Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules

Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules

Accepted Manuscript Title: Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules A...

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Accepted Manuscript Title: Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules Author: Ming Wu, Chao Xu, Yaling He PII: DOI: Reference:

S1359-4311(15)01060-1 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.10.014 ATE 7130

To appear in:

Applied Thermal Engineering

Received date: Accepted date:

17-3-2015 1-10-2015

Please cite this article as: Ming Wu, Chao Xu, Yaling He, Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.10.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

1

Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded

2

phase change material capsules

3 Ming Wu1, Chao Xu2*, Yaling He1*

4 1

5

Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

6 7

State Key Laboratory of Multiphase Flow in Power Engineering, School of Energy and Power

2

Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of MOE, School

8

of Energy Power and Mechanical Engineering, North China Electric Power University,

9

Beijing 102206, China

10 11

Highlights

12

>Cyclic behaviors of a TES system packed with cascaded PCM capsules are investigated.

13

>Non-cascaded system suffers from a low charging ratio and a long charging time.

14

>The cyclic process of the cascaded system can reach to a repeatable state after some cycles.

15

>Practical storage capacity depends on the threshold temperature to stop the operation.

16

Abstract

17

A transient, one-dimensional dispersion-concentric model to numerically study the cyclic behaviors

18

of the molten-salt packed-bed thermal energy storage system filled with cascaded phase change

19

material (PCM) capsules is presented. Three different storage systems are investigated which

20

include the non-cascaded system, the cascaded systems with 3 and 5 cascaded phase change

21

temperatures (PCTs). Detailed characteristics of heat transfer between molten salt and the packed

22

PCM capsules are discussed, and various numerical results are presented, including the temperature

23

distributions of molten salt and PCM capsules, the variations in the molten-salt outlet temperature,

24

the accumulated efficiency of each cycle. The results show that the non-cascaded system suffers

25

from a low charging ratio and a long charging time due to the constrains of PCT while the cascaded

26

systems especially with 5 cascaded PCTs are found to have both a fast discharging rate and a fast

27

charging rate. The cyclic process of the cascaded system with 5 cascaded PCTs can reach to a *Corresponding author. Tel.: +86 29 82665930; fax: +86 29 82665445. E-mail address: [email protected] (C. Xu); [email protected] (Y.-L. He)

Page 1 of 29

28

repeatable state after some cycles, at which high accumulated efficiencies can be achieved. It is also

29

found that the practical storage capacity of the storage system with cascaded PCM capsules depends

30

highly on the threshold temperatures to stop the charging/discharging process.

31 32

Kew words: Thermal energy storage, Solar energy, Packed bed, Phase change material

33

1. Introduction

34

Thermal energy storage (TES) is very crucial for large-scale applications of concentrating

35

solar power (CSP) systems, because CSP systems with TES can not only generate stable and

36

dispatchable electricity, but also enable higher overall penetrations of solar photovoltaic (PV) and

37

wind power [1]. Presently, the two-tank molten-salt TES system is the only one that has been

38

applied in large-capacity CSP plants such as Andasol 1-3 in Europe. However, the two-tank system

39

has a relatively high cost and limited room for cost reduction, and thus alternative cost-effective

40

TES systems are in urgent need [2-4].

41

The one-tank packed-bed thermocline TES system has been regarded as a promising TES

42

alternative since it may save 35% of capital cost compared to the two-tank TES system [2]. The

43

first pilot-scale molten-salt packed-bed thermocline tank has been successfully established in

44

Sandia National Laboratories [5], and quartzite rock combined with silica sand were screened out as

45

the most practical cheap solid fillers. Valmiki et al. [6] also built a lab-scale packed-bed

46

thermocline TES tank and experimentally investigated the heat transfer behaviour during the

47

charging and discharging processes. In addition to the experimental research work, increasing

48

numerical investigations about the packed-bed thermocline TES system were reported recently.

49

Yang et al. [7-8] developed a two-temperature model for the molten-salt packed-bed thermocline

50

system and carried out a series of numerical investigations. Li et al. [9] numerically investigated

51

various scenarios of thermal energy charging and discharging processes for the packed-bed

52

thermocline tank based on the developed one-dimensional thermal model. Xu et al. [2-3] presented

53

a transient two-dimensional two-phase model to investigate the characteristics of the discharging 2 Page 2 of 29

54

process of the packed-bed thermocline system. Xu et al. [4] also developed a modified transient

55

two-dimensional dispersion-concentric (D-C) model to study the heat transfer characteristics within

56

spherical solid fillers for the discharging process. Flueckiger et al. [10] developed a new model to

57

provide a comprehensive simulation of thermocline tank operation, and incorporated it into a

58

system-level model of a 100 MWe power tower plant to investigate the storage performance during

59

long-term operation. The efficiency of the thermocline tank at charging and discharging heat was

60

found to be above 99% throughout the year.

61

Compared to solid fillers, capsules filled with phase change material (PCM) have been

62

considered as a better option to be used in packed-bed TES systems. The benefits of PCM include

63

the utilization of latent heat, which may result in a higher energy storage density and a smaller

64

storage volume. Packed-bed TES systems filled with PCM capsules have been extensively studied

65

both experimentally and numerically for low-temperature storage applications such as space and

66

water heating, cooling and air-conditioning etc. Arkar and Medved [11] investigated the free

67

cooling of a low-energy building using a latent heat TES device integrated into a mechanical

68

ventilation system. The cylindrical TES device was filled with spheres of encapsulated paraffin.

69

The results showed that free cooling with an latent heat TES was an effective cooling technique.

70

Nallusamy et al. [12] experimentally studied the thermal behavior of a packed-bed of combined

71

sensible and latent heat TES unit. Paraffin was used as the PCM filled in spherical capsules and

72

water was used as the heat transfer fluid (HTF). Effects of both constant and varying heat sources

73

on the charging/discharging performance were investigated. Bédécarrats et al. [13-14] carried out

74

experimental investigations on the performance of a TES system packed by spherical capsules filled

75

with water as the PCM. Effects of the temperature and flow rate of the inlet HTF, kinetics of

76

cooling and heating on the charging/discharging performance were investigated. A numerical study

77

was also presented to complement with the experimental investigations. Amin et al. [15] developed

78

a semi-analytical mathematical model based on the effectiveness-NTU method for a TES system

79

filled with PCM spheres. The formulation enables quick design and simulation of a packed bed 3 Page 3 of 29

80

PCM system without the need for numerical modelling. Regin et al. [16] numerically investigated

81

the thermal behavior of a packed-bed storage system filled with paraffin capsules for solar water

82

heating application. The Schumann-like model was developed and the enthalpy method was used to

83

analyze the phase change process inside of capsules. Xia et al. [17] numerically studied the fluid

84

flow through the voids of packed capsules and thermal gradients inside of the PCM capsules for the

85

packed-bed TES tank filled with PCM capsules. The effect of arrangement of the PCM capsules

86

was also analyzed based on the developed model. Oró et al. [18] numerically investigated the heat

87

charging performance of a packed bed storage with PCM capsules using two different models. The

88

results indicated that free convection was not as important as forced convection in the studied case.

89

Recently, packed-bed TES systems filled with high-temperature PCM capsules have been

90

identified as a promising compact and cost-effective TES technology for CSP plants, and molten

91

salt, whose phase change temperature (PCT) can range from below 100 oC to above 600 oC

92

depending on the ingredients, has great potential to be used as the PCM. Nithyanandam et al.

93

[19-21] carried out a numerical analysis of the dynamic behaviour of a molten-salt packed-bed TES

94

system with PCM capsules for repeated charging and discharging cycles for CSP power plants. The

95

effects of the configuration design and constraints on the charging and discharging temperature as

96

encountered in a CSP plant operation on the system dynamic responses were discussed. The effect

97

of PCT of PCM on the system utilization was found to be non-monotonic, with higher latent

98

utilization when the PCT is either greater than the discharging cut-off temperature or lesser than the

99

charging cut-off temperature. A methodology for system design and optimization was also provided

100

based on the systematic parametric studies and consideration of target design requirements on the

101

dynamic operation of a CSP plant. Galione et al. [22] numerically investigated the performance of

102

different thermocline-like storage concepts including a pure thermocline tank, tanks filled with a

103

single PCM, multi-layered solid-PCM and cascaded PCM arrangements. They suggested the

104

multi-layer solid-PCM thermocline system could be utilized due to its cost-effectiveness and high

105

efficiency in the use of the overall thermal capacity of the system. Tumilowicz et al. [23] developed 4 Page 4 of 29

106

an enthalpy-based model of thermocline operation applicable to both single phase and encapsulated

107

PCM using the method of characteristics. Various possible heat transfer conditions along with

108

placement of PCM filler phase state interface were investigated. Flueckiger et al. [24] also

109

presented a new finite volume approach to simulate mass and energy transport into a latent heat

110

thermocline tank and integrated the model into a system-level model of a molten-salt power tower

111

plant. PCMs with different PCTs and heats of fusion were evaluated and the performance of a TES

112

tank filled with multiple PCMs with cascaded PCTs along the tank height was discussed. Bellan et

113

al. [25] numerically investigated the effect of capsule size, fluid temperature, tank size, fluid flow

114

rate on the performance of a packed bed TES system using sodium nitrate as the PCM and synthetic

115

oil as the HTF. The dynamic behaviour subjected to partial charging and discharging cycles was

116

also analysed. Wu et al. [26] recently presented a transient two-dimensional dispersion-concentric

117

(D-C) model for the packed-bed TES system with PCM capsules to study the dynamic performance

118

characteristics. The introduction of the D-C model enables determination of the temperature

119

distribution and phase change front within each PCM capsule during the heat charging/discharging

120

processes. Detailed characteristics of heat transfer between molten salt and the packed PCM

121

capsules were investigated and a parametric sensitivity analysis was presented. A similar model was

122

also developed by Peng et al. [27] to analyze the effects of physical properties and operational

123

conditions on the thermal performance of a TES tank with PCM capsules.

124

Based on the developed D-C model in our prior work [26], this study aims at investigating

125

the dynamic behaviours for the charging/discharging cyclic processes of a molten-salt packed-bed

126

TES system filled with PCM capsules. The benefits of utilizing PCM capsules with cascaded PCTs

127

will also be explored. To this goal, a modified transient one-dimensional D-C model is developed.

128

The heat transfer characteristics of three different packed-bed systems filled with PCM capsules

129

with different PCT configurations are investigated and various working modes including the

130

charging process, the discharging process and the multiple charging/discharging processes are

131

considered. 5 Page 5 of 29

132 133

2. Model formulation

134

The present study investigates three different molten-salt packed-bed TES systems filled with

135

PCM capsules, which are illustrated in Fig. 1. Each system is composed of a vertically standing

136

cylindrical tank which has two ports on the top and bottom for the flow of hot and cold molten salt,

137

respectively. Spherical PCM capsules with the same diameter are packed in each tank, and molten salt

138

flows through the void space of the packed-bed region. The volume fraction of the packed-bed region

139

taken up by molten salt is termed as the void fraction and is given as 

140

distributors adjacent to the two ports are equipped to guarantee a uniform fluid flow through the void

141

space of the packed-bed region. As illustrated in Fig. 1, System NC is a TES system filled with

142

non-cascaded PCM capsules, which have a uniform PCT of 375 oC. The chosen of the PCT of 375 oC

143

is to achieve a high discharging efficiency [26]. Two systems filled with cascaded PCM capsules (i.e.,

144

System C3 and System C5) are investigated. The PCM capsules in System C3 are divided evenly into

145

three layers, which have cascaded PCTs of 375 oC, 340 oC and 305 oC, respectively. And the PCM

146

capsules in System C5 are divided evenly into five layers, which have cascaded PCTs of 375 oC, 360

147

o

148

in this study in order to study the performance characteristics of TES systems with cascaded PCM

149

capsules. Using PCM with artificial PCTs enables extensive investigation about the effect of PCT

150

on the thermal performance of the TES system, and this approach has been widely adopted by other

151

researchers [20, 21, 24]. Practically, the PCT of PCM can be adjusted by using salt eutectic

152

compositions [28], and the artificial PCTs chosen in the present work have already been satisfied by

153

some salt eutectic compositions. For example, LiCl(54.2mol.%)-BaCl2(6.4mol.%)-KCl(39.4mol.%)

154

has the PCT of 320 oC, LiF(7.0mol.%)-LiCl(41.5mol.%)-LiVO3(16.4mol.%)-Li2CrO4(35.1mol.%)

155

has

156

Li2MoO4(27.1-27.6wt.%)- Li2SO4(17.3-17.8wt.%)- LiF(6.1-6.2wt.%) has the PCT of 360 oC [28].

 V ms / V tank

. Two short

C, 340 oC, 320 oC and 305 oC, respectively. It should be pointed out that artificial PCTs are chosen

the

PCT

of

340

o

C,

and

LiCl(23.4-24.2wt.%)-

LiVO3(24.8-25.3wt.%)-

6 Page 6 of 29

157

Three working modes are investigated in this study, which are the single charging process, the

158

single discharging process and the multiple charging/discharging cyclic process. During the single

159

charging process, hot molten salt flows into the cold tank through the top port, and flows downside

160

through the packed-bed region releasing heat to the packed PCM capsules. The solid PCM in capsules

161

melts to liquid phase after absorbing enough heat from the hot molten salt, and thus heat is stored in the

162

PCM capsules. While during the single discharging process, cold molten salt flows reversely from the

163

bottom to the top and is heated by the hot PCM capsules, in which liquid PCM is solidified after

164

releasing heat. The cyclic process includes multiple consecutive charging/discharging cycles, during

165

which hot molten salt flows into the cold tank through the top port during charging processes while

166

cold molten salt flows into the hot tank through the bottom port during discharging processes.

167 168 169

2.1 Governing equations

170

In our prior work [26], we had developed a transient two-dimensional D-C model for the

171

discharging process of the TES system filled with non-cascaded PCM capsules like System NC. The

172

D-C model enables identification of the phase change front and the temperature distribution within

173

each capsule, and thus detailed characteristics of heat transfer between molten salt and the packed

174

PCM capsules can be investigated. The model had also been validated based on the results shown in

175

Ref. [29]. The results in Ref. [26] showed that the differences of heat and mass transfer in the radial

176

direction are negligibly small with good thermal insulation, and thus a simplified transient

177

one-dimensional D-C model is used in the present study to save the calculation time. The following

178

assumptions are employed in the modeling:

179 180 181 182

1) There is no difference of heat and mass transfer in the radial direction, and thus the governing equations for mass and heat transfer become one-dimensional. 2) The capsules are PCM spherical particles with the same diameter, and the capsule wall is too thin to be considered.

7 Page 7 of 29

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3) The packed PCM capsules form a continuous, homogeneous, and isotropic porous region for

184

fluid flow, and the void fraction of the packed bed region is arbitrarily chosen as 0.25 [20, 24].

185

4) The PCM is assumed to be homogeneous and isotropic on the physical properties, and the

186

physical properties of solid and liquid phase of the PCM are considered to be same [19-20].

187

The governing equations of the modified transient one-dimensional D-C model are presented as

188

follows.

189



Conservation of mass equation for molten salt:  (  l )

190

t



 (  lu )

0

x

(1)

191

where  l is the molten-salt density, u is the superficial velocity, x means the tank axial distance and

192

the origin of the x coordinate is at the bottom surface of the packed-bed region as shown in Fig. 1 .

193



Conservation of momentum equation for molten salt:  (  lu )

194

 ( t )



 (  l uu )

 x 2





(

 u

x  x

)

p x

 lg  (





CF 

K

(2)

u )u

K

195

where K is the intrinsic permeability of the packed-bed region, C F is the inertial coefficient, and  is

196

the molten-salt viscosity.

197



Conservation of energy equation for molten salt:  (  l c p,lTl )

198

t



 x

(  l c p,1uTl ) 

 x

(  l,eff

 Tl x

)  h v ((T p ) R  Tl )

(3)

199

where T l is the molten-salt temperature,

200

molten-salt specific heat capacity,

201

term on the right side accounts for the heat transfer between molten salt and PCM capsules with a

202

volumetric interstitial heat transfer coefficient

203



204

 l, eff

(T p ) R is

the surface temperature of PCM capsules,

c p, l is

the

is the molten-salt effective thermal conductivity, and the last

hv .

Conservation of energy equation for PCM capsules:  (  p h p (T p )) t



 

( k p (T p )

 Tp 

)

2 k p (T p )  T p





(4)

8 Page 8 of 29

205

where  is the radial coordinate inside each capsule,

206

density and thermal conductivity of PCM, respectively.

h p is

the enthalpy of PCM,

 p and k p

are the

207 208

2.2 Material properties and constitutive correlations

209

The molten salt used in this study is the binary molten salt (60wt% NaNO3 and 40wt% KNO3),

210

and its thermo-physical properties can be found in Ref. [2]. The properties of PCM are listed in Table

211

1. The inertial coefficient and the permeability of the packed-bed region can be expressed as [2]:

212

1 . 75

CF 

150 

dp  2

213

214 215 216

K 

3

150 (1   )

(6)

2

where d p is the diameter of the spherical capsule. The interstitial heat transfer coefficient between molten salt and PCM capsules, h v , and the molten-salt effective thermal conductivity,

 l, eff

, are given as [26]:

0.6 1/ 3 6(1   ) k l  2  1.1 R e p P r  hv  2 dp

217

 0.7  k l , R e p  0.8  l,eff    0.5 P rR e p k l , R e p  0.8

218 219

(5)

3

(7)

(8)

where the Prandtl number and Reynolds number are expressed as below:

220

Pr 

c p ,l  kl

;

R ep 

 ld p u 

(9)

221 222

When the PCM is in liquid phase, natural convection which enhances heat transfer may exist. The

223

following effective thermal conductivity of liquid PCM is adopted to account for the natural

224

convection effect [17]:

225

k p, n  0.18 k p R a

0.25

(10)

9 Page 9 of 29

226

where the Rayleigh number, Ra, is expressed as

227

kinematic viscosity, thermal diffusivity, and thermal expansion coefficient of liquid PCM, respectively.

g  (Tp  Tm elt )( d p / 2) /  3

, and

 , , 

are the

228 229 230

2.3 Boundary conditions and initial conditions Boundary conditions.

231

The boundary conditions of the molten salt for the different working processes are listed as

232

follows.

233



Single charging process:

234

x 0

:

u / x

235

xH

:

u

237

x 0

:

u

238

xH

:

u / x

236

239









 0 ,  Tl /  x

  u in

,

 u in

Tl

Tl



0



 Tin,high

(11) (12)

Single discharging process: 



,

0



,

 Tin,low  Tl /  x

(13) 

0

(14)

Cyclic process:

240

The cyclic process is composed of multiple consecutive charging/discharging processes. Eqs.

241

(11-12) are used as the boundary conditions of molten salt during each charging process, while Eqs.

242

(13-14) are the boundary conditions of molten salt during each discharging process.

243

The boundary condition for PCM capsules at each position is listed as below:

244 245

kp



 hs ( T l  T p

 dp /2

)

(15)

where hs is the convective heat transfer coefficient at the capsule surface and can be expressed as [26]:

246 247

 Tp

hs  h v / (6(1   ) / d p )

(16)

Initial conditions.

248

Initially, it is assumed that the storage tank is fully charged with thermal energy for the single

249

discharging process, and the molten salt and the packed PCM capsules have the same hot temperature

10 Page 10 of 29

250

of

251

discharged, and the molten salt and the PCM capsules have the same cold temperature of

252

the cyclic process, initially it is assumed that the molten salt and the PCM capsules have the same cold

253

temperature of

254

increases to exceed a threshold value

255

charging rate becomes very low. And thus the charging process is stopped when the molten-salt outlet

256

temperature gets to

257

the charging process is stopped is used as the initial conditions of the consecutive discharging process.

258

On the other hand, when the molten-salt outlet temperature drops below a threshold value

259

Tdischarge,cut - off

260

molten salt may fail to generate useful steam for power generation effectively. The discharging process

261

is stopped when the molten-salt temperature gets to

262

molten salt and PCM capsules when the discharging process is stopped is used as the initial conditions

263

of the consecutive charging process. The threshold values for the charging and discharging processes

264

are restrained by the operation of a CSP plant. In the present study, the threshold values are set as

265

Tcharge,cut-off = Tin,low +  T

266

analyzed.

Tin , h ig h .

At the beginning of the single charging process, it is assumed that the storage tank is fully

Tin ,lo w

Tin ,lo w

. For

, and the charging process starts first. When the molten-salt outlet temperature

T ch arg e,cu t-o ff

T ch arg e,cu t-o ff

, most of the PCM capsules are fully charged and the

. The corresponding temperature of molten salt and PCM capsules when

during the discharging process, the discharging rate becomes very low and the discharged

and

T discharge,cut-off  Tin, high   T

Tdischarge,cut - off

, and the corresponding temperature of

, and the effect of  T on the cyclic performance is

267 268

2.4 Numerical method

269

The same numerical method which has been described in detail in Ref. [26] has been used.

270

Briefly, the above described equations are discretized using the finite volume method and solved with

271

the SIMPLER (Semi-Implicit Method for Pressure-Linked Equations Revised) algorithm. During

272

each iteration, after updating the molten-salt temperature (Tl) from Eq. (3), the temperature of PCM

273

capsule (Tp) corresponding to each grid is iteratively computed using the Temperature-Transforming

274

method proposed by Cao and Faghri [30]. The transformation form of the governing equation of PCM 11 Page 11 of 29

275

capsules (Eq. (4)) can be referred to Ref. [26]. The grid and time-step independences have also been

276

validated, and the used convergence criteria at each time step are that the residuals for all variables

277

drop below 10-4. The above-described model for the single discharging process of System NC has been

278

validated in Ref. [26] based on a packed-bed storage tank using paraffin wax as the PCM capsules.

279

The following analysis are based on a hypothetical 50 MWht molten-salt TES tank filled with

280

spherical PCM capsules, the geometric parameters of which are summarized in Table 1. The total

281

storage capacity of 50 MWht is the sum of the sensible heat of both the HTF and the PCM capsules

282

with the temperature range of 290 to 390 oC and the latent heat of PCM capsules. Several parameters

283

are defined to evaluate the effectiveness of the various working processes. For the single charging

284

process, the accumulated charging ratio which is defined as the ratio of the amount of heat storage to

285

the total storable energy provided by the hot molten salt is expressed as:

286

 charge  1 

 

t 0

t 0

m c p,l (T l, x  0  290 C ) dt o

m c p,l (390 C  290 C ) dt o

o

(17)

287

While for the single discharging process, the accumulated discharging ratio which is defined as the

288

ratio of the useful discharged energy from the TES tank to the total energy initially stored in the

289

TES tank is expressed as:  d isch arg e 

290 291 292 293 294



t 0

m c p ,l (3 9 0

o

C  T l, x  H ) d t

T o tal en erg y in itially sto red in th e T E S tan k

(18)

For the cyclic process, accumulated input storable energy ( Q in ) and the accumulated charging energy ( Q charge ) within each charging process are defined as: Q in 



tc 0

m c p,l (390 C  290 C ) dt

Q charge  Q in 

o



tc 0

o

m c p,l (Tl, x  0  290 C ) dt o

(19) (20)

12 Page 12 of 29

295

where t c is the consumed time at each charging process when the molten-salt outlet temperature

296

reaches to the threshold value

297

discharging process is expressed as:

298

T ch arg e,cu t-o ff

Q dis charge 



. While the accumulated discharging energy within each

td 0

m c p,l (390 C  T l, x  H ) dt o

(21)

299

where t d is the consumed time at each discharging process when the molten-salt outlet temperature

300

reaches to the threshold value

301

cycle is defined as:

Tdis charge,cut-off

302

. The accumulated efficiency for each charging/discharging

 cycle  Q d is ch arg e / Q in

(22)

303 304

3. Results and discussion

305

3.1 Single discharging behavior

306

The single discharging processes of the three TES systems are investigated in this section. Each

307

tank is assumed to be fully charged at the beginning, and during the discharging process cold molten

308

salt with a temperature of 290 oC is continuously pumped into the tank through the bottom port. Let’s

309

first analyze the variations of the capsule temperature during the discharging process. Fig. 2 shows the

310

distributions of the capsule centre temperature along the tank height at various discharging time of 1 h,

311

3 h, and 5 h. As shown for System NC, generally five different regions can be identified, i.e., low

312

temperature region, below-PCT thermocline region, quasi-isothermal region, above-PCT thermocline

313

region, and high temperature region. This behavior has already been reported in our prior work [26].

314

Only one quasi-isothermal region exists for System NC and it moves upward with the discharging

315

time. However, multiple quasi-isothermal regions can be found for systems with cascaded PCM

316

capsules. For instance, 3 and 5 quasi-isothermal regions can be identified for System C3 and System

317

C5, respectively. These multiple quasi-isothermal regions obviously result from the cascaded PCTs.

13 Page 13 of 29

318

On the other hand, the capsule centre temperatures for System C3 and System C5 do not always

319

keep increasing or stable along the tank height, which is different from that for System NC. For

320

example, 5 quasi-isothermal regions still exist for System C5 at 5 h, while between neighboring

321

quasi-isothermal regions concave distribution occurs for the capsule centre temperature. This is

322

because during the discharging process in each layer that has a uniform PCT, the capsule centre

323

temperature drops quickly after it is fully solidified while it remains at the PCT before it is melted, as

324

can be seen in Fig. 3. For the region covered by the capsules that are fully solidified, the capsule centre

325

temperature becomes close to the capsule surface temperature, and there is little difference between the

326

capsule surface temperature and molten-salt temperature indicating negligible heat transfer. While for

327

the region covered by the capsules that are not fully solidified, the capsule centre temperature remains

328

at the PCT and there is evident difference between the capsule surface temperature and molten-salt

329

temperature indicating normal heat discharge. As a result, the region covered by the capsules that are

330

fully solidified always expands from the tank bottom to the top during the discharging process for the

331

system with non-cascaded PCM capsules, while for the systems with cascaded PCM capsules there can

332

exist an expanding region that is covered by fully solidified capsules in each layer that has a uniform

333

PCT.

334 335

The solidification process of PCM capsules during the discharging process can be further

336

investigated by inspecting the changes of the capsule temperature. Fig. 4 shows the variations in the

337

centre temperature of the middle capsule at x=0.5 H with the discharging time for the three TES

338

systems. The capsule centre temperature for System NC shows four different periods before

339

completely discharging the stored heat: high temperature period before discharging, the first

340

temperature-dropping period during which only sensible heat in the liquid PCM is discharged,

341

isothermal phase change period during which latent heat is discharged, the second temperature

342

dropping period during which only sensible heat in the solid PCM is discharged. This behavior has also

343

been revealed in Ref. [26].

14 Page 14 of 29

344

A similar trend can be found for the systems with cascaded PCM capsules. The main difference is

345

that during the period of discharging sensible heat in the solid PCM, the capsule centre temperature for

346

the systems with cascaded PCM capsules first drops sharply and then it decreases slowly (for System

347

C5) or much slightly (for System C3) for quite a long time, after which it drops slowly to 290 oC. This

348

is caused by the fact that during that period the molten-salt temperature at x=0.5 H already drops to 290

349

o

350

temperature difference between the PCM capsule and molten salt, which can be seen in Fig. 5.

C for System NC, while it is above 290 oC for System C3 and System C5 resulting in a smaller

351

Figure 5 shows the molten-salt temperature distributions along the tank height at the discharging

352

time of 1 h, 3 h and 5 h. The quasi-isothermal region during which the molten-salt temperature is very

353

close to the PCT of PCM capsules can be found for all the systems. However, only one

354

quasi-isothermal region can be found for System NC, while 3 and 5 quasi-isothermal regions can be

355

identified for System C3 and System C5, respectively. As a result, the systems with cascaded PCM

356

capsules show a more linear distribution of the molten-salt temperature (especially for System C5).

357

The variations in the molten-salt outlet temperature and the accumulated discharging ratio are

358

presented in Fig. 6. The three systems all show a period of constant outlet temperature near the highest

359

PCT (i.e., 375 oC) after which the molten-salt outlet temperature all drops rapidly. After the plateau, the

360

molten-salt outlet temperature drops earlier for System C3 and System C5 compared to System NC.

361

That is because for the systems with cascaded PCM capsules more PCM capsules near the tank top

362

have already been solidified during the later discharging period as can be found in Fig. 2 (c), and

363

correspondingly the molten-salt temperatures near the tank top are lower. The molten-salt outlet

364

temperatures drop earlier after the plateau for System C3 than System C5, which is caused by that the

365

average PCT for System C5 is larger than that of System C3. When the molten-salt outlet temperature

366

drops below a threshold value, the discharged molten salt may fail to effectively generate useful steam

367

for power generation and the discharging process should be stopped, which means that in practical

368

applications the TES systems will not be fully discharged and the storage capacity of the TES system

369

may not be fully utilized. As a result, the operational storage capacity of the TES system depends on 15 Page 15 of 29

370

the discharging behavior. The above findings in Fig. 6 indicate that for TES systems with cascaded

371

PCM capsules, the chosen PCTs and system geometric parameters should be optimized to improve the

372

discharging process.

373 374

3.2 Single charging behavior

375

The charging characteristics of the three TES systems are discussed in the following section. Each

376

tank is assumed to be fully discharged at the beginning. At that condition all PCM capsules are at solid

377

state. During the charging process hot molten salt with a temperature of 390 oC enters the tank

378

continuously through the top port and flows downward through the void space in the storage tank. Fig.

379

7 shows the distributions of capsule centre temperature along the tank height at various charging time

380

of 1 h, 3 h, and 5 h. It can be seen that the centre temperature of capsules near the inlet of the hot

381

molten salt increases first, and the centre temperature of more capsules in the downstream region is

382

increased with the charging time. Isothermal regions which correspond to the melting process of PCM

383

capsules can also be found during the charging process. Only one isothermal region exists for System

384

NC and it can cover quite a long region. However, multiple isothermal regions can be found for

385

systems with cascaded PCM capsules, and the temperature of the isothermal regions corresponds to the

386

cascaded-PCTs of PCM capsules in the systems.

387

It can also be found that the PCM melting time for the systems with cascaded PCM capsules is

388

generally shorter than that for the system with uniform PCM capsules. For instance, most of PCM

389

capsules for System C3 and System C5 have been completely melted at 5 h while only PCM capsules

390

in the region between 12 to 14 m have been completely melted for System NC. That is caused by the

391

fact that the temperature difference between molten salt and the PCM capsules is lower for System NC

392

than those of System C3 and System C5.

393

To further investigate the melting process of PCM capsules during the charging process, the

394

variations in the centre temperature of the middle capsule at x=0.5H with the charging time for the

395

three TES systems which are shown in Fig. 8 are examined. From Fig. 8 an isothermal period during 16 Page 16 of 29

396

which the temperature is very close to the PCT of the middle capsule can be found for the three TES

397

systems. The isothermal period is from about 3 h to 13.4 h for System NC, while it is from 1.5 h to 3.5

398

h and from 1.5 h to 4.4 h for System C3 and System C5, respectively. This clearly demonstrates that

399

the middle capsules can be melted much faster in the systems with cascaded PCM capsules.

400 401

Figure 9 shows the molten-salt temperature distributions along the tank height at the charging time

402

of 1 h, 3 h and 5 h. The variations in the molten-salt temperature along the flow direction behave

403

differently for the three TES systems. It increases faster for System NC than for the systems with

404

cascaded PCM capsules, and the increment for System C5 is the slowest. For example, the molten-salt

405

temperature for System NC becomes as high as about 375 oC from the tank height of 11.5 m to 1 m at 3

406

h, while it steps down from about 375 oC to 305 oC for the same tank region for System C3 and System

407

C5. That is obviously because the melting processes of capsules with lower PCTs in the cascaded

408

systems drops down the temperature of flowing molten salt undergoing heat transfer with the PCM

409

capsules.

410

The variations in the molten-salt outlet temperature and the accumulated charging ratio with time

411

are presented in Fig. 10. After a short period (about 1 h) of flowing out of low temperature molten salt

412

at 290 oC, the molten-salt outlet temperature for System NC increases rapidly to about 375 oC and

413

maintains at that temperature for quite a long time (from 3 to 22 h). However, the accumulated

414

charging ratio for System NC decreases significantly. When the molten-salt outlet temperature reaches

415

380 oC, the charging process takes 23.6 h and the charged ratio is only about 23%. This indicates that

416

the charging rate for the TES system with non-cascaded PCM capsules is very slow, which is possibly

417

due to that the uniform PCT is high and thus the heat transfer rate from the molten salt to the PCM

418

capsules is low.

419 420

Contrarily, for the systems with cascaded PCM capsules, the molten-salt outlet temperature firstly

421

climbs to about 305 oC, which is close to the PCT of the capsules near the outlet, and maintains at that 17 Page 17 of 29

422

temperature for less than three hours. It then increases rapidly to 375 oC after the isothermal period,

423

and dwells at that temperature for a short period before increasing rapidly again. When the molten-salt

424

outlet temperature reaches 380 oC, the charging time takes 8.6 h and the accumulated charging ratio is

425

about 59% for System C3, while the charging time takes only 5.6 h and the accumulated charging ratio

426

is about 77% for System C5. In other word, after charging the systems for the same time of 5.6 h, the

427

accumulated charging ratio is only 40% for System NC, while it is about 70% and 77% for System C3

428

and System C5, respectively.

429

As has been found in our prior work [26], the TES system with non-cascaded PCM capsules must

430

have a high PCT which is above the interest of application. However, Fig. 10 clearly shows that

431

System NC with a high PCT suffers from a low charging rate and a long charging time, meaning the

432

system with non-cascaded PCM capsules may be inappropriate to be used as TES systems utilizing

433

liquid as the HTF. From the above results, the systems with cascaded PCM capsules, especially System

434

C5, show both a fast discharging rate and a fast charging rate, and thus they are very promising to be

435

used as the compact TES system using liquid as the HTF.

436 437 438

3.3 Cyclic behavior Since System C5 shows the best performance considering both the charging and discharging of 25 oC and 50 oC.

439

behaviors, the cyclic behavior is investigated only for System C5 with different

440

As thus, the threshold values are

441

charging processes, respectively, when

442

discharging and charging processes when

443

temperature along the tank height at the end of some charging/discharging processes during the cyclic

444

process for

445

 T  25  C ,

446

and it increases from about 315 to 390 oC with a roughly five ladder-like distribution along the tank

Tdischarge,cut-off  365 C o

 T  25  C

 T  25 C o

Tcharge,cut-off  315 C

T

o

and

for the discharging and

. While the threshold values are both 340 oC for the

 T  50 C o

. Fig. 11 shows the distributions of molten-salt

(Fig. 11a) and  T  50  C (Fig. 11b). For the cycle process with

not all the molten-salt temperature reaches 390 oC at the end of the first charging process,

18 Page 18 of 29

447

height. While at the end of the first discharging process, the molten-salt temperature increases from

448

290 to 365 oC with a roughly five-ladder like distribution along the tank height. With the increase in

449

the cycle number, the molten-salt temperature at the end of each charging process decreases and it

450

tends to a fixed distribution. While for the temperature at the end of each discharging process, it

451

increases with the increase in the cycle number and also tends to a fixed distribution. It is seen that the

452

molten-salt temperature distributions for the 9th cycle are nearly the same with that for the 25th cycle,

453

indicating that the cycle process reaches to a repeatable state after 9 cycles. A similar trend can also be

454

found for the cycle process with

455

only after 3 cycles, which indicates that the required cycle number needed to reach to a repeatable

456

cycle is influenced by the threshold temperature to stop the charging/discharging process.

457

 T  50  C .

However, the cycle process reaches to a repeatable state

Figure 12 shows the variations in the molten-salt outlet temperature with the time during some

458

charging/discharging processes for

459

process with

 T  25  C

(Fig. 12a) and  T  50  C (Fig. 12b). For the cycle

 T  25  C , the molten-salt outlet temperature keeps at the low temperature of 290

o

C for

460 461 462

a short period of about 1 h, after which it increases to about 305 oC and maintains at that temperature

463

during most of the first charging time. The first hour’s charge with the molten-salt outlet temperature

464

of 290 oC during the first charging process is caused by the fact that the whole system is assumed to

465

have the temperature of 290 oC initially. For the subsequent charging processes, the period during

466

which the molten-salt outlet temperature keeps at 290 oC shrinks to be very small, and the temperature

467

starts to increase soon after the start of each charging process. On the other hand, the period during

468

which the molten-salt temperature maintains at about 305 oC decreases slightly with the increase in the

469

cycle number when the cycle number is smaller than 9. The molten-salt outlet temperature shows an

470

isothermal discharging period with the temperature of about 375 oC for each discharging process, and

471

the isothermal period decreases from about 2.7 h to 1.4 h when the cycle number increases from 1 to 9.

19 Page 19 of 29

472

After 9 cycles, the variations in the molten-salt outlet temperature with the time for both the charging

473

process and the discharging process become repeatable. The cycle process with

474

shows a similar phenomenon, and the variations become repeatable only after 3 cycles.

 T  50  C

also

475 476

Figure 13 shows the variations in the accumulated energy and the accumulated efficiency with the  T  25  C , Q in , Q charge

477

cycle number. For the cyclic process with

478

increase in the cycle number, and become stable when the cycle number is larger than 9. This is

479

because as discussed in Figs 11a and 11a the cyclic process reaches to a repeatable state after 9 cycles.

480

It is also seen that the corresponding accumulated efficiency increases from about 81% to 93% when

481

the cycle number is increased from 1 to 27. The limiting accumulated efficiency can be determined to

482

be

483

should be caused by the fact that some molten salt exiting from the system has a temperature above

484

290 oC during each charging process, meaning the input thermal energy has not be fully stored. For the

485

cyclic process with

486

since the cycle process reaches to a repeatable state at that time. The corresponding accumulated

487

efficiency increases from about 88.5% to 92.6% when the cycle number increases from 1 to 27, and the

488

limiting accumulated efficiency is calculated to be

489

be concluded that a high accumulated efficiency can be achieved by the TES system filled with

490

cascaded PCM capsules, and the efficiency will be slightly lowered when increasing the threshold

491

temperature to stop the charging process.

492

Q discharge / Q in  95.1%

using the stable values of

 T  50  C ,

Q in , Q charge

Q discharge

and

Q discharge

and

Q in .

and

Q discharge all

decreases with the

The efficiency loss of about 4.9%

all decreases to stable values after 3 cycles,

Q discharge / Q in  92.8%

. Therefore, from Fig. 13 it can

On the other hand, when the cyclic process reaches to a repeatable state the useful discharged  T  25  C and  T  50  C ,

493

energy ( Q discharge ) is 82 GJ and 152 GJ for the cyclic processes with

494

respectively, which take up only 45.5% and 84.4% of the maximum storage capacity of the system (50

495

MWh=180GJ). This is mainly because during the cyclic process the system is not fully

496

charged/discharged at each charging/discharging process. Generally, increasing

T

is beneficial to

20 Page 20 of 29

497

enlarge the practical storage capacity of the TES system with cascaded PCM capsules. When designing

498

such a TES system, the influence of the threshold temperature on the practical storage capacity, which

499

is smaller than the total storable capacity, has to be considered. And a larger system may be necessary

500

to achieve the required storage capacity.

501 502 503

4. Conclusions

504

We have presented a transient, one-dimensional dispersion-concentric (D-C) model to numerically

505

investigate the dynamic behaviors for the charging/discharging cyclic processes of the molten-salt

506

packed-bed TES system filled with high-temperature PCM capsules. Three different storage systems

507

including the non-cascaded system, the 3-cascaded system and the 5-cascaded system have been

508

studied using various working modes. Salient findings of the present work include:

509

(a) The characteristics of heat transfer for cascaded systems are more complicated than the

510

non-cascaded system. Multiple isothermal regions for the temperatures of PCM capsules and

511

molten salt exist during both the charging and discharging processes of the cascaded systems. As a

512

result, the molten-salt temperature along the tank height for the cascaded systems shows more

513

linear distributions during both the charging and the discharging processes.

514

(b) The packed-bed system with non-cascaded PCM capsules may be inappropriate to be used as

515

TES systems because it suffers from a low charging ratio and a long charging time due to the

516

constrains of PCT. While the cascaded systems especially with 5 cascaded PCTs are very

517

promising since they show both a fast discharging rate and a fast charging rate.

518

(c) The cyclic process of the cascaded system with 5 PCTs can reach to a repeatable state after some

519

cycles, at which high accumulated efficiencies can be achieved. The required cycle number to

520

get to the equilibrium, the satisfied accumulated efficiencies and the practical storage capacity

521

all depend highly on the threshold temperatures to stop the charging/discharging process.

522 523 21 Page 21 of 29

524

ACKNOWLEDGMENT

525 526

This work is supported by the National Natural Science Foundation of China (51522602), and the National Key Basic Research Program of China (973 Program) (2013CB228304).

527 528 529

Nomenclature CF

inertial coefficient

cp

specific heat capacity, J kg-1 K-1

dp

spherical capsule diameter, m

g

acceleration due to gravity, m s-2

H

Tank height, m

hp

enthalpy of PCM, J kg-1

hs

heat transfer coefficient at the capsule surface, W m-2 K-1

hv

volumetric interstitial heat transfer coefficient, W m-3 K-1

K

intrinsic permeability of porous medium, m2

k

Thermal conductivity, W m-1 K-1

m

mass flow rate, kg s-1

Nu

Nusselt number

p

pressure, Pa

Pr

Prandtl number

Q

energy, J

Ra

Rayleigh number

Re

Reynolds number

T

temperature, K

22 Page 22 of 29

t

time, s consumed time during charging processes when the HTF outlet

tc temperature reaches to the threshold value consumed time during discharging processes when the HTF outlet td temperature reaches to the threshold value u

velocity, m s-1

V

tank volume, m3

x

location along the axis of the tank, m

Greek 

thermal diffusivity, m2 s-1



thermal expansion coefficient, K-1



Porosity of packed-bed region



Viscosity, kg m-1 s-1

r

Density, kg m-3



effective thermal conductivity, W m-1 K-1



radial coordinate inside each capsule



ratio; efficiency

Subscripts charge

value for the charging process

cut-off

threshold value

discharge

value for the discharging process

eff

effective value

high

high temperature

in

inlet; input

23 Page 23 of 29

l

molten salt

low

low temperature

ms

molten salt

n

natural convection

p

PCM

R

radius

tank

storage tank

530 531 532

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533

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611 612 613 614 615 616 617 618 619 620

Figurer caption

621 622

Fig. 1. Schematic of the molten-salt packed-bed TES systems using spherical PCM capsules: (a)

623

System NC, (b) System C3, and (c) System C5. (only color on the web)

27 Page 27 of 29

624

Fig. 2. Distributions of the capsule centre temperature along the tank height at different discharging

625

time: (a) 1 h, (b) 3 h, (c) 5 h. (only color on the web)

626

Fig. 3. Distributions of temperature of capsule centre, capsule surface and molten salt along the tank

627

height at discharging time of 5 h for System NC and System C5. (only color on the web)

628

Fig. 4. Variations in the centre temperature of the middle capsule (x=0.5 H) with the discharging time.

629

(only color on the web)

630

Fig. 5. Distributions of the molten-salt temperature along the tank height at different discharging time:

631

(a) 1 h, (b) 3 h, (c) 5 h. (only color on the web)

632

Fig. 6. Variations in the molten-salt outlet temperature and the accumulated discharging ratio with the

633

discharging time. (only color on the web)

634

Fig. 7. Distributions of the capsule centre temperature along the tank height at different charging time:

635

(a) 1 h, (b) 3 h, (c) 5 h. (only color on the web)

636

Fig. 8. Variations in the centre temperature of the middle capsule (x=0.5 H) with the charging time.

637

(only color on the web)

638

Fig. 9. Distributions of the molten-salt temperature along the tank height at different charging time: (a)

639

1 h, (b) 3 h, (c) 5 h. (only color on the web)

640

Fig. 10. Variations in the molten-salt outlet temperature and the accumulated charging ratio with the

641

charging time. (only color on the web)

642

Fig. 11. Distributions of molten-salt temperature along the tank height at the end of some  T  25  C

 T  50  C (b).

643

charging/discharging processes during the cyclic process for

644

(only color on the web)

645

Fig. 12. Variations in the molten-salt outlet temperature with the time during some  T  25  C

(a) and

(a) and

 T  50  C (b).

646

charging/discharging processes within the cyclic process for

647

(only color on the web)

648

Fig. 13. Variations in the accumulated input storable energy, the accumulated charging energy, the

649

accumulated discharging energy and the accumulated efficiency with the cycle number. (only color on

650

the web)

651 652 653 654 655

Table 1 Geometric parameters and properties used in the model.

28 Page 28 of 29

Parameters

Values

Tank height, m Tank radius, m

14.0 2.45

Diameter of PCM capsule, m

0.04

Porosity

0.25 o

Tank initial temperature before charging, C

290 o

Tank initial temperature before discharging, C

390

-3

Density of PCM, kg m

2110 -1

Specific heat capacity of solid PCM, J kg K

-1 -1

1220

-1

-1

0.5

Specific heat capacity of liquid PCM, J kg K

Thermal conductivity of solid PCM, W m K -1

Thermal conductivity of liquid PCM, W m K PCM latent heat of fusion, kJ kg

1220

-1

-1

226

Thermal expansion coefficient of liquid PCM, K Dynamic viscosity of liquid PCM, Pa s Absolute inlet velocity, m s

0.5

-1

-1

-1

0.001 2.59e-3 1.85e-3

Time step, s

0.01

656 657

29 Page 29 of 29