-
rlt
sh
ica
ormine
ciat
(Cohen, 2006; Frier, 1999; Kearney, 1989; Price, 2002).For
instance, the Solar Electric Generating Stations(SEGS) I plant used
Caloria as the HTF. Caloria is in
ate up to a higher temperature range of 450500 C withvery low
vapor pressures. The use of a molten salt as theHTF can achieve a
higher output temperature from the col-lector eld, resulting in the
generation of steam at temper-atures above 450 C for use in the
turbine, which in turnraises the Rankine cycle eciency to
approximately 40%.
* Corresponding author. +1 765 494 5621.E-mail address:
[email protected] (S.V. Garimella).
Available online at www.sciencedirect.com
Solar Energy 84 (20101. Introduction
Parabolic-trough solar thermal electric technology isone of the
promising approaches to providing the worldwith clean, renewable
and cost-competitive power on alarge scale. In a solar
parabolic-trough plant, solar thermalenergy is collected by troughs
in a collector eld, and thendelivered by a heat transfer uid (HTF)
into a steam gen-erator to generate steam for producing electricity
in a Ran-kine steam turbine. In early studies and applications of
thistechnology, synthetic oils with operating temperaturesbelow 400
C were used as the HTF in prototype plants
a liquid state at atmospheric pressures at temperaturesbelow 315
C. Although higher HTF operating tempera-tures are desired in order
to achieve higher Rankine cycleeciencies, currently available
candidate oils are limitedto operating below approximately 400 C;
the pressuriza-tion needed to operate at higher temperatures is
prohibi-tively expensive. Hence, fossil fuels need to be used
tofurther superheat the steam generated by the oils to thehigher
temperatures desired in the turbine.
More viable candidates for high-temperature HTFs aremolten
salts, such as the commercially available HITEC(binary) and HITEC
XL (ternary). Molten salts can oper-Abstract
A comprehensive, two-temperature model is developed to
investigate energy storage in a molten-salt thermocline. The
commerciallyavailable molten salt HITEC is considered for
illustration with quartzite rocks as the ller. Heat transfer
between the molten salt andquartzite rock is represented by an
interstitial heat transfer coecient. Volume-averaged mass and
momentum equations are employed,with the BrinkmanForchheimer
extension to the Darcy law used to model the porous-medium
resistance. The governing equations aresolved using a nite-volume
approach. The model is rst validated against experiments from the
literature and then used to systemat-ically study the discharge
behavior of thermocline thermal storage system. Thermal
characteristics including temperature proles anddischarge eciency
are explored. Guidelines are developed for designing solar
thermocline systems. The discharge eciency is foundto be improved
at small Reynolds numbers and larger tank heights. The ller
particle size strongly inuences the interstitial heat transferrate,
and thus the discharge eciency. 2010 Elsevier Ltd. All rights
reserved.
Keywords: Solar thermal energy; Energy storage; Thermocline;
Molten saltThermal analysis of solain a molten-sa
Zhen Yang, Sure
Cooling Technologies Research Center, NSF I/UCRC, School of
Mechan
Received 19 June 2009; received in revised fAvailable onl
Communicated by: Asso0038-092X/$ - see front matter 2010
Elsevier Ltd. All rights
reserved.doi:10.1016/j.solener.2010.03.007thermal energy
storagethermocline
V. Garimella *
l Engineering, Purdue University, West Lafayette, IN 47907-2088,
USA
22 February 2010; accepted 8 March 20102 April 2010
e Editor Halime Paksoy
www.elsevier.com/locate/solener
) 974985
-
larIn comparison, current high-temperature oils generatesteam at
393 C with a corresponding cycle eciency of37.6% (Kearney et al.,
2003). The use of molten salts asthermal storage media allows for
higher storage tempera-tures, thereby reducing the volume of the
thermal storageunit for a given storage capacity. Moreover, molten
saltsare cheaper and more environmentally friendly than cur-
Nomenclature
CP specic heat, J kg1K1
d diameter of thermocline tank, md0 diameter of connecting tube
at the inlet and out-
let of thermocline tank, mds diameter of ller particles, me*r
unit vector in the r direction,
e*x unit vector in the x direction,
F inertial coecient, g acceleration due to gravity, m/s2
h thermocline tank height, mh0 distributor region height, mhi
interstitial heat transfer coecient, W m
3K1
K permeability, m2
k thermal conductivity, W m1K1
p pressure, PaT temperature, Kt time, su*
velocity vector, ms1
Z. Yang, S.V. Garimella / Sorently available high-temperature
oils. The major disadvan-tage of molten salts is their relatively
high meltingtemperature (149 C for HITEC XL relative to 15 C
forCaloria and 12 C for Therminol VP-1), which necessi-tates
special measures such as the use of fossil fuels or elec-tric
heating to maintain the salts above their meltingtemperatures in
order to avoid serious damage to theequipment when solar power is
unavailable at night or inpoor weather conditions.
Thermal energy storage (Gil et al., 2010; Medrano et al.,2010;
Esen and Ayhan, 1996) for solar thermal powerplants (Laing et al.,
2006; Lovegrove et al., 2004; Michelsand Pitz-Paal, 2007; Luzzi et
al., 1999) oers the potentialto deliver electricity without fossil
fuel backup as well as tomeet peak demand, independent of weather
uctuations.The current baseline design for SEGS plants uses
Thermi-nol VP-1 as the heat transfer uid in the collector
eld.Therminol VP-1 has a low freezing point of 12 C, andis stable
up to 400 C, which is higher than the operatingtemperature possible
with Caloria. However, it is still dif-cult to use Therminol VP-1
as the HTF near or above400 C in practical applications, due to its
undesirably highvapor pressure (>1 MPa) which can incur
signicant costsfor pressurization of the system. A near-term
solution forthermal storage in solar-trough plants is to use
indirectthermal storage wherein solar thermal energy deliveredby
the Therminol oil from the collector eld is transferred,through a
heat exchanger, to molten salt which serves asthe storage medium.
The expensive heat exchanger maybe eliminated by employing direct
thermal storage. In adirect molten-salt thermal storage system, a
single uid,e.g., the molten salt, serves as both the HTF and the
stor-
umag velocity magnitude, ms1
um mean velocity magnitude at the inlet of ller re-gion, ms1
Greek
a thermal diusivity of molten salt, m2s1
e porosity, l viscosity of molten salt, kgm1s1
m kinematic viscosity of molten salt, m2s1
q density, kgm3
s**
stress tensor, Nm2
Subscripts
c at the inlet low temperatureh at the outlet high temperaturel
molten salt phases solid ller phasee eective
Energy 84 (2010) 974985 975age medium, and ows directly between
the collector-eldpipes and the thermal storage tanks. The direct
solar ther-mal energy storage approach is attractive for future
para-bolic-trough solar thermal power plants both in terms ofhigher
eciency and lower cost.
In both indirect and direct molten-salt thermal storagesystems,
there are two prevailing design options: two-tankstorage, and
single-tank thermocline storage. In a two-tankstorage system, the
molten-salt HTF ows from a coldtank, through the oil-salt heat
exchange (indirect system)or the collector eld (direct system), to
a hot tank duringa charge cycle, and ows back from the hot tank,
thoughthe steam generator, to the cold tank during a
dischargecycle. The two-tank molten-salt storage design was usedin
the Solar Two demonstration plant (Pacheco and Gil-bert, 1999), and
was shown to be a low-risk and cost-eec-tive approach. Compared to
the two-tank storage system,single-tank thermocline storage oers
the potential for sig-nicantly reducing storage costs. The
thermocline storageapproach uses a packed bed (Sanderson and
Cunningham,1995; Mawire and McPherson, 2009; Mawire et al.,
2009;Singh et al., 2010) in a single tank that is marginally
largerthan one of the tanks in a two-tank thermal storage systemas
used in Solar Two. Buoyancy forces help maintain stablethermal
stratication between hot and cold molten salts in
-
the upper port. The thermal energy stored in the ller med-ium is
thus retrieved by the cold uid for further use.
Since energy storage in a thermocline depends on buoy-ancy to
maintain thermal stratication, a uniform ow atthe inlet and outlet
contributes to eective thermal strati-cation and for improved
performance of the thermocline.Therefore, measures for maintaining
a uniform ow condi-tion at the inlet and outlet are needed in
practice. In Fig. 1,two distributor regions (free of ller material)
are includedat the upper and lower ends of the ller region in the
stor-age tank. Due to their low ow resistance (compared to theller
material region), the distributor regions are expectedto lead to a
uniform distribution of the ow at the inletand outlet.
The volume-averaged governing continuum andmomen-tum equations
for the HTF phase are:
larthe same tank in this one-tank approach. A low-cost
llermaterial is used to ll most of the thermocline tank volumeand
acts as the primary thermal storage medium; this helpsreduce the
quantity of the relatively more expensive moltensalt, and presents
a signicant cost advantage over the two-tank approach. It was shown
using system-level models(Price, 2003; Kearney and Associates,
2001) that thermo-cline storage may oer the lowest-cost energy
storageoption, saving 35% of the cost relative to the two-tank
stor-age system.
Ideal ller materials for thermocline thermal energystorage
should meet several requirements: low cost, wideavailability, high
heat capacity, and compatibility withthe molten-salt HTFs. A wide
range of materials, includingquartzite, taconite, marble, NM
limestone, apatite, corun-dum, scheelite and cassiterite, have been
considered as can-didates for the ller material in a HITEC XL
molten-saltthermocline storage system (Brosseau et al., 2005).
Quartz-ite rock and silica sand were found to withstand the
moltensalt environment with no signicant deterioration thatwould
impact the performance or operability of a thermo-cline thermal
storage. A demonstration on such a thermo-cline on a pilot-scale
(2.3 MW h) was reported in Pachecoet al. (2002).
Although a few studies of molten-salt thermocline ther-mal
energy storage for parabolic-trough solar thermalplants have been
reported, the thermal behavior and e-ciency of these systems under
dierent operating conditionsis not yet well-understood. A model
that is capable of pre-dicting the charge/discharge eciency is
needed, as areguidelines for the design of molten-salt thermocline
systemsfor parabolic-trough solar thermal electric plants.
The present work develops a comprehensive analysis ofthe
discharge dynamics of molten-salt thermocline thermalenergy storage
for parabolic-trough solar thermal electricplants. HITEC molten
salt is considered as the HTF andquartzite rock as the ller in the
computations, althoughthe analysis methodology is valid for any
combination ofsalt and ller. The thermal behavior, including
temperatureproles and discharge eciency, are specically
investi-gated. Based on results from the model, guidelines
aredeveloped for the design of thermocline thermal energystorage
systems.
2. Development of a thermocline model
The thermocline unit considered for analysis is schemat-ically
illustrated in Fig. 1. The height of the ller region isdenoted h,
h0 is the height of the distributor region, d thediameter of the
cylindrical tank, and d0 the diameter ofthe ports, as shown in the
gure. An axisymmetric coordi-nate system is used as indicated. The
cylindrical thermo-cline thermal storage tank has inlet/exit ports
at thecenter of the top and bottom surfaces. The bulk of the tankis
occupied by a ller material, quartzite rock, at a porosity
976 Z. Yang, S.V. Garimella / Soof e. A molten-salt heat
transfer uid, HITEC, lls the porevolume as well as the unlled
portions at the top and bot-tom of the tank as shown in the gure.
HITEC is a eutecticmixture of water-soluble, inorganic salts:
potassium nitrate(53 wt.%), sodium nitrite (40 wt.%) and sodium
nitrate(7 wt.%). It is in a liquid state above 149 C (its
meltingtemperature) and very stable up to 538 C. Its
physicalproperties, such as viscosity and thermal
conductivity,change with temperature. HITEC is nonammable,
non-explosive and evolves no toxic vapors under
recommendedconditions of use, and therefore is considered a
potentialcandidate for molten-salt HTFs used in
parabolic-troughsolar thermal electric plants (Costal Chemical
Co.).
During the charging (heating) period, hot molten saltfrom the
collector eld enters the storage tank from theupper port, transfers
heat to the cold ller material, andexits the storage tank at a
lower temperature through thebottom port. Thermal energy from the
collector eld isthus stored in the ller medium of the storage tank.
Duringdischarge, cold liquid is pumped into the storage tankthrough
the bottom port, heated by the hot ller medium,and drawn from the
tank at a higher temperature through
Fig. 1. Schematic diagram of the thermocline thermal energy
storagesystem under analysis and the axisymmetric coordinate system
used.Energy 84 (2010) 974985@eql@t
r ql u* 0 1
-
Z. Yang, S.V. Garimella / Solar Energy 84 (2010) 974985 977@ql
u*
@tr ql
u*u*
e
! erp r s*
*
eql g*
e lK
u* F
Kp qlumag u
*
2
where s**
2l S**
23lSkk I
**
, S**
r u*r u* T
2and r e*r @@r
e*hr
@@h e
*x@@x. In the axisymmetric coordinate system shown
in Fig. 1, the problem is two-dimensional, and the velocity
vector is u* ur e*r ux e*x and its derivatives in the
h-direc-
tion are all zeros, i.e., @ur@h @ux@h 0.
Since the HTF and the ller material may be at
dierenttemperatures due to their distinct thermal conductivitiesand
heat capacities, the energy equation is applied separatelyto the
two phases. For the HTF, the energy equation is:
@eqlCP ;lT l T c@t
r ql u*CP ;lT l T c
r kerT l pr u*tr r u*
e
! s**
" # u
* u*2e
@ql@t
hiT s T l 3
and for the ller, it is:
@
@t1 eqsCP ;sT s T c hiT s T l 4
The heat transfer between the HTF and the ller is ac-counted for
with a volumetric interstitial heat transfer coef-cient hi, which
appears as a source term on the right sideof Eqs. (3) and (4).
Heating of the HTF caused by compres-sion work due to volume
expansion/shrinkage, viscous ef-fects and kinetic energy changes,
as respectively shown inthe second, third and fourth terms on the
right side ofEq. (3), is small and less than 104 times the
conductionor convection terms, but is included for
completeness.
In a thermocline using quartzite rock as the ller, the l-ler
particles are completely surrounded by the HTF (a con-tinuous
phase) and have poor thermal contact withneighboring particles;
therefore, the ller is treated as a dis-persed phase embedded in a
continuous HTF phase. Theeective thermal conductivity ke of the
HTF-ller mixturein Eq. (3) can then be expressed as (Gonzo,
2002)
ke kl 1 2b/ 2b3 0:1b/2 /30:05 exp4:5b
1 b/ 5
where / 1 e and b ksklks2kl. Eq. (5) provides a good esti-mate
for the eective conductivity of liquid-saturated por-ous media with
/ ranging from 0.15 to 0.85 and b from0.499 to 1. Thermal
conduction of the ller phase is, how-ever, neglected in Eq. (4)
because of the large thermal con-tact resistance between ller
particles; conduction withinthe ller particles is also neglected
due to their small size(
-
Da2 Da
The non-dimensional parameters included in Eqs. (9)(12)
s tmc ; X x ; R r ; U* u*
; H h ;
H d; D
d; D
d;
Re mc
; P lcum
; Gr mcum
; Da ds
;
ql;cCP ;l;c lum
~r ex@X
R @h
er@R
:
978 Z. Yang, S.V. Garimella / Solar Energy 84 (2010)
974985Coecients Uq, Ul, UCpl, Ukl, Uke, Uqs and UCps account forthe
temperature dependence of the density, viscosity, spe-cic heat,
thermal conductivity, eective thermal conduc-tivity of the molten
salt, and the density and specic heatof the ller material,
respectively. These coecients canbe expressed as follows, according
to the data in CostalChemical Co.:* @ e*h @ * @A u2m
CP ;l;cT h T c ; Nui hid
2s
kl;c;
Pr mcac CP ;l;clc
kl;c; Hl T l T cT h T c ; Hs
T s T cT h T c ;
X qs;cCP ;s;c ; T**
s**
dss s s
umds pds gd2s
K
pd2s ds ds um ds
0 h0 d 0 d
0are dened as follows:Energy equation for the molten salt:
Pr@
@seUqUCplHl PrRe ~r UqUCplHl U
*
~r Uke ~rHl PrA P ~r U* tr ~rU* T*
*
=e UU2
@Uq@s
" #
UklNuiHs Hl 11
Energy equation for the ller phase:
Pr@
@s1 eXUqsUCpsHs UklNuiHs Hl 12@Uq U*
@s Re ~r Uq U
*
U*
e
!
e ~rP ~r ~T* eUqGre*x
e Ul U*
FReUqUmag U*
!10Uq 1 0:732T h T c2084:4 0:732T cHl
Ul exp4:343 2:0143 lnT h T cHl T c 10:094exp4:343 2:0143 ln T c
10:094
Ukl 6:53 104T h T cHl T c 0:5908
6:53 104T c 0:5908Uke Ukl 1 2b/ 2b
3 0:1b/2 /30:05 exp4:5b1 b/
UCpl 1; UCps 1; Uqs 1
According to Wakao and Kaguei (1982), the interstitialNusselt
number for liquid ow through particle beds canbe expressed by
Nui 61 e2 1:1Re0:6L Pr1=3L 13where ReL and PrL are the local
Reynolds and Prandtlnumbers, respectively.
Assuming the distributor regions are properly designedso that
uniform ows at the inlet and outlet of the llerregion have been
achieved, the appropriate boundary con-ditions are as follows.
At the inlet:
UX 1; UR 0; Hl 0 14and at the outlet:
@UX@X
@UR@X
@Hl@X
0 15
Eqs. (9)(13) show that heat transfer and uid ow in athermocline
storage tank is decided by Re and materialproperties, i.e., Uq, Ul,
Ukl, Uks, Uke, UCpl, UCps and Pr.Once the HTF and the ller
particles are selected and thematerial properties are determined,
the characteristics ofthe thermal energy storage process are solely
determinedby Re.
The computational domain is discretized into nitevolumes. All
the variables are stored at the centers ofthe square mesh cells. A
second-order upwind scheme isused for the convective uxes, while a
central-dierencingscheme is used for discretizing the diusion uxes.
A sec-ond-order implicit scheme is used for time
discretization.Pressurevelocity coupling is implemented through
thePISO algorithm (Issa, 1986). Iterations at each time stepare
terminated when the dimensionless residuals for allequations drop
below 104. The computations are per-formed using the commercial
software FLUENT (FLU-ENT 6.1 Documentation). User-dened
functions(UDFs) are developed to account for Eqs. (11) and(12).
Grid and time-step dependence are checked byinspecting results from
dierent grid densities and timeintervals. Based on this, DX = DR =
0.01 andDs = 1 103 are chosen as this setting results in a
tem-perature along the line R = 0 throughout the discharge
-
process that is within 1% of that for the case withDX = DR =
0.005 and Ds = 5 104.
3. Model validation
The experimental results of Pacheco et al. (2002) areused here
to validate the numerical model. A small pilot-scale, 2.3 MW h,
thermocline system was designed andbuilt for their experiments. The
storage tank was lled witha mixture of quartzite rock and silica
sand resulting in aporosity of 0.22. A nearly eutectic mixture of
soldiumnitrate and potassium nitrate was used as the HTF.
Thenon-dimensional parameters for the experiments were asfollows: H
= 67, H = 1.1, D = 33, D = 3.3, Re = 220,Pr = 13.4, Gr = 9.59 107,
Da = 0.01, A = 1.21 1012.
The numerical results for the axial temperature prolesare
compared with the experimental ones in Fig. 2. Simula-tion 1 uses
the same conditions as in the experiment. Prop-erty parameters Uq,
Ul, Ukl, Uke, UCpl and Pr are taken as
HTF and the ller particles takes values of as much as0.1; this
is consistent with the extent of scatter in the exper-imental
measurements and the deviation (0.1) betweenthe experimental and
the numerical temperature prolesin Fig. 2. Within the experimental
uncertainty, therefore,the results from the simulations are seen to
agree well withthe experiments. The ow distributor regions are seen
to bequite eective from the results of simulation 1, since theaxial
temperature proles at dierent times in simulation1 are almost
identical to those for the ideal uniform inletand exit ow assumed
in simulation 2. It is clear from theseresults that uid ow and heat
transfer in a thermoclinethermal energy storage tank with
well-designed distributorregions are equivalent to those under
uniform inlet andoutlet ow conditions.
4. Results and discussion
The validated numerical code discussed above isemployed here to
systematically investigate the discharge
cussed above, this condition is readily achieved in
practice.
Z. Yang, S.V. Garimella / Solar Energy 84 (2010) 974985 979Fig.
2. Comparison between the numerical and experimental (Pachecoet
al., 2002) axial temperature proles during discharge of a
thermoclinethose of HITEC salt, since properties for the exact
eutecticmixture (whose composition is close to that of HITEC)used
in Pacheco et al. (2002) were not provided. In orderto understand
the eectiveness of the ow distributor inrendering uniform ow to the
ller region, another case(simulation 2) is considered; conditions
for simulation 2are identical to those for simulation 1, except
that the mol-ten-salt ow eld is not solved for in the distributor
region,and instead, the ow is set to be uniform at the entranceand
exit of the ller region.
As shown in Fig. 2, the experimental results displaysome scatter
in the temperature proles. This may havebeen caused by the contact
of some of the thermocoupleswith the rock while others may have
been located squarelyin the pore centers. Results from the model
show that thenon-dimensional temperature dierence DH between
thethermal energy storage unit (2.3 MW h): Simulation 1 with
distributors,Simulation 2 with uniform ow at the inlet and outlet
of the ller region.Fig. 3. Axial temperature proles at dierent
times during a discharge4.1. Temperature proles
Typical temperature histories of the molten salt and theller
material during a discharge cycle are shown in Fig. 3.The
temperature proles at any given time, e.g., s = 1.5,can be divided
into three zones. In the constant, low-tem-characteristics of a
thermocline energy storage unit. Basedon the numerical results, a
procedure is proposed fordesigning thermocline thermal storage
systems. In theresults presented in this section, it is assumed
that eectiveow distributors have led to the establishment of
uniformow of molten salt in the ller region in all cases. As
dis-cycle at Re = 50 and H = 250: Hl molten salt temperature, Hs
llertemperature.
-
perature zone near the inlet (X = 0) at the bottom of thestorage
tank, both Hl and Hs take values of zero. The nextzone is
characterized by signicant temperature changes inboth phases (0
< Hl < 1 and 0 < Hs < 1). The nal zone isthe constant,
high-temperature zone near the exit at thetop of the storage tank,
where both Hl and Hs take valuesof unity. In the rst zone, the ller
is completely cooled bythe cold molten salt (Hl = 0) pumped into
the storage tank,and thermal equilibrium exists between the two
phases. Inthe second zone (referred to hereafter as the
heat-exchangezone), the temperature of the quartzite rock is higher
thanthat of the molten salt, and thermal energy is transferred
tothe cold salt. In the third zone, the salt is fully heated up
toHl = 1 and is once again in thermal equilibrium with the l-ler
material.
As time progresses, the intermediate, heat-exchangezone advances
from the inlet towards the outlet, leavingbehind an expanding
constant-low-temperature zone andcausing the
constant-high-temperature zone in front toshrink, as shown in Fig.
3. It is convenient to track the
l;c c l;c c h s c s h c
16where DE is the thermal energy change in the control vol-ume,
Ac is the cross-section area of the storage tank, u
0
(=um/e v) is the relative speed of molten salt in the mov-ing
coordinate system, and v is the speed of the travelingcoordinate
system which is equal in magnitude to the rela-tive speed of the
ller. Although temperature proles in themolten salt in the
heat-exchange zone change with time,they are essentially symmetric
about the mid-temperaturepoint Xm, as will be discussed later. This
indicates thatthe thermal energy of the salt in this zone changes
littlewith time, which is also true for the thermal energy ofthe
ller material in this zone. Therefore, DE is close tozero so that
Eq. (16) becomes
ume v
AceCpl;cql;cT h T c 1 evAcCpsqsT h T c
17which yields
v Cpl;cql;cumeCpl;cql;c 1 eCpsqs
18
980 Z. Yang, S.V. Garimella / Solarlocation Xm, where the molten
salt is at temperatureHl = 0.5, as being representative of the
heat-exchange zone.Fig. 4 illustrates the change in the position of
the heat-exchange zone with time at dierent Reynolds numbers.All
the results are seen to be well represented by a singlelinear t
passing through the origin, when plotted againstthe product of s
and Re. The slope of this line obtainedby linear regression is
1.29.
The slope of the line in Fig. 4 can also be obtained via asimple
energy balance on a control volume that covers themolten salt and
ller in the entire heat-exchange zone, asshown in Fig. 5. The
moving coordinate system has its ori-gin xed at the location Xm,
and travels with the controlvolume from the bottom to the top of
the storage tank.
Fig. 4. Representative location Xm in the heat-exchange zone for
dierent
Reynolds numbers at dierent times. The results are well
represented by asingle straight line passing through the origin.In
this moving coordinate system, the ller enters the con-trol volume
at the high temperature Th and exits at the lowtemperature Tc; the
molten salt enters the control volumein the opposite direction as
the ller at the low temperatureTc and exits at the high temperature
Th. The net thermalenergy ux of the salt and the ller changes the
total ther-mal energy in the control volume, according to
DE q u0A e Cp T T 1 eq vA Cp T T
Fig. 5. Control volume xed at the mean-temperature location ofHl
= 0.5.
Energy 84 (2010) 974985Since v is the speed of the traveling
coordinate system withits origin xed in the heat-exchange zone, it
is also the
-
speed of advance of this zone, i.e., dxm/dt = v, where xm isthe
dimensional form of Xm. The slope in Fig. 4 can then berewritten
as
dXmds Re
dxmdtum
vum
Cpl;cql;ceCpl;cql;c 1 eCpsqs
1:29
19
This result depends only on the physical properties, andis
identical to the slope obtained from the linear t tothe numerical
data in Fig. 4. This validates the assump-tion made earlier that
the total thermal energy in theheat-exchange zone is essentially
invariant, i.e., DE = 0,during the discharge cycle. Both the
analysis above andthe data in Fig. 4 indicate that the
heat-exchange zoneadvances at a constant speed from the inlet on
the bot-tom to the outlet at the top in a thermocline
thermalstorage tank.
Fig. 6 shows the development of the axial temperatureproles
plotted in the moving coordinate system, with thehorizontal axis
being (X Xm). All the temperature pro-les pass through the point
(0, 0.5) in Fig. 6, and appear
changes little, i.e., DE 0 in Eq. (16), which supports
theearlier assumption in the derivation of Eq. (17).
Increasing the Reynolds number results in an expansionof the
heat-exchange zone. For instance, the temperatureproles at Re = 10
change more gradually in the heat-exchange zone than at Re = 1 when
compared at the sameposition Xm, resulting in a wider heat-exchange
zone, asshown in Fig. 6. At the higher Reynolds number, a longerow
distance is needed for the uid to be heated by the l-ler phase,
leading to a more gradual temperature rise and acorresponding
increase in the extent of the heat-exchangezone. Since the molten
salt in the heat-exchange zone isat a relatively lower temperature,
an expanded heat-exchange zone can lead to signicant waste of
thermalenergy if the salt delivered at lower temperatures is not
use-ful for further application. This points to the importanteects
of Reynolds number on the design of a thermoclinethermal energy
storage system.
The eect of tank height is illustrated in Fig. 7 in termsof its
eect on the temperature history of the molten salt.Prior to the
heat-exchange zone reaching the tank outlet,
Z. Yang, S.V. Garimella / Solar Energy 84 (2010) 974985 981to be
symmetrical about this point. As the discharge pro-cess proceeds
(and the position of the heat-exchange zoneXm increases in Fig. 6),
the thermal energy decrease (tem-perature drop) in the region to
the right of the point (0,0.5) is eectively compensated by an
increase (temperaturerise) in the region to left of the point, as
shown by a com-parison of the proles at Xm = 65 and 322 at Re = 1
or 10.This causes the thermal energy of the molten salt in
theheat-exchange zone to be maintained at a near-constantlevel.
This conclusion also holds for the ller phase. There-fore, the
total thermal energy in the heat-exchange zone
Fig. 6. Molten salt temperature proles in the heat-exchange
zone.
Sharper changes in temperature prole occur at lower Reynolds
numberand small Xm.salt at a constant high-temperature level is
available atthe outlet, i.e., Hl = 1. As the heat-exchange zone
arrivesat the outlet, the salt temperature begins to drop,
nallyreaching the constant low temperature level (Hl = 0) whenthe
thermal energy stored in the ller particles has beencompletely
depleted. Thermocline tanks with a largerheight can eectively
extend the discharge stage whereinthe salt temperature is
maintained at a high level. Forinstance, the salt temperature
begins to drop at s = 5 whentank height H is 450, whereas this time
is prolonged totwice the period (s = 10) with H = 850, as shown
inFig. 7. Since the quality of low-temperature salt is not
Fig. 7. Output temperature history of the molten salt with Re =
50 at
dierent tank heights. A thermocline tank of a larger height
exhibits aprolonged constant-high-temperature-discharge stage.
-
acceptable for generating superheated steam in the tur-bines, it
is desired that most of the stored thermal energybe retrieved at a
high-temperature level in order to meetthe design conditions; this
also helps to maintain higherthermal-to-electrical conversion
eciency of the turbinegenerator. It may be noted that only thermal
energy withtemperature above a certain level, e.g., Hl > 0.95 as
chosenfor this work and shown in Fig. 7, is usually considered
asuseful energy.
4.2. Discharge eciency
It is of interest to quantify the amount of useful energythat a
thermocline system can deliver during a dischargecycle. The
discharge eciency of a thermocline thermalenergy storage system is
dened in this work as follows
g Output energy with Hl > H0Total energy initially stored in
the thermocline tank
982 Z. Yang, S.V. Garimella / Solar20where H0 is a threshold
value determined by the applica-tion of interest. A value of 0.95
for H0 is chosen in thiswork, implying that thermal energy
delivered at tempera-tures greater than (Tc + 0.95(Th Tc)) qualies
as usefulenergy. If Th = 450 C and Tc = 250 C, for example, HI-TEC
liquid delivered at temperatures above 440 C is con-sidered useful
in generating superheated steam for thesteam turbine.
The eciency dened by Eq. (20) varies depending onthe
construction and working conditions of the thermo-cline system.
Fig. 8 shows the discharge eciency calcu-lated for dierent Re for
thermoclines of dierent heightsH. It is clear that the eciency
increases with tank heightH, and decreases with a rise in the
Reynolds number. AFig. 8. Discharge eciency g of a thermocline at
dierent H and Re. gincreases with H and decreases as Re
increases.tank with a larger height extends the constant
high-temper-ature discharge stage, as shown earlier in Fig. 7,
thusincreasing the fraction of initial stored energy that is
recov-ered as high-temperature thermal energy. At a higher
Rey-nolds number, the heat-exchange zone expands greatly, asshown
in Fig. 6. For instance, the heat-exchange zone forRe = 10 at Xm =
579 extends over an X Xm of 200; fora particle diameter of 5 cm,
this would imply a zone lengthof 10 m. Since the salt temperature
in the heat-exchangezone is lower than the constant
high-temperature level,an expanded heat-exchange zone reduces the
amount ofhigh-temperature molten salt delivered, and thus
decreasesthe discharge eciency g.
The numerical results for the eciency in Fig. 8 are
wellrepresented by the following correlation:
g 1 0:1807Re0:1801H=100m 21where m 0:00234Re0:6151 0:00055Re
0:485.
This correlation can predict the numerical data within amaximum
error of 1% for Reynolds number between 1 and50 and H between 10
and 800, as shown by the solid-linepredictions from the equation
included in Fig. 8.
Three other important parameters which capture theperformance of
the thermocline system, i.e., dischargepower per unit
cross-sectional area (P/A), useful thermalenergy per unit
cross-sectional area (Q/A), and total storedthermal energy per unit
cross-sectional area (Qt/A), may bedened as follows:
PA umql;cCpl;cT h T c kl;c
T h T cds
RePr 22
QA eqlCpl 1 eqsCpsT hT h T chg eqlCpl 1 eqsCpsT hT h T cds Hg
23
QtA eqlCpl 1 eqsCpsT hT h T ch eqlCpl 1 eqsCpsT hT h T cds H
24
where Q is the useful thermal energy delivered at a temper-ature
above H0, and the thermal properties included in thesquare brackets
subscripted by Th are calculated at temper-ature Th. The importance
of parameters (P/A) and (Q/A) indesigning a thermocline storage
system will be demon-strated in the following.
From Eqs. (22)(24), a non-dimensional dischargepower may be
dened as RePr, a non-dimensional usefulenergy as Hg, and a
non-dimensional total energy as H(equaling the non-dimensional
height of the storage tank).Fig. 9 plots the eciency under
conditions of dierent dis-charge power and total energy, which can
serve as a guide-line for the design of thermocline storage
systems. Thedischarge eciency is seen to increase with an increase
inthe total stored thermal energy and decrease with anincrease in
discharge power. If high discharge eciency is
Energy 84 (2010) 974985desired, a thermocline storage unit
should be designed tohave a large height and operate at a low
discharge power.
-
Fig. 9. Discharge eciency at dierent discharge powers (RePr) and
totalthermal energies H. A high discharge eciency occurs at a low
discharge
Z. Yang, S.V. Garimella / SolarHowever, this may not be
practically feasible as the dis-charge power would need to be
maintained above a certainvalue and the tank height would need to
be limited for costconsiderations as well as to reduce heat loss
from the cor-respondingly higher tank surface area. The
dischargepower and the amount of useful thermal energy would
typ-ically be determined by the application, leaving
otherparameters to be decided during the design of a storageunit.
To facilitate the design under such conditions,Fig. 10 shows the
total thermal energy H under conditions
power and a high total thermal energy.of dierent discharge power
and useful thermal energy.From this gure, the total thermal energy
(or tank height)
Fig. 10. Total thermal energy H at dierent discharge power RePr
anduseful thermal energy Hg. The value of the useful thermal energy
is alwayslower than that of the total thermal energy.required to
meet the discharge power and thermal energyoutput demands may be
determined. For instance, a ther-mocline storage unit with a
non-dimensional dischargepower of 600 and a non-dimensional useful
thermal energyof 400 calls for a non-dimensional total thermal
energy (ornon-dimensional tank height) of 470.
4.3. Design procedure and examples
The analyses presented thus far are used in this sectionto
develop procedures for designing a thermocline thermalenergy
storage system with HITEC as the molten salt andquartzite rock for
the ller particles, although the proce-dure itself is generally
applicable to other materials sys-tems. It is assumed that
discharge power P and usefulthermal energy Q are predetermined by
the application,and that the rock can be packed to a porosity of
0.22 inthe ller region (Pacheco et al., 2002). The
recommendeddesign procedure follows.
1. Choose tank diameter d and ller particle size ds basedon
practical requirements.
2. Calculate the cross-sectional area of the storage tankA =
0.25d2, and then the discharge power per unitcross-sectional area
(P/A) and total thermal energy perunit cross-sectional area
(Q/A).
3. Calculate the non-dimensional discharge power RePrand useful
thermal energy Hg, using Eqs. (22) and(23), respectively.
4. Calculate Re from the value of RePr and assumingH = Hg.
5. Use the Re and H obtained in step 4 to calculate g fromEq.
(21).
6. Obtain H by dividing Hg with the eciency g obtainedin step
5.
7. Repeat steps 5 and 6 until the dierence between thenewly
obtained H and that in last iteration is smallerthan 0.1%.
8. The nal H is the required height for the thermoclinestorage
tank; also obtained is the discharge eciency g.
9. The dimensional height of the tank h is calculated ash = ds
H.
Table 1 shows some examples of thermocline designsbased on this
procedure. The storage tank is initially at450 C, and cold HITEC at
250 C (Tc) is fed into the tank.The output HITEC is at a
temperature level of 450 C (Th)during the early discharge phase,
and later drops in temper-ature as the thermal energy stored in the
tank is depleted.Thermal energy delivered at a temperature
exceeding440 C (H0 = 0.95) is regarded as useful energy.
It is observed that an increase in discharge power Pdecreases
the discharge eciency g, as evident from acomparison of cases 1, 2,
3, and 4 in Table 1 with cases5, 6, 7, and 8, respectively. This
trend is due to expansion
Energy 84 (2010) 974985 983of the heat-exchange zone at larger
powers (also largerRe values) as shown in Fig. 6, which reduces the
amount
-
8 5 2 5 0.1 57.6 3.52
larof useful thermal energy delivered. For a speciedamount of
useful thermal energy Q, choosing a largertank diameter can
eectively reduce the required tankheight; however, this also
decreases the discharge e-ciency. This decrease in discharge
eciency is related tothe importance of the relatively large extent
of the tankoccupied by the heat-exchange zone in a short
storagetank. Increasing the useful thermal energy Q, with
thedischarge power, the tank diameter and the ller sizebeing xed,
needs an increase in the tank height, as canbe seen from a
comparison of cases 18 with cases 916, respectively. The discharge
eciency is also increaseddue to an increase in the storage tank
height (as shown inFig. 8). The eciency of a design with a small
tank diam-eter can be increased by using a larger height.
However,such a design can be more expensive in terms of
materialscost, and also oers more surface area for heat loss tothe
environment. These practical considerations wouldfurther inform
design trade-os.
9 10 1 2 0.05 88.0 28.810 10 1 2 0.1 81.6 31.111 10 1 5 0.05
80.1 5.0712 10 1 5 0.1 70.5 5.7613 10 2 2 0.05 86.4 29.414 10 2 2
0.1 79.1 32.115 10 2 5 0.05 77.8 5.2216 10 2 5 0.1 67.3 6.03Table
1Results for various thermocline design examples.
Case No. Q (MW h) P (MW) d (m) ds (m) g () (%) h (m)
1 5 1 2 0.05 83.6 15.22 5 1 2 0.1 75.4 16.83 5 1 5 0.05 73.4
2.774 5 1 5 0.1 61.4 3.315 5 2 2 0.05 81.6 15.66 5 2 2 0.1 72.4
17.57 5 2 5 0.05 70.5 2.88
984 Z. Yang, S.V. Garimella / SoIt is also noted that the ller
particle size strongly aectsthe eciency. The use of small-sized
ller particlesincreases the eciency greatly, as can be seen by
comparingcases 1, 3, 5, 7 with cases 2, 4, 6, 8, respectively. The
contactarea between HITEC and quartzite rock is increased
withsmaller particles, which increases the heat exchange
ratebetween HITEC and quartzite rock, leading to increaseddischarge
eciency.
5. Conclusions
A two-temperature model is developed for investigatingenergy
discharge from a thermocline thermal energy stor-age system using
molten salt as the heat transfer uidand inexpensive rock as the
ller. Thermal characteristics,including temperature proles and
discharge eciency ofthe storage tank, are systematically
explored.
During discharge, the heat-exchange zone expands withtime and
Reynolds number, and its rate of travel is con-stant and can be
precisely predicted by Eq. (18).Discharge eciency of the
thermocline storage tank iswell predicted by the correlation
developed in Eq. (21)for Reynolds numbers in the range of 150 and
non-dimen-sional tank heights of 10800. The eciency increases
withtank height and decreases as Reynolds number increases.
Procedures for designing thermocline storage tanks areproposed.
The use of smaller ller particles can greatlyincrease the discharge
eciency. For instance, a thermo-cline storage unit (2 MW, 5 MW h
and d = 5 m) with a l-ler particle size of 5 cm has a discharge
eciency thatexceeds that with a particle size of 10 cm by
12.9%.
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Z. Yang, S.V. Garimella / Solar Energy 84 (2010) 974985 985
Thermal Analysis analysis of Solar Thermal Energy Storage solar
thermal energy storage in a Molten-Salt Thermoclinemolten-salt
thermoclineIntroductionDevelopment of a thermocline modelMODEL
VALIDATIONModel validationRESULTS AND DISCUSSIONResults and
discussionTemperature profilesDischarge efficiencyDesign procedure
and examples
ConclusionsReferences