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: sureshg@purdue.edu (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%.

References

Brosseau, D., Kelton, J.W., Ray, D., Edgar, M., 2005. Testing ofthermocline ller materials and molten-salt heat transfer uids forthermal energy storage systems in parabolic trough power plants. J.Sol. Energy Eng. 127, 109116.

Cohen, G., 2006. Nevada rst solar electric generating system. In: IEEEMay Technical Meeting. Solargenix Energy, Las Vegas, Nevada..

Esen, M., Ayhan, T., 1996. Development of a model compatible with solarassisted cylindrical energy storage tank and variation of stored energywith time for dierent phase-change materials. Energy Convers.Manage. 37 (12), 17751785.

FLUENT 6.1 Documentation. .Frier, S., 1999. An overview of the kramer junction SEGS recent

performance. In: Parabolic Trough Workshop. KJC Operating Com-pany, Ontario, California. .

Gil, A., Medrano, M., Martorell, I., Lazaro, A., Dolado, P., Zalba, B.,Cabeza, L.F., 2010. State of the art on high temperature thermalenergy storage for power generation. Part 1 Concepts, materials andmodellization. Renew Sust. Energy Rev. 14, 5672.

Gonzo, E.E., 2002. Estimating correlations for the eective thermalconductivity of granular materials. J. Chem. Eng. 90, 299302.

Specic Heat Capacities of Some Common Substances. The EngineeringToolBox. .

HITEC Heat Transfer Salt. Costal Chemical Co., L.L.C., BrenntagCompany. .

Issa, R.I., 1986. Solution of implicitly discretized uid ow equations byoperator splitting. J. Comput. Phys. 62, 4065.

Kearney, D., 1989. Solar electric generating stations (SEGS). IEEE PowerEng. Rev. 9, 48.

Kearney and Associates. 2001. Engineering evaluation of a molten saltHTF in a parabolic through solar eld. NREL Contract No. NAA-1-30441-04. .

Kearney, D., Herrmann, U., Nava, P., 2003. Assessment of a molten saltheat transfer uid in a parabolic through solar eld. J. Sol. EnergyEng. 125, 170176.

Laing, D., Steinmann, W.D., Tamme, R., Richter, C., 2006. Solid mediathermal storage for parabolic trough power plants. Sol. Energy 80,12831289.

Launder, B.E., Spalding, D.B., 1972. Lectures in Mathematical Models ofTurbulence. Academic Press, London, England.

Lovegrove, K., Luzzi, A., Soldiani, I., Kreetz, H., 2004. Developingammonia based thermochemical energy storage for dish power plants.Sol. Energy 76, 331337.

Luzzi, A., Lovegrove, K., Filippi, E., Fricker, H., Schmitz-Goeb, M.,Chandapillai, I., Kane, S., 1999. Techno-economic analysis of a10 MWe solar thermal power plant using ammonia-based thermo-chemical energy storage. Sol. Energy 66, 91101.

Mawire, A., McPherson, M., 2009. Experimental and simulated temper-

Energy 84 (2010) 974985ature distribution of an oil-pebble bed thermal energy storage systemwith a variable heat source. Appl. Therm. Eng. 29, 10861095.

Mawire, A., McPherson, M., van den Heetkamp, R.R.J., Mlatho, S.J.P.,2009. Simulated performance of storage materials for pebble bedthermal energy storage (TES) systems. Appl. Energy 86,12461252.

Medrano, M., Gil, A., Martorell, I., Potau, X., Cabeza, L.F., 2010. Stateof the art on high-temperature thermal energy storage for powergeneration. Part 2 case studies. Renew Sust. Energy Rev. 14,3155.

Michels, H., Pitz-Paal, R., 2007. Cascaded latent heat storage forparabolic trough solar power plants. Sol. Energy 81, 829837.

Pacheco, J.E., Gilbert, R., 1999. Overview of recent results of the solar twotest and evaluations program. In: Hogan, R., Kim, Y., Kleis, S.,ONeal, D., Tanaka, T. (Eds.), Renewable and Advanced EnergySystems for the 21st Century. ASME Int., New York.

Pacheco, J.E., Showalter, S.K.,Kolb,W.J., 2002.Thermocline thermal storagesystem for parabolic trough plants. J. Sol. Energy Eng. 124, 153159.

Price, H., 2002. Parabolic Trough Technology Overview. Trough Tech-nology Algeria, NREL. .

Price, H., 2003. A parabolic trough solar power plant simulation model..

Sanderson, T.M., Cunningham, G.T., 1995. Performance and ecientdesign of packed bed thermal storage systems part 1. Appl. Energy 50,119132.

Singh, H., Saini, R.P., Saini, J.S., 2010. A review on packed bed solarenergy storage systems. Renew. Sust. Energy Rev. 14 (3), 10591069.

Wakao, N., Kaguei, S., 1982. Heat and Mass Transfer in Packed Beds.Gordon and Beach, New York.

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