Proceedings of the ASME 2012 6th International Conference on Energy Sustainability
ES2012
July 23-26, 2012, San Diego, CA, USA
ES2012-91389
ANALYSIS OF A LATENT THERMOCLINE ENERGY STORAGE SYSTEM FOR CONCENTRATING SOLAR
POWER PLANTS
1
1
2
Karthik Nithyanandam , Ranga Pitchumani * and Anoop Mathur
Advanced Materials and Technologies Laboratory, Department of Mechanical Engineering, Virginia Tech, Blacksburg,
2
th
Virginia 24061, USA; Terrafore Inc., 100 South 5 Street, Suite 1900, Minneapolis 55402, USA.
1
ABSTRACT:
The primary purpose of a thermal energy storage system in
a concentrating solar power (CSP) plant is to extend the operation of plant at times when energy from the sun is not adequate by dispatching its stored energy. Storing sun’s energy in
the form of latent thermal energy of a phase change material
(PCM) is desirable due to its high energy storage density
which translates to less amount of salt required for a given
storage capacity. The objective of this paper is to analyze the
dynamic behavior of a packed bed encapsulated PCM energy
storage subjected to partial charging and discharging cycles,
and constraints on charge and discharge temperatures as encountered in a CSP plant operation. A transient, numerical
analysis of a molten salt, single tank latent thermocline energy
storage system (LTES) is performed for repeated charging and
discharging cycles to investigate its dynamic response. The
influence of the design configuration and operating parameters
on the dynamic storage and delivery performance of the system is analyzed to identify configurations that lead to higher
utilization. This study provides important guidelines for designing a storage tank with encapsulated PCM for a CSP plant
operation.
(sensible heat). Thus thermal storage systems using PCM as
storage medium have the advantage of being compact in size.
However, a major technology barrier that is limiting the use of
latent thermal energy of PCM is the higher thermal resistance
provided by its intrinsically low thermal conductivity. This
requires large heat transfer surface area of interaction between
the working fluid and PCM in order to maintain high heat
rates, typically required in power plants. Several efforts [1–6]
were made to improve the heat transfer rates. However, a
promising approach is to increase the heat transfer area by
incorporating the PCM mixture in small capsules using suitable shell materials. For example, PCM stored in capsule diameters of 10 mm possess surface area of more than 600 square
meters per cubic meter of capsules. Research to find suitable
materials and process to encapsulate high temperature PCM
mixtures is underway [7]. In this paper, we discuss the effectiveness of using latent heat when PCM melts and solidifies
inside small capsules by direct contact with a heat transfer
fluid.
A single-tank thermocline storage system packed with
spherical capsules containing PCM is considered in the present work. The working of latent thermocline energy storage
(LTES) system in a CSP involves the exchange of heat between the HTF and the packed bed of spherical PCM capsules.
The operation of a LTES constitutes the charging and discharging processes. During charging, hot HTF from the solar
power tower enters the LTES from the top and heat transfer
between the HTF and PCM takes place thus effecting the
melting of PCM at a constant temperature. As hot HTF enters
the tank, the existing cold fluid in the tank is forced from the
bottom to return to the solar field. During discharging, cold
fluid is pumped from the bottom of the LTES resulting in the
solidification of the PCM within the capsules and the hot fluid
exiting the top of the tank is directed to the power block for
steam generation. Buoyancy forces ensure stable thermal stratification of hot and cold fluids within the tank. The charging
process takes place during the day when solar energy is available while discharging is effected whenever the sun is not
available or when there is a peak demand in electricity. The
charging and discharging process combined is referred to as
one cycle and repeated cycles subjected to partial charging and
INTRODUCTION
Concentrating solar power (CSP) generation is becoming
attractive for meeting current and future energy needs. A key
requirement to make this energy option competitive is through
the use of a thermal energy storage unit. Storing energy for
future use allows the power plant to operate continuously during periods of intermittent sun, reduces the mismatch between
the energy supply and demand by providing load leveling and
helps to conserve energy by improving the reliability and performance of energy system Thermal energy can be stored as
either sensible or latent heat. Most of the thermal energy storage systems in operation are based on sensible heat storage.
However, storing heat in the form of latent heat of fusion of
phase change material (PCM) in addition to sensible heat significantly increases the energy density. For example, the energy required to melt one kilogram of sodium nitrate (latent
heat) is 75 times higher compared to the energy required to
raise the temperature of one kilogram of sodium nitrate by 1K
* Corresponding author. +1 540 231 1776; [email protected]
1
Copyright © 2012 by ASME
discharging process may limit the rate of phase change of
PCM and decrease the utilization of the tank. This paper focuses on investigating the dynamic thermal behavior of LTES
to develop guidelines for the design of latent thermocline
thermal energy storage tank for a CSP plant.
Numerous works on the numerical modeling of sensible
heat storage in packed beds are found in the literature [8–15].
As a pioneering work, Schumann et al. [9] presented the first
numerical study on modeling of the packed bed which is widely adopted in the literature. The model enables prediction of
the temporal and axial variation of the HTF and filler bed
temperatures in a thermocline tank. Van Lew et al. [14] adopted the Schumann model to analyze the performance of thermocline energy storage system embedded with rocks as filler
material. The efficiency of solving the governing equations
using the method of characteristics was discussed. Ismail and
Henriquez [16] presented a mathematical model for predicting
the thermal performance of cylindrical storage tank containing
spherical capsules filled with water as PCM. The model was
used to investigate the influence of the working fluid inlet
temperature, flow rate of the working fluid and material of the
spherical capsule of 77 mm diameter during the solidification
process. Felix Regin et al. [17] and Singh et al. [18] presented
a brief review of the works performed in the thermocline storage system till date. Felix Regin et al. [19] also reported the
modeling of thermocline energy storage system with embedded PCM capsules. The modeling follows the Schumann’s
equation except that the dependent variable for energy equation of filler bed is enthalpy and not temperature. The resistance developed during the solidification phase change process was accounted for by a decrease in the heat transfer coefficient between the HTF and the filler bed. Hänchen et al. [20]
employed the Schumann’s equation to discuss the effects of
particle diameter, bed dimensions, fluid flow rate and the solid
filler material on the dynamic performance of thermocline
storage system. Uniform charging and discharging times were
considered and the efficiency of the system as a function of
cycles was monitored. Wu and Fang [21] analyzed the discharging characteristics of a solar heat storage system with a
packed bed of spherical capsules filled with myristic acid as
PCM. The influence of HTF mass flow rate, inlet temperature
and the porosity of packed bed were studied.
Although several articles on the thermocline tank packed
with sensible filler materials is reported, relatively few works
on the performance of a latent thermocline energy storage
system is found in the literature. To the author’s knowledge, a
thorough modeling of solidification and melting process of
encapsulated PCM in a thermocline energy storage system and
a comprehensive study of the dynamic performance of the
system subjected to constraints dictated by the power plant
operation is lacking in the literature. To this end, the objective
of the present study is to develop a detailed model of a thermocline storage system containing spherical capsules filled
with PCM and investigate the influence of the design and operating parameters on the dynamic performance of the system
to identify configurations that lead to higher system utilization. A further contribution is that while most of the studies in
the literature pertain to low temperature LTES, the present
study focuses on a high temperature LTES system which can
be installed in CSP plants.
MATHEMATICAL MODEL
Figure 1a illustrates a schematic of a thermocline storage
tank of height Ht and radius Rt packed with spherical capsules.
For the sake of clarity in illustration, the capsules are schematically shown to be arranged in an ordered fashion. However,
in reality, as the PCM capsules are piled up pressing each other from the top to bottom the packing scheme may vary and
the porosity of the packed bed for a fixed diameter of spherical
capsules can range from 0.26–0.476 [22]. The red colored
arrows indicate the direction of hot HTF during charging
while the blue colored arrows indicate the direction of cold
HTF as it enters the storage system during discharging. The
inner radius of the capsules filled with PCM (yellow shade) is
represented by Rc, while the thickness of the capsule wall is
denoted by b as depicted in Fig. 1b.
The flow of the HTF is considered incompressible. The
PCM is assumed to be homogeneous without any impurities
and isotropic such that the physical properties are independent
of direction. This assumption affects the melting (solidification) rate of the PCM although the effect of which on microencapsulated PCM as considered here would be negligible.
The outer surface of the thermocline tank is considered to be
adiabatic and a uniform radial distribution of the HTF flow is
assumed which was also confirmed from a detailed computational analysis of the system (not discussed here). Since the
Peclet number of the HTF flow in the thermocline tank is large
(Pe >> 100) the axial heat conduction in the HTF is negligible
[23]. The Biot number of the transient heat conduction in a
single PCM spherical capsule is small enough that lumped
heat capacitance method is applicable; however a transient
radial energy equation in the PCM is solved for to calculate
the spatial and temporal temperature variation and melt interface location. Thermal expansion and shrinkage of PCM in the
spherical capsules is not accounted for in the present study and
the density of solid and liquid phase of the PCM is considered
to be same. Thermal conduction between the spherical PCM
capsules is neglected because of the large contact resistance.
The melting and solidification process within a PCM is modeled by the enthalpy-porosity technique as introduced by
Voller et al. [24]. By this approach, the porosity in each cell is
set equal to the liquid fraction,  in the cell, which takes either
the value of 1 for a fully liquid region, 0 for a solid region, or
0 <  < 1 for a partially solidified region (mushy zone). Based
on the foregoing assumptions, the governing energy equations
in the axi-symmetric coordinate system (z-r) shown in Fig. 1a
for the HTF and encapsulated PCM phase are as follows:
 c
f f
T
T
 c m T
p, r  Rc
f
3(1   )
f
f f
f


t
  R 2 z
4 ( R  b)3 RT1  RT2
f
t
c
T



 p  c p  hl

T p
 T p
T p
1 

 2
(k p , eff r 2
)
 t
r
r r

(1)
(2)
where RT1 and RT2 in Eq. (1) denote the thermal resistance
offered by radial heat conduction in the capsule wall and convective heat transfer between the HTF and filler phase
2
Copyright © 2012 by ASME
Di appearing in Eq. (3) represents the thickness of the liquid
layer in the PCM. Since the thickness of the liquid layer is
very small initially, heat transfer across the liquid layer occurs
primarily by conduction although ultimately, convection becomes important as the melt region expands. Therefore, heat
transfer through the melt is calculated by evaluating both (i) a
conduction heat transfer rate using kp and (ii) a rate associated
with the use of keff,p for free convection in a spherical enclosure. The expression that yields the largest heat transfer rate
was used in the computations.
In order to generalize the model and the corresponding results, Eqs. (1) and (2) are non-dimensionalized as follows:
3(1   )(
f )

p , r *  R c*

*
b
Nu
b*
 f  f  b* (1  * ) 2

(
1

)
 *  * 
(4)
Rc 2( Rc*  b* )
Rc*
t
z

Nu

 Re Prf  2( Rc*  b* ) Rc*
Hot HTF
r
z
Rt
b
Ht
Rc
(b)
(a)
(1  St
Cold HTF
FIGURE 1 (a) Schematic of LTES, (b) PCM spherical capsules
 f  1 (0), z *  0 (1); Ch arg ing ( Disch arg ing )
 f
z *
 p
r
*
 p
r
c
*
 0, z *  1 (0); Ch arg ing ( Disch arg ing )

( p   f )
1
 *
* *
R


b k
 2 Rc k f
c
*
*   
*
* 

(
R

b
)
Nu

(
R

b
)
c
c

 

*
; r  Rc*
* *
w
(6)
 0; r *  0
The non-dimensional parameters appearing in Eqs. (4)–(6)
are defined as follows:
hand side of Eq. (1) denotes the PCM temperature calculated
at the internal radius of the PCM capsules as shown in Fig.
1(b).
The circulation of liquid due to buoyancy driven natural
convection currents during the melting of PCM are modeled
using empirical correlations to determine the enhanced thermal conductivity of the PCM melt front, kp,eff. The effective
thermal conductivity is evaluated using the correlation given
in [26] which covers both the conduction and convection regimes and is expressed as k p , eff  k p  Nu conv , where kp is the

R
z *
r *
m t
b
;r 
;t 
; b* 
; Rc*  c
Ht
Ht
Ht
Ht
 f Rt2 H
z* 
f 

T f  TD
TC  TD
 f cf
 pc p
; p 
;k 
*
w

kp
kw
T p  TD
; St 
TC  TD
;k 
*
f
kp
kf
Nu  2  2.87 ( Rc*  b* ) Re
molecular thermal conductivity of PCM and Nuconv is calculated from
1/ 4
Ra1/ 4
 D  Di 

Nu conv  1.16 f (Pr) o
54

3/ 5
 2 Di  Di / Do   ( Do / Di ) 4 5
(3)
2.012
f (Pr) 
4
/
9
3  1  (0.492 Pr p ) 9 /16

(5)
The boundary conditions during the charging and discharging process are specified as
respectively
which
can
be
expressed
as
b
1
RT1 
and RT2 
. The cor4k w Rc ( Rc  b)
4h( Rc  b) 2
relation for convective heat transfer coefficient, h between the
HTF and porous packed bed is obtained from Galloway and
Sage [25]. The notations  , c, k and T correspond to density,
specific heat, thermal conductivity, and temperature respectively of either the HTF denoted by subscript ‘f’ or the encapsulated PCM denoted by subscript ‘p’. hl denotes the latent
 represents the
heat of fusion of the PCM, t denotes time, m
mass flow rate of the heat transfer fluid, and  denotes the
porosity of the packed bed. The term, T p, r  R on the right

*
f L  p   k f  Nu conv   * 2  p 
r

) * 
 p t
Re . Prf
r * 
r * 

hl
;
c p (TC  TD )
(7)
;
1/ 2
Pr1f / 3  0.098( Rc*  b* ) RePr1f / 2 ;

 f cf
H m
Re  t 2 ; Prf 
kf
 f Rc

The interstitial Nusselt number, Nu thermally couples the
HTF with the spherical PCM capsules, the expression for
which is obtained from Galloway and Sage [25]. The other
characteristic non-dimensional parameters that appear in Eq.
(7) are the Reynolds number, Re, Prandtl number of HTF, Prf
and the Stefan number of PCM, St. Subscripts C and D corre-

This correlation is valid for a wide range of Prandtl (Prp)
number and Rayleigh number (Ra) of the PCM. The term Do-
3
Copyright © 2012 by ASME
spond to the hot inlet HTF temperature during charging and
the cold inlet HTF temperature during discharging, respectively.
The numerical simulations started from a charge process
assuming that the tank is completely discharged resulting in
the following initial conditions for the HTF and filler phase
 f  0;  p  0
(8)
The complete set of governing equations is discretized using the finite volume approach and the melting/solidification
of the PCM is modeled using the fixed-grid enthalpy approach
as presented by Voller et al. [24]. In order to accurately predict the liquid fraction in the fixed grid enthalpy-based procedure, the liquid fraction in each computational cell, in conjunction with the temperature predicted by the equation for
encapsulated PCM, should be updated at each iteration within
a time step. In the present case, the enthalpy iterative updating
scheme of the liquid fraction takes the following form for a
pure PCM, which melts at constant temperature:
a
 in 1   in  0i c p  pn,i  F 1( in )
(9)
ai
In the above equation, ai is the coefficient of  i for the radial nodal point i in the discretized equation of the energy
equation for PCM, n is the iteration number,  is a relaxation
factor, which is set to 0.01 for the present case, and F-1 is the
inverse of latent heat function which takes the value of Tm for
a pure substance. The coupled system of governing equations
is solved by implicit method and the solution is advanced in
time using Runge-Kutta time stepping scheme. After careful
examination of the grid refinement process, a grid interval size
of 0.003 is chosen in the axial direction within the thermocline
tank and the encapsulated PCM within the spherical capsules
is discretized into 10 uniform zones in the radial direction. The
non-dimensional time step chosen for the study was
tion ( U T  QL* , D QL* , max ) where QT* ,D ( Q L* ,D ) denote the total
(latent) energy discharged in a cycle which is obtained by subtracting the total, QT* (latent, Q L* ) energy available within the
system, at the end of the discharging process form the total
energy available within the system at the end of the charging
process of the corresponding cycle. QT* ,max and QL* ,max represent the maximum total and latent storage capacity of the tank
which can be easily obtained from Eqs. (10a) and (10b) assuming  f ,  p  1 and   1 .
RESULTS AND DISCUSSIONS
The model was validated with experimental results obtained
from Pacheco et al. [27] for a small pilot scale, 2.3 MW h sensible thermocline storage tank as illustrated in Fig. 2a. A eutectic molten salt of NaNO3 and KNO3 and Quartzite rocks
were used as the HTF and filler material, respectively. The
other properties of the material could be obtained from [27].
(a) 1.0
avg

Average Temperature, 

sules respectively. The performance metrics characterizing the
behavior of the system analyzed in the present work are the
cyclic total utilization ( U T  QT* , D QT* , max ) and latent utiliza-
t  0.0001.
*
o
Temperature, T [ C]
 
QL*   
j 1i 1
(1   ) St iVi z
R  
* 3
c
t = 1.0 h
0.4
t = 1.5 h
0.2
t = 2.0 h
0.2
0.4
0.6
Axial Position, z*
0.8
1.0
HTF, z/H = 0.25
T
Q L*
*
t = 0.5 h
0.6
(b) 80
composed of sensible energy ( ) and latent energy ( )
components calculated as the summation of energy stored in
all the PCM capsules and the HTF which can be determined
from the following expressions
*
*
p 
q (1   ) p , iVi z 
*
*

(10a)
QS    f z  
3
j 1
i 1

Rc* 


p q
0.8
0.0
0.0
The numerical model allowed for modeling all the physical
heat transfer processes that occur within the system namely,
the convective heat transfer between the HTF and the filler
phase, the radial thermal conduction in the wall, the conduction in the solid PCM, conduction and natural convection
within the liquid PCM. The outputs from the model comprise
the transient axial variation of temperature in the HTF, the
transient radial variation of temperature and the melt fraction
contour of PCM within the capsule at any axial location. The
transient total energy available within the system ( QT* ) is
Q S*
t = 0.0 h
70
60
(10b)
Conduction
PCM, z/H = 0.5
40
30
0
*
Conduction
+
Convection
50
T
20
40
60
80 100 120 140 160
Time, t [min]
FIGURE 2 Comparison of numerical results obtained for
(a) axial variation of temperature with experimental data of
[27] and (b) transient temperature
Figure 2 variation of HTF and
PCM at various axial positions with experimental data of
[28].
where i represents the radial node at any axial location, j. p
and q denotes the total number of discretized finite volumes in
the axial direction of the tank and radial direction of the cap-
4
Copyright © 2012 by ASME
b*  5  108 ;
Re  6000;
HTF Temperature, 
Rc*  0.0005;
goes to the solar field reaches a certain maximum temperature
as dictated by the solar power tower operation. For a given
solar heat flux, as the inlet temperature of the HTF into the
solar power tower increases, the outlet temperature of the HTF
from the tower which is directed towards the power block also
increases. In order to maintain the CSP plant design outlet
temperature, correspondingly the HTF mass flow rate has to
be decreased which will affect the overall efficiency of the
plant operation in generating the required power output. The
charging cut-off temperature, referred to as  C from this point
on, is thus established by the above mentioned constraint.
After the charge process, the temperature distribution in the
tank is taken as the initial condition for the subsequent discharge process. During discharge, cold HTF is directed into
the tank bottom at z* = 1 and the exiting hot HTF collected
from the top of the tank is pumped to the power block for
Rankine cycle superheated steam generation. Similar to charging, the discharge process is stopped after the temperature
exiting the top of the tank reaches a certain minimum cut-off
temperature,  D below which the Rankine cycle efficiency
decreases significantly. The combined charge and discharge
process is referred to as one cycle. In the present study,  C
and  D were selected to be 0.15 and 0.85 respectively representative of restrictions imposed on 100 MWe CSP plant operation [30]. Subsequent cycles were carried out until the
(a) 1.0
f
The experimental results obtained for the transient discharging
profile of the HTF temperature for every 30 minutes up to a
maximum of 2 hours are denoted by markers. The initial condition corresponds to the final charging state of the first cycle,
which was also carried out for 2 hours. To analyze the performance of sensible thermocline system with the developed
model for latent thermocline energy storage system, the nondimensional PCM melting temperature,  m is set to a value
greater than 1 and the Stefan number of the filler material, St
is set to 0. The numerically simulated axial temperature distributions of the average temperature between the HTF and filler
particle for the various time instants as reported in [27] are
represented by the colored lines in Fig. 2a. Within the experimental uncertainty, the agreement between experimental data
and numerical results is quite satisfactory. Fig. 2b shows the
comparison of the numerical results obtained from the present
model with experimental data obtained from Nallusamy et al.
[28] for a packed bed thermocline system filled with spherical
capsules of diameter 55 mm. The capsules were filled with
paraffin wax which melts at 60 °C and water was selected as
the HTF. It is observed that prediction of melting rate of the
PCM with convection assisted model leads to a sound agreement with the experimental data than a conduction only model. Neglecting the free convection effects within the PCM predicts a slower melting rate which is not in accordance with the
obtained experimental data. Hence it is important to account
for the buoyancy driven natural convection currents which
ensues during the charging process by suitably varying the
effective thermal conductivity of the PCM as discussed in the
previous section. Acceptable agreement with experimental
results ensures the validity of the model and the parametric
studies conducted using the model is discussed in the reminder
of this section.
The operating and design parameter considered in the present study are the Reynolds number, Re and non-dimensional
capsule radii, Rc* respectively. The default case pertains to
Ste  0.25;
0.6
Total Utilization, U
T
0.4
0.2
Discharge
t* = 0.0
m  0.125; Prf  5;   1; k  1; k  1 . The Reynolds
number and the capsule radius have a significant effect on the
pressure drop across the tank which dictates the parasitic
pump power and cost. Hence the non-dimensional pump work
during discharge is also monitored in the present study to
study the effects of Reynolds number and the non-dimensional
capsule radius ( Rc* ) on the pump work. The non-dimensional
pump work during discharge can be obtained from,
W p*  p *t D* (Re . Pr)2 where the non-dimensional pressure
*
p
0.0
0.0
0.2
0.4
0.6
Axial Position, z*
0.8
1.0
f,e
(b) 1.0
HTF Exit Temperature, 
*
w
Charge
0.8
drop can be expressed as, p*  pRt2 m and the pressure
drop p for flow through a porous obtained from Ergun’s
expression [29].
Figure 3a shows the axial temperature distribution of the
HTF,  f at the end of charging and discharging process of the
latent thermocline storage system corresponding to fourth cycle. Initially at t* = 0, the tank is in a completely discharged
state as established by Eq. (8). The numerical computation
started from a charge process with the hot HTF entering the
top of the tank at z* = 0. Charging was continued until the
temperature of the cold HTF which exits the tank at z* = 1 and
Discharge
0.8
0.6
0.4
0.2
0.0
0.0
Charge
0.3
0.6
*
Time, t
0.9
1.2
FIGURE 3 (a) Axial variations of the charge and discharge
temperature profile of the HTF and (b) transient variation
of the HTF charge and discharge exit temperature
5
Copyright © 2012 by ASME
HTF axial temperature distribution within the tank reached a
cyclic quasi-steady state independent of the initial condition. It
was found that, with the current conditions the solution
reached cyclic steady state after four charge and discharge
cycles for the various range of parametric values considered in
the present study and the results presented pertain to the system performance at the end of fourth cycle. The percentage of
shaded area in Fig. 3a gives a visual representation of the total
utilization, UT of the LTES system.
From Fig. 3a it can be seen that, the discharge temperature
profile at any given time can be divided into four zones: a
constant low-temperature zone (  f  0 ) near the discharge
(a) 1.0
Melt Fraction, 
0.8
Charge
Discharge
0.6
Latent
Utilization, U
0.4
L
0.2
t* = 0.0
0.0
0.0
inlet, a constant high-temperature zone (  f  1 ) which pre-
0.4
0.6
Axial Position, z*
Sensible Energy Charged (Discharged),
*
*
(Q
Q
)
S,C
S,D
(b) 1.2
0   f  1 ). In the constant low- and high-temperature zones
the molten salt and PCM capsules are in thermal equilibrium
while in the heat exchange zone energy in the form of sensible
heat is transferred from the PCM capsules to the HTF during
discharge and in the constant melt-temperature zone, energy is
transferred in the form of latent heat from the PCM to the
HTF.
The exit temperatures of the HTF during the charge and
discharge process are portrayed in Fig. 3b. The solid red colored line corresponds to the exit temperature profile during the
first cycle while the dashed red colored line correspond to the
exit temperature profile established during the fourth cycle.
During the charge process, the exit temperature remains at the
high temperature after which it increases and then stays steady
at the melting temperature of the PCM until it increases to the
cut-off temperature within a short duration. Thus possessing a
PCM which melts at a temperature below the charging cut-off
temperature is seen to extend the operation of a LTES. Similar
exit temperature profile for the discharge process is represented by solid and dashed blue colored lines, albeit, the delineation between the curves is hardly discernible as a cyclic quasisteady state was achieved within the first two cycles for the
default design and operating conditions.
Figure 4a depicts the axial variation of melt fraction within
the encapsulated PCM in the thermocline tank at the end of the
charge and discharge process of the fourth cycle. The percentage of the shaded area depicts the latent utilization of the system which is effectively the amount of PCM in the storage
tank that undergoes alternate melting and solidification during
the cyclic charge and discharge process respectively. It is seen
that during the first charge process almost all the PCM is
completely molten except for some amount of PCM near the
exit of the tank, as the HTF temperature at z* = 1 reaches the
charging cut-off temperature. During the subsequent discharge
process, only 40 % of the PCM is solidified before the temperature of the HTF exiting the top of the tank at z* = 0 decreases from  f  1 to  f   D . This is attributed to the low
0.8
1.0
0.2
Charge
Discharge
1.1
0.1
1.0
0.9
1
2
3
Latent Energy Charged (Discharged),
*
*
(Q
Q
)
L,C
L,D
vails near the discharge outlet, a constant melt-temperature
zone (  f   m ) and an intermediate heat exchange zone (
0.2
0
4
Cycle, i
FIGURE 4 (a) Axial variation of the PCM melt fraction during the charge and discharge process and (b) cyclic sensible and latent energy charged and discharged.
of energy charged at the first cycle is higher than the rest of
the cycles while the energy discharged by the thermocline tank
is almost the same throughout the four cycles which is in accordance with the trends observed in Figs. 3a and 4a. Thus the
performance of the thermocline tank degrades from the first
cycle and hence the performance of the tank is explored only
after a cyclic quasi-steady state is achieved.
Figure 5 portrays the effects of Reynolds number on the
Nusselt number for various non-dimensional capsule radii.
The influence of Reynolds number and the non-dimensional
capsule radius on the Nusselt number is obtained from the
empirical correlation suggested by Galloway and Sage [25]. It
is observed that both Reynolds number and capsule radius
have a pronounced effect on the Nusselt number and the heat
transfer rate between the HTF and spherical PCM capsules is
observed to be higher for larger radii capsules and higher HTF
 . Also it is important to observe that the
mass flow rate, m
Nusselt number levels off after a certain Reynolds number
after which increasing the HTF mass flow rate does not have a
significant impact on the heat transfer rate between the HTF
and the spherical PCM capsules. The trends reported in Fig. 5
will be referred to in the discussions pertaining to the rest of
the figures.
Figure 6a shows the axial discharge temperature profile of
the HTF at the end of the fourth cycle for various Re. It is observed that with increase in Reynolds number the heat exchange zone expands. At the higher Reynolds number, a
temperature difference between the HTF discharge inlet temperature,  D and the PCM melting temperature,  m compared
to the charge process and also the slow conduction dominated
discharge mechanism. Figure 4b portrays the energy charged
and discharged by the tank as a function of the cycles. For this
particular default case, the thermocline settles into a cyclic
quasi-steady state by the end of the second cycle. The amount
6
Copyright © 2012 by ASME
(a)
(b)
1500
1.0
*
(a)
R = 0.0080
Re = 60
Re = 600
Re = 6000
Re = 60000
Re = 300000
Re = 600000
c
900
f
*
HTF Temperature, 
Nusselt Number, Nu
1200
*
R = 0.001
R = 0.0040
c
c
600
*
300
R = 0.0003 *
c
R = 0.0001
c
*
R = 0.0005
c
600
0.4
0.2
D
Charge (Discharge) Time, t
1.0
400
(b)
Charge
Discharge
1.0
300
0.8
200
0.6
100
0.4
0
(c)
L
Total (Latent) Utilization, U (U ) [%]
Nusselt Number, Nu
0.8
p
longer flow distance is required for the HTF to be heated by
80 spherical capsules
the PCM
which results in a gradual temper*
R = 8.000
c
ature increase and a corresponding
expansion of the heat exchange zone. Also, the constant melt-temperature zone is ob60
served to reduce in height as the Reynolds number increases.
*
*
= 4.000
R = 0.125
For instance at Re =R600000,
the discharge temperature
profile
c
c
depicted
by
the
solid
red
colored
line
* does not possess the
40
R = 0.250
c
constant melt-temperature * zone reflecting
an inefficient exR = the
0.500
traction of latent
energy
from
PCM.
Figure
6b shows that
c
*
R = 1.000
the charge
time decreases with increase in Reyn20 (discharge)
c
olds number. Since the heat exchange zone is at a lower temperature than the higher temperature, the discharging cut-off
0
temperature
is reached quicker for higher Re as the heat ex0
10
20
30
40
change zone expands. Consequently, the utilization and latent
HTF
Prandtl
Number,
Pr
utilization of the system also decreases
in Fig. 6c.
f
Figure 2 as portrayed
As seen in Fig. 6c, beyond a Re = 150000, the utilization and
also the latent utilization does not decrease much because of
the higher heat transfer rate between the HTF and spherical
PCM capsules concomitant with increase in Nusselt number,
Nu observed in Fig. 5. Although the non-dimensional pump
work, W*p depends on Re2 , it is observed in Fig. 6b that the
discharge time decreases drastically with increase in Re, resulting in an almost linear increase in the pump work.
Similarly, Fig. 7a presents the axial discharge temperature
profile of the HTF at the end of the fourth cycle for the various
non-dimensional capsule radii values, R*c. Similar to the effect
of Re, it was observed that increasing R*c results in an expansion of the heat exchange zone and restricts the formation of
constant melt-temperature zone. This is attributed to the fact
that for a given height of the tank, increasing the capsule radius, results in an increased resistance to the conduction dominated PCM solidification which occurs during discharge process. Also, the surface contact area between the HTF and capsules per unit tank volume decreases with larger R*c, which
limits the heat exchange rate and leads to a poor thermocline
performance. Figure 7b presents the effect of the nondimensional capsule radius on the charge and discharge time
of the thermocline tank. It is observed that the charge and discharge time of the thermocline tank almost levels off beyond
0.4
0.6
Axial Position, z*
*
15
Pump Work, W [x 10 ]
*
0.2
1.2
C
*
(t )
150
300
450
3
Reynolds Number, Re [x 10 ]
FIGURE
100 5 Variation of Nusselt number with Re and R c
Rc*
0.6
0.0
0.0
*
0
0
0.8
Latent
T
75
Total
50
25
0
0
150
300
450
3
Reynolds Number, Re [x 10 ]
600
FIGURE 6 Variation of (a) axial HTF discharge temperature
profile (b) charge (discharge) time and pump work, and (c)
total and latent utilization with Reynolds number
R*c, the heat exchange rate decrease and the conduction resistance within the PCM increases which results in a negligible utilization of the latent energy in the capsules. Thus only a
smaller portion of the PCM adjoining the capsule wall alone is
solidified and the thermocline typically operates only in the
sensible energy regime as seen by the absence of constant
melt-temperature zone in the violet and red colored lines in
Fig. 7a. This results in faster discharge time as the HTF temperature exiting the tank reaches the cut-off temperature faster.
Further it is observed from Fig. 7c that between Rc*  0.00013
and Rc*  0.004 the utilization decreases quite drastically with
increase in R*c, due to the increase in the conduction resistance
 0.004 . This is because of the fact that with increase in
7
Copyright © 2012 by ASME
in spite of the increase in Nusselt number (Fig. 5). On observing the utilization of the thermocline storage system, it can be
seen that larger diameter capsules possess a lower utilization
(Fig. 7c) and hence smaller diameter capsules are preferred for
stable dynamic operation of the system. But, with decrease in
R*c, the pressure drop across the bed increases, which, coupled
with a longer discharge time for R*c below 0.00041, leads to a
drastic increase in the pump work (Fig. 7b). Based on the
competing effects between the pump work and latent utilization with smaller R*c, it can be observed from Figs. 7b and c
that the non-dimensional radius of the capsule should not be
smaller than Rc*  0.00041 , which
is selected by carefully monitoring the change in slope of the
pump work curve. For the purpose of illustration, if the height
of the tank is considered to be Ht = 14 m as commonly employed in a 3000 MWh-th power plant [30], the capsule radius
should be approximately 5.77 mm to realize simultaneous
benefits of high utilization and low pump work.
Figure 8 portrays the total utilization of the LTES system
calculated for different Re and different non-dimensional capsule radius, Rc* . The range of the Reynolds number and the
non-dimensional capsule radius values chosen for this plot
corresponds to the practical design of a LTES system for CSP
plant. It is clear from Fig. 8 that utilization decreases with
increase in Re and Rc* . At higher Reynolds number, the mass
flow rate is higher. Hence the existing hot fluid in the tank is
discharged faster, after which due to insufficient residence
time of the cold inlet HTF within the tank, heat exchange between the HTF and spherical PCM capsules do not take place
efficiently, resulting in a faster decay of the HTF discharge
temperature and contributing to low system utilization. With
increase in capsule radius, the thermal conduction resistance
within the PCM increases resulting in a decrease in the latent
utilization and hence the total system utilization also decreases
with increase in R*c. This highlights the important effects of
the Reynolds number and capsule radius, R*c on the design of
a latent thermocline storage system. Thus for a given HTF
Reynolds number established by the discharge power requirements of the CSP plant, and for an assumed height of the tank,
Fig. 8 can be used to determine the total utilization of the
LTES for various capsule radii.
1.0
*
R c = 0.00100
0.6
*
R c = 0.00400
*
R = 0.00800
0.4
c
0.2
0.8
1.0
25
(b)
1.2
Charge
Discharge
20
0.9
15
0.6
10
0.3
5
0.0
0
(c)
80
T
1.5
Total Utilization, U [%]
D
0.4
0.6
Axial Position, z*
Total
L
Latent
75
Re = 60
60
Re = 600
40
Re = 3000
20
Re = 6000
Re = 30000
0
0
50
25
0
0
2
4
6
*
-3
Capsule Radius, R [x 10 ]
c
8
FIGURE 8 Utilization of a LTES at different Re and
*
R c 80
2
4
6
*
-3
Capsule Radius, R [x 10 ]
8
T
*
C
(t )
*
0.2
Total Utilization, U [%]
f
HTF Temperature, 
c
*
p
Charge (Discharge) Time, t
c
R* = 0.00050
*
15
Pump Work, W [x 10 ]
T
R = 0.00025
c
0.8
0.0
0.0
Total (Latent) Utilization, U (U ) [%]
*
R = 0.00013
(a)
c
FIGURE 7 Variation of (a) axial HTF discharge temperature
profile (b) charge (discharge) time and pump work, and (c)
*
total and latent utilization with R c
8
60
= 1.0
= 2.0
40
20
0
0
= 0.5
Copyright © 2012 by ASME
2
4
*
6
-3
8
CONCLUSIONS
A thermocline model accounting for axial variation of temperature in the HTF and radial temperature variation in the
PCM at any axial position is solved and the effects of various
non-dimensional variables on the dynamic performance of the
thermocline storage system are analyzed. Important results
pertaining to the analysis above can be summarized as follows: Smaller radii capsules yield higher total and latent utilization of the latent thermocline storage system. But on the
other hand, the pressure drop increases as capsule radius decreases which results in a higher pump work and cost. Thus a
minimum R*c exists, that trades off between the competing
effects of the increasing pump work and total utilization with
decrease in R*c. Monitoring the change in slope of the pump
work curve, a minimum bound on the value of nondimensional capsule radii is established which is calculated to
be Rc*  0.00041 . Extrapolating the value for a 14 m tall tank,
commonly used in CSP plants, the corresponding capsule radius amounts to 5.77 mm. Higher Reynolds number and consequently higher mass flow rate also leads to decrease in the
utilization of the system due to expansion of the heat exchange
zone. Based on the parametric studies, an informative design
plot characterizing the utilization of the system as a function
of both Re and R*c is illustrated. A preliminary calculation of
the exergy efficiency, defined as the ratio of exergy recovered
by the HTF during discharging to the total exergy content of
the HTF at the inlet of the thermocline during charging for the
default design and operating parametric values yielded 66.17
%. A detailed exergy analysis and optimization of a cascaded
latent thermocline storage tank will be presented in a future
work.
D
discharging
f
heat transfer fluid
L
latent
p
phase change material
S
sensible
t
tank
T
total
eff
effective
Greek Symbols

porosity of the packed bed

dynamic viscosity

density

melt fraction
REFERENCES
[1]
LeFrois, R. T., Mathur, A. K., 1982, “Active Heat Exchanger Evaluation for Latent Heat Thermal Energy
Storage Systems,” New York : The American Society
of Mechanical Engineers, 82-HT-7.
[2]
“Heat Transfer and Latent Heat Storage in Inorganic
Molten Salts for Concentrating Solar Power Plants,”
Department Of Energy, Terrafore, Inc., U.S. DOE Contract: DE-FG36-08GO18148
[3]
Nithyanandam, K., Pitchumani, R., 2011, “Analysis
and Optimization of a Latent Thermal Energy Storage
System with Embedded Heat Pipes,” Int. J. Heat and
Mass Transfer, 54, pp. 4596–4610.
[4]
Nithyanandam, K., Pitchumani, R., 2010, “Numerical
Modeling of a Latent Heat Thermal Energy Storage
System with Integral Heat Pipes," Proceedings of the
ASME International Mechanical Engineering Congress
and Exposition, Paper No. IMECE2010-38682, Vancouver, British Columbia, Canada, 8 pp.
[5]
Nithyanandam, K., Pitchumani, R., 2012, “Computational Studies on a Latent Thermal Energy Storage
System with Integral Heat Pipes for Concentrating Solar Power,” Applied Energy, In Review.
[6]
Nithyanandam, K., Pitchumani R., 2011, “Analysis of
latent heat thermal energy storage system with integral
heat pipes under steady state and dynamic conditions, ”
5th International Conference on Energy Sustainability,
Paper No. ESFuelCell2011-54501, Washington, DC,
USA, 10 pp.
[7]
“Using Encapsulated Phase Change Material in Thermal Storage for Baseload Concentrating Solar Power
Plants,” Terrafore Inc., U.S. DOE Contract: DEEE0003589
[8]
Beasley, D. E., Clark, J. A., 1984, “Transient response
of a packed bed for thermal energy storage,” Int. J.
Heat Mass Transfer, 27, pp. 1659–1669.
[9]
Schumann, T. E. W., 1929, “Heat transfer: A liquid
flowing through a porous prism,” J. Franklin Inst., 208,
pp. 405–416.
[10] Shitzer, A., Levy, M., 1983, “Transient behavior of a
rock-bed thermal storage system subjected to variable
inlet air temperature: Analysis and Experimentation,”
ASME J. Sol. Energy Eng., 105, pp. 200–206.
[11] McMahan, A. C., 2006, “Design and optimization of
organic rankine cycle solar-thermal power plants,” MS
ACKNOWLEDGMENTS
This work was supported by a grant from the U.S. Department of Energy under Award Number DE-EE0003589. Their
support is gratefully acknowledged.
NOMENCLATURE
b
capsule wall thickness [m]
c
specific heat [J/kg-K]
h
convective heat transfer coefficient [W/m2-K]
hl
latent heat of fusion of PCM [J/kg]
H
height [m]
k
thermal conductivity [W/m-K]
mass flow rate [kg/s]
m˙
Nu
Nusselt number
Pe
electrical power output [MWe]
Pr
Prandtl number
Pth
thermal power output [MW-th]
Q
energy [MJ]
R
radius [m]
Re
Reynolds number
t
time [s]
T
temperature [K]
Tm
melting temperature [K]
Subscripts and Superscripts
c
capsule
C
charging
9
Copyright © 2012 by ASME
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
thesis, University of Wisconsin-Madison, Wisconsin.
Kolb, G. J., Hassani, V., 2006, “Performance analysis
of thermocline energy storage proposed for the 1 MW
Saguaro solar trough plant,” ASME Conf. Proc., 1.
Yang, Z., Garimella, S. V., 2010, “Thermal analysis of
solar thermal energy storage in a molten-salt thermocline,” Solar Energy, 84, pp. 974–985.
Van Lew, J. T., Li, P., Chan, C. L., Karaki, W., Stephens, J., 2011, “Analysis of heat storage and delivery
of a thermocline tank having solid filler material,” J.
Sol. Energy Engineering, 133, pp. 021003-1–10.
Yang, Z. Garimella, S. V., 2011, “Molten-salt thermal
energy storage in thermoclines under different environmental boundary conditions,” App. Energy, 87, pp.
3322–3399.
Ismail, K. A. R., Henriquez, J. R., 1999, “Numerical
and experimental study of spherical capsules packed
bed latent heat storage system,” App. Thermal Eng., 19,
pp. 757–788.
Felix Regin, A., Solanki, S. C., Saini, J. S., 2008, “Heat
transfer characteristics of thermal energy storage system using PCM capsule: a review,” Renew and Sus.
Ener. Reviews, 12, pp. 2438–2458.
Singh, H., Saini, R .P, Saini, J. S., 2011, “A review on
packed bed solar energy storage system,” Renew and
Sus. Ener. Reviews, 14, pp. 1059–1069.
Felix Regin, A., Solanki, S. C., Saini, J. S., 2009, “An
analysis of a packed bed latent heat thermal energy
storage system using PCM capsules: Numerical investigation,” Renew. Ener., 34, pp. 1765–1773.
Hänchen, M., Brückner, S., Steinfeld, A., 2011, “Hightemperature thermal storage using a packed bed of
rocks – Heat transfer analysis and experimental validation,” App. Thermal Eng., 31, pp. 1798–1806.
Wang, S., Fang, G., 2011, “Dynamic performance of
solar heat storage system with packed bed using
myristic acid as phase change material,” Energy and
Buildings, 43, pp. 1091–1096.
Hales, T.C., 2006, “Historical overview of the Kepler
conjecture, Discrete & Computational Geometry,” International Journal of Mathematics and Computer Science, 36, pp. 5–20.
Kays, W. M., Crawford, M. E., Weignand, B., 2005,
Convective Heat and Mass Transfer, 4th Ed., McGrawHill, New York.
Voller, V.R., Cross, M., Markatos, N.C., 1987, “An
enthalpy method for convection/diffusion phase
change,” Int. J. Numer. Methods, 24, 271–284.
Galloway, T. R., Sage, B. H., 1970, “A model of the
mechanism of transport in packed, distended, and fluidized beds,” Chemical Engg. Sci., 25, pp. 495–516.
Yang, K. T., 1987, Natural convection in enclosures,
in: S. Kakac, R. Shah, W. Aung (Eds.), Handbook of
Single-Phase Convective Heat Transfer, Wiley, New
York.
Pacheco, J. E., Showalter, S. K., Kolb, W. J., 2002,
“Development of a molten salt thermocline thermal
storage system for parabolic trough plants,” ASME J.
Sol. Energy Eng., 124 (2002) 153 – 159.
Nallusamy, N., Sampath, S., Velraj, R., 2007, “Experimental investigation on a combined sensible and latent
[29]
[30]
10
heat storage system integrated with constant/varying
(solar) heat sources,” Renewable Energy, 32, pp. 1206–
1227.
Ergun, S., 1952, “Fluid Flow through Packed Columns,” Chem. Eng. Prog., 48, pp. 89–94.
“Solar Thermocline Storage Systems – Preliminary
design study, ” EPRI, 2010 Public Copy
Copyright © 2012 by ASME