Accepted Manuscript Title: Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules Author: Ming Wu, Chao Xu, Yaling He PII: DOI: Reference:
S1359-4311(15)01060-1 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.10.014 ATE 7130
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
Please cite this article as: Ming Wu, Chao Xu, Yaling He, Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.10.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded
phase change material capsules
3 Ming Wu1, Chao Xu2*, Yaling He1*
Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
State Key Laboratory of Multiphase Flow in Power Engineering, School of Energy and Power
Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of MOE, School
of Energy Power and Mechanical Engineering, North China Electric Power University,
Beijing 102206, China
>Cyclic behaviors of a TES system packed with cascaded PCM capsules are investigated.
>Non-cascaded system suffers from a low charging ratio and a long charging time.
>The cyclic process of the cascaded system can reach to a repeatable state after some cycles.
>Practical storage capacity depends on the threshold temperature to stop the operation.
A transient, one-dimensional dispersion-concentric model to numerically study the cyclic behaviors
of the molten-salt packed-bed thermal energy storage system filled with cascaded phase change
material (PCM) capsules is presented. Three different storage systems are investigated which
include the non-cascaded system, the cascaded systems with 3 and 5 cascaded phase change
temperatures (PCTs). Detailed characteristics of heat transfer between molten salt and the packed
PCM capsules are discussed, and various numerical results are presented, including the temperature
distributions of molten salt and PCM capsules, the variations in the molten-salt outlet temperature,
the accumulated efficiency of each cycle. The results show that the non-cascaded system suffers
from a low charging ratio and a long charging time due to the constrains of PCT while the cascaded
systems especially with 5 cascaded PCTs are found to have both a fast discharging rate and a fast
charging rate. The cyclic process of the cascaded system with 5 cascaded PCTs can reach to a *Corresponding author. Tel.: +86 29 82665930; fax: +86 29 82665445. E-mail address: [email protected]
(C. Xu); [email protected]
Page 1 of 29
repeatable state after some cycles, at which high accumulated efficiencies can be achieved. It is also
found that the practical storage capacity of the storage system with cascaded PCM capsules depends
highly on the threshold temperatures to stop the charging/discharging process.
Kew words: Thermal energy storage, Solar energy, Packed bed, Phase change material
Thermal energy storage (TES) is very crucial for large-scale applications of concentrating
solar power (CSP) systems, because CSP systems with TES can not only generate stable and
dispatchable electricity, but also enable higher overall penetrations of solar photovoltaic (PV) and
wind power . Presently, the two-tank molten-salt TES system is the only one that has been
applied in large-capacity CSP plants such as Andasol 1-3 in Europe. However, the two-tank system
has a relatively high cost and limited room for cost reduction, and thus alternative cost-effective
TES systems are in urgent need [2-4].
The one-tank packed-bed thermocline TES system has been regarded as a promising TES
alternative since it may save 35% of capital cost compared to the two-tank TES system . The
first pilot-scale molten-salt packed-bed thermocline tank has been successfully established in
Sandia National Laboratories , and quartzite rock combined with silica sand were screened out as
the most practical cheap solid fillers. Valmiki et al.  also built a lab-scale packed-bed
thermocline TES tank and experimentally investigated the heat transfer behaviour during the
charging and discharging processes. In addition to the experimental research work, increasing
numerical investigations about the packed-bed thermocline TES system were reported recently.
Yang et al. [7-8] developed a two-temperature model for the molten-salt packed-bed thermocline
system and carried out a series of numerical investigations. Li et al.  numerically investigated
various scenarios of thermal energy charging and discharging processes for the packed-bed
thermocline tank based on the developed one-dimensional thermal model. Xu et al. [2-3] presented
a transient two-dimensional two-phase model to investigate the characteristics of the discharging 2 Page 2 of 29
process of the packed-bed thermocline system. Xu et al.  also developed a modified transient
two-dimensional dispersion-concentric (D-C) model to study the heat transfer characteristics within
spherical solid fillers for the discharging process. Flueckiger et al.  developed a new model to
provide a comprehensive simulation of thermocline tank operation, and incorporated it into a
system-level model of a 100 MWe power tower plant to investigate the storage performance during
long-term operation. The efficiency of the thermocline tank at charging and discharging heat was
found to be above 99% throughout the year.
Compared to solid fillers, capsules filled with phase change material (PCM) have been
considered as a better option to be used in packed-bed TES systems. The benefits of PCM include
the utilization of latent heat, which may result in a higher energy storage density and a smaller
storage volume. Packed-bed TES systems filled with PCM capsules have been extensively studied
both experimentally and numerically for low-temperature storage applications such as space and
water heating, cooling and air-conditioning etc. Arkar and Medved  investigated the free
cooling of a low-energy building using a latent heat TES device integrated into a mechanical
ventilation system. The cylindrical TES device was filled with spheres of encapsulated paraffin.
The results showed that free cooling with an latent heat TES was an effective cooling technique.
Nallusamy et al.  experimentally studied the thermal behavior of a packed-bed of combined
sensible and latent heat TES unit. Paraffin was used as the PCM filled in spherical capsules and
water was used as the heat transfer fluid (HTF). Effects of both constant and varying heat sources
on the charging/discharging performance were investigated. Bédécarrats et al. [13-14] carried out
experimental investigations on the performance of a TES system packed by spherical capsules filled
with water as the PCM. Effects of the temperature and flow rate of the inlet HTF, kinetics of
cooling and heating on the charging/discharging performance were investigated. A numerical study
was also presented to complement with the experimental investigations. Amin et al.  developed
a semi-analytical mathematical model based on the effectiveness-NTU method for a TES system
filled with PCM spheres. The formulation enables quick design and simulation of a packed bed 3 Page 3 of 29
PCM system without the need for numerical modelling. Regin et al.  numerically investigated
the thermal behavior of a packed-bed storage system filled with paraffin capsules for solar water
heating application. The Schumann-like model was developed and the enthalpy method was used to
analyze the phase change process inside of capsules. Xia et al.  numerically studied the fluid
flow through the voids of packed capsules and thermal gradients inside of the PCM capsules for the
packed-bed TES tank filled with PCM capsules. The effect of arrangement of the PCM capsules
was also analyzed based on the developed model. Oró et al.  numerically investigated the heat
charging performance of a packed bed storage with PCM capsules using two different models. The
results indicated that free convection was not as important as forced convection in the studied case.
Recently, packed-bed TES systems filled with high-temperature PCM capsules have been
identified as a promising compact and cost-effective TES technology for CSP plants, and molten
salt, whose phase change temperature (PCT) can range from below 100 oC to above 600 oC
depending on the ingredients, has great potential to be used as the PCM. Nithyanandam et al.
[19-21] carried out a numerical analysis of the dynamic behaviour of a molten-salt packed-bed TES
system with PCM capsules for repeated charging and discharging cycles for CSP power plants. The
effects of the configuration design and constraints on the charging and discharging temperature as
encountered in a CSP plant operation on the system dynamic responses were discussed. The effect
of PCT of PCM on the system utilization was found to be non-monotonic, with higher latent
utilization when the PCT is either greater than the discharging cut-off temperature or lesser than the
charging cut-off temperature. A methodology for system design and optimization was also provided
based on the systematic parametric studies and consideration of target design requirements on the
dynamic operation of a CSP plant. Galione et al.  numerically investigated the performance of
different thermocline-like storage concepts including a pure thermocline tank, tanks filled with a
single PCM, multi-layered solid-PCM and cascaded PCM arrangements. They suggested the
multi-layer solid-PCM thermocline system could be utilized due to its cost-effectiveness and high
efficiency in the use of the overall thermal capacity of the system. Tumilowicz et al.  developed 4 Page 4 of 29
an enthalpy-based model of thermocline operation applicable to both single phase and encapsulated
PCM using the method of characteristics. Various possible heat transfer conditions along with
placement of PCM filler phase state interface were investigated. Flueckiger et al.  also
presented a new finite volume approach to simulate mass and energy transport into a latent heat
thermocline tank and integrated the model into a system-level model of a molten-salt power tower
plant. PCMs with different PCTs and heats of fusion were evaluated and the performance of a TES
tank filled with multiple PCMs with cascaded PCTs along the tank height was discussed. Bellan et
al.  numerically investigated the effect of capsule size, fluid temperature, tank size, fluid flow
rate on the performance of a packed bed TES system using sodium nitrate as the PCM and synthetic
oil as the HTF. The dynamic behaviour subjected to partial charging and discharging cycles was
also analysed. Wu et al.  recently presented a transient two-dimensional dispersion-concentric
(D-C) model for the packed-bed TES system with PCM capsules to study the dynamic performance
characteristics. The introduction of the D-C model enables determination of the temperature
distribution and phase change front within each PCM capsule during the heat charging/discharging
processes. Detailed characteristics of heat transfer between molten salt and the packed PCM
capsules were investigated and a parametric sensitivity analysis was presented. A similar model was
also developed by Peng et al.  to analyze the effects of physical properties and operational
conditions on the thermal performance of a TES tank with PCM capsules.
Based on the developed D-C model in our prior work , this study aims at investigating
the dynamic behaviours for the charging/discharging cyclic processes of a molten-salt packed-bed
TES system filled with PCM capsules. The benefits of utilizing PCM capsules with cascaded PCTs
will also be explored. To this goal, a modified transient one-dimensional D-C model is developed.
The heat transfer characteristics of three different packed-bed systems filled with PCM capsules
with different PCT configurations are investigated and various working modes including the
charging process, the discharging process and the multiple charging/discharging processes are
considered. 5 Page 5 of 29
2. Model formulation
The present study investigates three different molten-salt packed-bed TES systems filled with
PCM capsules, which are illustrated in Fig. 1. Each system is composed of a vertically standing
cylindrical tank which has two ports on the top and bottom for the flow of hot and cold molten salt,
respectively. Spherical PCM capsules with the same diameter are packed in each tank, and molten salt
flows through the void space of the packed-bed region. The volume fraction of the packed-bed region
taken up by molten salt is termed as the void fraction and is given as
distributors adjacent to the two ports are equipped to guarantee a uniform fluid flow through the void
space of the packed-bed region. As illustrated in Fig. 1, System NC is a TES system filled with
non-cascaded PCM capsules, which have a uniform PCT of 375 oC. The chosen of the PCT of 375 oC
is to achieve a high discharging efficiency . Two systems filled with cascaded PCM capsules (i.e.,
System C3 and System C5) are investigated. The PCM capsules in System C3 are divided evenly into
three layers, which have cascaded PCTs of 375 oC, 340 oC and 305 oC, respectively. And the PCM
capsules in System C5 are divided evenly into five layers, which have cascaded PCTs of 375 oC, 360
in this study in order to study the performance characteristics of TES systems with cascaded PCM
capsules. Using PCM with artificial PCTs enables extensive investigation about the effect of PCT
on the thermal performance of the TES system, and this approach has been widely adopted by other
researchers [20, 21, 24]. Practically, the PCT of PCM can be adjusted by using salt eutectic
compositions , and the artificial PCTs chosen in the present work have already been satisfied by
some salt eutectic compositions. For example, LiCl(54.2mol.%)-BaCl2(6.4mol.%)-KCl(39.4mol.%)
has the PCT of 320 oC, LiF(7.0mol.%)-LiCl(41.5mol.%)-LiVO3(16.4mol.%)-Li2CrO4(35.1mol.%)
Li2MoO4(27.1-27.6wt.%)- Li2SO4(17.3-17.8wt.%)- LiF(6.1-6.2wt.%) has the PCT of 360 oC .
V ms / V tank
. Two short
C, 340 oC, 320 oC and 305 oC, respectively. It should be pointed out that artificial PCTs are chosen
6 Page 6 of 29
Three working modes are investigated in this study, which are the single charging process, the
single discharging process and the multiple charging/discharging cyclic process. During the single
charging process, hot molten salt flows into the cold tank through the top port, and flows downside
through the packed-bed region releasing heat to the packed PCM capsules. The solid PCM in capsules
melts to liquid phase after absorbing enough heat from the hot molten salt, and thus heat is stored in the
PCM capsules. While during the single discharging process, cold molten salt flows reversely from the
bottom to the top and is heated by the hot PCM capsules, in which liquid PCM is solidified after
releasing heat. The cyclic process includes multiple consecutive charging/discharging cycles, during
which hot molten salt flows into the cold tank through the top port during charging processes while
cold molten salt flows into the hot tank through the bottom port during discharging processes.
167 168 169
2.1 Governing equations
In our prior work , we had developed a transient two-dimensional D-C model for the
discharging process of the TES system filled with non-cascaded PCM capsules like System NC. The
D-C model enables identification of the phase change front and the temperature distribution within
each capsule, and thus detailed characteristics of heat transfer between molten salt and the packed
PCM capsules can be investigated. The model had also been validated based on the results shown in
Ref. . The results in Ref.  showed that the differences of heat and mass transfer in the radial
direction are negligibly small with good thermal insulation, and thus a simplified transient
one-dimensional D-C model is used in the present study to save the calculation time. The following
assumptions are employed in the modeling:
179 180 181 182
1) There is no difference of heat and mass transfer in the radial direction, and thus the governing equations for mass and heat transfer become one-dimensional. 2) The capsules are PCM spherical particles with the same diameter, and the capsule wall is too thin to be considered.
7 Page 7 of 29
3) The packed PCM capsules form a continuous, homogeneous, and isotropic porous region for
fluid flow, and the void fraction of the packed bed region is arbitrarily chosen as 0.25 [20, 24].
4) The PCM is assumed to be homogeneous and isotropic on the physical properties, and the
physical properties of solid and liquid phase of the PCM are considered to be same [19-20].
The governing equations of the modified transient one-dimensional D-C model are presented as
Conservation of mass equation for molten salt: ( l )
( lu )
where l is the molten-salt density, u is the superficial velocity, x means the tank axial distance and
the origin of the x coordinate is at the bottom surface of the packed-bed region as shown in Fig. 1 .
Conservation of momentum equation for molten salt: ( lu )
( t )
( l uu )
where K is the intrinsic permeability of the packed-bed region, C F is the inertial coefficient, and is
the molten-salt viscosity.
Conservation of energy equation for molten salt: ( l c p,lTl )
( l c p,1uTl )
) h v ((T p ) R Tl )
where T l is the molten-salt temperature,
molten-salt specific heat capacity,
term on the right side accounts for the heat transfer between molten salt and PCM capsules with a
volumetric interstitial heat transfer coefficient
(T p ) R is
the surface temperature of PCM capsules,
c p, l is
is the molten-salt effective thermal conductivity, and the last
Conservation of energy equation for PCM capsules: ( p h p (T p )) t
( k p (T p )
2 k p (T p ) T p
8 Page 8 of 29
where is the radial coordinate inside each capsule,
density and thermal conductivity of PCM, respectively.
h p is
the enthalpy of PCM,
p and k p
2.2 Material properties and constitutive correlations
The molten salt used in this study is the binary molten salt (60wt% NaNO3 and 40wt% KNO3),
and its thermo-physical properties can be found in Ref. . The properties of PCM are listed in Table
1. The inertial coefficient and the permeability of the packed-bed region can be expressed as :
1 . 75
214 215 216
150 (1 )
where d p is the diameter of the spherical capsule. The interstitial heat transfer coefficient between molten salt and PCM capsules, h v , and the molten-salt effective thermal conductivity,
, are given as :
0.6 1/ 3 6(1 ) k l 2 1.1 R e p P r hv 2 dp
0.7 k l , R e p 0.8 l,eff 0.5 P rR e p k l , R e p 0.8
where the Prandtl number and Reynolds number are expressed as below:
c p ,l kl
ld p u
When the PCM is in liquid phase, natural convection which enhances heat transfer may exist. The
following effective thermal conductivity of liquid PCM is adopted to account for the natural
convection effect :
k p, n 0.18 k p R a
9 Page 9 of 29
where the Rayleigh number, Ra, is expressed as
kinematic viscosity, thermal diffusivity, and thermal expansion coefficient of liquid PCM, respectively.
g (Tp Tm elt )( d p / 2) / 3
228 229 230
2.3 Boundary conditions and initial conditions Boundary conditions.
The boundary conditions of the molten salt for the different working processes are listed as
Single charging process:
u / x
u / x
0 , Tl / x
Single discharging process:
Tin,low Tl / x
The cyclic process is composed of multiple consecutive charging/discharging processes. Eqs.
(11-12) are used as the boundary conditions of molten salt during each charging process, while Eqs.
(13-14) are the boundary conditions of molten salt during each discharging process.
The boundary condition for PCM capsules at each position is listed as below:
hs ( T l T p
where hs is the convective heat transfer coefficient at the capsule surface and can be expressed as :
hs h v / (6(1 ) / d p )
Initially, it is assumed that the storage tank is fully charged with thermal energy for the single
discharging process, and the molten salt and the packed PCM capsules have the same hot temperature
10 Page 10 of 29
discharged, and the molten salt and the PCM capsules have the same cold temperature of
the cyclic process, initially it is assumed that the molten salt and the PCM capsules have the same cold
increases to exceed a threshold value
charging rate becomes very low. And thus the charging process is stopped when the molten-salt outlet
temperature gets to
the charging process is stopped is used as the initial conditions of the consecutive discharging process.
On the other hand, when the molten-salt outlet temperature drops below a threshold value
Tdischarge,cut - off
molten salt may fail to generate useful steam for power generation effectively. The discharging process
is stopped when the molten-salt temperature gets to
molten salt and PCM capsules when the discharging process is stopped is used as the initial conditions
of the consecutive charging process. The threshold values for the charging and discharging processes
are restrained by the operation of a CSP plant. In the present study, the threshold values are set as
Tcharge,cut-off = Tin,low + T
Tin , h ig h .
At the beginning of the single charging process, it is assumed that the storage tank is fully
Tin ,lo w
Tin ,lo w
, and the charging process starts first. When the molten-salt outlet temperature
T ch arg e,cu t-o ff
T ch arg e,cu t-o ff
, most of the PCM capsules are fully charged and the
. The corresponding temperature of molten salt and PCM capsules when
during the discharging process, the discharging rate becomes very low and the discharged
T discharge,cut-off Tin, high T
Tdischarge,cut - off
, and the corresponding temperature of
, and the effect of T on the cyclic performance is
2.4 Numerical method
The same numerical method which has been described in detail in Ref.  has been used.
Briefly, the above described equations are discretized using the finite volume method and solved with
the SIMPLER (Semi-Implicit Method for Pressure-Linked Equations Revised) algorithm. During
each iteration, after updating the molten-salt temperature (Tl) from Eq. (3), the temperature of PCM
capsule (Tp) corresponding to each grid is iteratively computed using the Temperature-Transforming
method proposed by Cao and Faghri . The transformation form of the governing equation of PCM 11 Page 11 of 29
capsules (Eq. (4)) can be referred to Ref. . The grid and time-step independences have also been
validated, and the used convergence criteria at each time step are that the residuals for all variables
drop below 10-4. The above-described model for the single discharging process of System NC has been
validated in Ref.  based on a packed-bed storage tank using paraffin wax as the PCM capsules.
The following analysis are based on a hypothetical 50 MWht molten-salt TES tank filled with
spherical PCM capsules, the geometric parameters of which are summarized in Table 1. The total
storage capacity of 50 MWht is the sum of the sensible heat of both the HTF and the PCM capsules
with the temperature range of 290 to 390 oC and the latent heat of PCM capsules. Several parameters
are defined to evaluate the effectiveness of the various working processes. For the single charging
process, the accumulated charging ratio which is defined as the ratio of the amount of heat storage to
the total storable energy provided by the hot molten salt is expressed as:
m c p,l (T l, x 0 290 C ) dt o
m c p,l (390 C 290 C ) dt o
While for the single discharging process, the accumulated discharging ratio which is defined as the
ratio of the useful discharged energy from the TES tank to the total energy initially stored in the
TES tank is expressed as: d isch arg e
290 291 292 293 294
m c p ,l (3 9 0
C T l, x H ) d t
T o tal en erg y in itially sto red in th e T E S tan k
For the cyclic process, accumulated input storable energy ( Q in ) and the accumulated charging energy ( Q charge ) within each charging process are defined as: Q in
m c p,l (390 C 290 C ) dt
Q charge Q in
m c p,l (Tl, x 0 290 C ) dt o
12 Page 12 of 29
where t c is the consumed time at each charging process when the molten-salt outlet temperature
reaches to the threshold value
discharging process is expressed as:
T ch arg e,cu t-o ff
Q dis charge
. While the accumulated discharging energy within each
m c p,l (390 C T l, x H ) dt o
where t d is the consumed time at each discharging process when the molten-salt outlet temperature
reaches to the threshold value
cycle is defined as:
. The accumulated efficiency for each charging/discharging
cycle Q d is ch arg e / Q in
3. Results and discussion
3.1 Single discharging behavior
The single discharging processes of the three TES systems are investigated in this section. Each
tank is assumed to be fully charged at the beginning, and during the discharging process cold molten
salt with a temperature of 290 oC is continuously pumped into the tank through the bottom port. Let’s
first analyze the variations of the capsule temperature during the discharging process. Fig. 2 shows the
distributions of the capsule centre temperature along the tank height at various discharging time of 1 h,
3 h, and 5 h. As shown for System NC, generally five different regions can be identified, i.e., low
temperature region, below-PCT thermocline region, quasi-isothermal region, above-PCT thermocline
region, and high temperature region. This behavior has already been reported in our prior work .
Only one quasi-isothermal region exists for System NC and it moves upward with the discharging
time. However, multiple quasi-isothermal regions can be found for systems with cascaded PCM
capsules. For instance, 3 and 5 quasi-isothermal regions can be identified for System C3 and System
C5, respectively. These multiple quasi-isothermal regions obviously result from the cascaded PCTs.
13 Page 13 of 29
On the other hand, the capsule centre temperatures for System C3 and System C5 do not always
keep increasing or stable along the tank height, which is different from that for System NC. For
example, 5 quasi-isothermal regions still exist for System C5 at 5 h, while between neighboring
quasi-isothermal regions concave distribution occurs for the capsule centre temperature. This is
because during the discharging process in each layer that has a uniform PCT, the capsule centre
temperature drops quickly after it is fully solidified while it remains at the PCT before it is melted, as
can be seen in Fig. 3. For the region covered by the capsules that are fully solidified, the capsule centre
temperature becomes close to the capsule surface temperature, and there is little difference between the
capsule surface temperature and molten-salt temperature indicating negligible heat transfer. While for
the region covered by the capsules that are not fully solidified, the capsule centre temperature remains
at the PCT and there is evident difference between the capsule surface temperature and molten-salt
temperature indicating normal heat discharge. As a result, the region covered by the capsules that are
fully solidified always expands from the tank bottom to the top during the discharging process for the
system with non-cascaded PCM capsules, while for the systems with cascaded PCM capsules there can
exist an expanding region that is covered by fully solidified capsules in each layer that has a uniform
The solidification process of PCM capsules during the discharging process can be further
investigated by inspecting the changes of the capsule temperature. Fig. 4 shows the variations in the
centre temperature of the middle capsule at x=0.5 H with the discharging time for the three TES
systems. The capsule centre temperature for System NC shows four different periods before
completely discharging the stored heat: high temperature period before discharging, the first
temperature-dropping period during which only sensible heat in the liquid PCM is discharged,
isothermal phase change period during which latent heat is discharged, the second temperature
dropping period during which only sensible heat in the solid PCM is discharged. This behavior has also
been revealed in Ref. .
14 Page 14 of 29
A similar trend can be found for the systems with cascaded PCM capsules. The main difference is
that during the period of discharging sensible heat in the solid PCM, the capsule centre temperature for
the systems with cascaded PCM capsules first drops sharply and then it decreases slowly (for System
C5) or much slightly (for System C3) for quite a long time, after which it drops slowly to 290 oC. This
is caused by the fact that during that period the molten-salt temperature at x=0.5 H already drops to 290
temperature difference between the PCM capsule and molten salt, which can be seen in Fig. 5.
C for System NC, while it is above 290 oC for System C3 and System C5 resulting in a smaller
Figure 5 shows the molten-salt temperature distributions along the tank height at the discharging
time of 1 h, 3 h and 5 h. The quasi-isothermal region during which the molten-salt temperature is very
close to the PCT of PCM capsules can be found for all the systems. However, only one
quasi-isothermal region can be found for System NC, while 3 and 5 quasi-isothermal regions can be
identified for System C3 and System C5, respectively. As a result, the systems with cascaded PCM
capsules show a more linear distribution of the molten-salt temperature (especially for System C5).
The variations in the molten-salt outlet temperature and the accumulated discharging ratio are
presented in Fig. 6. The three systems all show a period of constant outlet temperature near the highest
PCT (i.e., 375 oC) after which the molten-salt outlet temperature all drops rapidly. After the plateau, the
molten-salt outlet temperature drops earlier for System C3 and System C5 compared to System NC.
That is because for the systems with cascaded PCM capsules more PCM capsules near the tank top
have already been solidified during the later discharging period as can be found in Fig. 2 (c), and
correspondingly the molten-salt temperatures near the tank top are lower. The molten-salt outlet
temperatures drop earlier after the plateau for System C3 than System C5, which is caused by that the
average PCT for System C5 is larger than that of System C3. When the molten-salt outlet temperature
drops below a threshold value, the discharged molten salt may fail to effectively generate useful steam
for power generation and the discharging process should be stopped, which means that in practical
applications the TES systems will not be fully discharged and the storage capacity of the TES system
may not be fully utilized. As a result, the operational storage capacity of the TES system depends on 15 Page 15 of 29
the discharging behavior. The above findings in Fig. 6 indicate that for TES systems with cascaded
PCM capsules, the chosen PCTs and system geometric parameters should be optimized to improve the
3.2 Single charging behavior
The charging characteristics of the three TES systems are discussed in the following section. Each
tank is assumed to be fully discharged at the beginning. At that condition all PCM capsules are at solid
state. During the charging process hot molten salt with a temperature of 390 oC enters the tank
continuously through the top port and flows downward through the void space in the storage tank. Fig.
7 shows the distributions of capsule centre temperature along the tank height at various charging time
of 1 h, 3 h, and 5 h. It can be seen that the centre temperature of capsules near the inlet of the hot
molten salt increases first, and the centre temperature of more capsules in the downstream region is
increased with the charging time. Isothermal regions which correspond to the melting process of PCM
capsules can also be found during the charging process. Only one isothermal region exists for System
NC and it can cover quite a long region. However, multiple isothermal regions can be found for
systems with cascaded PCM capsules, and the temperature of the isothermal regions corresponds to the
cascaded-PCTs of PCM capsules in the systems.
It can also be found that the PCM melting time for the systems with cascaded PCM capsules is
generally shorter than that for the system with uniform PCM capsules. For instance, most of PCM
capsules for System C3 and System C5 have been completely melted at 5 h while only PCM capsules
in the region between 12 to 14 m have been completely melted for System NC. That is caused by the
fact that the temperature difference between molten salt and the PCM capsules is lower for System NC
than those of System C3 and System C5.
To further investigate the melting process of PCM capsules during the charging process, the
variations in the centre temperature of the middle capsule at x=0.5H with the charging time for the
three TES systems which are shown in Fig. 8 are examined. From Fig. 8 an isothermal period during 16 Page 16 of 29
which the temperature is very close to the PCT of the middle capsule can be found for the three TES
systems. The isothermal period is from about 3 h to 13.4 h for System NC, while it is from 1.5 h to 3.5
h and from 1.5 h to 4.4 h for System C3 and System C5, respectively. This clearly demonstrates that
the middle capsules can be melted much faster in the systems with cascaded PCM capsules.
Figure 9 shows the molten-salt temperature distributions along the tank height at the charging time
of 1 h, 3 h and 5 h. The variations in the molten-salt temperature along the flow direction behave
differently for the three TES systems. It increases faster for System NC than for the systems with
cascaded PCM capsules, and the increment for System C5 is the slowest. For example, the molten-salt
temperature for System NC becomes as high as about 375 oC from the tank height of 11.5 m to 1 m at 3
h, while it steps down from about 375 oC to 305 oC for the same tank region for System C3 and System
C5. That is obviously because the melting processes of capsules with lower PCTs in the cascaded
systems drops down the temperature of flowing molten salt undergoing heat transfer with the PCM
The variations in the molten-salt outlet temperature and the accumulated charging ratio with time
are presented in Fig. 10. After a short period (about 1 h) of flowing out of low temperature molten salt
at 290 oC, the molten-salt outlet temperature for System NC increases rapidly to about 375 oC and
maintains at that temperature for quite a long time (from 3 to 22 h). However, the accumulated
charging ratio for System NC decreases significantly. When the molten-salt outlet temperature reaches
380 oC, the charging process takes 23.6 h and the charged ratio is only about 23%. This indicates that
the charging rate for the TES system with non-cascaded PCM capsules is very slow, which is possibly
due to that the uniform PCT is high and thus the heat transfer rate from the molten salt to the PCM
capsules is low.
Contrarily, for the systems with cascaded PCM capsules, the molten-salt outlet temperature firstly
climbs to about 305 oC, which is close to the PCT of the capsules near the outlet, and maintains at that 17 Page 17 of 29
temperature for less than three hours. It then increases rapidly to 375 oC after the isothermal period,
and dwells at that temperature for a short period before increasing rapidly again. When the molten-salt
outlet temperature reaches 380 oC, the charging time takes 8.6 h and the accumulated charging ratio is
about 59% for System C3, while the charging time takes only 5.6 h and the accumulated charging ratio
is about 77% for System C5. In other word, after charging the systems for the same time of 5.6 h, the
accumulated charging ratio is only 40% for System NC, while it is about 70% and 77% for System C3
and System C5, respectively.
As has been found in our prior work , the TES system with non-cascaded PCM capsules must
have a high PCT which is above the interest of application. However, Fig. 10 clearly shows that
System NC with a high PCT suffers from a low charging rate and a long charging time, meaning the
system with non-cascaded PCM capsules may be inappropriate to be used as TES systems utilizing
liquid as the HTF. From the above results, the systems with cascaded PCM capsules, especially System
C5, show both a fast discharging rate and a fast charging rate, and thus they are very promising to be
used as the compact TES system using liquid as the HTF.
436 437 438
3.3 Cyclic behavior Since System C5 shows the best performance considering both the charging and discharging of 25 oC and 50 oC.
behaviors, the cyclic behavior is investigated only for System C5 with different
As thus, the threshold values are
charging processes, respectively, when
discharging and charging processes when
temperature along the tank height at the end of some charging/discharging processes during the cyclic
T 25 C ,
and it increases from about 315 to 390 oC with a roughly five ladder-like distribution along the tank
Tdischarge,cut-off 365 C o
T 25 C
T 25 C o
Tcharge,cut-off 315 C
for the discharging and
. While the threshold values are both 340 oC for the
T 50 C o
. Fig. 11 shows the distributions of molten-salt
(Fig. 11a) and T 50 C (Fig. 11b). For the cycle process with
not all the molten-salt temperature reaches 390 oC at the end of the first charging process,
18 Page 18 of 29
height. While at the end of the first discharging process, the molten-salt temperature increases from
290 to 365 oC with a roughly five-ladder like distribution along the tank height. With the increase in
the cycle number, the molten-salt temperature at the end of each charging process decreases and it
tends to a fixed distribution. While for the temperature at the end of each discharging process, it
increases with the increase in the cycle number and also tends to a fixed distribution. It is seen that the
molten-salt temperature distributions for the 9th cycle are nearly the same with that for the 25th cycle,
indicating that the cycle process reaches to a repeatable state after 9 cycles. A similar trend can also be
found for the cycle process with
only after 3 cycles, which indicates that the required cycle number needed to reach to a repeatable
cycle is influenced by the threshold temperature to stop the charging/discharging process.
T 50 C .
However, the cycle process reaches to a repeatable state
Figure 12 shows the variations in the molten-salt outlet temperature with the time during some
charging/discharging processes for
T 25 C
(Fig. 12a) and T 50 C (Fig. 12b). For the cycle
T 25 C , the molten-salt outlet temperature keeps at the low temperature of 290
460 461 462
a short period of about 1 h, after which it increases to about 305 oC and maintains at that temperature
during most of the first charging time. The first hour’s charge with the molten-salt outlet temperature
of 290 oC during the first charging process is caused by the fact that the whole system is assumed to
have the temperature of 290 oC initially. For the subsequent charging processes, the period during
which the molten-salt outlet temperature keeps at 290 oC shrinks to be very small, and the temperature
starts to increase soon after the start of each charging process. On the other hand, the period during
which the molten-salt temperature maintains at about 305 oC decreases slightly with the increase in the
cycle number when the cycle number is smaller than 9. The molten-salt outlet temperature shows an
isothermal discharging period with the temperature of about 375 oC for each discharging process, and
the isothermal period decreases from about 2.7 h to 1.4 h when the cycle number increases from 1 to 9.
19 Page 19 of 29
After 9 cycles, the variations in the molten-salt outlet temperature with the time for both the charging
process and the discharging process become repeatable. The cycle process with
shows a similar phenomenon, and the variations become repeatable only after 3 cycles.
T 50 C
Figure 13 shows the variations in the accumulated energy and the accumulated efficiency with the T 25 C , Q in , Q charge
cycle number. For the cyclic process with
increase in the cycle number, and become stable when the cycle number is larger than 9. This is
because as discussed in Figs 11a and 11a the cyclic process reaches to a repeatable state after 9 cycles.
It is also seen that the corresponding accumulated efficiency increases from about 81% to 93% when
the cycle number is increased from 1 to 27. The limiting accumulated efficiency can be determined to
should be caused by the fact that some molten salt exiting from the system has a temperature above
290 oC during each charging process, meaning the input thermal energy has not be fully stored. For the
cyclic process with
since the cycle process reaches to a repeatable state at that time. The corresponding accumulated
efficiency increases from about 88.5% to 92.6% when the cycle number increases from 1 to 27, and the
limiting accumulated efficiency is calculated to be
be concluded that a high accumulated efficiency can be achieved by the TES system filled with
cascaded PCM capsules, and the efficiency will be slightly lowered when increasing the threshold
temperature to stop the charging process.
Q discharge / Q in 95.1%
using the stable values of
T 50 C ,
Q in , Q charge
Q in .
Q discharge all
decreases with the
The efficiency loss of about 4.9%
all decreases to stable values after 3 cycles,
Q discharge / Q in 92.8%
. Therefore, from Fig. 13 it can
On the other hand, when the cyclic process reaches to a repeatable state the useful discharged T 25 C and T 50 C ,
energy ( Q discharge ) is 82 GJ and 152 GJ for the cyclic processes with
respectively, which take up only 45.5% and 84.4% of the maximum storage capacity of the system (50
MWh=180GJ). This is mainly because during the cyclic process the system is not fully
charged/discharged at each charging/discharging process. Generally, increasing
is beneficial to
20 Page 20 of 29
enlarge the practical storage capacity of the TES system with cascaded PCM capsules. When designing
such a TES system, the influence of the threshold temperature on the practical storage capacity, which
is smaller than the total storable capacity, has to be considered. And a larger system may be necessary
to achieve the required storage capacity.
501 502 503
We have presented a transient, one-dimensional dispersion-concentric (D-C) model to numerically
investigate the dynamic behaviors for the charging/discharging cyclic processes of the molten-salt
packed-bed TES system filled with high-temperature PCM capsules. Three different storage systems
including the non-cascaded system, the 3-cascaded system and the 5-cascaded system have been
studied using various working modes. Salient findings of the present work include:
(a) The characteristics of heat transfer for cascaded systems are more complicated than the
non-cascaded system. Multiple isothermal regions for the temperatures of PCM capsules and
molten salt exist during both the charging and discharging processes of the cascaded systems. As a
result, the molten-salt temperature along the tank height for the cascaded systems shows more
linear distributions during both the charging and the discharging processes.
(b) The packed-bed system with non-cascaded PCM capsules may be inappropriate to be used as
TES systems because it suffers from a low charging ratio and a long charging time due to the
constrains of PCT. While the cascaded systems especially with 5 cascaded PCTs are very
promising since they show both a fast discharging rate and a fast charging rate.
(c) The cyclic process of the cascaded system with 5 PCTs can reach to a repeatable state after some
cycles, at which high accumulated efficiencies can be achieved. The required cycle number to
get to the equilibrium, the satisfied accumulated efficiencies and the practical storage capacity
all depend highly on the threshold temperatures to stop the charging/discharging process.
522 523 21 Page 21 of 29
This work is supported by the National Natural Science Foundation of China (51522602), and the National Key Basic Research Program of China (973 Program) (2013CB228304).
527 528 529
specific heat capacity, J kg-1 K-1
spherical capsule diameter, m
acceleration due to gravity, m s-2
Tank height, m
enthalpy of PCM, J kg-1
heat transfer coefficient at the capsule surface, W m-2 K-1
volumetric interstitial heat transfer coefficient, W m-3 K-1
intrinsic permeability of porous medium, m2
Thermal conductivity, W m-1 K-1
mass flow rate, kg s-1
22 Page 22 of 29
time, s consumed time during charging processes when the HTF outlet
tc temperature reaches to the threshold value consumed time during discharging processes when the HTF outlet td temperature reaches to the threshold value u
velocity, m s-1
tank volume, m3
location along the axis of the tank, m
thermal diffusivity, m2 s-1
thermal expansion coefficient, K-1
Porosity of packed-bed region
Viscosity, kg m-1 s-1
Density, kg m-3
effective thermal conductivity, W m-1 K-1
radial coordinate inside each capsule
value for the charging process
value for the discharging process
23 Page 23 of 29
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611 612 613 614 615 616 617 618 619 620
Fig. 1. Schematic of the molten-salt packed-bed TES systems using spherical PCM capsules: (a)
System NC, (b) System C3, and (c) System C5. (only color on the web)
27 Page 27 of 29
Fig. 2. Distributions of the capsule centre temperature along the tank height at different discharging
time: (a) 1 h, (b) 3 h, (c) 5 h. (only color on the web)
Fig. 3. Distributions of temperature of capsule centre, capsule surface and molten salt along the tank
height at discharging time of 5 h for System NC and System C5. (only color on the web)
Fig. 4. Variations in the centre temperature of the middle capsule (x=0.5 H) with the discharging time.
(only color on the web)
Fig. 5. Distributions of the molten-salt temperature along the tank height at different discharging time:
(a) 1 h, (b) 3 h, (c) 5 h. (only color on the web)
Fig. 6. Variations in the molten-salt outlet temperature and the accumulated discharging ratio with the
discharging time. (only color on the web)
Fig. 7. Distributions of the capsule centre temperature along the tank height at different charging time:
(a) 1 h, (b) 3 h, (c) 5 h. (only color on the web)
Fig. 8. Variations in the centre temperature of the middle capsule (x=0.5 H) with the charging time.
(only color on the web)
Fig. 9. Distributions of the molten-salt temperature along the tank height at different charging time: (a)
1 h, (b) 3 h, (c) 5 h. (only color on the web)
Fig. 10. Variations in the molten-salt outlet temperature and the accumulated charging ratio with the
charging time. (only color on the web)
Fig. 11. Distributions of molten-salt temperature along the tank height at the end of some T 25 C
T 50 C (b).
charging/discharging processes during the cyclic process for
(only color on the web)
Fig. 12. Variations in the molten-salt outlet temperature with the time during some T 25 C
T 50 C (b).
charging/discharging processes within the cyclic process for
(only color on the web)
Fig. 13. Variations in the accumulated input storable energy, the accumulated charging energy, the
accumulated discharging energy and the accumulated efficiency with the cycle number. (only color on
651 652 653 654 655
Table 1 Geometric parameters and properties used in the model.
28 Page 28 of 29
Tank height, m Tank radius, m
Diameter of PCM capsule, m
Tank initial temperature before charging, C
Tank initial temperature before discharging, C
Density of PCM, kg m
Specific heat capacity of solid PCM, J kg K
Specific heat capacity of liquid PCM, J kg K
Thermal conductivity of solid PCM, W m K -1
Thermal conductivity of liquid PCM, W m K PCM latent heat of fusion, kJ kg
Thermal expansion coefficient of liquid PCM, K Dynamic viscosity of liquid PCM, Pa s Absolute inlet velocity, m s
0.001 2.59e-3 1.85e-3
Time step, s
29 Page 29 of 29