Effects of PCM arrangement and natural convection on charging and discharging performance of shell-and-tube LHS unit

International Journal of Heat and Mass Transfer 115 (2017) 99–107

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Effects of PCM arrangement and natural convection on charging and discharging performance of shell-and-tube LHS unit Y.B. Tao ⇑, Y.K. Liu, Ya-Ling He Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049. China

a r t i c l e

i n f o

Article history: Received 1 April 2017 Received in revised form 14 June 2017 Accepted 21 July 2017

Keywords: Latent heat storage Performance enhancement PCM arrangement Natural convection

a b s t r a c t The low thermal conductivity of phase change material (PCM) seriously weakens the heat charging and discharging rates of latent heat storage (LHS) system. High efficient performance enhancement method is urgently needed. In present study, three-dimensional simulation models with and without natural convection were established for a shell-and-tube LHS unit to investigate the effects of PCM arrangements and natural convection on the charging and discharging performance. The results show that compared ot the commonly used shell-and-tube LHS unit with PCM in shell side, the LHS unit with PCM in tube side can significantly enhance heat storage rate under the same working conditions and overall dimensions. Natural convection has significant effects on charging performance, espeically when PCM is arranged in tube side. When natural convection is neglected, PCM melting time can be reduced by 25.4% and latent heat storage rate can be enhanced by 36.6% with PCM arranged in tube side. When natural convection is considered, PCM melting time can be reduced by 34.4% and latent heat storage rate can be enhanced by 54.2% with PCM arranged in tube side. However, natural convection has little effects on discharging performance even if for the model with PCM in tube side. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction With the developments of renewable energy and industrial waste heat recovery technologies, thermal energy storage (TES) is more and more important to ensure the energy system operation with high efficiency and stability. Generally speaking, there are three kinds of TES technologies, including sensible heat storage (SHS), latent heat storage (LHS) and thermochemical heat storage (TCHS). Where, LHS system uses PCM as thermal energy storage medium, thermal energy is stored or released during PCM melted from solid to liquid or solidified from liquid to solid. Comparing to SHS system, LHS has larger energy storage density and smaller temperature variation. Comparing to TCHS system, LHS has excellent repeatability and controllability. LHS has been considered as the most promising TES method in the present stage. Trp [1] experimentally and numerically investigated the performance of paraffin melting and solidification in a shell-and-tube LHS unit with PCM in shell side. The effects of heat transfer fluid (HTF) working conditions and geometric parameters on LHS performance were investigated. Wang et al. [2] experimentally studied the thermal behavior and heat transfer performance of a

⇑ Corresponding author. E-mail address: [email protected] (Y.B. Tao). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.07.098 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

vertical shell-and-tube latent heat thermal storage unit with erythritol as storage media and air as HTF. The effects of the natural convection, HTF inlet temperature and mass flow rate were examined. Adine and Qarnia [3] numerically studied the LHS performance of a shell-and-tube LHS unit filled with P116 and n-octadecane. The impact of HTF inlet temperature, HTF mass flow and the proportion mass of PCMs on the thermal performances of the latent heat storage units were revealed. The above studies mostly focused on the effects of working conditions on LHS performance. However, the PCM’s low thermal conductivity seriously weakens the thermal energy charging and discharging rates. In order to improve the thermal performance of LHS system, a lot of researches on performance enhancement have been carried out. The mostly used performance enhancement methods for LHS can be classified into two categories: enhancing PCM thermal conductivity and changing LHS unit structure. However, both of them are either complicated to applications or have some negative impacts on the comprehensive thermal performance. High thermal conductivity porous media (e.g., metal foams and expanded graphite) was commonly used to enhance PCM thermal conductivity. The available results show that the adding of porous media can enhance PCM thermal conductivity up to dozens of times [4–6], which is benefit to improve the thermal performance

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Nomenclature cp d f g Henthalpy h k L _ m Pr r Ri Ro Re T Tm t tm V w

specific heat, J kg
1 K
1 inner diameter of the tube, m liquid fraction gravitational acceleration, ms
2 enthalpy of the PCM, kJ kg
1 heat transfer coefficient, Wm
2 K
1 thermal conductivity, Wm
1 K
1 length of the PCM unit, m mass flow rate, kg s
1 Prandtl number radial coordinate, m inner radius of the inner tube, m inner radius of the out tube, m Reynolds number temperature, K PCM melting temperature, K time, min melting time of PCM, min velocity of liquid PCM, ms
1 heat transfer fluid velocity, ms
1

of LHS system [7,8]. However, the existing of metal foams severely restricts the natural convection of liquid PCM, which causes complex effects on total thermal performance of LHS system. Also it will reduce the PCM volume and the total thermal storage capapcity. Tao et al. [9] numerically investigated the LHS performance of copper metal foams/paraffin CPCM with lattice Boltzmann method. The results show that the CPCM heat transfer performance is determined by both heat conduction and natural convection. The geometric parameters of metal foams have great effects on heat transfer performance, e.g., increasing pore density can enhance heat conduction, but weaken natural convection. Xu et al. [10] performed numerical study on a shell-and-tube LHS unit with partial filled porous media and also found that pore size and porosity of metal foams have great effects on LHS performance. Kumar and Saha[11] performed energy and exergy analyses of LHS system with high porosity metal matrix. The restuls show the charging, discharging and overall efficiency are increased with decreasing porosity, but the effects of pore diameter are marginal. Zhao et al. [12] numerically studied the solid-liquid phase change in open-cell metal foams and found that Rayleigh number, porosity and pore density have great influence on the solid-liquid phase change. Bahraseman et al. [13] experimentally investigated the charging performance of expanded graphite/paraffin CPCM. The results show that the response rate to charging can be enhance 7 times with about 30% energy storage reduction as the penalty. There must be a sweet spot where response rate improvement and energy storage reduction are at their optimum condition for a particular application. High conductivity nanomaterial (e.g., carbon nanotubes and metal oxide nanoparticles) is also used to enhance PCM thermal conductivity. The available results show that the nanomaterial additives can enhance PCM thermal conductivity up to 1.2 times [14–18] and improve the LHS thermal performance [19], but the enhancement effect greatly depends on the mass fraction and dispersion of nanomaterials. With small mass fraction, the enhancement effect is weak; with high mass fraction, the dspersion of nanomaterial is worse and it will restrict the natural convection of liquid PCM and reduce PCM volume. Li et al. [20] prepared three CPCMs with stearic acid and different carbon additives (MWCNTs, graphene, graphite). The experimental results indicate that the addition of carbon additives can improve the heat conduction of

z

axial coordinate, m

Greek symbols b thermal expansion coefficient, K
1 h circumferential coordinate, m l dynamic viscosity, Pa s q density, kg m
3 DH melting enthalpy, kJ kg
1 U heat flux, W Subscripts f heat transfer fluid i initial state in inlet boundary l liquid out outlet boundary p phase change material s solid r,z,h r, z, h-direction

stearic acid effectively, but it also weakens the natural convection of stearic acid in liquid state. Tao et al. [21] experimentally investigated the effects of nanomaterial dispersion and surface active agent (SAA) on thermal performance of carbonate salt/MWCNTs CPCM. The results show that the dispersion of nanomaterial in PCM has great influence on the CPCM thermal performance and the effect of SAA on CPCM thermal performance has duality: on the positive side, SAA can improve nanomaterial dispersion and enhance CPCM thermal performance; on the negative side, SAA and its decomposition products may weaken CPCM thermal performance. A compound porous-foam/nanoparticles enhancement technique was used to improve melting of a PCM in a triplextube by Mahdi and Nsofor [22]. Results show that the metal foam porosity and nanoparticle volume fraction should be proper selection to have a good contribution by both conduction and convection heat transfers and also to ensure minimal PCM volume reduction. Improving the structure of LHS unit is another commonly used method to enhance the LHS performance, such as using finned tubes and cascaded LHS technology. Although the fins can efficiently enhance PCM melting rate [23], it also restricts natural convection and reduces PCM volume. Tao and He [24] numerically investigated the effects of liquid PCM natural convection on performance of a shell-and-tube LHS unit. Based on the results, a local enhanced fin tube was designed, the dimension optimization results show the fin dimensions should be appropriately selected to achieve better performance. Mahdi and Nsofor [25] investigated the melting enhancement of PCM in triplex-tube LHS system with nanoparticles-fins combination. The resutls show that a much better improvement can be achieved by employing fins alone for the same volume usage. But the fin dimensions should be properly selected to ensure good performance within minimal PCM volume reduction. Shinde et al. [26] examined the solidification performance of shell and tube heat exchanger-based LHS with and without fin. The effect of geometrical parameters of fin, such as fin thickness, fin height, and number of fin on the thermal performance of LHS was studied. The results show the fin thickness and fin number play significant role on the solidification process of PCM. With the cascaded LHS technology, the uniform heat transfer temperature difference between HTF and PCM can be achieved,

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but the selection and arrangemnt of PCM have directly influence on the comprehensive performance. Fang and Chen [27] numerically investigated the performance of a shell-and-tube LHS unit using multiple PCMs and found that PCMs’ fractions and melting temperatures play important roles in the performance of the LHS unit. Appropriate choosing of multiple PCMs is very significant for the performance improvement. Tao et al. [28] numerically analyzed the effects of PCM melting temperatures on the LHS performance of a two-stage cascaded LHS unit. The optimization for the match of two-stage PCMs melting temperatures was performed based on the entransy theory. The results show that there is an optimal match of the two-stage PCMs melting temperatures to achieve the maximum heat transfer rate or the minimum entransy dissipation rate. And the formulas for the optimum two-stage PCMs temperatures were presented. Xu and Zhao [29,30] performed optimization for a cascaded LHS system with steady and unsteady HTF inlet temperature. The correlations for optimum PCM phase change temperature were derived, which are benificial for PCM selection. A compound enhancement method to improve the LHS performance of a shell-and-tube LHS unit was proposed by Tao and He [31,32], which consists of internal enhanced tube (ET) and multiple PCMs. A comparative study on the LHS performances with smooth tube (ST), simple enhancement method (ET), and the compound enhancement method (ET & multiple PCMs) were performed. The results show that the compound enhancement method can further reduce the PCM melting time and total charging time compared with simple enhancement method. However, the enhancement effect is greatly depended on the selected PCM thermal properties. After that, Tao and Carey [33] systematically investigated the effects of PCM thermal properties on shell-andtube LHS unit based on the orthogonal method. And the selection cretieria for PCM were established. The foregoing literature review shows that a lot of studies have been performed on the LHS performance and its enhancement. There also exists some problems in applications. For metal foams or nanomaterial CPCMs, the additives severely restrict the natural convection of liquid PCM and cause the decreasing of LHS density, furthermore it is difficult to ensure the nanomaterial fully dispersed in PCM. For finned tubes, the natural convection is also restricted and the LHS density is reduced due to the existing of fins. For cascaded LHS system, the performance greatly depends on the selected PCM thermal properties and the arrangements, it is difficult to carry out. So, a simple and efficient performance enhancement method without negative impacts is urgently needed. In present paper, in order to provide a better LHS unit structure without negative impacts, three-dimensional simulation models for a shell-and-tube LHS unit were established. Comparative studies on two PCM arrangements (with PCM in tube side and shell side respectively) were performed. And the effects of liquid PCM natural convection on charging and discharging performance were examined. A better PCM arrangement was recommended to enhance the charging and discharging performance, which has no negative impacts on comprehensive thermal performance and is easy to carry out.

2. Model description 2.1. Physical model The physical model for a horizontal shell-and-tube LHS system is shown in Fig. 1 (a), one of the LHS tube is commonly selected as the object of numerical study due to the symmetry. In most of the available shell-and-tube LHS systems, PCM is arranged in shell side and HTF flows in tube side as shown in Fig. 1(b), which is named model A in present paper. In order to reveal the effects of PCM

HTF

PCM tube wall HTF

(a) Schematic of a shell-and-tube LHS unit

r

r

z

θ

PCM (b) Model A (PCM in shell side)

PCM (c) Model B (PCM in tube side) Fig. 1. Schematic for PCM arrangements in shell-and-tube LHS unit.

arrangement on LHS performance, another LHS model with PCM in tube side and HTF flowing in shell side was designed as shown in Fig. 1(c), name model B. The geometric parameters for model A are as follows: length for the LHS unit (L) is 1.0 m, the inner radius for the inner tube (Ri) is 12.5 mm, and inner radius for the outer tube (Ro) is 25.0 mm. For model B, in order to keep the same amount of PCM filling with model A, the inner radius for the inner tube (Ri) is set as 21.65 mm and all the other parameters are the same as model A. The thermophysical properties for HTF and PCM are shown in Table 1 [34,35]. All the operation parameters are the same for model A and B: HTF inlet velocity is 15.0 m/s and the inlet temperature is 1090.0 K; the initial temperatures both for PCM and HTF are 823.0 K for the charging process. In order to simplify the mathematical model and save the computational time, the axial heat conduction and viscous dissipation in the HTF are neglected and the HTF flow is treated as one dimensional fluid flow. Due to the symmetry, half of the tube is chosen as the computational domain. The axial direction is z-direction which is horizontal, the radial direction is r-direction, and the circumferential direction is h-direction. 2.2. Governing equations For HTF region, one dimensional fluid flow and heat transfer model is adopted. The governing equation is shown in Eq. (1).

Table 1 Thermophysical properties of HTF and PCM. HTF (He/Xe) [34]

PCM (LiF/CaF2) [35]

kf (W/m K) qf (kg/m3)

0.133 1.862

kp (W/m K) qp (kg/m3)

3.8 2390.0

cp;f (J/kg K)

lf  106 (kg/m s)

502.2 59.82

cp;p (J/kg K) T m (K)

1770.0 1040.0

Pr

0.24

DH (kJ/kg)

816.0 1.86

lp  103 ; kg/(ms)

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_ f @T f @T f 2h m ðT f
T  Þ ¼

@t qf pR2i @z ðqcÞf pRi

ð1Þ

where T f is the HTF temperature and T  is the average PCM temperature at inner tube surface and the last time layer; h is the forced convection heat transfer coefficient of HTF, h ¼ dk 0:022Pr 0:6 Re0:8 . For PCM region, a three dimensional model is used to investigate the effects of natural convection on LHS performance. And the governing equations are as follows. Continuity equation

@ q 1 @ðrqV r Þ 1 @ðqV h Þ @ðqV z Þ þ þ ¼0 þ @r r @h @z @t r

ð2Þ

Momentum equations for the liquid PCM region




! @V h VrVh 1 @p 2 @V r V h þ m r2 V h þ 2 þ ðV rÞV h þ ¼ gh

2 r @h @t r qr @h r

ð4Þ

@V z 1 @p þ mðr2 V z Þ þ ðV rÞV z ¼
@t q @z

ð5Þ

The energy equation (6) is formulated by the enthalpy method, where, Henthalpy ¼ cp T þ f DH. And the melting fraction is determined as,

ð7Þ

The detailed process for the determination of melting fraction can be found in Ref. [3], which will not be presented here to avoid duplication.

The initial conditions are,

T f ðz; t ¼ 0Þ ¼ Tðh; r; z; t ¼ 0Þ ¼ T i : The boundary conditions for HTF region are, inlet boundary,

T f ðz ¼ 0; tÞ ¼ T f;in ; wðz ¼ 0; tÞ ¼ wf;in surface boundary between HTF and PCM,


kp

@Tðh; r ¼ Ri ; z; tÞ ¼ hðT f ðz; tÞ
Tðh; r ¼ Ri ; z; tÞÞ: @r

The boundary conditions for PCM region are: h-direction,

uðh ¼ 0; r; z; tÞ ¼ uðh ¼ p; r; z; tÞ ¼ 0; @ v ðh ¼ 0; r; z; tÞ @ v ðh ¼ p; r; z; tÞ ¼ ¼ 0; @h @h @wðh ¼ 0; r; z; tÞ @wðh ¼ p; r; z; tÞ ¼ ¼ 0; @h @h

wðh; r ¼ Ri ; z; tÞ ¼ wðh; r ¼ Ro ; z; tÞ ¼ 0;
kp

@Tðh; r ¼ Ri ; z; tÞ ¼ hðT f ðz; tÞ
Tðh; r ¼ Ri ; z; tÞÞ @r

uðh; r ¼ Ri ; z; tÞ ¼ 0;

v ðh; r ¼ Ri ; z; tÞ ¼ 0;


kp

@Tðh; r ¼ Ri ; z; tÞ ¼ hðT f ðz; tÞ
Tðh; r ¼ Ri ; z; tÞÞ @r

z-direction,

!

ð6Þ

2.3. Initial conditions and boundary conditions

v ðh; r ¼ Ri ; z; tÞ ¼ v ðh; r ¼ Ro ; z; tÞ ¼ 0;

wðh; r ¼ Ri ; z; tÞ ¼ 0;

@T u @T @T @T k 1 @ 2 T 1 @ @T @ 2 T DH @f þv þw ¼ þ þ ðr Þ þ 2
@t r @ x @r @z qcp r2 @ x2 r @r @r @z cp @t

8 f ¼ 0; T < Tm > > > < 0 < f < 1; T ¼ T m > > > : f ¼ 1; T > Tm

uðh; r ¼ Ri ; z; tÞ ¼ uðh; r ¼ Ro ; z; tÞ ¼ 0;

r-direction (for model B),


 ! @V r V2 1 @p 2 @V h V r þ m r2 V r
2 þ ðV rÞV r
h ¼ g r

2 r @h @t r q @r r

where g h ¼ gbðT
T m Þ sin h, g r ¼
gbðT
T m Þ cos h. Energy equation

r-direction (for model A),

@Tðh; r ¼ Ro ; z; tÞ ¼ 0; @r

 ð3Þ

!

@Tðh ¼ 0; r; z; tÞ @Tðh ¼ p; r; z; tÞ ¼ ¼ 0; @h @h

uðh; r; z ¼ 0tÞ ¼ uðh; r; z ¼ L; tÞ ¼ 0

v ðh; r; z ¼ 0tÞ ¼ v ðh; r; z ¼ L; tÞ ¼ 0; wðh; r; z ¼ 0tÞ ¼ wðh; r; z ¼ L; tÞ ¼ 0; @Tðh; r; z ¼ 0tÞ @Tðh; r; z ¼ L; tÞ ¼ ¼ 0: @z @z 3. Model validation Based on the above governing equations and boundary conditions, the heat transfer process between PCM and HTF can be numerically investigated. For the model with natural convection, the governing equations of Eqs. (1)–(6) should be solved integrated in the whole computational domain. When natural convection is neglected, only the Eqs. (1) and (6) need be solved. In order to validate the independencies of grid system and time step, the predicted PCM melting time are examined under different grid systems and time steps. After that, the grid number 30(h)  30 (r)  60(z) and time step 5 s are adopted. The comparison between the present numerical predictions and the experimental results [36] were performed under the same conditions to validate the reliability of the simulation code. The validation result is shown in Fig. 2. It can be seen that the predicted PCM temperatures for the two reference points are good accordant with the experimental values. The validation results prove the present physical model and simulation code are correct and reliable. 4. Results and discussions In order to investigate the PCM arrangements on LHS performance of shell-and-tube LHS unit, the comparison studies on two LHS units were performed. The operating and geometric parameters are kept the same, except that the inner tube radius changes from 12.5 mm (model A) to 21.65 mm (model B) to ensure the same amount of PCM filling. The comparison results will be presented in the following sections. And in order to reveal the effects of liquid PCM natural convection, the comparisons between the

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50

1400

45

1200

40

1000

Model A (PCM in shell side) Model B (PCM in tube side)

predicted T

800

predicted T

2

experimental T [32]

30

/W

T /°C

1

35

1

experimental T [32]

600

2

25

400

20

200

15

0

5

10

15

20

25

30

35

t /min

40

45

50

55

60

0

65

Fig. 2. Model validation results.

0

50

100

150

200

250

t /min

300

350

400

450

Fig. 4. Comparison of heat storage rate without natural convection.

simulation results obtained by numerical model with natural convection and without natural convection will also be performed.

3.0

4.1. Comparisons of charging performance without natural convection 2.5

1.0 0.9 0.8 0.7 0.6

f

0.5 0.4

Model A (PCM in shell side)

0.3

Model B (PCM in tube side)

0.2 0.1 0.0

0

50

100

150

200

t /min

250

300

350

400

Fig. 3. Comparison of PCM melting fraction without natural convection.

2.0

Q /MJ

Fig. 3 shows the variations of PCM melting fraction with time. Due to the initial PCM temperature is lower than melting temperature. At the beginning of the charging process, the melting fraction both for model A and B is zero, which means the PCM keeps in solid state and this stage is sensible heat storage stage. PCM temperature quickly increases with more and more thermal energy transferred to PCM. When PCM temperature reaches the melting temperature, the melting process begins, PCM melting fraction increases from zero to 1. This stage is latent heat storage stage. For model A with PCM in shell side, the melting process begins at t = 30 min. For model B with PCM in tube side, the PCM melting process begins at t = 15 min. Then, with the melting process ongoing, the melting fraction increase both for model A and B, but the increasing tendency of model B is larger than model A. For model A, the melting process ends at t = 355 min; for model B, the melting process ends at t = 265 min. The PCM melting time can be reduced about 25.4% with PCM arranged in tube side. This is because the heat transfer area between HTF and PCM in model B is larger than

1.5 SHS (Model A)

1.0

LHS (Model A) SHS (Model B) LHS (Model B)

0.5

0.0

0

50

100

150

200

250

t /min

300

350

400

450

Fig. 5. Comparison of latent and sensible heat storage capacity without natural convection.

that in model A, which results in the heat transfer rate of model B larger than model A as shown in Fig. 4. The comparisons for heat transfer rates are shown in Fig. 4. From the figure, it can be seen in the first sensible heat storage process, due to the larger temperature difference between HTF and PCM, the heat transfer rate is very high. And the heat transfer rate of model B is always larger that model A, which causes the melting process of model B beginning earlier than model A and PCM melting rate of model B is higher than model A, as shown in Fig. 3. The whole heat storage process ends at t = 453 min and 297 min for model A and B respectively. During the latent heat storage process, the average heat transfer rate is 170.3 W for model A and 232.6 W for model B, which means the latent heat storage rate can be enhanced by 36.6% with PCM arranged in tube side. Fig. 5 shows the comparisons of sensible and latent heat storage capacity for model A and B. The total sensible and latent heat storage capacities are the same, because the two models have the same PCM mass and working conditions. But the increasing tendencies of model B are always higher than model A, especially for the latent heat storage capacity due to the higher heat transfer rate as shown in Fig. 4. So, the model B can quickly reach the maximum heat storage capacity and reduce the heat storage time.

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1.0

0.8

0.8

0.6

0.6

f

1.0

0.4

0.4 Model A (PCM in shell side) Model B (PCM in tube side)

0.2

0.0

Model A (PCM in shell side)

0.2

Model B (PCM in tube side)

0

50

100

150

200

250

t /min

300

350

400

0.0

450

50

100

150

200

250

300

350

400

450

t /min

Fig. 6. Comparison of heat storage efficiency without natural convection.

Fig. 7. Comparison of PCM melting fraction with natural convection.

Fig. 6 shows the effects of PCM arrangements on heat storage efficiency. The definition for the heat storage efficiency is shown in equation (8).

1400 1200

ð8Þ

where Q t is the total thermal energy stored in PCM from the initial time to the present time, which includes the energy stored with sensible heat and latent heat. Q max is the maximum possible heat storage capacity. From the figure it can be seen the charging efficiency of model B is always higher than model A, which means the model B has better heat storage performance. From the above discussions, it can be concluded that with PCM arranged in tube side, both the PCM melting rate and heat storage rate can be enhanced and the total heat storage capacity are the same. The corresponding melting time can be reduced about 25.4% and the latent heat transfer rate can be enhanced 36.6%. So, model B has a better LHS efficiency. 4.2. Comparisons of charging performance with natural convection Fig. 7 shows the comparisons of PCM melting fractions for model A and B when the natural convection of liquid PCM is taken into account. The melting process ends at t = 305 min for model A and 200 min for model B, which means the PCM melting time can be reduced 34.4% with PCM arranged in tube side. Comparing to Fig. 3, it can be found that when the natural convection is considered, the enhancement of PCM melting rate of model B is more significant. For model A, the PCM melting time is reduced from 355 min to 305 min by natural convection, which is reduced only 14.1%. For model B, the PCM melting time is reduced from 265 min to 200 min by natural convection, which is reduced 24.5%. This is because the natural convection in model B is stronger than that in model A due to the larger natural convection space in model B. Fig. 8 shows the comparisons of heat storage rate for model A and B with natural convection. When the natural convection is considered, the average heat transfer rate during the latent heat storage process is 193.9 W for model A and 299.0 W for model B, which means the latent heat storage rate can be enhanced by 54.2% with PCM arranged in tube side. And compared to Fig. 4, the latent heat storage rate is enhanced only 13.9% by natural convection for model A, but it is enhanced up to 28.5% by natural con-

Model A (PCM in shell side)

1000

/W

Q e¼ t Q max

0

Model B (PCM in tube side)

800 600 400 200 0

0

50

100

150

200

250

t /min

300

350

400

450

Fig. 8. Comparison of heat storage rate with natural convection.

vection for model B. The effects of natural convection on model B is more significant than model A. Fig. 9 shows the comparisons of solid-liquid interface distributions in different cross sections along axial direction for model B with and without natural convection, where the PCM melting fraction is 0.25. When the natural convection is neglected, the solidliquid interface in circumferential direction is uniform as shown in Fig. 9(a). The PCM melting fraction decrease along the axial direction, the solid-liquid surface moves to the tube surface. When the natural convection is considered, the high temperature liquid PCM flows to the upside due to the effect of natural convection, which enhances the PCM melting rate in upside and weakens the melting rate in downside. So, the natural convection causes nonuniform distribution of solid-liquid interface as shown in Fig. 9(b).

4.3. Effects of natural convection on discharging process In order to be consistent with the charging process, during the discharging process, HTF inlet velocity is the same as the charging

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0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05

z =0.1

0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05

0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05

z =0.5

z =0.9

(a) solid-liquid interface without natural convection

0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05

0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05

z =0.1

0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05

z =0.5

z =0.9

(b) solid-liquid interface with natural convection Fig. 9. Comparison of solid-liquid surface (f = 0.25).

1.0 Model B without natural convection

0.8

Model B with natural convection

0.6

f

process, 15.0 m/s; HTF inlet temperature is set to 823.0 K. The initial temperatures both for PCM and HTF region are 1090.0 K. Fig. 10 shows comparisons of PCM liquid fraction for model B with and without natural convection during the discharging process. From the figure, it can be seen that the liquid fraction of PCM gradually decreases with time due to the solidification of liquid PCM. And the existing of natural convection can also enhance the PCM solidification rate. When natural convection is considered, the liquid fraction of PCM is always lower than that without natural convection. But, in totally, the effect of natural convection on PCM liquid fraction during the discharging process is very weak. The PCM solidification time is 70 min for the model without natural convection and 65 min for the model with natural convection. Compared to the charging process, the PCM solidification rate is higher than melting rate because the temperature difference between the HTF inlet temperature (823 K) and the PCM melting temperature (1040 K) in discharging process is higher than that in charging process. The effects of natural convection on heat transfer rate during the discharging process are shown in Fig. 11. Compared to the charging process, the high heat transfer rate stage can last for a long time, due to the large temperature difference between the HTF inlet temperature and the PCM melting temperature, which

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t /min

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Fig. 10. Effects of natural convection on PCM liquid fraction.

results in the discharging rate higher than charging rate. And it also can be seen that the effects of natural convection on discharging rate is weak compared to the charging process, as shown in Fig. 4.

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review of the manuscript entitled ‘‘Effects of PCM arrangement and natural convection on charging and discharging performance of shell-and-tube LHS unit”.

Model B without natural convection Model B with natural convection

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/W

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t /min

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Fig. 11. Effects of natural convection on heat release late.

5. Conclusion In present study, the three-dimensional simulation models with and without natural convection were established for a shell-andtube LHS unit. Comparative studies on two PCM arrangement models were performed. The effects of liquid PCM natural convection on charging and discharging performance were also examined. Based on the present work, the following conclusions can be derived. (1) Under the same operating conditions and overall dimensions, the LHS unit with PCM in tube side can enhance charging rate compared to that with PCM in shell side regardless of whether natural convection is considered. And it has no any negative impacts on heat storage capacity. (2) When natural convection is neglected, PCM melting time is reduced by 25.4% and latent heat storage rate is enhanced by 36.6% with PCM arranged in tube side. When natural convection is considered, PCM melting time is reduced by 34.4% and latent heat storage rate is enhanced by 54.2% with PCM arranged in tube side. (3) Natural convection has significant effects on charging performance, especially when PCM is arranged in tube side. The latent heat storage rate is enhanced 13.9% by natural convection for the model with PCM in shell side and 28.5% for the model with PCM in tube side. However, the effects of natural convection on discharging performance can be neglected even if for the model with PCM in tube side. (4) In practical applications, PCM should be arranged in tube side to achieve better heat storage performance and the natural convection during charging process must be taken into account.

Acknowledgments The present work is supported by the National Natural Science Foundation of China (No. 51376146). Conflict of interest statement We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. There is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the

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