thermal analytical model of latent thermal storage with heat pipe heat exchanger for concentrated...

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Solar Energy xxx (2013) xxx–xxx

Thermal analytical mode of latent thermal storage with heat pipeheat exchanger for concentrated solar power

Eui Guk Jung a,⇑, Joon Hong Boo b

a SAC Laboratory, SAC Business Unit, AE Division, LG Electronics Inc., 76, Seongsan-dong, Changwon, Gyeongnam 641-713, Republic of Koreab School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang, Gyeonggi-do 412-791, Republic of Korea

Received 19 May 2013; received in revised form 3 November 2013; accepted 11 November 2013

Communicated by: Associate Editor Doerte Laing

Abstract

An analytical model is developed for predicting the transient thermal behavior of a latent thermal energy storage (LTES) system inwhich circular fins are attached to the heat pipes. Thermal energy is stored or released by the heat pipe heat exchanger, and pure con-duction is assumed for the charging and discharging modes. Considering the thermal environment required to concentrated solar power(CSP), potassium nitrate (KNO3), which has a phase-change temperature of 335 �C, is used as the phase-change material (PCM). Themalmodel used to estimate the heat transfer rate and the transient temperature variation in the PCM contained in each row of the heat pipeheat exchanger. Both melting and solidification are simulated under pure conduction. Row-by-row heat transfer is considered to assistestimation of row number of the entire LTES system. The developed model is also evaluated by comparing its predictions with the exper-imental results of a valid previous study. The discrepancies were observed to be less than 8%.� 2013 Elsevier Ltd. All rights reserved.

Keywords: Latent thermal storage; Phase-change material; Solar power plant; Heat pipe; Thermal modeling; Thermal resistance

1. Introduction

To improve the management and supply of solar power,many studies have been conducted on the design and fab-rication of systems used for collecting, transporting, andstoring solar energy (Michels and Pitz-Paal, 2007;Kamimoto et al., 1980; Vaivudh et al., 2008; Monteset al., 2009; Duffie and Beckman, 1980). Among the studiedsystems is the latent thermal energy storage (LTES) system,which is used to store thermal energy during the day andrelease it at night, thereby enabling the continuous utiliza-tion of solar power. LTES technology is used to store andrelease the latent heat generated during the melting andsolidification of a phase-change material (PCM). A

0038-092X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2013.11.008

⇑ Corresponding author. Tel.: +82 55 269 3630; fax: +82 55 269 3739.E-mail addresses: [email protected] (E.G. Jung), [email protected]

(J.H. Boo).

Please cite this article in press as: Jung, E.G.,, Boo, J.H. Thermal analyticalcentrated solar power. Sol. Energy (2013), http://dx.doi.org/10.1016/j.solen

material that undergoes phase change within a specific tem-perature range can be used for LTES if it satisfies a numberof criteria regarding, for example, its procurement andhandling costs and the operation temperature of the sys-tem. It has particularly been established that, in theabsence of quality degradation such as decompositionwithin the temperature range of the phase change, anLTES system has a higher heat storage capacity than sin-gle-phase and pack-bed energy storage systems (Duffieand Beckman, 1980).

The temperature of the heat transfer fluid (HTF; gener-ally vapor or air) used for LTES in a concentrated solarpower (CSP) system should be maintained between250 �C and 500 �C (Michels and Pitz-Paal, 2007). Tradi-tionally, alkali nitrate salts or chloride eutectic composi-tions, which have phase-change temperatures above250 �C, have been used as thermal storage materials(Kenisarin, 2010; Ferri et al., 2008). Although there are

mode of latent thermal storage with heat pipe heat exchanger for con-er.2013.11.008


mailto:[email protected]

mailto:[email protected]



Nomenclature

A area (m2)c specific heat (kJ/kg C)D fin density (fins/m)d diameter (m)f friction factorG mass velocity (kg/s m2), G ¼ _m=rAfr

h heat transfer coefficient (W/m2 �C) or enthalpy(kJ/kg)

H height (m)HP heat pipeHPHEX heat pipe heat exchangerHTF heat transfer fluidj index of number of row or Colburn factork thermal conductivity (W/m �C)L length (m)_m mass flow rate (kg/s)N heat pipe number per rowp pipe or fin pitchP pressure (Pa)pr Prandtl numberQ heat transfer rate (W)R thermal resistance (�C/W)Re Reynolds numberr radial position (m) or radius (m)s fin space (m)St Stanton numbert time (s)T temperature (�C)u velocity (m/s)V volume (m3)v specific volume (m3/kg)X tube bank pitch (m)XD tube bank diagonal pitch (m),

½ðX T=2Þ2 þ X 2L�

1=2

Greek symbols

d fin thickness (m)g fin efficiencyl fluid dynamic viscosity (m2/s)

/ porosity of capillary screen wick structurej local volume fraction of fins at the LTESq density (kg/m3)t specific volume (m3/kg)

Subscripts

a ambientc chargingd dischargingcap capillary structurecap-HPHEX capillary structure in the HPHEXcap-LTES capillary structure in the LTEScap-o capillary structure outer diametercap-i capillary structure inner diametereff effectiveeq equivalentevap evaporatorf fluid or finf-fin between HTF and finsfin-pcm between fin and pcmfr frontalh hydraulici innerj HP row inexL lengthW widthl liquidsl solid–liquid phase changem mean valuemax maximum valuemin minimum valueo outer or overallp pipe or pressurepcm phase change materialT totalwf working fluid within HPw-HPHEX HP wall in the HPHEXw-LTES HP wall in the LTES

2 E.G. Jung, J.H. Boo / Solar Energy xxx (2013) xxx–xxx

PCMs that can be used at various operation temperatures,their detailed thermophysical properties are not fullyunderstood (Kenisarin, 2010; Shabgard et al., 2010).

To control the time of the temperature rise of a PCMand enhance its thermal performance, an extended surfaceis used in many applications (Bergantz, 1992; Lacroix,1993; Hamada et al., 2003; Agyenim et al., 2010; Liuet al., 2006). PCMs with better thermophysical propertieshave also been developed by mixing different PCMs in spe-cific proportions (Kenisarin, 2010).

Shell-and-tube heat exchangers are commonly used inLTES systems (Bergantz, 1992; Lacroix, 1993; Hamada


et al., 2003; Agyenim et al., 2010). Additionally, an LTESsystem with a heat pipe heat exchanger (HPHEX) that pos-sess an excellent heat transfer efficiency has also been suc-cessfully developed (Liu et al., 2006; Shabgard et al., 2012;Robak et al., 2011).

Theoretical studies were conducted on a heat pipe (HP)-based LTES system. Sharifi et al. (2012) conducted a studyon the heat transfer numerical model of an LTES systemusing a single HP and using sodium nitrate as the PCM.The numerical model was used to derive detailed governingequations for continuity, momentum, and energy of theHP, HTF, and PCM.



E.G. Jung, J.H. Boo / Solar Energy xxx (2013) xxx–xxx 3

Another heat transfer model of an HP system that actsas an extended surface in an HTF pipe was proposed(Shabgard et al., 2010; Nithyanandam and Pitchumani,2011, 2013; Nithyanandam, 2013). Shabgard et al. (2012)developed a heat transfer and exergy analysis model foran LTES system with an HPHEX. This analytical modeldid not take the extended surface in the HP into consider-ation and conducted energy analysis of the system primar-ily based on the HTF temperature at the inlet and exitpoints. Liu et al. (2006) conducted an experimental studyon an LTES system in which 5 HPs were mounted in acylindrical container and thermal storage performancewas investigated. Additionally, the study introduced corre-lation relations between the effectiveness of the system andthe Stefan number.

By expanding the underlying concept of an LTES modelwith the HPHEX with a staggered tube bank configura-tion, an analytical model of the entire system that enabledCSP application was proposed (Jung et al., 2010; Shabgardet al., 2012). Although the heat transfer model enabled theprediction of the transient temperature variation of eachrow, a systemized design method was not developed andthe effects of changing the geometric shape were notinvestigated.

Although the basic concept of LTES using the HPHEXwas introduced by Liu et al. (2006) and Shabgard et al.(2012), a theoretical analysis model of the heat transferfrom a system design viewpoint is yet to be developed.

In this paper, by expanding the works of Liu et al.(2006), Jung et al. (2010) and Shabgard et al. (2012), wepropose an analytical model that can be used to design areal CSP application. We use the model to predict the tran-sient temperature variation and heat transfer rate in eachrow of an LTES system with the purpose of integratingthe system with an HPHEX. Furthermore, the applicationin the solar power tower with 200 kW is currently underprogress in Korea and thermal analytical model of thisstudy is used as the design and analysis tool of the latentthermal storage on the project.

Fig. 1 illustrates the HP operation principle. As shownin the figure, the working fluid within the evaporator isvaporized by thermal energy absorption, and the vapor istransported to the condenser by the vapor pressure. Thevapor is condensed by the cooling medium in the condenserand the condensed liquid is then returned to the evaporatorby the capillary pressure generated in the screen capillary

Fig. 1. Schematic illustration of the heat pipe operation.


structure. This HP operation involving repeated evapora-tion and condensation in the evaporator and condenser isdescribed in detail by Peterson (1994).

To estimate the size of an LTES system required for thedesired charging and discharging performance of a CSPsystem, the transient variation in the PCM temperatureand the heat transfer rate in each HPHEX row should beobtained by a row-by-row heat transfer analysis. The anal-ysis model of heat transfer with respect to the LTES systemwith the HPHEX was derived on the basis of thermal resis-tance and temperature under pure conduction.

The thermal expansion coefficient of potassium nitrate(KNO3) could not be found but recent studies (Nithyanan-dam and Pitchumani, 2013; Shabgard et al., 2010) tooknatural convection into consideration using the thermalexpansion coefficient of sodium chloride (NaCl). In thepresent study, the applications of the physical properties(thermal expansion coefficient of potassium nitrate(KNO3)) are still limited and hence, the heat transfer isextended under the pure conduction approach (Zhangand Faghri, 1996; Horbaniuc et al., 1999; Hamada et al.,2003; Jian-you, 2008; Long and Zhu, 2008; Nakaso et al.,2008; Tardy and Sami, 2009; Nithyanandam and Pitchu-mani, 2011).

The heat transfer rate, HTF temperature, and transientvariation in the PCM temperatures were determined byrow-by-row analysis for specific temperature and pressureconditions at the HPHEX inlet and outlet, and specific geo-metric dimensions. The pitch of the circular fins attached tothe HP of the LTES was adopted as the main variable, andthe corresponding temperature characteristics and heattransfer performance were evaluated.

2. Heat transfer analysis model of LTES for CSP that has

HPHEX

Fig. 2 illustrates the operation principle of the LTESsystem of this study. The system consists of an HPHEXfor thermal charging (lower part of Fig. 2), an LTES (mid-dle part of Fig. 2), and an HPHEX for thermal discharging(upper part of Fig. 2). An HP with attached circular finswas employed. In the charging mode, thermal energy isstored in the PCM while a high-temperature HTF is passedthrough the HPHEX. In the discharging mode, the thermalenergy stored in the PCM is transferred to a low-tempera-ture HTF through the HPHEX.

The following basic assumptions were made regardingthe heat transfer model:

(1) The PCM is an isotropic material and its thermo-physical properties are the same in the liquid andsolid phases, and are independent of temperature.

(2) The thermal energy interaction between the rows hasno effect.

(3) The outer wall of the LTES system is adiabatic;hence, there re is no heat exchange with theatmosphere.



Fig. 2. Schematic representation of the latent thermal storage system for CSP with the HP arrangement: (a) side view and (b) frontal view.


(4) The mass flow rate into the HPHPX is uniform withrespect to the frontal area.

(5) The HP has zero internal thermal resistance consider-ing its high isothermal performance (Peterson, 1994).

(6) Contact thermal resistances between PCM andtube-fin assembly and thermal radiation of the LTESand HPHEX are ignored.

Eqs. (1)–(4) are the geometric relationships regardingthe arrangement of the HP with attached fins. As indicatedin Eq. (1), the primary area of each row is the sum of theareas of the HP and the common walls.

Ap;j ¼pdoH HPHEX NHP ;jð1�dDf ÞþðX LLW �pd2oNHP ;j=4Þ ð1Þ

where HHPHEX is the height of the HPHEX.The area of the fins in each row is given by

Af ;j ¼ pDf HHPHPX N HP ;j½ðd2f � d2

oÞ=2þ df d� ð2Þ

The total heat transfer area of each row is given by

AT ;j ¼ Ap;j þ Af ;j ð3Þ

Fig. 3. Thermal circuit o


The volume of the PCM filled into each row can bedetermined by subtracting the volume of the heat pipesand the fins from the total volume of each row as follow:

V pcm;j ¼H LTESX LLw�p4

NHP ;jHLTESd2o½1þDf dðd2

f =d2o�1Þ�

n oð4Þ

Fig. 3 shows the thermal flow circuit of the LTES andHPHEX. The directions of the heat transfer in the chargingand discharging modes are opposite. Eqs. (5)–(12) give thethermal resistance of the HTF, HP and PCM with respectto each low of the LTES.

The thermal resistance between fins and the HTF is asfollows:

RðtÞf -fin;j ¼1

go;jho;jAT ;jð5Þ

where go,j is the overall efficiency (including the finefficiency) of the extended surface, and ho,j is the convec-tive heat transfer coefficient between the HP and HTF ofthe LTES. The geometric shape of the HP arrangement isshown in Fig. 4a and b and the HP with circular fins is

f the LTES system.



XT

Lw

LL

(a)

XL

di dodf

XL

2aXT

dodi

bB

Bdf

(b) pf

Hf

Lp

s

di do

rx

(c)

df

δ

Fig. 4. LTES system with the HPHEX: (a) top view showing geometry of the HP arrangement, (b) unit of the HP arrangement with circular fins, and (c)HP with circular fins.


shown in Fig. 4c. Whereas the geometric shape of thearrangement is always the same in the HEX and LTES,the thermal performance of the LTES system can beflexibly controlled by the adoption of different typesand sizes of fins. The equations of the overall efficiencyand convective heat transfer coefficient are available inthe commonly referenced work of Shah and Sekulic(2003).

The thermal resistance of the HP wall is as follows:

RðtÞw-HPHEX ;j ¼lnðdo=diÞ

2pkHP H HPHEX N HP ;jð6Þ

The thermal resistance of the screen capillary structuresaturated with the working fluid in the HP container isgiven by

RðtÞcap-HPHEX ;j ¼lnðdi=dwiÞ

2pkeff ;jH HPHEX NHP ;jð7Þ

where keff ;j ¼ kwf ½ðkwfþkcapÞ�ð1�/Þðkwf�kcapÞ�ðkwfþkcapÞð1�/Þðkwf�kcapÞ

h iis the effective

thermal conductivity of the working fluid and the screencapillary structure with the porosity, /[=1 � pSNdw/4.The crimping factor, S is 1.05 (Peterson, 1994), and Nand dw are the mesh number and wire diameter,respectively.


Eqs. (8)–(12) give the thermal resistance between the HParrangement and the PCM in the LTES. The thermalresistance of the screen capillary structure inserted intothe HP in each row is as follows:

RðtÞcap-LTES;j ¼lnðdcap-o=dcap-iÞ

2pkeff ;jH LTESN HP ;jð8Þ

The thermal resistance of the HP wall is as follows:

RðtÞw-LTES;j ¼lnðdo=diÞ

2pkp;jH LTESNHP ;jð9Þ

If Tw-LTES,j is small than Tsl, the thermal resistance in theregion of the PCM and the fins and the thermal resistancein the region of the PCM alone can be represented by Eqs.(10) and (12), respectively.

RðtÞfin-pcm;j ¼lnðdf=doÞ

2pkfin-pcm;jH LTESNHP ;jð10Þ

where kfin-pcm,j[=kfin,jjj + (1 � jj)kpcm,j] is the effective ther-mal conductivity of the PCM and jj is the local volume ra-tio of the fins.

The Schmidt method (Schmidt, 1949; Perrotin andClodic, 2003) of determining the circular radius (Eq. (11))




equivalent to the hexagonal configuration in Fig. 3a wasemployed in this study.

rpcm;eq ¼ 0:635X T

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX D

X T� 0:3

rð11Þ

Using the equivalent radius in Eq. (11), the thermalresistance in the region of the pure PCM can be expressedas follows:

RðtÞpcm;j ¼lnðrpcm;eq=rf Þ

2pkpcm;jHLTESNHP ;jð12Þ

Eq. (13) gives the total thermal resistance of each row.

RðtÞT ;j¼RðtÞf -fin;jþRðtÞw-HPHEX ;jþRðtÞcap-HPHEX ;j

þRðtÞcap-LTES;jþRðtÞw-LTES;jþRðtÞfin-pcm;jþRðtÞpcm;j ð13Þ

The temperatures of the HP wall in the regions of theHPHEX and the LTES can be obtained by energy conser-vation at the corresponding nodes, and are respectivelygiven by

T w-HPHEX ;j ¼T pcm;jðRðtÞf -fin;j þ RðtÞw-HPHEX ;jÞ þ T f ;jðRðtÞcap-HPHEX ;j þ RðtÞcap LTES;j þ RðtÞw-LTES;j þ Rfin-pcm;j þ Rpcm;jÞh i

RðtÞT ;jð14Þ

T w-LTES;j ¼T pcm;jðRðtÞf -fin;j þ RðtÞw-HPHEX ;j þ RðtÞcap-HPHEX ;j þ RðtÞcap LTES;j þ RðtÞw-LTES;jÞ þ T f ;jðRðtÞfin-pcm;j þ RðtÞpcm;jÞh i

RðtÞT ;jð15Þ

If Tw-LTES,j P Tsl, the PCM solid–liquid interface can beestimated using Eqs. (16) and (17) on the basis of energyconservation at the nodes during melting and solidification(Shabgard et al., 2010; Nithyanandam and Pitchumani,2011). To solve Eqs. (16) and (17), the initial values ofTfin-pcm,j and Tpcm,j are obtained to be those when Tw-LTES,j

is larger than or equal to Tsl, and the initial radius of themelting/solidification interface is assumed to be ro + 5 lm.The phase-change mass flow rate _msl;j can be expressed as2pqpcm,jHLTES(rsl,j � ro)drsl,j/dt.If rsl,j < rf,j,

qpcm;jðrsl;j � roÞ½hsl þ cp;pcm;jðT m;j � T slÞ�drsl;j

dt

¼ � kfin;pcm;jðT sl � T fin-pcm;jÞlnðrf=rsl;jÞ

ð16Þ

where Tm,j was obtained by iterative solution to adjustPCM temperature and position of the melting or solidifica-tion layer.

If rsl,j P rf,j,

qpcm;jðrsl;j � roÞ½hsl þ cp;pcm;jðT m;j � T slÞ�drsl;j

dt

¼ � kpcmðT sl � T pcm;jÞlnðrpcm;eq=rsl;jÞ

ð17Þ


where Tpcm,j represents the temperature at the center region(rpcm,j) between the rows.

If Tw-LTES,j P Tsl,j, the thermal resistance in the regionof the PCM and fins and the thermal resistance of the purePCM can be represented by Eqs. (18) and (19), respectively.The thermal resistance of the latent and sensible heat isassumed to be zero because the phase change occurs underisothermal conditions of the solid and liquid PCM.

RðtÞfin-pcm;j¼lnðrsl;j=roÞ

2pkfin-pcm;jH LTESN HP ;jþ lnðrf =rsl;jÞ

2pkfin-pcm;jH LTESN HP ;jð18Þ

RðtÞpcm;j ¼lnðrsl;j=rf Þ

2pkpcmH LTESNHP ;jþ lnðrpcm;eq;j=rsl;jÞ

2pkpcmHLTESNHP ;jð19Þ

The thermal energy charged (or discharged) by the solidPCM (or liquid PCM) at a particular temperature condi-tion is composed of sensible energy and latent energy isdetermined by summing the energies stored in all thePCM rows as follows (Tardy and Sami, 2009; Shabgardet al., 2010; Nithyanandam and Pitchumani, 2011):

QT ;j¼Xj

j¼1

T f ;j�T pcm;j

RT ;j¼�

Xj

j¼1

_msl;jhsl; T w-LTES;j < T sl ð20Þ

QT ;j ¼Xj

j¼1

T f ;j�T pcm;j

RT ;j¼�

Xj

j¼1

_msl;j½hslþcp;pcmðT m;j�T slÞ�; T w-LTES;j P T sl ð21Þ

Eqs. (20) and (21) indicate that the total thermal energyadded to a latent thermal storage system may be equal tothe sum of the latent heat and the sensible heat. Whereaslatent heat and sensible heat are stored in the LTES duringthe phase change of the PCM in the charging mode, onlysensible heat is stored after completion of the phasechange. Therefore, the latent heat is excluded from Eq.(21) after completion of melting and then Eq. (21) is simpli-fied to QT ;j½¼ �

Pjj¼1 _mslcp;pcmðT m;j � T slÞ�.

The transient total energy conservation in each row ofthe LTES is given by

½ðqcpV Þeff þðqcpV Þpcm�dT pcm

dt

��j

¼� _msl;jhsl T w-LTES;j < T sl ð22Þ

½ðqcpV Þeff þ ðqcpV Þpcm�dT pcm

dt

��j

¼ � _msl;j½hsl þ cp;pcmðT m;j � T slÞ� T w-LTES;j P T sl ð23Þ




where (qcpV)eff[=jj(qVcp)fin + (1 � jj)(qVcp)pcm] is theeffective heat capacity, and Tpcm,j is the PCM temperatureat r is equal to rpcm,eq.

In Eqs. 16, 17, 20, 22, and 23, the negative sign impliesdischarging mode, in which case the inequality is reversedin the discharge mode. The HTF temperatures of eachrow for the charging/discharging modes are written asEqs. (24) and (25), respectively.

T f ;jþ1 ¼ T f ;j � ðT f ;j � T pcm;jÞ=RT ;j _mf cp ð24Þ

T f ;j ¼ T f ;jþ1 þ ðT f ;j � T pcm;jÞ=RT ;j _mf cp ð25Þ

The pressure drop equations for the arrangement ofthe HP shown in Fig. 4 are available in the commonly ref-erenced work of Shah and Sekulic (2003), and total pres-sure drop in each row of the HPHEX is represented byEq. (26).

Xj

j¼1

Dpj ¼Xj

j¼1

G2mj

2ð1þ r2Þ mjþ1

vj� 1

� �þ f

aV j;HPHEX

rAfr

mm

mj

� �

ð26Þ

0 20 40 60 80 100 120 140 160 180 20025

30

35

40

45

50

55

60

65

70

75(a)

T pcm

,c [

o C]

position (r) exp.(Liu et al., 2006) predicted 31 mm 41 mm 48 mm 55 mm

Charging time [min]

25

30

35

40

45

50

55

60

65

70

75

80 (b)

T pcm

, c[o C

]

HTF inlet temp. exp.(Liu et al., 2006) predicted

90oC:

80oC:

70oC:

Charging time [min]

0 20 40 60 80 100 120 140 160 180 200

80

Fig. 5. Comparison of the experimental and theoretical PCM temperaturevariations in the charging mode: (a) radial position and (b) HTF inlettemperature.


where Afr[=HHPHEXWHPHEX] and mm[=(mj + mj+1)/2], andfor the friction factor f, many related equations have beenintroduced in literatures (Shah and Sekulic, 2003; Incroper-a and Dewitt, 2002) in detail.

3. Results and discussion

3.1. Experimental validation of the LTES thermal design

model

Liu et al. (2006) developed an experimental LTES sys-tem in which the HPs were arranged side by side (k = 1and j = 4 in Fig. 2) and investigated the heat responsecharacteristics in the charging and discharging modes.Their experimental results are compared with thoseobtained using our theoretical model in Figs. 5–7 withthe purpose of evaluating the validity of the model. ThePCM properties, input conditions, and the geometricdimensions of the system used by Liu et al. are describedin detail in their work referenced above. The PCM wasparaffin wax (#52), which had a phase-change tempera-ture of 52.1 �C.

0 30 60 90 120 150 180 21025

30

35

40

45

50

55

60

65

70

75

80 (a) position (r) exp.(Liu et al., 2006) predicted 31 mm 41 mm 48 mm 55 mm

PCM

tem

pera

ture

[o C]

Discharging time [min]

25

30

35

40

45

50

55

60

65

70

75

80 (b) inlet temp. exp.(Liu et al., 2006) predicted

10oC:

17oC:

25oC:

T pcm

, d[o C

]


0 30 60 90 120 150 180 210

Fig. 6. Comparison of the experimental and theoretical PCM temperaturevariations in the discharging mode: (a) radial position and (b) HTF inlettemperature.



60 70 80 90 100 110 1200

10

20

30

40

50

60

70

80

exp.(Liu et al., 2006) Predicted

r sl [

mm

]

Charging time [min]

Fig. 7. Comparison of the variations in the experimental and theoreticalPCM melting front locations in the charging mode.

Table 1Properties of the PCM used in this study.

Items Unit Potassium nitrate (KNO3)

Melting temperature �C 335Density kg/m3 2100Latent heat kJ/kg 95Specific heat kJ/kg K 953Thermal conductivity W/m K 0.425


The experimental and theoretical PCM temperatures inthe charging mode are compared in Fig. 5a and b. InFig. 5a, the comparison is with respect to the variation inthe PCM temperature at radii (r) of 31 mm, 41 mm,48 mm, and 55 mm (see Fig. 4c) for inlet temperature andmass flow rate of 80.1 �C and 2.5 kg/min, respectively.The discrepancies can be attributed to the occurrence ofnatural convective heat transfer between the PCM andthe HP wall and fin assembly during melting in the exper-iment. When the radius is relatively small, melting is faster;hence, the relative maximum error of 7.1% corresponded tothe smallest radius of 31 mm and occurred 60 min into theexperiment. As the melting of the PCM progressed beyond120 min, the errors increased in all regions, although theywere still below 2%. Between 70 min and 120 min, theerrors in all regions were below 0.6%, indicating goodagreement.

The experimentally and theoretically determined PCMtemperatures at a radius of 48 mm are compared inFig. 5b as a function of the HTF temperature. Melting atthe HTF inlet temperature of 90 �C was faster than at otherinlet temperatures, resulting in higher errors, although theywere still below 2.4%.

Fig. 6 is a comparison of the experimentally and theoret-ically determined locations of the melting interface. Themean values of the time-dependent locations (z coordinate)in the work of Liu et al. (2006) are used for the experimen-tal data. From Fig. 7, the relative errors of the experimen-tal and theoretical locations are below 15%, rangingbetween 4% and 14.8% over time.

The variations in the experimental and theoretical PCMtemperatures in the discharging mode are compared inFig. 7a and b. Fig. 7a corresponds to the same regions inFig. 5a for HPHEX inlet temperature and mass flow rateof 17 �C and 1.67 kg/min, respectively. Although the errorsare slightly high due to the occurrence of natural convec-tion cooling before the PCM phase-change temperaturewas attained in each region, they are still below 2.4%. As


solidification progressed, thermal energy was transferredby pure conduction, thereby decreasing the errors to below0.6% in all regions.

The variations in the experimental and theoreticalPCM temperatures at a radius of 48 mm are comparedin Fig. 7b with respect to the HTF inlet temperature.The maximum error of 2.7% occurs 60 min into the exper-iment, which coincides with the attainment of the phase-change temperature. Beyond this point, the errors reduceto below 0.3%.

3.2. LTES charging mode

Listed in Tables 1 and 2 are the properties and specifica-tions of the PCM of the analytical model used for estimat-ing the temperature variation in the CSP LTES system. ThePCM was potassium nitrate, which has a phase-changetemperature of 335 �C (Kenisarin, 2010; Shabgard et al.,2010). For convenience, the height and width of the LTESsystem were fixed at 1 m and 0.9 m, respectively. The heightof LTES was 0.6 m, and the height of the charging and dis-charging HPHEX was 0.2 m. The values were the same inall cases. A total of 400 rows were used for charging anddischarging of the HTF, which utilized counter flow (seeFig. 2). The specifications of the fins of the HPHEX werefixed, whereas the pitches of the fins attached to the LTESregion were considered to be variable. The HTF was asuperheated vapor with pressure ranging between 2.5 and3 MPa, and its thermodynamic properties (Cengel andBoles, 2002) used for the calculation were obtained as func-tions of the temperature and pressure were. The pressure atthe inlet of each row was calculated from the pressure drop(Shah and Sekulic, 2003). The charging and dischargingtimes in the LTES system were set at 300 and 120 min,respectively.

Fig. 8 shows the variation in the PCM temperature inthe charging mode. As explained in Eq. (17), Tpcm,j repre-sents the PCM temperature (Tpcm,j in Fig. 3) at the centerregion (rpcm,eq) between the rows. Additionally, the PCMtemperature distribution in the HP without the fin is shownin Fig. 8c.

The fin pitches for the data shown in Fig. 8a and b were4 and 16 mm, respectively. As can be observed, the smallerthe pitch, the faster the PCM temperature increase. For thefin pitch of 4 mm, the temperature of all the rows reachedthe phase-change temperature within 232 min. In the case



Table 2Physical dimensions and input conditions of the LTES system.

Items Dimensions/materials

HPHEX 0.2 m (H) � 1 m (W)HP Stainless steel 316, O.D. = 25.4 mm, I.D. = 22.1 mm, L = 1 m,

working fluid = Dowtherm AScreen capillary structure Stainless steel 316, MESH number = 300, dw = 0.1 mmThermal storage container 0.6 m (H) � 1 m (W)Annular fins of the HPHEX df = 43.4 mm, d = 1 mm, Df = 270.3 fins/m, pf = 3.7 mm, s = 2.7 mmAnnular fins of the LTES df = 43.4 mm, d = 1 mm, Df = variable, pf = variable, s = variableArrangement of heat pipes XT = 58.4 mm, XL = 58.4 mm, staggered angle = 60�Number of heat pipes per row Odd rows: 14, even rows: 13, total rows: 400HTF Superheated vapor (2–3 MPa)Inlet mass flow rate of HPHEX 1.67 kg/sHPHEX inlet temperature and pressure (charging mode) 395 �C and 2.7 MPaHPHEX inlet temperature and pressure (discharging

mode)224 �C and 2.25 MPa

Charging/discharging time min Charging mode: 300 min, discharging mode: 120

0 50 100 150 200 250 300

50

100

150

200

250

300

350

400

(a)

row number 1 50 100 150 200 250 300 350 400

T pcm

, c[o C

]

Charging time [min]

0

50

100

150

200

250

300

350

400(b)

row number 1 50 100 150 200 250 300 350 400

T pcm

, c [

o C]

Charging time [min]

0 50 100 150 200 250 300

0 50 100 150 200 250 3000

50

100

150

200

250

300

350

400

(c)

row number 1 50

100 150 200 250 300 350 400

T pcm

, c [

o C]

Charging time [min]

0 50 100 150 200 250 3000

10

20

30

40

50

60

70 (d)

row number 1 50 100 150

200 250 300 350 400

PCM

tem

pera

ture

dif

fere

nce

[o C]

Charging time [min]

Fig. 8. Variation in the PCM temperature as function as row number in the charging mode: (a) LTES fin pitch: 4 mm, (b) LTES fin pitch: 16 mm, (c)without fin, and (d) PCM temperature difference.


of the fin pitch of 16 mm, the temperature in all the rowsreached the phase-change temperature within 298 min.The PCM temperature in Row 300 was 332.4 �C when afin was not attached to the HP. Because the PCM temper-ature did not reach the melting temperature, it was foundunsuitable for the design condition. Reaching melting tem-perature was not achieved in rows more than Row 300 even


after 300 min, and no melting occurred in Row 300. Asshown in Fig. 8c, the achievement of complete phasechange within the specified time requires adequate heattransfer area, which can be secured by attaching a fin withthe adequate pitch to the HP.

The differences between the respective PCM tempera-tures calculated for the fin pitch of 4 and without fin are



0.5

0.6

0.7

0.8

0.9

1.0

pf: 16 mm

(c)

row number 1 50 100 150 200 250 300 350 400

r sl, j /

rpc

m, e

q, j

0.4

30 60 90 120 150 180 210 240 270 3000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

pf: 16 mm

(d)

row number 1 50 100 150 200 250 300 350 400

Vsl

,j /

Vpc

m, j

Charging time [min]

0.4

0.5

0.6

0.7

0.8

0.9

1.0

pf : 4 mm(a)

row number 1 50 100 150 200 250 300 350 400

r sl /

r pcm

, eq

30 60 90 120 150 180 210 240 270 3000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

pf : 4 mm

(b)row number

1 50 100 150 200 250 300 350 400

Vm

elt/V

T, j

Charging time [min]

Fig. 9. Melting interface location and melting rate as a function of the row number: (a) melting interface location (LTES fin pitch: 4 mm), (b) melting rate(LTES fin pitch: 4 mm), (c) melting interface location (LTES fin pitch: 16 mm), and (d) melting rate (LETES fin pitch: 16 mm).

0 50 100 150 200 250 300150

180

210

240

270

300

330

360

390

420

row number: 400

LTES HP fin pitch [mm] 4 10 16 22 28 without fin

HT

F te

mpe

ratu

re [

o C]

Charging time [min]

Fig. 10. HTF temperature as function as LTES fin pitch (row number:400).


shown in Fig. 8d. The temperature differences are thosebetween corresponding rows (i.e., the PCM temperatureshown in Fig. 8a minus the corresponding PCM tempera-ture shown in Fig. 8d). The PCM temperatures in Fig. 8aare higher than those in Fig. 8d for all the rows. The max-imum difference between the temperatures was determinedto be 70 �C, which corresponded to Row 400 at 180 min ofthe charging time.

Fig. 9 shows the location of the melting interface andmelting rate in each row for fin pitches of 4 and 16 mm.As expected, it was observed that, the time taken for thegrowth of the melting interface to begin was proportionalto the row number and the fin pitch. For the 4 mm finpitch, the times were 32 and 80 min for Rows 1 and 400,respectively. The corresponding times taken for completionof melting when the melting interface was at rpcm,eq were150 and 232 min, respectively. In the case of the 16 mmfin pitch, the growth of the melting interface in Rows 1and 400 began after 41 and 103 min, and ended after 191and 297 min, respectively. As shown in Fig. 9c and d, themelting rate showed a similar trend with respect to thelocation of the melting interface. However, the slope oftime with respect to the melting rate increased initiallyand then decreased exponentially over time. As the numberof rows increased, the slope of the melting rate decreased.


When the number of rows is increased by increment ofthe 50, the calculated difference in slope was less than 1%.

Figs. 10 and 11 show the HTF and pressure dropchanges according to the charging time using the LTESfin pitch function. Table 2 shows physical dimensions andinput conditions of the LTES system. The HTF in thisstudy is in a state of superheated vapor and the inlet



0 50 100 150 200 250 30040

45

50

55

60

65

70

75

80

LTES HP fin pitch [mm] 4 10 16 22 28 without finT

otal

pre

ssur

e dr

op [

kPa]

Charging time [min]

Fig. 11. HTF total pressure drop as function as LTES fin pitch.

0 50 100 150 200 250 3000

200

400

600

800

1000

1200

1400

1600

TES HP fin pitch [mm] 4 10 16 22 28 without fin

QT

,c [

kW]

Charging time [min]

Fig. 12. Total heat transfer rate as function as LTES fin pitch for chargemode.


conditions are temperature and pressure. The HTF shouldsatisfy the superheated condition for all the rows (Cengeland Boles, 2002). The physical property of the HTF wasadjusted by restricting it to a range between 3 MPa and2 MPa and its error was less than 5%. The calculationresult presented in Fig. 10 shows the HTF temperature dis-tribution at Row 400, and Fig. 11 shows the total pressuredrop, calculated by summation of pressure drop in eachrow (refer Eq. (25)). The saturation temperature that corre-sponded to the inlet pressure of 2.7 MPa was 232 �C.Because the saturation temperature was less than the inlettemperature of 394 �C, the inlet temperature and pressureof the HTF with respect to the charging mode indicateda superheated condition. If the HTF at Row 400 was inthe state of superheated vapor, the HTF in all the rowsin between satisfied the superheated condition. As shownin Fig. 10, because the PCM temperature was at its lowestat the initial charging time, the HTF temperatures werealso at its minimum of all LTES fin pitches. Similarly,the minimum HTF temperature for all fin pitches was149 �C, and when the charging time reached 300 min, theminimum temperatures were close to the inlet HTF temper-ature. The saturation pressure for the minimum tempera-ture was approximately 0.47 MPa. The HTF pressurethat resulted in the pressure drop (41 kPa) was 2.66 MPaat the initial charging time. Because this pressure washigher than the saturation pressure (0.47 MPa), the HTFsatisfied the superheated condition at the minimum temper-ature. When the charging time reached 300 min, the totalamount of pressure drop and the HTF temperature haddifferent values according to the fin pitches. For fin pitchesof 4 mm and 28 mm, the HTF temperature and the pres-sure drop were 394.6 �C and 71 kPa and 390.2 �C and70.8 kPa, respectively. Because these values of the satura-tion temperature with respect to the pressure were less thanthe HTF temperature, they satisfied the superheated condi-tion. Because the pressure and temperature at first and endrows satisfied the superheated condition, the pressure andtemperature of the HTF in all the rows satisfied the super-


heated condition. As shown in Figs. 10 and 11, when the finpitch was smaller, the HTF temperature was higher andtotal pressure drop was high. As shown in Table 2,HPHEX fin pitch was fixed to a constant value of3.7 mm and main parameter for the thermal charging/dis-charging simulations described in present study is theLTES fin pitch. This means that heat transfer area of theHPHEX has constant value with respect to the heat trans-fer area on the LTES region with variation of the LTES finpitch. As explain in Fig. 8, a decrease in LTES fin pitch andconsequent increase in the heat transfer area of the LTESregion would be effective for raising PCM temperaturebut may cause negative result in term of HTF temperatureincrease including HPHEX region. This mean that heattransfer rate decrease with respect to increase of HTF tem-perature (refer to Eq. (20), (21), and (24)).

As shown in Table 2, because the fin pitches in theHPHEX region were fixed, the pressure drop dependedonly on the properties of the HTF with respect to the tem-perature. Because the specific volume increased as the HTFtemperature increased, the total pressure drop increased asthe working temperature was higher (refer to the Eq. (25)).For fin pitches between 4 mm and 22 mm, the total pres-sure drop increased discontinuously because of the discon-tinuity of the physical property after approximately152 mm of charging time. As shown in Fig. 10, when thefin pitch was 10 mm, the temperature of the HTF increaseddiscontinuously because of the discontinuity of the specificheat after 151 mm of charging time.

Fig. 12 shows the total heat transfer rate with respect tothe LTES fin pitch in charging. As the fin pitch increases,the volume the fins occupy decreases, thereby increasingthe PCM volume. As shown in Eqs. (22) and (23), theincrease in the PCM volume can increase the heat transferrate and the calculated heat transfer rate was the highestwhen the fin was not attached. As shown in Fig. 8, thetransit temperature of the PCM decreased as the fin pitchincreased and hence, though the time to reach the melting




temperature may have been longer, the heat transfer rateincreased. Therefore, as the PCM temperature rises to themelting temperature, the fin pitch of the LTES should beselected appropriately to secure the maximum possible heattransfer rate. Furthermore, as shown in Fig. 12, the heattransfer rate increased with larger fin pitch. However, themaximum difference in the heat transfer rate between the

0 20 40 60 80 100 120260

280

300

320

340

360

380

400 (a) row number 1 50 100 150 200 250 300 350 400

T pcm

, d [

o C]


0 20 40 60 80 100 120260

280

300

320

340

360

380

400 (b)

row number

1 50 100 150 200 250 300 350 400

T pcm

, d [

o C]


0 20 40 60 80 100 120260

280

300

320

340

360

380

400 (c)

row number

1 50 100 150 200 250 300 350 400

T pcm

, d [

o C]


Fig. 13. Variation in the PCM temperature as function as row number inthe discharging mode: (a) LTES fin pitch: 4 mm, (b) LTES fin pitch:16 mm, and (c) without fin.


case of a fin pitch of 28 mm and that without the fin wasless than 5.4%.

For a charging time of 150 min, as the pitch increasesfrom 4 mm to 16 mm, the heat transfer rate increases bymaximum 20.4%. Moreover, as the pitch increases from16 mm to without fin, the heat transfer rate increases bymaximum 9.2%.

3.3. LTES discharging mode

Fig. 13a–c shows the variation in the PCM temperaturein the discharging mode with respect to time for fin pitchesof 4 mm, 16 mm and without fin, respectively. The initialPCM temperature (at t = 0) of all the rows was fixed at387 �C and the subsequent temperatures were calculatedwith respect to the row number in the discharging mode.As shown in Fig. 2, the number of the HTF inlet row inthe discharge mode is 400. As can be observed from the fig-ures, the smaller the pitch, the higher the rate of tempera-ture decrease. In the case of the 400th row, the PCMtemperature after 120 min of discharging was 261.7, 276.8and 283 �C for the 4, 16 mm fin pitches and without fin,respectively. In the three cases of the discharging mode,the PCM temperatures reach to the solidification tempera-

0.4

0.5

0.6

0.7

0.8

0.9

1.0(a)

row number 400 350 300 250 200 150 100 50 1

Discharging time [min]20 30 40 50 60 70 80 90

30 40 50 60 70 80 90 100 110 1200.4

0.5

0.6

0.7

0.8

0.9

1.0

(b)

row number 400 350 300 250 200 150 100 50 1

r sl,

j / r pc

m, e

q, j


r sl,

j / r pc

m, e

q, j

Fig. 14. Solidification interface location as a function of the row number:(a) LTES fin pitch: 4 mm and (b) LTES fin pitch: 16 mm.



0 10 20 30 40 50 60 70 80 90 100 110 12043

44

45

46

47

48

49

50

51

52


Tot

al p

ress

ure

drop

[kP

a]


Fig. 16. HTF total pressure drop as function as LTES fin pitch.


ture during 120 min of the discharging time. However, asmentioned in Fig. 8, in the case without the fin, becausethe PCM temperature did not reach the melting tempera-ture, the design condition was not met.

Fig. 14 shows the solidification interface in each row forfin pitches of 4 and 16 mm. As LTES fin pitch increased,starting and completing time of the solidification aredelayed. It was observed that the row number and fin pitchwere positively correlated with the time at which the solid-ification interface growth began, which were respectively13.6 and 59 min in Rows 400 and 1 for the 4 mm fin pitchand the solidification was complete in 20 min and 76.5 min,respectively. For a fin pitch of 16 mm, the growth of thesolidification interface began in Rows 400 and 1 whenthe discharging times were 30.1 min and 89 min and solid-ification was complete in 40.8 min and 115.1 min,respectively.

Figs. 15 and 16 show the HTF temperature and pressuredrop changes according to the charging time using theLTES fin pitch function. The HTF should satisfy the super-heated condition for all rows (Cengel and Boles, 2002). Thecalculation result shown in Fig. 15 shows the HTF temper-ature distribution at Row 1, and Fig. 11 shows the amountof total pressure drop, summation of the pressure drop ineach row (refer to Eq. (26)). The saturation temperaturethat corresponds to the inlet pressure of 2.25 MPa is218 �C. Because the saturation temperature was less thanthe HTF inlet temperature of 224 �C, the inlet conditions(400th row) of the HTF with respect to the dischargingindicate a superheated condition. If the superheated condi-tion of the HTF at Row 1 is satisfied, the HTF of all therows are in the state of superheated vapor.

As shown in Fig. 15, because the PCM temperatureswere at its lowest at the end (discharging time of120 min) of the discharging time, the HTF temperature isalso at its minimum (refer to Fig. 13). The minimumHTF temperatures were different according to the fin pitch.When analyzing data based on the working pressure, satu-ration temperature, and saturation pressure, taking the

0 10 20 30 40 50 60 70 80 90 100 110 120270

280

290

300

310

320

330

340row number: 1


HT

F te

mpe

ratu

re [o C

]


Fig. 15. HTF temperature as function as LTES fin pitch (row number: 1).


working temperature and the total pressure drop into con-sideration with the HTF conditions as shown in Figs. 15and 16, the HTF in all the rows satisfied the superheatedcondition.

For example, in the case with no fin, at the dischargingtime of 120 min, the temperature of the HTF was 273.3 �C(which was its lowest) and the pressure drop was approxi-mately 43 kPa. Because the HTF temperature was higherthan the saturation temperature, the HTF was in the stateof superheated vapor. As shown in Figs. 10 and 11, whenthe fin pitch was larger, the HTF temperature and totalpressure drop were higher.

As shown in Figs. 15 and 16, when the fin pitch was lar-ger, the HTF temperature and total pressure drop werehigher. The heat transfer area of the HPHEX has constantvalue with respect to the heat transfer area on the LTESregion with variation of the LTES fin pitch. As explain inFigs. 10 and 11, a decrease in LTES fin pitch and conse-quent increase in the heat transfer area of the LTES regionwould be effective for falling PCM temperature but maycause negative result in term of HTF temperature decrease

0 10 20 30 40 50 60 70 80 90 100 110 120200

250

300

350

400

450

500

550

TES HP fin pitch [mm] 4 10 16 22 28 without fin

QT,d [

kW]


Fig. 17. Total heat transfer rate as function as LTES fin pitch.




including HPHEX region. This mean that heat transferrate decrease with respect to decrease of HTF temperature(refer to Eq. (20), (21), and (25)) at the discharging mode.

The total pressure drop with constant value of theHPHEX fin pitch depended only on the properties of theHTF with respect to temperature. The total pressure dropalso increased with the specific volume at higher HTFtemperature.

Fig. 17 shows the total heat transfer rate with respect tothe LTES fin pitch in discharging mode, respectively. Asthe fin pitch increases, the volume the fins occupydecreases, thereby increasing the PCM volume. Theincrease in the PCM volume can increase the heat transferrate. As shown in Fig. 17, for a charging time of 150 min,as the pitch increases from 4 mm to 16 mm, the heat trans-fer rate increases by 47%. Moreover, as the pitch increasesfrom 16 mm to 30 mm, the heat transfer rate increases by12%. The pitch increase is accompanied by a decrease inthe heat transfer area, and thereby produces a decrease inthe discharging heat transfer rate. As shown in Fig. 12b,as the pitch increases, the heat transfer rate decreases.

Fig. 17 shows the total heat transfer rate with respect tothe LTES fin pitch in discharging. As the fin pitchincreases, the volume the fins occupy decreases, therebyincreasing the PCM volume. As shown in Eq. (22), theincrease in the PCM volume can increase the heat transferrate and the calculated heat transfer rate was the maximumwhen the fin was not attached. The transient temperatureof the PCM (Fig. 13) was decreases and the heat transferrate increases with the LTES fin pitch increase. It is bene-ficial to have a larger LTES fin pitch as it allows for higherHTF temperatures and heat transfer rate while maintainingthe PCM temperature at an appropriate level based on thedischarging time. However, in a relative sense, the totalpressure drop increases as well.

The pitch increases from 4 mm to 16 mm, the heat trans-fer rate increases by maximum 18.4%. Moreover, as thepitch increases from 16 mm to without fin, the heat transferrate increases by maximum 4.2%. Furthermore, as shownin Fig. 17, the heat transfer rate increases with larger finpitch. However, the maximum difference in the heat trans-fer rate between the case of a fin pitch of 28 mm and thatthe no fin was less than 3%.

4. Conclusion

We developed an analytical model of the heat transferthat occurs during melting/solidification in an LTES sys-tem with the HPHEX for CSP applications, and evaluatedit by comparing its predictions with experimental results.The relationship between the thermal resistance and thetemperature difference between the HPHEX and the LTESwas established, and a row-by-row heat transfer was usedto estimate the total required row number of the LTES sys-tem. The validation of the analytical model was done usingthe results of a previous experimental study. The errors of


the temperature value were mostly below 8%, indicatinggood agreement.

The LTES fin pitch was adopted as the design variable,and the phase-change time and heat transfer rate must becontrolled using a geometrical shape of the LTES compo-nents that matched the operational environment. As LTESfin pitch was increased, the effect of the increase in the LTESfin pitch became minimal. Additionally, because the PCMtemperature did not reach the melting temperature in thecase of the no fin, the design condition was not met. The tran-sit temperature of the PCM decreased with the LTES finpitch increase, implying that though the time taken to reachthe melting temperature may be longer, heat transfer ratehave increased. Therefore, the LTES fin pitch should bedesigned appropriately based on the transient temperaturedistributions of the PCM, HTF temperatures in all rows,phase change interface growth, and the total pressure dropand appropriately to secure as much heat transfer rate aspossible in the duration when the PCM temperatureincreases up to the melting temperature.

Furthermore, heat transfer rate and high HTF tempera-ture could have been obtained as the fin pitch increased inthe discharging mode; however, the pressure dropincreased instead. The design condition in the chargingmode should consider the result obtained in the discharg-ing mode.

Acknowledgment

We sincerely appreciate the support of the Korea Insti-tute of Energy Research (KIER) for this study.

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