pipe length s . The interface
between the solid and the fluid is assumed to be at the melting
temperature of the material. The mass of solidified salt is found
by conducting a mass balance over a pipe section through the
following equation:
An in-house build freezing model was derived and applied
to simulate the experimental conditions found in the
experiments. Details of the freezing model can be found in (Le
Brun, 2016), here we summarise its most important features.
The model is a 1-D thermo-hydraulic model where momentum
and energy equation are solved at each time step in each section
of the channel. The freezing process of molten salts inside a
pipe is modelled by assuming that the salt solidifies
homogenously along the pipe walls. In this case, a uniform
layer of solidified salt is formed between the wall and the
molten salt. The layer is assumed to form when the temperature
of the wall drops below the melting temperature of the salt Tmelt.
The thermo-hydraulic equations describing the freezing
process where derived by considering a pipe section of length
ds. By conducting an energy balance over the liquid phase in
contact with a frozen layer of salt we can infer:
(Δ + ( − melt )p + (s , w ))
sf w ,

= ℎ( − melt ) −
where sf is the solid-side heat flux at the interface between
the fluid and the solidified mass of salt, Δ is the enthalpy of
fusion and (s , w ) is a function accounting for the energy
loss/gained during transitions from different quasi-steady-states
caused by a change in the mass of solidified salt per unit length
s . The expression for (s , w ) was calculated as the first
order term of the Taylor series of the energy differential
between two different quasi-steady-states caused by a change in
mass ds :
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(s )
(s , w ) = p (melt − w ) ( ln
0 2
(s ) (s )2
+ ln
0 2
(s )
depends on the inlet conditions of the water flow, increasing
with the inlet temperature and the water flow-rate. The presence
of this buffer period can be easily explained: it is related to the
time needed to cool the copper plate below the melting
temperature of water. Once the temperature of the copper plate
is below the melting temperature of water, the water in contact
with the plate is sub-cooled and solidification starts. The newly
formed layer of ice grows steadily until cooling power is
ceased. The thickness of the ice layer grows almost linearly
with time and ends abruptly towards the end of the experiment
when no more liquid nitrogen is present in the cavity.
Curves similar to one in Fig. 4, were observed for all the
experimental conditions used in the study. The linearity of such
curves is somewhat counter-intuitive as one would expect that
the thicker the ice-layer is, the higher is the resistance to the
heat transfer, and thus, the slower the growth. The linearity of
the curves is however easily explained when we take into
account the thermal mass of the plate. Indeed the copper plate
is subjected to continuous cooling throughout the experiment
and its temperature continuously decreases, similarly to what
happens in the buffer period. The effect of the steady
temperature drop of the copper plate is to increase the
temperature difference between the plate and the water, which
compensate for the larger resistance to heat transfer offered by
the growing ice layer. These two opposite effects balance each
other leading to an almost linear growth rate of the ice layer.
This analysis underlines the importance of accurately modelling
the wall thermal mass which was not accounted for in previous
model (Savino, 1967).
Eq. 1-5 where combined with standard 1-D thermohydraulics equations, see for example Vijayan and Austregesilo
The model derived was applied to the experiment by
simulating a 20 cm long channel, divided along its length in
increments of length ds = 1 mm. The system of equations
comprising the model were solved for each space increment
using the FTUS scheme (first order upwind explicit) to find the
lumped fluid temperature T, plate wall temperature Tw and
thickness of the solid layer Xs, proportional to the mass of fluid
solidified in the channel. With respect to the boundary
conditions, the bottom surface of the channel was considered
adiabatic while the top surface, representing the 1 mm copper
plate, was assumed in contact with boiling liquid nitrogen Tw =
-197 °C). The heat transfer coefficient between the plate and
boiling liquid nitrogen h given in W/m2/K, was taken from Jin
et al. (2009). The fluid, initially at a constant temperature T0,
was assumed to have a constant Re which was taken equal to
the average Re measured in the experiments. The inlet
temperature of the fluid was also taken to be T0. The expression
for the thermal properties of ice, water, and copper were taken
from Green et al. (2008). The thermal properties were
calculated at each iteration based on the mean temperature of
the material. Specifically for water, whose properties vary
significantly with temperature, they were evaluated at the
average temperature between the bulk temperature and the
melting temperature. The value of the water/ice heat transfer
coefficient h was taken from the correlations for laminar flow
in non-circular pipes (Wibulswas, 1966), using a Nusselt
number Nu of 8.2 when no ice layer is formed (constant heat
flux boundary condition) and Nu = 7.5 when ice is formed
(constant temperature boundary condition).
From the experimental setup and methods described before
the thickness of the solidified layer and the local Re was
acquired as a function of time; this, for different average flowrates of water and inlet temperatures. Knowledge of the local
Re was important to accurately calculate the local heat transfer
coefficient used in the model. The results of the measurements
are shown in Fig. 4 which reports the measured thickness of the
solidified layer versus time, and the corresponding simulation
for an inlet water temperature of 8 °C and a Reynolds number
of 20. As visible by looking at the profile, water does not start
solidifying as soon as liquid nitrogen is poured in the cavity
(time = 0); the solidification is delayed and takes place later.
This is shown in the picture by an initial "buffer" period where
the thickness of the ice layer is zero even if liquid nitrogen has
been poured in the cavity. The extension of this buffer period
Figure 4. Measured and calculated thickness of the
solidified layer for an inlet water temperature of 8 °C and a
Reynolds number of 20.
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particular, at the start of each experiment, the temperature of
the plate would not be immediately decreased by placing it in
contact with the liquid nitrogen. This is probably due to the
formation of an insulative layer of liquid nitrogen vapour
between the plate and the boiling liquid nitrogen. Also at the
end of each experiment the boiling liquid nitrogen was not
dispersed uniformly over the plate so that using an uniform heat
wall-side, transfer coefficient is unrealistic. Another source of
error relates to the uncertainty in the knowledge of the waterside heat transfer coefficient. The correlation used to calculate
the heat transfer coefficient was indeed developed for fully
developed laminar flow of a fluid with an uniform viscosity,
which, for some conditions, proved unrealistic. It is important
to mention that the modelling methodology, which has been
validated in this study against the experimental results, should
be applicable to molten salt flows. Molten salts are considered
Newtonian fluids and follow standard heat transfer correlations
(Ambrosek, 2008). The difference temperature of operation
between water and molten salts should not affect the reliability
of the model prediction. What is important are the temperature
differences with respect to the melting point of the salt (e.g.
Tmelt – Twall), whose order of magnitude is replicated by the
experiments conducted in this study. The reliability of the
results can however be improved by designing scaled-up
experiments which can match all the dimensionless numbers
encountered in real systems.
Figure 5. Growth rates of the solidified layer (experiments
and simulations) for different experimental conditions
Thanks to their linearity, each curve can be characterized
by a growing rate, which is its slope. Fig. 5 reports these
growth rates of the ice layer as a function of the inlet water
condition, namely its temperature and flow-rate. As showed in
Fig. 5, the growth rates of the solid layer are similar for low
fluid inlet temperatures, T0, irrespective of the velocity of the
flow. This is understandable as, at low inlet temperature, both
the heat transfer between the solidified layer and the bulk of the
fluid and the sensible heat in the fluid are low. The growth rates
seem also bounded between two curves, Re =10 and Re = 100.
In particular, for low Re, all the data would collapse on an
asymptote, similar to the Re=10 profile, which represent the
case of freezing in a warm stagnant fluid. In addition, it is
evident how, for each velocity (or Re), there exists an inlet
temperature for which no solid layer is formed at the wall. This
limiting value of the inlet temperature is particularly important
in the MSR as if the wall temperature in the NDHX is kept
below such temperature, solid formation is prevented, and so
any danger of clogging.
Overall the model reproduced with fairly well the
experimental observation. A sensitivity analysis conducted on
the major source of uncertainty in the model revealed that,
provided that the knowledge of the heat transfer coefficient are
correct, the discrepancy between the model and the experiments
is less than 20%. One main source of error between the
experiments and the model was the uncertainty related to when
the liquid nitrogen cooling power is initiated and stopped. In
In this study we described the experimental setup used to study
transient freezing under condition of high wall heat fluxes and
high temperature difference between the hot and cold fluid,
typical of the air/molten salt of DRACS. The main results from
the experiment and the corresponding numerical simulations
are here summarised:
Accurate tracking of the ice/water interface and
velocity profile in the liquid under freezing was
possible by measuring the intensity of the scattered
signal from the interface and the fluid through PIV and
The growth of the ice thickness with time is
approximately linear. This is due to the steady drop in
the wall temperature throughout the experiment which
partially offset the increased resistance to the heat
transfer caused by the growing layer of ice.
The growth rate of the solid layer was characterised as
a function of the inlet fluid velocity and Re. The
growth rates were found to decrease with increasing
inlet fluid temperature and velocity.
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the direct reactor auxiliary cooling system (DRACS), Appl
Energy (2016), in press.
The thermo-hydraulic model derived can reasonably
predict the experimental data with the major sources of
error being the time-delay in providing cooling power
at the start and end of the experiment, and the
uncertainty in the heat transfer coefficient.
Q. Lv, X. Sun, R. Chtistensen, T. Blue, G. Yoder, and D.
Wilson, Design, testing and modelling of the direct reactor
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Energy Alliance, LLC, Idaho Falls, ID, United States, (2015).
The thermo-hydraulic model validated in the present study can
be used to simulate the transient freezing of molten salt in the
new generation MSR.
J. Serp, M. Allibert, O. Benes, S. Delpech, O. Feynberg, V.
Ghetta, D. Heuer, D. Holocomb, V. Ignatiev, J. L. Kloosterman,
et al. The molten salt reactor (msr) in generation IV: overview
and perspectives, Progress in Nuclear Energy, 77 (2014), pp.
The authors gratefully acknowledge the UK Centre for Nuclear
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