This document summarizes a paper that analyzes heat storage using a thermocline tank for concentrated solar power plants. It presents: - A simulation model of the charging and discharging processes in a thermocline tank that uses molten salt and quartzite rock as storage media. - Validation of the model by comparing its results to experimental data and other models, showing good agreement. - Application of the model to design an alternative storage system for the AndaSol I solar plant using a single thermocline tank instead of two separate tanks. - Analysis of how the tank height-to-diameter ratio affects energy storage efficiency. - Comparison of three thermal fluids to determine the best

1. Analysis of Heat Storage with a Thermocline Tank for Concentrated
Solar Plants: Application to AndaSol I
Abstract— The storage system in a concentrated solar
plant is considered as an important concern to increase the
capacity factor of the plant by producing power during the
night or in cloudy days. This paper presents the analysis of
a thermocline system, which consists of a single tank that
typically works with molten salt and quartzite rock as
storage media. A simulation model of heat charging and
discharging process is developed with the numerical
solution of non-dimensional convection-diffusion
equations. These equations describe the heat transfer in
the fluid and between the fluid and the filler material. The
model is validated with experimental data, and the results
are compared with other models. The proposed model is
used for the design of an alternative storage system for
AndaSol I. Moreover, the model is used to analyze the
influence of the ratio between height and diameter of the
tank on the energy storage efficiency. Finally, a
comparison between three thermal fluids is made in order
to find out which heat transfer fluid (HTF) is better for the
designed thermal storage tank.
I. INTRODUCTION
It is widely known that we live in an unsustainable world,
and that the increase of population predicted for the next
decades will require much more amount of energy. Moreover,
the natural resources are limited and some of them are
beginning to disappear. For these reasons, the goals for the
next years in the energy security are clear and a consensus is
reached for the most part among the academia and the public:
significant improvements on the efficiency of energy
processes and an increase in the use of renewable energy
sources which not require limited natural resources are
necessary.
Solar power plants are a good alternative for conventional
thermal power stations to produce sustainable electricity.
However, they should deal with the problem of producing
power during the periods when sun is not available.
Consequently, to improve the efficiency of solar plants, most
of investigations focus efforts on the thermal storage system.
A review of the state of art on thermal energy storage and
important concepts and materials are presented in [1]. There
are already quite a few different types of storage, but the
thermocline tank system has significant advantages compared
to the other systems because of its low-cost in comparison
with the two-tank system. Herrman et al. [2] offer an overview
on different storage systems and Flueckiger et al. [3]
investigated a simulation model for the thermocline tank.
Here, a model is developed in order to simulate charge and
discharge process, and used in the design of an alternative heat
storage system for AndaSol I solar plant. The storage system
currently used in this plant consists of two separate tanks
which store the hot and cold fluid independently. Therefore, a
storage system with one single thermocline tank with the same
heat capacity will be proposed as a low-cost alternative.
II. MODEL DEVELOPMENT
This section presents the governing heat equations of the
model. A detailed explanation of the development of the
dimensionless governing equations for the model can be found
in [4].
Energy balance in the heat transfer fluid is given by the
convection-diffusion equation:
( )* * * *
1f f f
s f eff
r
k
t z z z
∂θ ∂θ ∂θ ∂
+ = θ −θ +  
τ∂ ∂ ∂ ∂ 
(1)
where,
2
r
f f
s
C Ru
H hS
ρ επ
τ = (2)
and
2
(1 )s
s
f R
S
r
π − ε
= (3)
Energy balance between the filler material and the HTF is
given by:
( )*
s CR
s f
r
H
t
∂θ
= − θ − θ
τ∂
(4)
where HCR is the ratio of heat capacities,
(1 )
f f
CR
s s
C
H
C
ρ ε
=
ρ − ε
(5)
and θf and θs are the non-dimensional temperatures of the fluid
and the solid phases:
f c
f
h c
T T
T T
−
θ =
−
, s c
s
h c
T T
T T
−
θ =
−
(6)
Lastly, the non-dimensional position and time are given by:
Serhat Yesilyurt
Mechatronics Department
Sabanci University
Istanbul, Turkey
syesilyurt@sabanciuniv.edu
Albert Graells Vilella
Exchange Student from Technical University of Catalonia
Sabanci University
Istanbul, Turkey
agraellsvilella@gmail.com

2. * *
,
z u
z t t
H H
 
= =  
 
(7)
A. Numerical solution
The model below is based on dimensionless governing
equations (1) and (4). The aim is to solve two equations with
two unknown vectors with the finite difference method. The
transient term is expressed with the Backward Euler implicit
method and central differences are used for the derivatives
with respect to axial position:
, 1 , 1 * *
* *
* *
,
2
k
f f k f k
k
z z
z k z
z z
+ −
=
∂θ θ − θ
≈ = ∆
∂ ∆
(8)
, 1 , , 1
* * *2
* *
2
k
f f k f k f k
z z
z z z
+ −
=
∂θ θ − θ + θ ∂
≈ 
∂ ∂ ∆ 
(9)
As the simulation is considered one dimensional in the axis
direction, the axial position in the tank is represented with N
nodes placed vertically in the axis of the tank. The linear
system of equations that represent the energy balance in the
fluid is obtained as:
( ) ( )*
1 1
2
f
f s f
r zt
∂
+ + = − +
τ ∆∂
θ
B C θ θ θ b (10)
where B is the matrix that corresponds to the second-order
accurate convective term in (8), C is the second-order accurate
conduction term in (9) and ,0 ,0,f = θ b ⋯ is the vector that
helps to impose Dirichlet boundary conditions at the inlet.
First-order unconditionally stable Backward Euler method
is used for the derivative of the temperature:
( ) ( ), 1 ,
, 1 , 1 , 1
1f j f j
f j s j f j
rt
+
+ + +
−
+ + = − +
∆ τ
θ θ
B C θ θ θ b (11)
Then, (11) is reordered to put the terms , 1f j+θ in the left
side of the equality, and after a few steps we obtain a simple
equation from which we can obtain the solution.
1
, 1f j
−
+ =θ A f (12)
where,
1 1
rt
  
= + + +   ∆ τ  
A B C I (13)
and
, 1 , *
1 1 1
2
s j f j
r t z
+= + +
τ ∆ ∆
f θ θ b (14)
A similar, but simpler, procedure is repeated for solving
(4) for the filler material using the first order differences in
time with Backward Euler implicit algorithm.
, 1 ,
*
s j s js
tt
+ −∂
≈
∆∂
θ θθ
(15)
We obtain:
, 1 , , 1
1 1CR CR
s j s j f j
r r
H H
t t
+ +
 
+ = + 
∆ τ ∆ τ 
θ θ θ (16)
Finally, the initial and boundary conditions for the
charging and discharging process must be defined. In the
charging period, the boundary conditions show that HTF
enters from the top of the tank at Th, while in the discharging
period the HTF enters from the bottom of the tank at Tc.
Therefore, the initial and boundary conditions for both energy
equations are defined respectively as:
i) Discharge Process:
10 ( )s ft f z= → θ = θ = , ( )*
0 0 0ft z> → θ = = (17)
ii) Charge Process:
20 ( )s ft f z= → θ = θ = , ( )*
0 1 1ft z> → θ = = (18)
III. MODEL VALIDATION
In this section, the results will be compared with
experimental data in order to validate model designed.
Moreover, a comparison with analytical results will be done as
well.
A. Comparisons with Experimental Data
For this comparison, the model is run with parameters
presented in [4]. Fig. 1 shows the predicted dimensionless
temperature distribution of the HTF obtained with our model
every half an hour during 2 hours of discharging process. One
can easily see that the agreement with experimental points is
quite satisfactory.
Figure 1. Comparison of modeling predicted results with experimental data
from [4].
B. Comparison with Analytical Results
Before using the model for new designs, some other
validation studies are needed in order to improve the
reliability of the model. In this case, we will repeat the
analytical results in [4].
First, we simulate the dimensionless fluid temperature in
the tank for 5 cycles. Each cycle includes charging and
discharging which take 4 hours each. Each process is repeated
for 10 cycles and the dimensionless temperature distribution is
plotted every half hour. After 10 cycles, the initial condition
does not affect the temperature distribution in the tank. The
initial condition of the simulation was is an ideal, fully

3. charged tank, for which after several cycles the initial and
final temperature distributions remain constant.
Fig. 2 shows the agreement between the HTF and the filler
material temperatures after a discharge process. As it was
expected, both distributions are practically the same.
However, there is a slight temperature difference from z* =
0.7 to z* = 1 caused by the sudden temperature decrease. The
temperature difference in z* = 1 is 0.03 which is the same as
observed in [4].
The next analysis is the influence under different number
of discretized nodes in the dimensionless temperature
distribution. As one can see in Fig. 3, modeling error increases
considerably with decreasing number of nodes. However, the
accuracy of the model is satisfactory between 100 and 1000
nodes.
Figure 2. HTF and Filler Material dimensionless temperature distribution in
the tank after 4 hours of discharge process.
Figure 3. Comparison of dimensionless temperature distribution after 4 hours
discharging under different number of nodes.
I. SIZING THERMAL STORAGE TANKS
The design of a thermocline tank consists of determination
of the size (length and diameter) that satisfies the required
energy storage of the solar plant. The size of the storage tank
is dictated by the required operational conditions which are:
electrical power output, thermal efficiency, duration of heat
discharge period, high temperature of the HTF and low
temperature of HTF returned, properties of HTF, properties of
the filler material, and the packing porosity [5].
A. Tank Sizing
The first step is to consider the tank as an ideal
thermocline tank and to calculate the baseline volume for this
case. The difference between an ideal thermocline tank and
the real one is the presence of a filler material in the
thermocline. The presence of a packed bed will explain why
the distribution of the temperature is stratified, as it can be
seen in Fig. 4. In order to avoid the temperature degradation, it
is necessary to use an ideal thermocline tank or to have a
system which stores much more thermal energy than needed.
Thus, during the discharge time period, the temperature
degradation must be minimal. However, in a real thermal
energy storage system, when the cold fluid is pumped into the
bottom of the tank, it extracts heat from the filler material.
After some time, the HTF could not heat up because the filler
material would become cold as well. Therefore, in a thermal
storage design, the goal is to minimize the temperature
degradation during the required operational period of time
such that the temperature of the HTF varies from the filler
temperature, Th, minimally.
Figure 4. Illustration of a single tank thermal storage system, [4]
Required total energy storage is obtained from the values
of the electric power output, Pe, the thermal efficiency, ηT, of
the power plant and the operation time period:
( ) ( ) e
total P h cf
T
P
Q V C T T t= ρ − = ∆
η
(19)
Moreover, to meet the requirement of minimum
temperature degradation, one needs to store large amount of
thermal energy than in an ideal tank. The mathematical
expression of this requirement is given by:
( ) ( )1s s f f real f f idealC C V C V ρ −ε +ρ ε = ρ  (20)
The second step consists of using a model in order to evaluate
the heat transfer and observe the temperature degradation for a
fully charged tank with packed bed.
B. Alternative Design for AndaSol I
First, we determined the minimum required volume for a
single storage tank based on the ideal thermocline. We use
(19) in order to obtain the total heat storage required, which is
1000 MWhth.
The operation time period is 7.5 hours because it is the
same storage capacity of AndaSol I plant [6]. Here we aim to
optimize the design of the tank maintaining the same required

4. operational conditions. With (23) we get the ideal volume
which is 14.695 m3
for the specifications of the AndaSol I
plant.
( ) ( )
total
ideal
P h cf
Q
V
C T T
=
ρ −
(21)
Moreover, in order to consider a bigger volume which
minimizes the temperature degradation, we use the following
requirement:
( )1
f f
real ideal
s s f f
C
V V
C C
ρ
=
ρ − ε + ρ ε
(22)
The next step is to choose the diameter, D, and the height,
H, that satisfy the minimum volume. With these dimensions,
the parameters τr and HCR can be evaluated and the
temperature distribution in the tank can be simulated during a
discharge process. The dimensions of the tank with a volume
of 17.611 m3
are: H = 15.2 m and D = 38.5 m. For choosing
these dimensions, we considered the same diameter/height as
the previous tank which was 36/14.
In Table I, model parameters and values are presented. The
HTF used in AndaSol has the same composition as the fluid
used in the comparison with the experimental data presented
in [4]. For this reason, the thermodynamic properties of the
HTF and the filler material are obtained from the literature.
The flow rate, the hot and cold temperatures, and the required
time period of energy discharge are operational parameters are
fixed for the AndaSol I plant as design constraints.
Surprisingly, the first design has better results than we
expected. In Fig. 5, one can see the dimensionless temperature
distribution of the HTF during a discharge process. The
simulation was run for 10 cycles in order to stabilize the initial
conditions.
In order to figure out the temperature degradation of HTF
during discharge, we plotted the dimensionless temperature
TABLE I. DIMENSIONS AND PARAMETERS OF THE THERMOCLINE TANK
Parameters Values
H [m] 15.2
D [m] 38.5
ε 0.22
dT [ h ] 7.5
Heat Transfer Fluid
ᆑf [ kg / m3
] 1733
kf [ W / (m K) ] 0.57
Cf [ J / (kg K) ] 1520
µf [ Pa s ] 0.0021
݉ሶ [ kg / s ] 948
Th [ ºC ] 384
Tc [ºC ] 291
Filler Material
ᆑs [ kg / m3
] 2500
ks [ W / (m K) ] 5
Cs [ J / (kg K) ] 830
dr [ m ] 0.015
histories of at the exit, z* = 1, during a discharge process,
which can be seen in Fig. 6. The temperature degradation is
not significant and it seems that this design would work well.
However, improvements are necessary for the design
observing the effects produced by the modification of some
parameters, based on the thermal energy efficiency which is
expressed in:
( )
arg
( , )
0
arg
disch et
f x H t c
h c disch e
T T dt
T T t
= − 
η =
−
∫
(23)
In the first attempt, the thermal energy efficiency was
0.9928. Therefore, when improving the design, we should pay
attention not to deteriorate this parameter.
C. Optimization Studies
1) Ratio H/D:
First, the ratio between height and diameter of the tank is
varied in order to find out if the geometry could affect the
efficiency of the thermal storage. Simulations are carried out
with the model for different values of this ratio, and the effect
on the thermal storage efficiency is calculated.
Figure 5. Dimensionless temperature of HTF every 30 min during a discharge
process
Table II shows the results for different ratios which are
plotted in Fig. 7 as well. As one can see, the energy storage
efficiency increases with the H/D-ratio. In other words, higher
energy efficiencies are obtained for taller tanks.
The principal conclusion inferred from this observation is
that, if we need to increase the volume of the tank in order to
reduce the temperature degradation, it is better to increase it
by increasing the height, and consequently, the ratio H/D.
Therefore, the first design is modified based on this
observation. In order to decrease the HTF temperature
degradation, volume needs to be increased. Thus, we decided
to increase the height to 18 m. With this adjustment, the HTF
temperature degradation shown in Fig. 8 is considerably
reduced and the thermal storage efficiency is increased to
0.9992.
2) Heat Transfer Fluid:
The last investigation is about the HTF. The aim of this
last question is to analyze two alternatives for the solar salt as
storage fluid. The two fluids selected are called: Hitec XL and
Therminol . The last one is a heat conductive oil. Hitec XL is
a molten salt composed with 7% NaNO3, 45% KNO3 and 48%

5. Ca(NO3)2. Table III illustrates the average properties at 300ºC
for the thermal energy storage (TES) materials.
TABLE II. THERMAL STORAGE EFFICIENCY UNDER DIFFERENT RATIOS
Figure 6. Dimensionless temperature histories of exit fuid at z* = 1 for a
discharge process
Figure 7. Effect of the Ratio H/D on the Thermal Storage Efficiency
Figure 8. Dimensionless temperature histories of exit fuid at z* = 1 for a
discharge process with the new design
The simulation of the new tank designed previously is
repeated for the three storage materials, and the results are
shown in Fig. 9. Each graph is the result of the same
simulation, only changing the properties of the HTF. The fluid
temperature distribution plotted represents the inside
temperature after 20 cycles of charge and discharge process
from a fully tank. 20 cycles are required in order to be sure
that the initial condition does not affect the temperature
distribution. The melting point and the upper temperature are
also indicated in Table III because the HTF must work in a
temperature range between the two temperatures in order to
remain in liquid phase during the charge-discharge processes.
As Th is 384 ºC and Tc is 291 ºC [6], all three fluids fulfill this
requirement.
As one can see in the Fig. 9, if the mass flow rate is kept
the same the Solar Salt seems to be the choice for the HTF.
However, for constant thermal mass flow rate, i.e. ,p lmcɺ , all
three HTF are comparable, with lowest mass flow rate for
Therminol, which will also have the least parasitic pumping
loss.
Moreover, Table IV sums up the energy storage efficiency
for each example. For the same thermal mass flow rate all
three have comparable efficiencies. However, if one considers
the cost of each HTF, the Solar Salt becomes the best thermal
energy storage material. Furthermore, complete analysis is
necessary by considering the effect of parasitic pumping loses
and other properties of the fluids.
TABLE III. CHARACTERISTICS OF TWO MOLTEN SALTS (SOLAR SALT AND
HITEC XL) AND ONE HEAT CONDUCTIVE OIL (THERMINOL) [7]
TES materials Solar Salt Hitec XL Therminol
Density, kg/m3
1899 1992 815
Heat Capacity, J/kg·K 1460 1800 2300
Thermal conductivity, W/m·K 0.52 0.53 0.21
Viscosity, Pa·s 0.00326 0.00637 0.0002
Melting Point, ºC 220 120 13
Upper Temperature, ºC 600 500 400
Cost of the material, $/kg 0.49 1.19 2.20
Cost of the heat storage, $/kWh 5.8 15.2 57.5
TABLE IV. ENERGY STORAGE EFFICIENCY FOR EACH HTF
HTF
η (constant
flow rate)
η (constant thermal
flow rate)
Solar Salt 0.9979 0.9899
Hitec XL 0.9925 0.9911
Therminol 0.8369 0.9814
CONCLUSIONS
This work presents the modeling of a thermocline storage
tank with a solid-filler packed bed. We developed and
validated a model that can be used for future storage systems
designs. Moreover, the model is also useful to investigate the
influence of different parameters of the tank. In this paper we
studied the influence of the ratio between the height and the
diameter of the tank to the thermal storage efficiency. We
conclude that an increase in this ratio causes an increase in the
thermal storage efficiency. The scientific justification is that a
smaller diameter corresponds to a higher flow velocity for the
HTF trough the filler material, and consequently, the heat
transfer coefficient would be also higher.
The model has also been used to propose a new
configuration of storage system for a real solar power plant.
H/D η H/D η
0.3948 0. 9928 2.3948 0.9995
1.3948 0.9994 3.3948 0.9995

6. AndaSol I has been the solar plant selected because its storage
system contains two separate tanks which store the hot and
cold fluid independently. Thus, a thermocline storage tank
would be a low-cost alternative to the current, because a single
tank requires a lower quantity of materials and space.
Moreover, the HTF in AndaSol I is the same molten salt used
in the model. Therefore, a storage system consisting on a
thermocline tank with 18 m height and 38.5 m diameter has
been obtained in this work as an alternative storage system for
AndaSol I. Moreover, the new design offers smaller fluid
temperature degradation.
Furthermore, a comparison between a Solar Salt, Hitec XL
and Therminol is presented here. This evaluation shows that
the best thermal storage fluid for this design seems to be Solar
Salt because of its lower temperature degradation and its low
cost. However, other factors such as pumping of the fluid and
melting point must be considered as well: for the former
Therminol is best because of its low viscosity and high heat
capacity (but also costs higher), and for the latter Hitec XL
would be a good alternative because its lower melting point.
Figure 9. Dimensionless temperature distribution and exit histories at z* = 1
during a discharge process for each HTF for constant mass flow rate.
Figure 10. Dimensionless temperature distribution and exit histories at z* = 1
during a discharge process for each HTF for constant thermal mass flow rate.
ACKNOWLEDGMENT
The author gratefully acknowledges the financial help
received from the Erasmus Mundus and the hospitality of the
Sabanci University.
NOMENCLATURE
CP Specific heat (J/kg·K)
D Diameter of the storage tank (m)
fs Surface shape factor (2-3)
H Height of the storage tank (m)
HCR Dimensionless parameter
k Thermal conductivity (W/m·K)
mɺ Mass flow rate (kg/s)
N Number of nodes
R Radius of the storage tank (m)
r Equivalent radius of a rock (m)
S Surface area (m2
)
T Temperature (K)
t Time (s)
u Fluid velocity in the axial tank direction (m/s)
z Location along the axis of the tank
Greek symbols
ε Porosity of packed bed in storage tank
η Efficiency
µ Dynamic viscosity (Pa·s)
τr Dimensionless parameter
ρ Density (kg/m3
)
θ Dimensionless temperature
Subscript
c Cold
eff Effective
f Thermal fluid
h Hot
j Discretized variable of time
k Discretized variable of space, Node position
s Filler material
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