Analysis of a Latent Thermocline Energy Storage System for

* Corresponding author. +1 540 231 1776; [email protected]

ANALYSIS OF A LATENT THERMOCLINE ENERGY STORAGE SYSTEM FOR CONCENTRATING SOLAR POWER PLANTS

Karthik Nithyanandam1, Ranga Pitchumani1* and Anoop Mathur2 1Advanced Materials and Technologies Laboratory, Department of Mechanical Engineering, Virginia Tech, Blacksburg,

Virginia 24061, USA; 2 Terrafore Inc., 100 South 5

th Street, Suite 1900, Minneapolis 55402, USA.

ABSTRACT: The primary purpose of a thermal energy storage system in

a concentrating solar power (CSP) plant is to extend the opera-

tion of plant at times when energy from the sun is not ade-

quate 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 en-

countered 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 sys-

tem is analyzed to identify configurations that lead to higher

utilization. This study provides important guidelines for de-

signing a storage tank with encapsulated PCM for a CSP plant

operation.

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 dur-

ing 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 per-

formance of energy system Thermal energy can be stored as

either sensible or latent heat. Most of the thermal energy stor-

age 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 sig-

nificantly increases the energy density. For example, the ener-

gy 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

(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 suita-

ble shell materials. For example, PCM stored in capsule diam-

eters 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 effec-

tiveness 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 pre-

sent work. The working of latent thermocline energy storage

(LTES) system in a CSP involves the exchange of heat be-

tween the HTF and the packed bed of spherical PCM capsules.

The operation of a LTES constitutes the charging and dis-

charging 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 strat-

ification of hot and cold fluids within the tank. The charging

process takes place during the day when solar energy is avail-

able 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

Proceedings of the ASME 2012 6th International Conference on Energy Sustainability ES2012

July 23-26, 2012, San Diego, CA, USA

ES2012-91389

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 fo-

cuses 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 wide-

ly 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] adopt-

ed the Schumann model to analyze the performance of ther-

mocline 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 stor-

age system till date. Felix Regin et al. [19] also reported the

modeling of thermocline energy storage system with embed-

ded PCM capsules. The modeling follows the Schumann’s

equation except that the dependent variable for energy equa-

tion of filler bed is enthalpy and not temperature. The re-

sistance developed during the solidification phase change pro-

cess was accounted for by a decrease in the heat transfer coef-

ficient 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 dis-

charging 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 ther-

mocline storage system containing spherical capsules filled

with PCM and investigate the influence of the design and op-

erating parameters on the dynamic performance of the system

to identify configurations that lead to higher system utiliza-

tion. 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 schemat-

ically shown to be arranged in an ordered fashion. However,

in reality, as the PCM capsules are piled up pressing each oth-

er 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 (solidifica-

tion) rate of the PCM although the effect of which on micro-

encapsulated 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 computa-

tional 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 inter-

face 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 mod-

eled 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:

21

,

3)(4

)1(3

2 RTRT

fT

pT

bc

Rz

fT

tR

f

mf

cf

t

fT

fc

fcRr

(1)

)(1 2

,2 r

Trk

rrt

T

Thc

p

effp

p

p

lpp

(2)

where RT1 and RT2 in Eq. (1) denote the thermal resistance

offered by radial heat conduction in the capsule wall and con-

vective heat transfer between the HTF and filler phase


FIGURE 1 (a) Schematic of LTES, (b) PCM spherical cap-sules

respectively which can be expressed as

)(41 bRRkbRT

ccw

and 22 )(4

1bRh

RTc

. The cor-

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 respec-

tively of either the HTF denoted by subscript ‘f’ or the encap-

sulated PCM denoted by subscript ‘p’. hl denotes the latent

heat of fusion of the PCM, t denotes time, m represents the

mass flow rate of the heat transfer fluid, and denotes the

porosity of the packed bed. The term, cRrpT

, on the right

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 ther-

mal 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 re-

gimes and is expressed as convpeffp Nukk , , where kp is the

molecular thermal conductivity of PCM and Nuconv is calculat-

ed from

9/416/9

45545/3

4/14/1

)Pr492.0(13

012.2(Pr)

)/(/2(Pr)16.1

p

iooii

ioconv

f

DDDD

Ra

D

DDfNu

(3)

This correlation is valid for a wide range of Prandtl (Prp)

number and Rayleigh number (Ra) of the PCM. The term Do-

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 be-

comes 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 enclo-

sure. The expression that yields the largest heat transfer rate

was used in the computations.

In order to generalize the model and the corresponding re-

sults, Eqs. (1) and (2) are non-dimensionalized as follows:

***

*

*

**

2

*

**

**,

**

)(2PrRe

)1()(2

)1(

))(1(3

ccf

ccc

fcRrp

ff

RbR

Nu

R

b

bR

Nu

R

bb

zt

(4)

*

2*

*

*

* Pr.Re)1(

rr

r

Nuk

t

fSt

p

f

convfp

p

L

(5)

The boundary conditions during the charging and discharg-

ing process are specified as

The non-dimensional parameters appearing in Eqs. (4)–(6)

are defined as follows:

f

ff

f

cf

t

fcfc

f

p

f

w

p

w

pp

ff

DCp

l

DC

Dp

p

DC

Df

f

t

cc

ft

k

c

R

mH

bRbRNu

k

kk

k

kk

c

c

TTc

hSt

TT

TT

TT

TT

H

RR

H

bb

HR

tmt

H

rr

H

zz

Pr;Re

;RePr)(098.0PrRe)(87.22

;;;

;)(

;;

;;;;

2

2/1**3/12/1**

**

*

t

*

2

t

**

t

*

(7)

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-

Rc

b

Hot HTF

Cold HTF

z

r

Rt

Ht

0;0

;

1

)(

2

)(

)(

)arg (arg);0 (1,0

)arg (arg);1 (0),0 (1

*

*

**

*

**

**

**

***

*

*

*

rr

Rr

R

bRNu

kR

bR

kbr

ingDischingChzz

ingDischingChz

p

c

c

c

fc

c

w

fpp

f

f

(6)

(a)

(b)


spond to the hot inlet HTF temperature during charging and

the cold inlet HTF temperature during discharging, respective-

ly.

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

The complete set of governing equations is discretized us-

ing 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 pre-

dict the liquid fraction in the fixed grid enthalpy-based proce-

dure, the liquid fraction in each computational cell, in con-

junction 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:

)(1,0

1 ni

nipp

i

ini

ni Fc

a

a

(9)

In the above equation, ai is the coefficient of i for the ra-

dial 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

0001.0* t .

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 conduc-

tion 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 ( *TQ ) is

composed of sensible energy ( *SQ ) and latent energy ( *

LQ )

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

j

q

ic

iip

fS

R

zVzQ

1 1

*

3*

*

,**)1(

(10a)

p

j

q

ic

iiL

R

zVStQ

1 1

*

3*

** )1(

(10b)

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-

sules respectively. The performance metrics characterizing the

behavior of the system analyzed in the present work are the

cyclic total utilization (*

max,

*

, TDTT QQU ) and latent utiliza-

tion (*

max,

*

, LDLT QQU ) where *,DTQ ( *

,DLQ ) denote the total

(latent) energy discharged in a cycle which is obtained by sub-

tracting the total, *TQ (latent, *

LQ ) 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. *max,TQ and *

max,LQ repre-

sent the maximum total and latent storage capacity of the tank

which can be easily obtained from Eqs. (10a) and (10b) as-

suming 1, pf 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 sen-

sible thermocline storage tank as illustrated in Fig. 2a. A eu-

tectic 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].

FIGURE 2 Comparison of numerical results obtained for (a) axial variation of temperature with experimental data of [27] and (b) transient temperature variation of HTF and PCM at various axial positions with experimental data of [28].

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Avera

ge T

em

pe

ratu

re, avg

Axial Position, z*

t = 0.0 h

t = 0.5 h

t = 1.0 h

t = 1.5 h

t = 2.0 h

30

40

50

60

70

80

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, T

[oC

]

Time, t [min]

HTF, z/HT = 0.25

Conduction +Convection

Conduction

PCM, z/HT = 0.5

Figure 2

(a)

(b)

0;0 pf (8)


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 con-

dition corresponds to the final charging state of the first cycle,

which was also carried out for 2 hours. To analyze the perfor-

mance of sensible thermocline system with the developed

model for latent thermocline energy storage system, the non-

dimensional 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 distri-

butions 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 experi-

mental 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 agree-

ment with the experimental data than a conduction only mod-

el. Neglecting the free convection effects within the PCM pre-

dicts 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 pre-

sent study are the Reynolds number, Re and non-dimensional

capsule radii, *

cR respectively. The default case pertains to

; 0005.0* cR

; 6000Re

;105 8* b

;25.0 Ste

; 125.0m

;5Pr f

;1

;1* wk

1* pk . 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 ( *

cR ) on the pump work. The non-dimensional

pump work during discharge can be obtained from, 2*** Pr).(ReDp tpW where the non-dimensional pressure

drop can be expressed as, mRpp t2* 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 cy-

cle. 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

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 dis-

charge 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 charg-

ing, 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 repre-

sentative of restrictions imposed on 100 MWe CSP plant op-

eration [30]. Subsequent cycles were carried out until the

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

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

HT

F T

em

pe

ratu

re, f

Axial Position, z*

t* = 0.0

Total Utilization, UT

Charge

Discharge

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.6 0.9 1.2

HT

F E

xit T

em

pera

ture

, f,e

Time, t*

Discharge

Charge

(a)

(b)


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 sys-

tem 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 ( 0f ) near the discharge

inlet, a constant high-temperature zone ( 1f ) which pre-

vails near the discharge outlet, a constant melt-temperature

zone ( mf ) and an intermediate heat exchange zone (

10 f ). 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 col-

ored 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 represent-

ed by solid and dashed blue colored lines, albeit, the delinea-

tion between the curves is hardly discernible as a cyclic quasi-

steady 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 percent-

age of the shaded area depicts the latent utilization of the sys-

tem 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 tem-

perature of the HTF exiting the top of the tank at z* = 0 de-

creases from 1f to Df . This is attributed to the low

temperature difference between the HTF discharge inlet tem-

perature, 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

FIGURE 4 (a) Axial variation of the PCM melt fraction dur-ing the charge and discharge process and (b) cyclic sen-sible 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 ac-

cordance 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

mass flow rate, m . Also it is important to observe that the

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 ob-

served that with increase in Reynolds number the heat ex-

change zone expands. At the higher Reynolds number, a

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Melt F

raction,

Axial Position, z*

Latent Utilization, U

L

Discharge Charge

t* = 0.0

Charge

Discharge

1 2 3 40

0.1

0.2

0.9

1.0

1.1

1.2

Cycle, i

La

ten

t Energ

y C

harg

ed

(Dis

ch

arg

ed

),

Q*L

,C (Q

*L,D

)

Sen

sib

le E

nerg

y C

ha

rged (

Dis

cha

rged

),

Q* S

,C (

Q* S

,D)

(a)

(b)


FIGURE 5 Variation of Nusselt number with Re and R*

c

longer flow distance is required for the HTF to be heated by

the PCM spherical capsules which results in a gradual temper-

ature increase and a corresponding expansion of the heat ex-

change zone. Also, the constant melt-temperature zone is ob-

served to reduce in height as the Reynolds number increases.

For instance at Re = 600000, the discharge temperature profile

depicted by the solid red colored line does not possess the

constant melt-temperature zone reflecting an inefficient ex-

traction of latent energy from the PCM. Figure 6b shows that

the charge (discharge) time decreases with increase in Reyn-

olds number. Since the heat exchange zone is at a lower tem-

perature than the higher temperature, the discharging cut-off

temperature is reached quicker for higher Re as the heat ex-

change zone expands. Consequently, the utilization and latent

utilization of the system also decreases as portrayed in Fig. 6c.

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 Re

2 , it is observed in Fig. 6b that the

discharge time decreases drastically with increase in Re, re-

sulting 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 expan-

sion 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 radi-

us, results in an increased resistance to the conduction domi-

nated PCM solidification which occurs during discharge pro-

cess. Also, the surface contact area between the HTF and cap-

sules 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 non-

dimensional capsule radius on the charge and discharge time

of the thermocline tank. It is observed that the charge and dis-

charge time of the thermocline tank almost levels off beyond

004.0* cR . This is because of the fact that with increase in

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 re-

sistance within the PCM increases which results in a negligi-

ble 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 tem-

perature exiting the tank reaches the cut-off temperature faster.

Further it is observed from Fig. 7c that between 00013.0* cR

and 004.0* cR the utilization decreases quite drastically with

increase in R*c, due to the increase in the conduction resistance

0

300

600

900

1200

1500

0 150 300 450 600

Nusse

lt N

um

ber,

Nu

Reynolds Number, Re [x 103]

R*

c = 0.0080

R*

c = 0.0040R

*

c = 0.001

R*

c = 0.0005

R*

c = 0.0003

R*

c = 0.0001

0

20

40

60

80

100

0 10 20 30 40

Nusse

lt N

um

ber,

Nu

HTF Prandtl Number, Prf

R*

c = 8.000

R*

c = 4.000

R*

c = 1.000

R*

c = 0.500

R*

c = 0.250

R*

c = 0.125

Figure 2

(a) (b)

Re = 60

Re = 600

Re = 6000

Re = 60000

Re = 300000

Re = 600000

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

HT

F T

em

pera

ture

, f

Axial Position, z*

0.4

0.6

0.8

1.0

1.2

0

100

200

300

400

Charge

Discharge

Cha

rge

(D

isch

arg

e)

Tim

e,

t* C (

t* D)

Pu

mp

Wo

rk, W

*p [x 1

01

5]

0

25

50

75

0 150 300 450 600

Latent

Total

Reynolds Number, Re [x 103]

To

tal (L

ate

nt)

Utiliz

atio

n,

UT (

UL)

[%]

(a)

(b)

(c)


in spite of the increase in Nusselt number (Fig. 5). On observ-

ing 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 utiliza-

tion 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 00041.0* cR , which

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

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 em-

ployed 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 cap-

sule radius, *

cR . 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*

cR . 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 be-

tween 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 require-

ments 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.

FIGURE 8 Utilization of a LTES at different Re and R

*c

R*

c = 0.00013 R

*

c = 0.00025

R*

c = 0.00050

R*

c = 0.00100

R*

c = 0.00400

R*

c = 0.00800

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

HT

F T

em

pera

ture

, f

Axial Position, z*

0.0

0.3

0.6

0.9

1.2

1.5

0

5

10

15

20

25

Charge

Discharge

Cha

rge

(D

isch

arg

e)

Tim

e,

t* C (

t* D)

Pu

mp

Wo

rk, W

*p [x 1

01

5]

0

25

50

75

0 2 4 6 8

Latent

Total

Capsule Radius, R*

c [x 10

-3]

To

tal (L

ate

nt)

Utiliz

atio

n,

UT (

UL)

[%]

(a)

(b)

(c)

0

20

40

60

80

0 2 4 6 8

To

tal U

tiliz

ation,

UT [%

]

Capsule Radius, R*

c [x 10

-3]

Re = 60

Re = 600

Re = 3000

Re = 6000Re = 30000

0

20

40

60

80

0 2 4 6 8

To

tal U

tiliz

ation,

UT [%

]

Capsule Radius, R*

c [x 10

-3]

= 0.5

= 2.0= 1.0


CONCLUSIONS A thermocline model accounting for axial variation of tem-

perature 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 fol-

lows: Smaller radii capsules yield higher total and latent utili-

zation of the latent thermocline storage system. But on the

other hand, the pressure drop increases as capsule radius de-

creases 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 non-

dimensional capsule radii is established which is calculated to

be 00041.0* cR . Extrapolating the value for a 14 m tall tank,

commonly used in CSP plants, the corresponding capsule ra-

dius amounts to 5.77 mm. Higher Reynolds number and con-

sequently 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.

ACKNOWLEDGMENTS This work was supported by a grant from the U.S. Depart-

ment 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]

˙ m mass flow rate [kg/s]

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

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 Ex-

changer 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 Con-

tract: 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, Van-

couver, British Columbia, Canada, 8 pp.

[5] Nithyanandam, K., Pitchumani, R., 2012, “Computa-

tional Studies on a Latent Thermal Energy Storage

System with Integral Heat Pipes for Concentrating So-

lar 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 Ther-

mal Storage for Baseload Concentrating Solar Power

Plants,” Terrafore Inc., U.S. DOE Contract: DE-

EE0003589

[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


thesis, University of Wisconsin-Madison, Wisconsin.

[12] 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.

[13] Yang, Z., Garimella, S. V., 2010, “Thermal analysis of

solar thermal energy storage in a molten-salt thermo-

cline,” Solar Energy, 84, pp. 974–985.

[14] Van Lew, J. T., Li, P., Chan, C. L., Karaki, W., Ste-

phens, 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.

[15] Yang, Z. Garimella, S. V., 2011, “Molten-salt thermal

energy storage in thermoclines under different envi-

ronmental boundary conditions,” App. Energy, 87, pp.

3322–3399.

[16] 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.

[17] Felix Regin, A., Solanki, S. C., Saini, J. S., 2008, “Heat

transfer characteristics of thermal energy storage sys-

tem using PCM capsule: a review,” Renew and Sus.

Ener. Reviews, 12, pp. 2438–2458.

[18] 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.

[19] 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 inves-

tigation,” Renew. Ener., 34, pp. 1765–1773.

[20] Hänchen, M., Brückner, S., Steinfeld, A., 2011, “High-

temperature thermal storage using a packed bed of

rocks – Heat transfer analysis and experimental valida-

tion,” App. Thermal Eng., 31, pp. 1798–1806.

[21] 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.

[22] Hales, T.C., 2006, “Historical overview of the Kepler

conjecture, Discrete & Computational Geometry,” In-

ternational Journal of Mathematics and Computer Sci-

ence, 36, pp. 5–20.

[23] Kays, W. M., Crawford, M. E., Weignand, B., 2005,

Convective Heat and Mass Transfer, 4th

Ed., McGraw-

Hill, New York.

[24] Voller, V.R., Cross, M., Markatos, N.C., 1987, “An

enthalpy method for convection/diffusion phase

change,” Int. J. Numer. Methods, 24, 271–284.

[25] Galloway, T. R., Sage, B. H., 1970, “A model of the

mechanism of transport in packed, distended, and fluid-

ized beds,” Chemical Engg. Sci., 25, pp. 495–516.

[26] 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.

[27] 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.

[28] Nallusamy, N., Sampath, S., Velraj, R., 2007, “Exper-

imental investigation on a combined sensible and latent

heat storage system integrated with constant/varying

(solar) heat sources,” Renewable Energy, 32, pp. 1206–

1227.

[29] Ergun, S., 1952, “Fluid Flow through Packed Col-

umns,” Chem. Eng. Prog., 48, pp. 89–94.

[30] “Solar Thermocline Storage Systems – Preliminary

design study, ” EPRI, 2010 Public Copy


Documents

Analysis of a Latent Thermocline Energy Storage System for