M. M. Valmiki

Wafaa Karaki

Peiwen Lie-mail: peiwen@email.arizona.edu

Jon Van Lew

Cholik Chan

Department of Aerospace

and Mechanical Engineering,

The University of Arizona,

Tucson, AZ 85721

Jake StephensUS Solar Thermal Storage LLC,

1000 E. Water Street,

Tucson, AZ 85719

Experimental Investigationof Thermal Storage Processesin a Thermocline TankThis paper presents an experimental study of the energy charge and discharge processesin a packed bed thermocline thermal storage tank for application in concentrated solarpower plants. A mathematical analysis was provided for better understanding and plan-ning of the experimental tests. The mathematical analysis indicated that the energy stor-age effectiveness is related to fluid and solid material properties, tank dimensions,packing schemes of the solid filler material, and the durations of the charge and dis-charge times. Dimensional analysis of the governing equations was applied to consoli-date many parameters into a few dimensionless parameters, allowing scaling from alaboratory system to an actual industrial application. Experiences on the system design,packing of solid filler material, system operation, and data analysis in a laboratory-scalesystem have been obtained in this work. These data are used to validate a recently pub-lished numerical solution method. The study will benefit the application of thermoclinethermal storage systems in the large scale concentrated solar thermal power plants inindustry. [DOI: 10.1115/1.4006962]

1 Introduction

Power generation using concentrated solar thermal energy(CSP) is one of the several promising, emerging renewable energytechnologies [1]. A great amount of research and developmentwork has been done in the last thirty years, including several testand commercial projects, some currently operational and someunder construction [2–5]. With the significant progression of theseefforts, CSP systems based on trough and tower concentratorscontinue to mature [6–9]. Expanded production of key compo-nents, innovation in system design, new technologies, and largerproposed project scales offer the potential for significant reductionin levelized electricity costs for CSP systems. These measureswill come in response to increased market demand for renewableenergy [2].

Nevertheless, the price of electricity generated from solar ther-mal energy is still not low enough to compete with conventionalfossil fuel technologies, including natural gas power. This and thedrop in cost of photovoltaic systems both drive the need for fur-ther cost reduction in solar thermal power generation [10,11] inorder to be competitive in the energy market.

Of the different approaches to cost reduction in solar thermalpower systems, thermal energy storage (TES)—if sufficientlycheap—is recognized as one of the best opportunities [1,12,13].The ability of TES to extend the daily operation of the powerplants beyond sunlight hours can ideally expand generation at alower per unit cost. It can also firm against resource intermittency,increasing energy value due to operational flexibility. If so, thecost of electricity from concentrated solar thermal power can bereduced and its value increased.

In a solar thermal power plant, heat transfer fluid (HTF) is typi-cally used to collect and deliver heat received from concentratedsunlight. In a direct thermal storage system, hot HTF is stored af-ter exiting the solar collection field. In an indirect system the heatis transferred to a secondary fluid for thermal storage in a separateloop via a heat exchanger. One TES possibility is to construct twotanks, one hot and one cold, in order to have an ideal high temper-ature supply [14]. This situation can be considered thermally ideal

since discharged fluid from the hot tank will continuously exit at ahigh temperature until completely emptied. There will be no tem-perature degradation at the outlet until the entire initial volumehas been withdrawn.

From the viewpoint of cost reduction, cutting the necessary ex-pensive HTF volume and the number of required tanks can beattractive. Thus, it is advantageous to combine a two tank systeminto a one tank system with a filler material. Using cheap, solidmaterial within such tanks as the primary thermal storage mediumis one possibility [15]. Such tanks are called thermocline tanksdue to their temperature stratified nature; in general, there are hotand cold sections separated by a temperature gradient, the thermo-cline. This stratification and the filler material reduces mixingwithin the tank, an important feature for maximizing TES effi-cacy. Thermocline tanks can be filled with sensible or phase-change heat storage materials [12]. Whereas, the cost reductionfrom cheaper filler material is a potential benefit, the heat transferbetween the fluid and filler material is a disadvantage from thepoint of view of energy storage effectiveness. The final merit of afiller-based approach depends on a design’s cumulative perform-ance and costs in achieving the desired storage goals.

There have been significant efforts in the modeling of packedbed thermal storage tank behavior. In general, most models areappropriate for any combination of fluid and sensible heat fillermaterial as all include material properties as parameters that canbe defined for any case. Some of these efforts use models basedon a variation of the one-dimensional Schumann energy equationsfor fluid flow through a porous medium [16–20]. Various numeri-cal solutions to the two-phase system have been demonstrated, yetthey tend to have both advantages and limitations. Computationaloverhead can be large, numerical stability issues can arise, andconditions are sometimes restricted due to numerics and assump-tions. Still, solutions are often in good agreement with experimen-tal data [21–24].

Other efforts use more comprehensive approaches which includeaspects such as two-dimensional flow, tank walls, temperature-dependent fluid properties, and environmental heat loss. Yang et al.,use commercial CFD software to solve a complete, dimensionlessmodel [25]. It is shown that for given tank dimensions, materialproperties, and cycle times the storage process characteristics aredependent on the Reynolds number, alone. Using the simulationresults and derived equations, a sizing procedure for thermocline

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL

OF SOLAR ENERGY. Manuscript received September 11, 2011; final manuscript receivedMay 26, 2012; published online July 5, 2012. Assoc. Editor: Rainer Tamme.

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TES tanks is suggested. One important conclusion is that the flowdistribution regions at the top and bottom of a thermocline tank caneffectively establish uniform flow into the packed bed. Furthermore,it was shown that structural failure due to thermal ratcheting can beavoided with proper tank design [26].

With a similar model, Xu et al., have presented a sensitivityanalysis using a finite volume method with a user-developed code[27]. The study showed that there was little dependence on thechoice of the interstitial heat transfer coefficient correlation and auniform cross-sectional temperature is possible with proper insu-lation layers. Like the previously mentioned work, it is shown thatthe thermocline length will grow in time during discharging. BothXu and Yang suggest that heat transfer to the wall will result inslightly depressed temperatures and even backflow.

While the comprehensive models are useful to gain full under-standing, they are computationally demanding and require muchtime and effort to simulate. It would be useful to have a quick andaccurate method for early design stages and for yearly simulationof complete power plants. A novel numerical approach presentedin our previous work uses the method of characteristics in anattempt to mitigate some numerical difficulties while maintaininghigh efficiency and accuracy [28]. This numerical scheme is theone used here and can accommodate arbitrary initial and boundaryconditions. Since the scheme is both accurate and efficient, a largeamount of results can be compiled with relative ease.

Packed bed thermal storage experiments of various scales havebeen carried out in order to gain operational experience and toprovide data for simulation validation. Most recently, an oil-pebble thermocline tank was used to model a parabolic dish cook-ing system [22]. A flow rate control algorithm maintained a con-stant temperature output from a variable power source meant tosimulate daily variation in solar irradiation. The experimentalresults were used to validate a Schumann model simulationmethod. However, the simulation used only five differential ele-ments in order to have a reasonable computational timeframe.Another setup used for validation was a packed pebble bed heatedvia a hot air flow [29,30]. Only several temperature readings alongthe axis were recorded and the dimensions demand that the exper-imental mass flow rates be adjusted for simulation. These datawere used to validate a finite difference solution method for theSchumann model [24].

A molten-salt thermocline column with quartzite and silicasand filler was built and studied under charge and discharge proc-esses [23]. This test has been commonly used for validation ofsimulations that do not directly accompany experimental worklargely because molten-salt is the most viable thermocline HTF.However, it is readily seen and acknowledged that the data exhibitconsiderable amounts of scatter in the temperature curves. Thescatter may be due to instrumentation deficiencies, yet the resultshave allowed for significant progress in the modeling of thermo-cline TES tanks.

In order to provide more data to facilitate comparison and vali-dation of mathematical modeling, this paper will focus on an ex-perimental study. The test uses a combination of materials andconditions that is unique in the literature. This experimental studywill be accompanied by a review of some basic analysis of thegoverning equations of the energy storage in a packed bed ther-mocline. The model will use dimensional analysis to definedimensionless parameters for similarity of scaled thermocline sys-tems as proposed by [28]. Results from a method of characteristicsnumerical scheme will be compared with the experimental resultsas means of validation of this novel solution.

2 Theoretical Analysis

Figure 1 shows a thermocline thermal storage tank in whichheat transfer fluid flows through a packed bed of solid filler mate-rial. During the heat charging process, hot HTF flows down thetank, transfers thermal energy to the solid material, and flows outat a low temperature. During the heat discharging process, cold

HTF flows up the tank, extracts thermal energy from the solid ma-terial, and flows out at a high temperature.

Clearly, the energy storage process of a thermocline tankdepends on many parameters, including: fluid and packed bed fil-ler material properties, tank dimensions, fluid velocities, and theenergy charge and discharge process times. A careful planning ofthe experimental test and data analysis is important to the presen-tation of the results of energy storage.

The following study will use dimensional analysis to convertthe governing equations into dimensionless form, consolidatingmany influential parameters into a few dimensionless parameters.

2.1 Energy Balance Equation for Fluid. As shown in Fig. 1,the fluid is assumed to be flowing into the tank at a uniform velocityand carries heat/enthalpy in and out of a typical control volume oflength dz. For convenience of analysis, the fluid inlet location isalways set to be z¼ 0. For the heat charging process the coordinateat the top of the tank is zero; for the heat discharging process thecoordinate at the bottom of the tank is zero.

An energy balance is presented for a volume of size dz; usingappropriate substitutions for enthalpy in the fluid energy balanceequation yields

@Tf

@tþ U

@Tf

@z¼ hSr

qf cf epR2ðTr � Tf Þ (1)

where h is the heat transfer coefficient between the solid filler ma-terial and HTF and U is the flow velocity. The parameter Sr is thetotal surface area of the solid, spherical particles per unit of length[28]. In order to make the equation dimensionless, variable trans-formations of temperature, time, and axial position are introduced

h ¼ T � TL

TH � TL; z� ¼ z

H; t� ¼ t

H=U(2)

where h can apply to either filler or fluid, TH and TL are high andlow reference temperatures and H is the tank height.

The final dimensionless equation for the energy conservation influid is

@hf

dt�þ @hf

@z�¼ 1

srðhr � hf Þ (3)

where the dimensionless parameter sr is defined by

sr ¼qf cf epR2

hSr H=Uð Þ (4)

Fig. 1 Schematic of a thermocline thermal storage tank with adischarging flow direction [28]

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2.2 Energy Balance Equation for Solid. For the same con-trol volume of size dz, an energy balance is applied to the fillermaterial. The internal energy change in the filler material is due tothe heat transfer from the filler material to the HTF. The govern-ing equation is then written as

@Tr

@t¼ � hSr

qrcrð1� eÞpR2ðTr � Tf Þ (5)

Using the dimensionless variables, the equation is converted to adimensionless form

@hr

@t�¼ � 1

srHCR hr � hf

� �(6)

where HCR is a dimensionless parameter indicating the ratio of theheat storage capacities of the fluid against the solid filler material.

HCR ¼qf cf e

qrcrð1� eÞ (7)

2.3 Heat Storage Effectiveness. During the heat charge pro-cess, hot HTF enters the top of the tank and the inlet boundarycondition is close to hf¼ 1.0; during the heat discharge process,cold HTF enters the bottom of the tank and the inlet boundarycondition is close to hf¼ 0.0.

The above analysis derived two dimensionless parameters, sr andHCR, consolidated parameters that determine the energy storageeffectiveness of a thermocline system. The required boundary con-dition for the solution of the governing Eqs. (3) and (6) is the inlettemperature of the fluid entering the tank while the initial conditionis the initial solid and fluid temperature distribution in the tank.

For an energy discharge process, the heat storage delivery effec-tiveness is the ratio of actual energy discharged at the outlet to thedischarged energy from an ideal thermocline. An ideal thermoclinewill have no temperature degradation at the outlet while an actualpacked bed thermocline will. This effectiveness is defined as

g ¼ 1

Pd

ðPd

0

hf z� ¼ 1; t�ð Þdt� (8)

where the dimensionless discharge time is

Pd ¼td

H=U(9)

Obviously the ideal value g in Eq. (8) should be 1.0, meaningthe discharged fluid should always have a temperature of Tf¼TH

for the entire discharging time. However, if the discharged fluidtemperature degrades, which is the typical case in reality, theenergy delivery effectiveness will be less than 1.0. Whether a the-mocline tank can deliver the maximum amount of thermal energyfor a designated discharge time will mostly depend on the amountof energy stored in the tank; therefore, the ratio of time length forenergy charge against that for energy discharge is an importantparameter that affects the energy delivery effectiveness of a ther-mocline tank.

In references [28], the method of solution to the governingequations was discussed. The energy delivery effectiveness hasbeen demonstrated to be a function of sr, HCR, and the ratio of thecharge and discharge time lengths [28,31].

The dimensionless governing equations and the dimensionlessparameters are of great significance to the experimental test. Thethermal storage performance of actual thermocline tanks can beexperimentally studied by using small scale thermocline tanks inthe laboratory, as long as the dimensionless parameters are keptthe same.

3 Experimental Study

3.1 Test System Design and Setup. The setup of the testsystem is shown in Fig. 2. The system consists of an aluminumthermocline tank with filler material connected to two thermal res-ervoirs, high temperature and low temperature. The HTF is a syn-thetic oil.

During a heat charge process, valves Vh3, Vc1, and Vc2 areclosed and hot HTF is pumped through the thermocline tank. Af-ter heat transfer to the packed bed, the oil goes to the cold reser-voir tank. During a heat discharge process, valves Vh1, Vc3, andVh2 are closed and cold oil is pumped back through the thermo-cline tank to extract heat from the packed bed. After obtainingheat from the filler, the oil returns to the hot reservoir.

The two reservoirs are 0.5 m in diameter and 1.0 m inheight. The thermocline tank is 0.241 m in diameter and 1.0 m inheight. The active thermal storage section in the thermocline tanksis 0.767 m with mesh filters and metal frames at the top and bot-tom to ensure the tight packing of the filler material. The entiresystem is insulated using multiple 6.35 mm thick fiberglass insula-tion layers and 31.75 mm thick fiberglass for pipe insulation. Thehot reservoir has an 11.0 kW heater to heat the oil to the temperatureTH, and a mixer ensures uniform temperature. Neglecting the tank

Fig. 2 Schematic of the experimental setup

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material, the energy required to heat or cool the reservoir oil vol-ume is predictable using

E ¼ Vresqf cf TH � TCð Þ (10)

The temperatures in the hot and cold oil reservoirs are moni-tored and controlled, according to the requirement of the test. Thehot reservoir is also connected to an expansion tank to accommo-date the increase in the volume of the oil as it heats.

The cold oil reservoir is connected to a copper brazed plate heatexchanger with a 1.04 m2 surface area to bring down the oil tem-perature to TL. A second mixer is used to ensure proper tempera-ture uniformity. The tanks and reservoirs are connected via 6.35mm pipes and stainless steel ball valves. Filtered fluid is drivenwith a 367.75 W pump. The pump section contains a feedbackloop and a control valve that allows control of the pressure andflow rate of the oil. An inline analog flow meter is used to monitorand measure the flow rate.

The working HTF used is Xceltherm 600VR

synthetic oil byRadco Industries. The filler materials chosen for this experimentare two types of rocks chosen for their low cost and high energydensity. River pebbles (RP) are on average around 2.0 cm in di-ameter and pea pebbles (PP) have an average diameter of around0.5 cm. The average density of each type of rocks was calculatedby weighing random samples and measuring their volumes. Thesample volumes were measured by displacing water volume in abeaker. This allows calculation of the volume and density of therocks as well as the void fraction of the packed bed. Table 1 liststhe density and individual porosity for the two types of rocksalong with the mass of each filled in the tank.

It is obvious in Table 1 that the porosity due to the packing of asingle type of rock is high. It is advantageous to reduce the poros-ity in order to minimize the amount of oil needed. Therefore,small and large rocks are packed in a mixed manner to reduce theoverall porosity of the packed bed. The void fraction is deter-mined by the equation

e ¼Vtan k �

Pmr=qr

Vtan k(11)

The packed masses of each rock type were weighed and arelisted in Table 1. The volume of rocks was then calculated.Finally, the porosity of the packed bed in the thermocline tankwas found to be 0.326 (in an active volume of 0.0350 m3 atH¼ 0.767 m and D¼ 0.241 m). The relevant tank parameters arelisted in Table 2.

3.2 Instrumentation. The instrumentation required for thisexperimental setup is for measuring temperatures and the oil flow

rate. Two grounded K-type OMEGACLADVR

XL thermocoupleprobes are used to measure the temperatures of oil in the reser-voirs. The thermocouple probes are 0.46 m long, immersed fromthe top of the oil reservoirs.

The temperatures in the center of thermocline tank along theaxial direction are measured using 14 thermocouples placed 5.0cm apart, vertically. For convention, the thermocouples are num-bered 1 to 14, from the top, down. This holds for both charge anddischarge. The thermocouples are K-type, ungrounded SuperOMEGACLAD

VR

with length of 0.41 m. The thermocouples areconnected through a DAQ to a computer station and real timemeasurements are monitored and stored via a LABVIEW

VR

program.

3.3 Procedures of Tests. Before any charging process, thethermocline tank and hot oil reservoir are checked to ensure theyare completely filled with oil. Then, both the heater and mixer inthe hot reservoir are activated. Once the desired temperature isreached, the heater is shut off and valves for test loop are man-ually turned to the position needed for the test. The pump is acti-vated, pumping the oil through the thermocline tanks andeventually dumping it in the cold reservoir. A LABVIEW

VR

programmonitors the thermocline axial temperatures and records the datato a spreadsheet file. The test continues for the necessary timebefore the pump is deactivated, concluding the charging process.

A discharge process must follow the charging. Due to thecharging process, the oil in the cold reservoir may have a tempera-ture which needs cooling to the desired cold temperature. This isdone through the oil-water heat exchanger shown in Fig. 2. Theoil from the cold reservoir is pumped through a heat exchangerand back to the reservoir. The heat exchanger extracts heat fromthe oil with running water slightly lower than room temperature.Once the oil in the cold reservoir is cool, the heat exchanger pumpsystem is turned off and a thermal discharge test may start. Theoil in the cold reservoir is pumped back through the thermoclinetank in the opposite direction, extracts heat, and returns to the hotreservoir.

Tests were conducted for a range of constant flow rates, chosenby the scaled parameters from a model parabolic CSP plant needs.The single cycle, single tank test list is compiled in Table 3.

4 Validation Method

The experimental data provide an opportunity for validation ofthermocline models. The governing equations were solved using anumerical method of characteristics [28] and compared to experi-mental data.

The simulation modeling is based on the conditions of theexperiment. The static conditions listed in Table 2 include theinner diameter of the tank, actual length of the measured packedbed (where temperatures were measured), void fraction of thepacked bed, and the nominal rock size. The test specific condi-tions include the high and low temperatures of heat transfer fluid,initial temperature distribution in the storage tank, and the temper-ature variation of the HTF at inlet. For comparison with the

Table 1 River and pea pebble properties and tank fill

Filler type Density (kg/m3) Porosity, e Filled mass (kg)

RP 2713.6 0.38 37.2PP 2506.3 0.34 25.0

Table 2 Static tank parameters

Packed bed length (m) 0.767Measured tank length (m) 0.650Tank inner diameter (m) 0.241Packed beck porosity, e 0.326Total tank length (m) 1.0Rock nominal diameter (m) 2632Rock specific heat (J/(kg K)) 790

Table 3 Single cycle test list

Charge Discharge

Flowrate (LPM) TL (�C) TH (�C) TH (�C) TL (�C)

0.75 26.1 120.6 117.9 41.41.00 38.9 124.9 124.6 44.41.00 22.9 125.0 124.8 38.31.25 32.1 126.8 126.5 40.41.50 26.5 133.4 133.1 44.41.75 23.5 131.6 131.5 41.72.00 32.1 133.9 133.3 44.12.00 30.6 136.1 135.6 45.8

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experimental data, the simulated local temperatures of rocks andoil are averaged based on Eq. (12).

Prior to comparison two differences between the experimentalsystem and the model must be considered: temperature measure-ment and the tank wall thermal mass.

The thermocouples are buried in thermocline rock bed. Theyactually measure local average temperatures of rocks and fluidbecause all thermocouples are certainly in simultaneous contactwith rocks and oil. Therefore, the thermocouple readings are con-sidered as a weighted average of the following form

havg ¼ ehf þ ð1� eÞhr (12)

The above model does include consideration of the thermalmass of the tank walls. This is an acceptable assumption for alarge thermocline tank, such as in a power plant, where the wallheat capacity is small relative to the filler material. However, theexperimental setup demands inclusion of the walls in the modelsince the wall’s thermal mass is significant. This considerationwill alter the dimensionless parameters used for simulation-experiment comparison.

Including the heat transfer to the tank walls to Eqs. (1) and (5)gives the governing system

@Tf

@tþ U

@Tf

@z¼

hSr Tr � Tf

� �þ hwSw Tw � Tf

� �qf cf epR2

(13a)

@Tr

@t¼ � hSr

qrcr 1� eð ÞpR2Tr � Tf

� �(13b)

@Tw

@t¼ � hwSw

qwcwp R2o � R2

� � Tw � Tf

� �(13c)

where Tw, qw, and cw are properties of the tank wall material, hw isthe wall heat transfer coefficient, Sw is the wall surface area perunit length, and Ro is the outer wall radius.

Assuming Tw� Tr, hw� h, and negligible Sw (since Sw� Sr)allows reduction of the governing system to a simpler form remi-niscent of the original model.

@Tf

@tþ U

@Tf

@z¼ hSr

pR2qf cf eTr � Tf

� �(14a)

@Tr

@t¼ � hSr

pR2qrcr 1� eð Þ þ p R2o � R2

� �qwcw

Tr � Tf

� �(14b)

Using the same dimensionless variables (Eq. (2)) as the previ-ous analysis, the governing equations are converted to the samedimensionless form (Eqs. (3) and (6)) with the same sr but modi-fied HCR.

HCRW ¼qf cf epR2

qrcr 1� eð ÞpR2 þ qwcwp R2o � R2

� � (15)

This definition modifies HCR by the addition of the tank wallheat capacity per unit length in the denominator. As the ratio ofpacked bed thermal mass to tank wall thermal mass increases, thecontribution from the walls becomes negligible and the originalHCR can be used. It can be seen in Fig. 3 that there is significantdifference between HCR and HCRW at the experimental diameterbut very little as the diameter increases. The equations for thecurves in Fig. 3 use the properties of the test setup. Figure 3 showsthat for validation purposes in using the lab scale data, it is impor-tant to use the modified equations but for large-scale thermoclinesthe original model is sufficient.

In models which do not use the dimensionless parameters pro-posed in this study, validation is still possible. It has been shownthat simply increasing the specific heat of the filler material to

account for the energy change in the tank is acceptable. In otherwords, cr is replaced with

crw ¼ cr þmw

mrcw (16)

5 Results and Discussion

The theoretical analysis has demonstrated that the dimension-less temperatures of the fluid and packed bed filler material can beexpressed in terms of dimensionless parameters sr and HCR. Forthe sake of completeness, the experimental data will be presentedin terms of actual temperatures as well as the dimensionless tem-peratures at conditions represented by dimensionless parameters.

5.1 Temperature Variations in a Typical Cycle. Manycharge/discharge cycles of varying testing conditions were per-formed to gather a full understanding of the testing proceduresand heat transfer. A representative cycle is presented, typical ofthe recorded testing results. The temperature curves for all 14thermocouples are shown in Fig. 4. The top curve is the reading atthe top of the thermocline; the bottom curve is the for bottomthermocouple.

For experimental purposes, charging or discharging is consid-ered complete when the temperatures are all within 5 �C of each

Fig. 3 Comparison of HCR and HCRW for varying thermoclinediameter with a wall thickness of 6.5 mm

Fig. 4 Temperatures of the tank along the length of 65 cm for asingle cycle (thermocouples were set every 5 cm)

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other. This, of course, would not necessarily hold true in a powerplant operation.

The comparison uses the measured length of 0.65 m betweenthe first and last thermocouples. The experimental and dimension-less conditions for the heat charge process are listed in Table 4.Initially, the thermocline tank has a uniform temperature of32.1 �C. The time-dependant temperature reading from the firstthermocouple on top of the measured 0.65 m length is consideredas the inlet fluid temperature in a charge process.Initially, the tem-perature in the tank increases rapidly when the driving tempera-ture difference between the inlet oil and thermocline is high. Thishigh heat transfer rate is reduced as the system moves towardequilibrium with the inlet oil.

Using the initial temperature distribution, inlet fluid tempera-ture, and the properties listed in Tables 2 and 4, numerical simula-tion results for the average temperatures given in Eq. (12) wereobtained. Figure 5 compares the temperatures at four locationsalong the tank axis as a function of time. The first curve is the firstreading after the inlet while the last curve is the outlet. Figure 6shows temperature distributions in the tank at various times. Thereal and dimensionless time points at intervals of Pc/5 are listedin Table 5. Obviously, the temperature on top of the tank (atz*¼ 0) rises fastest as it sees the hot fluid first. As expected, theremaining locations follow in time toward TH. It is reasonable forthe experimental curve to be below the simulated curve due to theassumptions of the model, including perfectly insulated bounda-ries. The agreement between experimental data and the modelingsimulation is very satisfactory, with an average percent error rela-tive to maximum temperature of 4.36%. The percent error is aver-aged for all thermocouples.

The experimental and dimensionless conditions for the dis-charging process are listed in Table 6. At initial time the thermo-cline tank had a nonuniform temperature distribution defined bythe end state of the charge. The time dependent temperature read-ing from the bottom thermocouple is considered the inlet fluidtemperature for discharging. The thermocouple at the top of thetank measures the temperature of the discharged fluid. The degra-dation of discharged fluid is clearly shown in Figs. 4 and 7.

Again, numerical and experimental results are compared withthe same method described for the charging results. The compari-

son is shown in Figs. 7 and 8. The real dimensionless time pointsfor Fig. 8 are listed in Table 5. Again, the agreement between ex-perimental data and the modeling simulation is good, with a per-cent error relative to the maximum temperature of 3.28%.

5.2 Energy Stored During a Cycle. When designing ther-mocline sizing for application, it is important to consider totalheat capacity of the tank. Therefore, one relevant way to validateexperimental and numerical results is to compare total energydelivered or extracted over time. In dimensionless terms, this totalenergy change at a time t from the initial state can be expressed as

DE�ðtÞ ¼ 1

TH � TL

XN

0

TiðtÞ � Ti;initial

� �(17)

where TH is the charged temperature, TL is the discharged temper-ature, Tt is the instantaneous temperature, and Tinitial is the initialtemperature. The index i represents the number of differential vol-umes represented by each thermocouple. Equation (17) is the nu-merical, axial integration of the dimensionless internal energy ofthe tank at any time, t. Figures 9 and 10 compares simulated andexperimental E* for a charging and discharging process, respec-tively. Again, the agreement is quite good in both cases. The

Table 4 Conditions of a charging test

Oil flow rate (LPM) 1.25 TH (�C) 126.8Charging time, tc (min) 80.42 TL (�C) 32.1sr 0.106 Pc¼ tc/(H/U) 10.04HCR 0.417 HCRW 0.347

Fig. 5 Charging temperatures for TC 2, 6, 10, and 14 (left toright). TC 1 is the inlet and 14 is the outlet. Solid lines are simu-lated and dashed lines are experimental.

Fig. 6 The charging temperature distribution along the heightin the tank at time intervals of Pc/5. Solid lines are simulatedand dashed lines are experimental.

Table 5 Real time and dimensionless time for both chargingand discharging, Dt 5 P/5

Charging Discharging

Time(min)

Dimensionlesstime t*

Time(min)

Dimensionlesstime t*

0 0 0 016.08 2.01 12.98 1.7332.17 4.02 25.95 3.4648.25 6.02 38.93 5.2064.34 8.03 51.90 6.9380.42 10.04 64.88 8.66

Table 6 Conditions of a discharge test

Oil flow rate (LPM) 1.25 TH (�C) 126.5Discharging period,td (min)

64.88 TL (�C) 40.4

sr 0.101 Pd¼ td/(H/U) 8.66HCR 0.418 HCRW 0.348

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percent error relative to the maximum stored energy is 3.28% forcharging and 2.56% for discharging.Finally, perhaps the most im-portant metric for validation is the measure of effectiveness givenby Eq. (8). The effectiveness describes the quality of energy comingout of the tank for a period of time. This quality must be sufficientlyhigh during discharge to suit application needs. A comparison of the

effectiveness for all tested flow rates is shown in Fig. 11. The sys-tem does not have high effectiveness because it is not optimized forany particular application. This is relatively unimportant becausethe objective of this study is to provide test data for validation ofmodels. The agreement of simulation and experiment is again quitegood. The average percent error relative to the experimental valuesis 5.63%. Optimization studies using the model will be presented inthe future.

6 Concluding Remarks

Sensible heat thermoclines are a simple, yet elegant and effec-tive solution for solar thermal plant energy storage, a necessarybridge to economic viability. In order to understand the physics ofthermal charge and discharge processes, the governing equationsfor the physical phenomenon were discussed. As the transienttemperatures and thermal storage effectiveness are functions ofmany parameters including fluid and solid properties, tank dimen-sions, fluid velocities, and charge and discharge time lengths,dimensionless governing equations were derived.

A packed bed thermocline thermal storage test system wasdeveloped in this work. The process provided valuable experiencein the design, assembly, and maintenance of a thermocline system.This knowledge could prove helpful for application in industry.Tests were run for a novel set of conditions including rock fillerwith oil HTF, constant inlet flow rates, inlet and outlet flow dis-tributors, and slightly degrading inlet temperature profiles overtime. Both single and multiple cycle tests were run. There were

Fig. 7 Discharging temperatures for TC 2, 6, 10, and 14 (left toright). TC 1 is the inlet and 14 is the outlet. Solid lines are simu-lated and dashed lines are experimental.

Fig. 8 The discharging temperature distribution along theheight in the tank at different times. Solid lines are simulatedand dashed lines are from experimental.

Fig. 9 Experimentally and simulated dimensionless storedenergy over a charging process

Fig. 10 Experimentally and simulated dimensionless storedenergy over a discharging process

Fig. 11 Experimentally and simulated effectiveness for dis-charging over a range of flowrates

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visible influences due to tank thermal mass, but these were consid-ered by modifying a term in the model and thus showed a good val-idation. A high resolution of temperature readings was taken; thetank length was divided into fourteen instrumented regions betweenthe flow ports. This provided smooth experimental curves.

The experimental data was presented in both dimensional anddimensionless forms. These experimental data provide a signifi-cant basis for the validation of mathematical models of thermo-cline thermal storage systems. A validation of a model andnumerical scheme based on the method of characteristics was per-formed. Over all the tests, the average percent error for tempera-ture readings was 3.49% and 5.63% for the effectiveness. Ingeneral, the simulation gives values slightly larger than the experi-ment due to the assumed ideal conditions of the model. Theseassumptions would likely be less influential in larger thermoclinetanks. The method of characteristics does not capture two-dimensional behavior in regions near the wall and near the inlet asmore comprehensive models have. Still, it has the obvious benefitof accurate, numerical stability, and efficient solutions.

This validation can help produce useful computational tools forthe design and understanding of thermoclines. Such tools canexpedite thermocline design and aid the optimization of thermalstorage systems on cost and storage effectiveness bases.

Acknowledgment

The authors are grateful to the supported by the US Departmentof Energy, National Renewable Energy Laboratory, under DOEAward No. DE-FC36-08GO18155, and US Solar Thermal StorageLLC. Thanks are also given to Mr. Lee Wilson and Eric Chang inDepartment of Aerospace and Mechanical Engineering at the Uni-versity of Arizona for their help on the experimental testing.

Nomenclaturec ¼ specific heat (J/kg�C)

CFD ¼ computational fluid dynamicsDAQ ¼ data acquisition system

E ¼ stored energy (J)h ¼ heat transfer coefficient between rocks and fluid

(W/m2�C)H ¼ thermocline tank height (m)

HCR ¼ dimensionless parameter, ratio heat capacity of fluid toheat capacity of rocks per unit length

HCRW ¼ modified dimensionless parameter to include tank wallheat capacity

LPM ¼ liters per minutem ¼ mass (kg)r ¼ average radius of filler material (m)R ¼ tank radius (m)S ¼ surface area per unit length along tank (m)T ¼ temperature (�C)

TC ¼ thermocouplest ¼ time (s)

U ¼ fluid velocity in the axial direction (m/s)Vtank ¼ reservoir volume (m3)

z ¼ location along axis of the tank (m)

Greek Symbols

e ¼ porosity of the packed bedg ¼ energy delivery effectivenessP ¼ dimensionless time period for charge or discharge processq ¼ density (kg/m3)sr ¼ dimensionless parameter in governing equationsh ¼ dimensionless temperature

Subscripts

avg ¼ weighted average, defined by Eq. (12)c ¼ energy charge process

d ¼ energy discharge processf ¼ transfer fluid

H ¼ high reservoirL ¼ low reservoiro ¼ outer radius of storage tankr ¼ filler material (rocks)

w ¼ thermocline tank wall

Superscript

* ¼ dimensionless variable

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