Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement

Applied Energy xxx (2014) xxx–xxx

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Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement q P. Zhang a,⇑, X. Xiao a, Z.N. Meng a, M. Li b a b

Institute of Refrigeration and Cryogenics, MOE Key Laboratory of Power Machinery and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Solar Energy Research Institute, Yunnan Normal University, Kunming 650092, China

h i g h l i g h t s  Heat storage and retrieval tests in a LTES unit were studied.  Molten salt and metal foam/salt composites were used as the PCMs comparatively.  Thermal non-equilibrium model was established to describe the heat transfer characteristics.  Time-duration with composite PCM during heat retrieval process was reduced more.  Slight temperature difference existed between the metal skeleton and PCM.

a r t i c l e

i n f o

Article history: Received 5 March 2014 Received in revised form 4 September 2014 Accepted 1 October 2014 Available online xxxx Keywords: Eutectic molten salt Metal foam Heat storage/retrieval Thermal non-equilibrium Heat transfer characteristics

a b s t r a c t Eutectic molten salt can be used as the latent thermal energy storage (LTES) medium in solar energy applications. In the present study, eutectic salt (50 wt% NaNO3, 50 wt% KNO3) with a melting temperature of about 220 °C was employed as the PCM for the middle-temperature solar energy application, which can be powered by the parabolic-trough solar collector using oil as the heat transfer fluid. There are many LTES units in which the molten salt is encapsulated in the thermal energy storage tank, where the heat transfer characteristic of the LTES unit is very important for the overall performance of the entire thermal energy storage tank. We experimentally and numerically investigated the heat transfer characteristics of the molten-salt in a LTES unit with and without heat transfer enhancement. Various heating temperatures of 240 °C, 250 °C, and 260 °C and cooling temperatures of 30 °C, 70 °C, and 110 °C were employed in the study, so as to extensively reveal the heat transfer characteristics during heat storage and retrieval. It was found that natural convection was very dominant during heat storage in the case of pure molten-salt, especially when the heating temperature was higher, and it was weakened in the case of molten-salt with metal foam; while the heat retrieval process was enhanced by the presence of the metal foam. The numerical results were compared with the experimental results, showing reasonable agreement, which indicated that such numerical model could be used for the further study of the performance of the LTES system. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction With the depletion of fossil fuels and the gradual increase of the energy consumptions, a lot of greenhouse gases have been emitted into atmosphere, which results in energy crisis and global warming simultaneously. Such energy and environment issues promote the development and utilization of renewable energy. Human society has made efforts on steering energy sources toward renewable energy. Solar energy as one of the renewable energy resources q This paper is included in the Special Issue of Energy Storage edited by Prof. Anthony Roskilly, Prof. Phil Taylor and Prof. Yan. ⇑ Corresponding author. Tel.: +86 21 34205505; fax: +86 21 34206814. E-mail address: [email protected] (P. Zhang).

shows potential to alleviate the energy issues. However, its intermittent and unstable characteristics are the major drawbacks, which restrict its extensive application. Energy storage is an appropriate method to overcome this time-dependent limitation. Thus thermal energy storage systems are perceived as indispensible components in solar energy applications [1–3]. Comparing with other thermal energy storage methods, latent thermal energy storage (LTES) is a hot research topic for the advantages of high density and small temperature variations during heat storage/retrieval processes. High temperature molten salt as phase change material (PCM) has been considered effective as a thermal storage medium for solar thermal power systems, which can significantly improve the stability of the system and make solar energy utilization more

http://dx.doi.org/10.1016/j.apenergy.2014.10.004 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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Nomenclature As asf C cp D Da df dk dp e Fl g H hsf K L p Pr R Ra Re T U u v

additional term in momentum equation interfacial surface area (m1) mushy zone constant specific heat (kJ/(kg K)) diameter (m) Dacry number fiber diameter (m) characteristic length (m) pore size (m) constant in model of Boomsma and Poulikakos inertial resistance (m1) gravitational acceleration (m/s2) height (m) interfacial heat transfer coefficient (W/(m2 K)) permeability (m2) latent heat (kJ/kg) pressure (Pa) Prandtl number thermal resistance (K/W) Rayleigh number Reynolds number temperature (°C) velocity vector (m/s) velocity in x direction (m/s) velocity in y direction (m/s)

practical [4–6]. For the middle temperature range of 200–300 °C in solar energy applications, nitrate mixtures with low melting point, low unit cost, high heat capacity and energy storage density have been used for decades in the concentrating solar power industry as heat transfer fluids and thermal storage media [7,8]. Solar salt with a certain mass fraction of sodium nitrate and potassium nitrate (NaNO3: KNO3 = 54:46 or 60:40) as a typical molten salt has been studied extensively [9–14]. Bauer et al. [12] reviewed the thermo-physical data of solar salt (60 wt% NaNO3, 40 wt% KNO3), and pointed out that the density, heat capacity, thermal conductivity of solar salt were temperature dependent. An overview of the various aspects of steel corrosion in molten nitrate salts was also given in their research. Iverson et al. [13] extensively investigated the thermal and mechanical properties of solar salt, including specific heat, coefficient of thermal expansion, thermal conductivity, latent heat, then the values of those parameters have been presented as a function of temperature. Normally, molten salt is with low thermal conductivity [9,10], and effectively improving its thermo-physical properties is of great interest in both academic research and applications. Impregnating PCMs into a continuous porous structure with high thermal conductivity appears to be an effective way to compensate the low thermal conductivity. Metal foam has been widely studied and used because of its good mechanical and thermo-physical properties. The attractive advantages include low bulk density due to its high open porosity which will not significantly increase the weight of the thermal storage system, high specific strength and stiffness, and especially high thermal conductivity for continuous skeleton structure. Thus composite PCMs fabricated by porous metal foams and pure PCMs have been used for LTES systems [15,16]. Several numerical studies have been performed to investigate the heat transfer characteristics of PCM in porous structure, and it was found that the hypothesis of local thermal equilibrium in porous media was not exactly valid [17]. As a result, the thermal non-equilibrium phenomenon should be considered in the numerical analysis. DeGroot and Straatman [18] proposed a model with the

w x,y,z

velocity in z direction (m/s) Cartesian coordinates

Greek symbols b thermal expansion coefficient (K1) c liquid fraction e porosity f small constant in additional term of momentum equation k thermal conductivity (W/(m K)) l dynamic viscosity (kg/(m s)) q density (kg/m3) s time (s) r parameter in model of Boomsma and Poulikakos v tortuosity coefficient x pore density (pore per inch, PPI) Subscript amb e f m sf s td

ambient effective value PCM melting surface solid skeleton thermal dispersion

volume-averaged energy equations under local thermal non-equilibrium conditions, which would be useful in analyzing the heat transfer in porous media. Liu et al. [19] established a numerical model to predict the melting characteristics of PCM in porous media, and the effects of the structural parameters of porous media and the inlet conditions of HTF on the thermal performance of a LTES unit were analyzed accordingly. Mesalhy et al. [20] numerically investigated the effects of impregnating porous matrix with high thermal conductivity of various porosities with PCM on the thermal performance of a LTES system. A two-temperature energy equation model was applied to analyze the local thermal non-equilibrium due to the large difference in thermo-physical properties between the solid matrix and PCM. Furthermore, the non-Darcy, Brinkman and Forchiemer effects were also considered in the investigation. Krishnan et al. [21] numerically investigated the natural-convection-coupled melting in a cavity filled with metal foam/PCM composite in the case of step change of the boundary temperature. A two-temperature energy equation to deal with the local thermal non-equilibrium between PCM and skeletons of the porous structure was used, and the heat transfer between PCM and metal foam was modeled by empirical correlations. Lafdi et al. [22] numerically analyzed the heat transfer process and the related liquid motion of the molten PCM by using thermal nonequilibrium model. It was shown that the graphite foam infiltrated with PCM significantly increased the heat transfer rate, and the decrease of the porosity largely accelerated the melting process due to high thermal conductivity of the graphite skeleton. Yang and Garimella [23] developed a two-temperature energy equation model to investigate the melting process of PCM impregnated into metal foams, and studied the effect of volume shrinkage/expansion of the PCM on the heat transfer between the foam and PCM. It can be seen from the above literature review that, however, very limited experimental data have been provided for the LTES system using metal foam/PCM composite, especially for metal foam/salt composite. And the heat transfer characteristics of the composite PCM in a LTES unit have not been understood, which is

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1.5

Heat Flow (W/g)

important for performance evaluation of a LTES system. Therefore, it is necessary to study the heat transfer characteristics of the LTES unit with metal foam/salt composite experimentally and numerically. According to the eutectic characteristics of sodium nitrate and potassium nitrate reported in the previous study [24], molten salt (50 wt% NaNO3 and 50 wt% KNO3) was applied as the PCM in the present study, copper foam and nickel foam with the porosity around 97% were used to enhance the thermal conductivity. Heat storage and retrieval experiments in a cylindrical LTES unit were conducted extensively both for pure molten salt and metal foam/ salt composites. Heat storage experiments were conducted at various heating temperatures from 240 °C to 260 °C, and heat retrieval experiments were conducted at various cooling temperatures from 30 °C to 110 °C. A three-dimensional model including enthalpy– porosity term, non-Darcy effect term and two-temperature energy equations were established to further describe the heat transfer characteristics inside the LTES unit. The performance of the LTES system can be improved with the application of metal foam, and the output power and heat storage/retrieval rates of the LTES system can be improved greatly with the composite PCM. Thus the energy efficiency of the LTES system increases, which benefits the applications of the LTES system.

endset 228.44°C

onset 218.10°C

0.0

onset 224.58°C

endset 215.85°C

-0.5

Extrapolated ending edge

-1.0

Melting curve Freezing curve

peak 219.14°C

-1.5 205

210 215

220

225

230

235 240

245

Temperature (°C) Fig. 1. Melting/freezing DSC curve of pure molten salt [24].

Table 2 Structural and thermo-physical characteristics of metal foams used in the present study. Type

Copper foam

Nickel foam

e x (PPI) qs (kg/m3) [26]

96.54 10 8930 398 386

97.48 10 8900 91.4 444

ks (W/(m K) [26] Cps (J/(kg K)) [26]

2. Experimental procedure

peak223.37°C

Extrapolated leading 1.0 edge Base line 0.5

2.1. Preparation of materials

2.2. Heat storage/retrieval experiments in a LTES unit

Molten salt (50 wt% NaNO3, 50 wt% KNO3) with a purity of 99.0% was used as the base PCM. Copper foam and nickel foam were used to enhance the low thermal conductivity of pure molten salt. The metal foams were machined into cylindrical shape with the diameter of about 72.0 mm in order to be encapsulated in the LTES unit. The diameter of the metal foam cylinder was slightly larger than the inner diameter of the LTES unit, which was to reduce the thermal contact resistance between the metal foam and wall of the LTES unit. The thermo-physical properties of the molten salt are listed in Table 1. The thermal conductivity of the molten salt was measured with a steady-state test rig in the previous study [25]. The latent heat and phase change temperatures were obtained from the melting/freezing curves of pure molten salt, as shown in Fig. 1, which was measured by a different scanning calorimeter (DSC) (DSC8000, PerkinElmer, Inc.) [24], and the phase change temperature and latent heat were obtained accordingly. While the specific heat, dynamic viscosity, and thermal expansion coefficient were obtained from the literature [11,13]. The structural characteristics of the metal foams are listed in Table 2, and the related thermophysical properties were from [26].

The heat storage/retrieval performances of pure molten salt and metal foam/salt composites were investigated in a LTES unit in the present study. And the melting/freezing characteristics were also numerically interpreted. Fig. 2 shows the schematic diagram of the LTES test system, and it can be seen that the LTES unit was immersed in a constant temperature thermostatic oil bath, while the top of the LTES unit was exposed to the surrounding because of the location of the wires and experimental safety. Fig. 3(a) shows the schematic illustration of the LTES unit, which is a vertical stainless steel tube with an outer diameter of 76.0 mm and a wall thickness of 3.0 mm. About 80% of the volume of the test tube was filled with the solid PCM at a room temperature of about 10 °C, and the remaining space was left empty to accommodate volume increase of the PCM during melting. About 2100.0 g pure salt was filled in the LTES unit without metal foam, while about 2020.0 g and 2040.0 g salt was filled in the LTES unit with copper foam and nickel foam, respectively. In order to investigate the heat transfer characteristics of the LTES unit, six platinum resistance thermometers (PT100, A–F) were fixed with a thin supporting rod along the central axis and wall of the LTES unit. The experiments of heat storage were started with the entire LTES unit at room temperature. And the tests were stopped when the LTES unit approximately reached the thermostatic oil bath temperatures of 240 °C, 250 °C and 260 °C, respectively. Subsequently the experiments of heat retrieval were started. During heat retrieval, the thermostatic oil bath temperatures were set at about 30 °C, 70 °C and 110 °C, respectively. All the temperature evolutions during heat storage and retrieval were monitored and collected by a data logger. The platinum resistance thermometers were pre-calibrated with the uncertainty of 0.1 °C, the uncertainty of the thermostatic oil bath temperature was 1.0 °C, and the uncertainty of the position of the platinum resistance thermometers was 1.0 mm, and the uncertainty of the liquid level of the thermostatic oil bath was 1.0 cm. The total uncertainty of the temperature evolutions can be obtained by the uncertainty propagation analysis, and it can be concluded that the maximum uncertainty for the temperature evolutions was determined to be 4.14%.

Table 1 Thermo-physical properties of molten salt used in the present study. Parameters

qf (kg/m3) Tm (°C) [24] L (kJ/kg) [24] kf (W/(m K))

Value Solid Liquid Melting Cooling Solid [25] Liquid [11]

Cpf (kJ/(kg K)) [13]

l (kg(m s)) [11] b (K1) [13]

Melting Cooling

2079.0 1884.0 218–228 215–225 122.89 0.705 0.478 1.05 (T 6 90) 1.85 (90 < T 6 228) 1.50(T > 228) 0.00506 5.47  10–5 7.06  10–5

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(1)

(2) (4)

(5) (6)

(3)

(7)

Fig. 2. Schematic of the LTES test system. (1) temperature control unit, (2) stirrer, (3) heater, (4) thermostatic oil bath, (5) heat storage unit, (6) data logger and (7) computer.

3. Mathematical model 3.1. Equations for flow and heat transfer Fig. 3(b) shows the computational domain, where the thickness of the stainless steel was ignored for the simplification of the numerical calculation. The LTES unit with the height H = 280.0 mm and diameter D = 70.0 mm was filled with solid molten salt with or without metal foam. The following assumptions were made in the numerical model in the present study:

As the porous metal foam and pure salt are not assumed to be in thermal equilibrium, two-temperature energy model describes the energy equations, in which one energy equation uses the thermophysical properties of PCM, another energy equation uses the thermo-physical properties of the metal, shown as follows [28]: For the PCM



  ~  rT f ¼ þ qf cpf U     kfe þ ktd r2 T f þ hsf asf T s  T f

eqf cpf þ L dTdcf



@T f @s

ð5Þ

For the metal skeleton: (1) The open-cell metal foam was assumed homogeneous and isotropic. (2) The liquid molten salt was considered isotropic, incompressible and Newtonian, and the Boussinesq approximation was applicable. (3) The natural convection was laminar flow in the liquid molten salt, and the volume variation of the salt during phase change process was negligible. (4) The influence of surface tension on the flow was negligible. In the numerical calculations, the enthalpy–porosity model and melting/solidification model were adopted [27]. Two-temperature energy equations were used to study the thermal non-equilibrium between the salt and metal foam skeleton. The set of governing equations can be formulated as follows. Continuity equation:

  @ qf ~ ¼0 þ r qf  U @s

ð1Þ

ð1  eÞqs cps









 lf qf F l qf @ v qf ~ @p lf þ 2 U  rv ¼  þ r2 v  þ pffiffiffiffi jv j v þ As v @y e e @s e K K ð3Þ  qf @w qf ~ @p þ 2 U  rw ¼  @z e @s e  lf 2 lf qf F l  þ pffiffiffiffi jwj w þ qf gbðT  T m Þ þ As w þ r w e K K

ð4Þ

ð6Þ

where qf, lf, b, L, cpf, kfe are the density, dynamic viscosity, thermal expansion coefficient, latent heat, specific heat and effective thermal conductivity of pure salt presented in Table 1, respectively. e, qs, cps, kse are the porosity, density, specific heat and effective thermal conductivity of metal foam presented in Table 2, respectively. K and Fl are the permeability and inertial resistance, respectively, which will be elaborately described in next section. Tf is the temperature of molten salt, and Ts is the temperature of metal skeleton. The source terms of viscous resistance and inertial resistance have been included in Eqs. (2)–(4). The second terms on the right side of Eqs. (2)–(4) belong to the viscous resistance, while the third and forth terms account for the extension of Darcy’s law to explain the non-Darcy effects. The direction of gravitational acceleration is in the negative direction of axis Z, as shown in Eq. (4). The rightmost terms in Eqs. (2)–(4) are related to the liquid fraction, which is expressed as follows:

Momentum equations:

 lf qf F l qf @u qf ~ @p lf U  ru ¼  þ r2 u  þ þ pffiffiffiffi juj u þ As u ð2Þ @x e @ s e2 e K K

  @T s ¼ kse r2 T s  hsf asf T s  T f @s

As ¼ C

ð1  cÞ2 c3 þ f

8 0; T f < T m1 > < c ¼ TTm2f TTm1m1 ; T m1  T f  T m2 > : 1; T m2 < T f

ð7Þ

ð8Þ

where c is the liquid fraction, C is the mushy zone constant, Tm1 and Tm2 are the temperature range of melting. As tends to be infinity when c tends to be zero, so f is a small constant used to avoid division by zero and designated to be 0.001. Three values including 104, 5  104 and 105 were adopted in a previous study [29] to investigate the effect of the constant C on the melting process of

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rffiffiffiffiffiffiffiffiffiffiffi 1e dp df ¼ 1:18 3p

(a)

asf ¼

D

F

ð10Þ

3pdf

ð11Þ

2

dp

The tortuosity coefficient v of metal foam is related to the porosity, and the characteristic length dk can be obtained accordingly, as shown in the following equations [31]:

C

v ¼ 2 þ 2 cos dk ¼

v 3v



4p 1 þ cos1 ð2e  1Þ 3 3



dp

ð12Þ

ð13Þ

B

E

3.2.2. Permeability and inertial coefficient The existence of pressure gradient impels the laminar flow inside the porous structure, which requests a relationship between the pressure gradient and velocity. Permeability indicating the transport performance of the fluid inside the porous media is always used to represent the relationship, but it is a complicated parameter and hardly experimentally determined. In the present study, the permeability K and inertial resistance Fl were determined by the following equations [30–31]. 1/K represents the viscous resistance, and was calculated correspondingly. Then the two values of 1/K and Fl were used in the enthalpy–porosity model.

A

(b) K¼

e2 d2k 36ðv  1Þv

 1:63 pffiffiffiffi F l ¼ 0:00212ð1  eÞ0:132 df =dp = K

ð14Þ ð15Þ

3.2.3. Interstitial heat transfer coefficient The heat transfer between PCM and metal foam skeleton is very important for heat transfer estimation. It is quite difficult to accurately predict the heat transfer between the molten salt and metal foam, where the simplification is necessary. The skeleton of the foam structure are usually considered as cylinders with the roughness neglected, so the laminar flow of liquid molten salt in porous structure is resembled as flow around cylinder. The empirical correlations of interstitial heat transfer coefficient can be found in the previous studies and were summarized in Table 3. Based on the application condition, the empirical correlations provided by Zhukauskas were adopted in the present numerical model [32]. Fig. 3. LTES unit and the location of platinum resistance thermometers (a) LTES unit and (b) computational domain. (unit: mm).

pure paraffin. It was found that the numerical results based on C = 104 showed the best agreement with the experimental data after a series of numerical calculation. Therefore, it can be concluded that the suitable value for molten salt was C = 104 and it was adopted in the present study. 3.2. Correlations of metal foam parameters 3.2.1. Structural parameters for metal foam Usually, the pore density x and porosity e are the basic parameters of metal foam, while the other parameters such as the pore size dp, fiber diameter df and interfacial surface area asf can be deduced from the following equations [30,31].

dp ¼

22:4  103

x

ð9Þ

3.2.4. Effective thermal conductivity and thermal dispersion conductivity For the thermal non-equilibrium model, the effective thermal conductivity of each phase should be given independently. A variety of theoretical models which considered the geometric parameters of the metal foams were proposed to predict the effective thermal conductivities of metal foams with thermal resistance analysis [39–42]. The unit cell model of hexagonal structure with the square intersection [39] or circular intersection [40] was usually used to estimate the effective thermal conductivities of metal foams. While threedimensional models including the cubic lattice model reported by Dul’nev [41] and the tetrakaidecahedron model reported by Boomsma and Poulikakos [42] were also used to predict the effective thermal conductivities of metal foams. The tetrakaidecahedron cell model was adopted to describe the effective thermal conductivity in the present study, as shown in the following equations.

ke ¼

pffiffiffi 2 2ðRA þ RB þ RC þ RD Þ

ð23Þ

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Table 3 Empirical equations of interstitial heat transfer coefficient [32–38]. Correlations 8 < 0:76Re0:4 Pr0:37 1 6 Re 6 40 hsf D 0:5 Pr0:37 4 0 6 Re 6 103 kf ¼ : 0:52Re 0:26Re0:6 Pr0:37 103 6 Re 6 2  105 h i hsf D 4ð1eÞ þ 12 ð1  eÞ1=2 Re0:6 Pr1=3 e kf ¼ 1 þ hsf D kf

¼ 0:376Re0:644 Pr0:37

hsf D kf

¼ 0:36 þ

hsf H kf

¼ 0:0159Re0:426 Pr1=3 Da0:787

hsf D kf

e

hsf D kf

RA ¼

RB ¼

¼ ½0:1 þ

0:518Ra1=4 ½1þð0:559=PrÞ9=16 

4=9

1

0:2555Re2=3 Pr1=3

¼ 6:820 þ 0:198Re



0:788

0:606

Pr

Application conditions

Eq. No.

References

Forced flow for cylinders in cross-flow

(16)

Zhukauskas [32]

Forced flow over spheres 0.2 < e < 0.9 Forced flow for metal foam, 40 < Re < 200

(17)

Kuwahara et al. [33]

(18)

Hwang et al. [34]

Natural convection across vertical plate

(19)

Churchill and Chu [35]

1000 < Re < 3000

(20)

Kim et al. [36]

Theoretical study for packed bed

(21)

Dixon and Cresswell [37]

Fitting from the numerical results, 0.1 < Re < 200

(22)

Haussener et al. [38]

4r ½2e2 þ prð1  eÞks þ ½4  2e2  prð1  eÞkf

ð e  2r

Þe2 ks

ðe  2rÞ2 þ ½2e  4r  ðe  2rÞe2 kf

pffiffiffi 2 2  2e  hpffiffiffi  RC ¼ pffiffiffi pffiffiffii 2pr2 1  2e 2 ks þ 2 2  2e  pr2 1  2e 2 kf RD ¼

2e e2 ks þ ð4  e2 Þkf

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i pffiffiffi upffiffiffih u 2 2  ð5=8Þe3 2  2e u   r¼t pffiffiffi p 3  4e 2  e

ð24Þ

ð25Þ

ð26Þ

ð27Þ

ð28Þ

where e = 0.339 is the constant. Then the effective thermal conductivities of the salt and metal foam can be expressed as:

kfe ¼ ke jks ¼0

kse ¼ ke jkf ¼0

ð29Þ

The heat transfer enhancement due to the fluid mixing in porous media at the pore scale should be considered, and it can be expressed as thermal dispersion. Georgiadis and Catton [43] proposed a thermal dispersion model based on the stochastic phenomena, as shown in the following equation:

ktd ¼

0:36 q cpf df 1e f

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi u2 þ v 2 þ w2

while the bottom and lateral surfaces were heated or cooled at constant temperature. The initial values of velocities for PCM at three directions were zero, and the non-slip velocity condition at the wall was applied. As the numerical result should be independent of the grids, the check of the grid sensitivity has been conducted firstly. Different grid sizes with 170,068 and 340,136 cells were tested, and the differences of the numerical results were within 0.1%, which indicated that the total amount of 170,068 grids was adequate enough to save the computing time without losing the numerical accuracy. Furthermore, the effects of time step on the solution were carefully examined in the preliminary calculations, where three time steps viz.: 0.5, 1 and 2 s were tested. As a compromise between the computational time and the accuracy, 1 s was adopted as the time step in the numerical calculation. Convergence of the solution was checked at each time step, and the convergence criteria for the residuals of continuity equation, velocity components, and energy equation were 105, 105 and 108, respectively. The solutions were obtained once the convergence criteria were satisfied.

ð30Þ

3.3. Numerical procedure In the present study, uniformly structured grid with hexahedral cells has been applied to investigate the heat storage and retrieval processes. The numerical calculation was performed using a commercial CFD program Fluent 6.3 [44]. The UDF (user define function) was adopted to improve the present porous media model in Fluent to account for the effect of variable quantity in the energy equations. The variable interstitial heat transfer between metal foam and salt was established, and the source term in the energy equation of metal foam was also programmed with the UDF in Fluent. The governing equations were discretized by the finite volume method. Pressure and velocity fields were computed by second Order Implicit Method for Pressure-Linked Equations (SIMPLE) algorithms. The initial condition in the model was a constant temperature for pure salt and metal foam/salt composites, as listed in Table 4. The origin of the coordinates was located at the center of the bottom surface. The top surface was regarded constant at ambient temperature, so as to consider the heat loss into the surrounding,

4. Results and discussion 4.1. Heat storage/retrieval processes of pure salt and metal foam/salt composites Fig. 4 shows an example of the temperature evolutions of heat storage and retrieval processes for pure salt. It can be seen that the temperatures of point A, E and F ascended more quickly than other points, while those points descended more quickly than other points. The reason was that points A, E and F were near the wall of the tube. As can be seen from the figure, the temperature evolution at point E displayed typical phase change characteristic in that there was a temperature plateau at around 225 °C, while the temperature evolutions at other points did not show such characteristics. It could be attributed to the effect of natural convection of liquid molten salt, resulting in phase change in the temperature curves inapparent. During heat retrieval of the pure salt, the heat transfer was dominated mainly by heat conduction. Therefore, the duration of heat retrieval was longer than that of heat storage. And the temperature evolutions at points C and D displayed temperature plateaus. Fig. 5 shows the comparison of temperature evolutions between pure salt and metal foam/salt composites during heat storage, while the heating temperature was kept constant at 240 °C, 250 °C and 260 °C, respectively. As it was found that the temperatures were only slightly different between pure salt and metal foam/salt composites for points A, E and F, respectively, the temperature evolutions of those points were not included in Fig. 5. The measuring temperature of point D was slightly lower than

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P. Zhang et al. / Applied Energy xxx (2014) xxx–xxx Table 4 Initial and boundary conditions for the governing equations. Definite conditions

Positions 2

2

x + y 6 (D/2) , 0 6 Z 6 H x2 + y2 = (D/2)2, 0 6 Z 6 H x2 + y2 < (D/2)2, Z = 0 x2 + y2 < (D/2) 2, Z = H

270

(a) 240

240

210

210

180

180

TA

150

TB TC

120

TD

90

TE

60

0

2000

4000

Temperature

Velocity

Tf = Ts = Tamb T = Theating/cooling T = Theating/cooling T = Tamb

u=v=w=0 u=v=w=0 u=v=w=0 u=v=w=0

150 Copper foam/salt T B

120

Copper foam/salt T C

90

Pure salt TB Pure salt TC Pure salt TD

60 30

TF

30 0

Temperature (oC)

Temperature (oC)

Initial condition Boundary condition

2

0 6000

8000

0

1000

2000

3000

Copper foam/salt T D

Nickel foam/salt T B Nickel foam/salt TC

Nickel foam/salt T D

4000

5000

6000

Time (s)

10000

Time (s) 210

Temperature (oC)

other points, especially for metal foam/salt composites, which was due to the heat loss from the top surface of the LTES unit to the surroundings. A discrepancy between the measuring results for pure salt and metal foam/salt composites was observed. As shown in Fig. 5(a) and (b), the temperature of point B ascended slightly more rapidly than those of points C and D during the melting of metal foam/salt composites, whereas the temperatures of points C and D ascended more quickly than that of point B during the melting of pure salt. These phenomena indicated different heat transfer mechanisms between metal foam/salt composites and pure salt during melting. The melting of pure salt was accelerated during heat storage because of the intensive natural convection in the liquid molten salt. However, the natural convection was weakened for metal foam/salt composites during heat storage, because the existence of metal foam constrained the flow of liquid molten salt. As can be seen from section ab in Fig. 5(c), the intensive natural convection of liquid molten salt was enhanced not only for pure salt, but also for nickel foam/salt composite because of the high heating temperature, which can be verified by the phenomena that the temperature of point C for nickel foam/salt composite ascended more quickly than that of point B at the end period of the heat storage process. The reason was that the porosity of nickel foam was larger than that of copper foam. In a word, the time-duration of heat storage of the composite PCM was reduced, e.g., the charging times were 3700 s, 2900 s and 3250 s for pure salt, copper foam/ salt composite and nickel foam/salt composite when the heating temperature was 240 °C, respectively, indicating about 21.6% and 12.2% reduction for copper foam/salt composite and nickel foam/ salt composite. Because of the high thermal conductivity of metal skeleton, the heat transfer process during heat storage was enhanced, although the natural convection was weakened. It was also showed that the enhancement of the copper foam/salt composite PCMs was more significant than that of the nickel foam/salt composite PCMs, which was due to the higher thermal conductivity of copper skeleton. However, it should be noted that copper is easier to be corroded than nickel, so a compromise should be considered to balance the heat transfer rate and thermal stability of the composite PCMs in practical application.

(b) 240 180 150

Copper foam/salt T B

120

Copper foam/salt T C

90

Pure salt TB Pure salt TC Pure salt TD

60 30 0

0

1000

2000

3000

Copper foam/salt T D Nickel foam/salt T B Nickel foam/salt T C Nickel foam/salt T D

4000

5000

6000

Time (s)

(c) 270 240 210

Temperature (oC)

Fig. 4. Experimental temperature evolutions of heat storage and retrieval processes. (pure salt, Theating = 260 °C, Tcooling = 30 °C).

a natural convection

b

180 150

Copper foam/salt T B

120

Copper foam/salt T C

90

Pure salt TB Pure salt TC Pure salt TD

60 30 0

0

1000

2000

3000

Copper foam/salt T D

Nickel foam/salt T B

Nickel foam/salt T C

Nickel foam/salt T D

4000

5000

6000

Time (s) Fig. 5. Experimental temperature evolutions of the LTES unit during heat storage (a) Theating = 240 °C, (b) Theating = 250 °C and (c) Theating = 260 °C.

It can also be seen form Fig. 5 that the heating temperature had strong influence on heat storage process. When the heating temperature was high, the time-duration could be reduced, e.g., the charging times for pure salt was 3700 s, 3200 s and 2600 s at the heating temperature of 240 °C, 250 °C and 260 °C, respectively. It was because that larger temperature difference between the heating fluid and PCM led to higher heat transfer rate, and enhanced the intensive natural convection of pure salt. Fig. 6 shows the comparison of temperature evolutions between pure salt and metal foam/salt composites during heat retrieval.

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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Due to the heat loss from the top of the LTES unit and fluctuation of the liquid level of oil bath, the temperature of point D was difficult to reach the heating temperature of oil bath, so the initial temperatures of point D for metal foam/salt composites were lower during heat retrieval, as shown in Figs. 5(a) and 6(a). In general, the effects of the slight temperature differences on the comparisons could be neglected, and the comparisons were reliable and reasonable. The temperature evolutions of the test points in pure salt were similar to those in metal foam/salt composites, which showed that the heat transfer mechanism in metal foam/salt composites resembled that in pure salt during heat retrieval. The time-durations of heat retrieval were considerably reduced for metal foam/salt composites which was attributed to the addition of metal foam, and the effect of metal foam was more significant for heat retrieval than for heat storage, e.g., the discharging times were 6180, 4400 and 4990 s for pure salt, copper foam/salt composite and nickel foam/ salt composite when the initial temperature was 240 °C, respectively, which were determined from the experimental data when

Copper foam/salt TC

Pure salt TC

Nickel foam/salt TB

o

Temperature ( C)

180

Nickel foam/salt TC

150

Nickel foam/salt TD

120 90 60 30 0

0

1000

2000

3000

4000

TB (30 oC) o

o

Temperature ( C)

210

Pure salt TB

Copper foam/salt T B

Pure salt TC

Copper foam/salt T C

Pure salt TD

Copper foam/salt T D Nickel foam/salt TB

180

Nickel foam/salt TC

150

TB (110oC)

TC (110oC)

150

TD (110oC)

100 50 1000 2000 3000 4000 5000 6000 7000 8000

0

Time (s)

Nickel foam/salt TD

120 90 60

(b) 300

o

TB (30oC)

TB (70 C) o

TC (30oC)

250

Temperature (oC)

240

TD (70oC)

TD (30 C)

Time (s)

(b)

TC (70oC)

TC (30 C)

200

0

5000

TB (70oC)

o

250

Copper foam/salt TD

Pure salt TD

Temperature (oC)

210

(a) 300

Copper foam/salt TB

Pure salt TB

(a) 240

the temperatures of all the test points were below 35 °C. The results indicated about 28.8% and 19.3% reduction in the timedurations of heat retrieval for copper foam/salt composite and nickel foam/salt composite, respectively, compared with that of pure salt. The reason was that the heat conduction dominated the heat transfer during heat retrieval. Furthermore, there were almost no apparent plateau sections for phase change during heat storage due to the effect of natural convection, while the plateau sections for phase change of pure salt were apparent during heat retrieval, as shown in Figs. 5 and 6. As the ambient temperature of about 10 °C was lower than that of the cooling fluid, the temperature of point D was expected to decrease more quickly than that of point B, which can be seen from the temperature evolutions of the metal foam/salt composites, as shown in Fig. 6. However, the temperature of point B decreased more quickly than that of point D for pure salt. The possible reason might be that the low thermal conductivity of pure salt restricted the heat transfer between the air and salt. As can be seen from

TC (70 C) o

TD (30oC)

200

TD (70 C) o

TB (110 C) o

TC (110 C)

150

TD (110oC)

100 50

30 0

0 0

1000

2000

3000

4000

5000

0

1000

2000

270

Pure salt TB

Copper foam/salt TB

240

Pure salt TC

Copper foam/salt TC

210

Pure salt TD

Copper foam/salt TD

(c) 300

Nickel foam/salt TC

150

Nickel foam/salt TD

120 90 60

Temperature (oC)

180

TB (30o C) TC (30o C)

250

Nickel foam/salt TB

o

Temperature ( C)

(c)

3000

4000

Time (s)

Time (s)

o

TD (30 C)

200

TB (70oC)

TC (70oC)

TD (70oC)

TB (110oC)

TC (110oC)

150

TD (110oC)

100 50

30 0

0

1000

2000

3000

4000

5000

Time (s) Fig. 6. Experimental temperature evolutions of the LTES unit for different initial temperatures during heat retrieval (a) Tinitial = 240 °C, (b) Tinitial = 250 °C and (c) Tinitial = 260 °C. (Tcooling = 30 °C).

0

0

1000

2000

3000

4000

5000

6000

Time (s) Fig. 7. Comparison of experimental temperature evolutions for different cooling temperatures during heat retrieval (a) pure salt, (b) copper foam/salt composite and (c) nickel foam/salt composite. (Tinitial = 260 °C).

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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P. Zhang et al. / Applied Energy xxx (2014) xxx–xxx

240

210

210

Exp TB

150

o

o

180

Exp TC

120

Exp TD

90

Num TB

60

Num TC

30

Num TD

0

Temperature ( C)

(a) 270

240

Temperature ( C)

(a) 270

0

1000

2000

3000

4000

5000

Exp TB Exp TC Exp TD

180

Num TB

150

Num TC

120

Num TD

90 60 30 0

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0

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240

210

210 Exp TB

150

Exp TC

120

Exp TD

90

Num TB

60

Num TC

30

Num TD 1000

2000

3000

4000

o

o

180

Temperature ( C)

(b) 270

Temperature ( C)

(b) 270

0

Exp TD Num TB

150

Num TC

120

Num TD

90 60

0

1000

3000

Exp TC

Exp TB

150

Exp TC

120

Exp TD

90

Num TB

60

Num TC

30

Num TD 4000

o

180

Temperature ( C)

210

3000

5000

Exp TB

240

2000

4000

Time (s)

210 o

2000

(c) 270

1000

6000

Exp TB

180

0

5000

240

0

5000

30

(c) 270

Temperature ( C)

4000

Exp TC

Time (s)

0

3000

Time (s)

Time (s)

0

2000

Exp TD

180

Num TB

deviation

150

Num TC

120

Num TD

90 60 30

5000

Time (s) Fig. 8. Comparisons of the experimental and numerical results for temperature evolutions during heat storage (Theating = 260 °C) (a) pure salt, (b) copper foam/salt composite and (c) nickel foam/salt composite. The numerical temperatures of metal foam/salt composites represent the temperatures of salt.

Fig. 6, there was a small temperature plateau at around 100 °C, which was due to the solid–solid phase transition of pure salt and was reported in the literature [13]. Fig. 7 shows the influence of the cooling temperature on the time-duration of heat retrieval. The time-duration could be reduced both for pure salt and metal foam/salt composites when the cooling temperature was low. The reason was that large temperature difference between the cooling fluid and PCM could accelerate the heat conduction process extensively.

4.2. Heat transfer characteristics of pure salt and metal foam/salt composites The numerical model with two-temperature energy equations was validated before applied to the present study. Figs. 8 and 9 show the comparisons of the experimental and numerical results

0

0

1000

2000

3000

4000

5000

Time (s) Fig. 9. Comparisons of the experimental and numerical results for temperature evolutions during heat retrieval (Tcooling = 30 °C) (a) pure salt, (b) copper foam/salt composite and (c) nickel foam/salt composite. The numerical temperatures of metal foam/salt composites represent the temperatures of salt. The deviation in (c) was caused by the non-uniform porous structure of nickel foam.

for temperature evolutions during heat storage and retrieval. It can be seen that the numerical results agreed with the experimental data generally, with a maximum deviation of about 18.0%. As shown in Fig. 8(a) and (c), both the experimental and numerical results of point C increased faster in temperature than those of point B at the end of the melting process. The reason was that the density of pure salt in solid state is larger than that in liquid state, leading to the solid salt moving down because of the influence of the gravity, and the melting rate in the upper portion of the LTES unit was faster than that in the lower portion. It can be seen that the numerical results of points B and C were almost the same before the temperatures of them ascended to the phase change temperature, which was due to the reason that the heat conduction dominated the heat transfer process around points B and C. However, the discrepancies between the numerical results

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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γ

T (°C)

1000 s

2500s

1000 s

4500 s

2500s

4500 s

(ΙΙ)

(Ι) Velocity (m/s)

1000 s 2500s (ΙΙΙ)

4500 s

Fig. 10. Temperature profile (I), solid/liquid interface (II) and velocity field (III) in pure salt during heat storage (Theating = 260 °C). The region on the top was caused by the heat loss from the top surface of the LTES unit to the surroundings.

and experimental data existed not only for pure salt, but for metal foam/salt composites. It can be seen from Fig. 8 (a) that the numerical results for pure salt ascended slowly than the experimental data, which could be attributed to the following reasons. On one hand, the top surface was taken constant at ambient temperature in the numerical model, which might be slight different from the situation in the experiments. On the other hand, the values of the thermo-physical properties used in the numerical calculation might deviate from the true values, in particular for the dynamic viscosity and specific heat. Moreover, the positions of the platinum resistance thermometers might not be at the center axis of the LTES unit exactly which also slightly affected the comparisons between the experimental and numerical results. The numerical results for metal foam/salt composites ascended more quickly than the experimental data, as shown in Fig. 8(b) and (c). In addition to the same reasons as pure salt, the possible non-uniform porous structure of the metal foams formed in manufacturing the specimens or filling them into the tubes might slightly distort the metal foam and weakened the heat transfer to a certain degree, and induced the deviation from the numerical results from experimental data. The temperature profiles, solid/liquid interfaces and velocity fields of pure salt and metal foam/salt composites are shown in Figs. 10–13. Figs. 10 and 12 show the comparisons of the temperature profiles for pure salt and metal foam/salt composites during

heat storage. Because of the low thermal conductivity of pure salt, the temperature distribution was non-uniform for the poor heat transfer performance. While heat transfer performance of the LTES unit was improved with the addition of metal foam, and the temperature distribution was more uniform in the case of metal foam/

T (°C)

500 s

1500s

2500 s

3500s

4500 s

Fig. 11. Temperature profile in pure salt during heat retrieval (Tcooling = 30 °C).

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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P. Zhang et al. / Applied Energy xxx (2014) xxx–xxx

Tsalt (°C)

Tcopper (°C)

500 s

1500s

2500 s

500 s

1500s

2500 s

500 s

1500s

2500 s

(Ι-a) Tsalt (°C)

Tnickel (°C)

500 s

1500s

2500 s (Ι-b)

γ

γ

500 s

1500s (ΙΙ-a)

2500 s

500 s

1500s

2500 s

(ΙΙ-b)

Fig. 12. Temperature profile (I), solid/liquid interface (II) and velocity field (III) in metal foam/salt composites during heat storage (a) copper foam/salt composite and (b) nickel foam/salt composite. (Theating = 260 °C).

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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P. Zhang et al. / Applied Energy xxx (2014) xxx–xxx

Velocity (m/s)

Velocity (m/s)

500 s

1500s

2500 s

500 s

1500s

2500 s

(ΙΙΙ-b)

(ΙΙΙ-a) Fig. 12 (continued)

salt composite. A funnel-like interface appears in Figs. 10 and 12, which was caused by the heat loss between the top of the LTES unit and surroundings. It can be seen from Fig. 10(II) that a solid cone appears near the bottom of the unit, which was due to the sinking of solid salt. The phenomena can also interpret that both the experimental and numerical results of point C increased faster in temperature than those of point B. As shown in Fig. 10, the temperature difference between the heating walls and the melting interface was maintained at a high value during the entire melting process, so the natural convection driven by the temperature difference was kept in the melting process. Whereas the natural convection was restricted due to the flow resistance of small pore size of the metal foam, as can be seen from Fig. 10(III) and Fig. 12(III). It can also be seen that the temperature gradient decreased because of the large effective thermal conductivity of the metal foam/salt composites. As a result, the mushy zone of the phase change was enlarged. Figs. 10 and 12 show the movement of the solid/liquid interface during heat storage. The interface was almost perpendicular to the bottom surface initially because it was dominated by heat conduction. When the molten salt was melted, the natural convection inside liquid molten salt started immediately. As the density of salt in solid state was larger than that in liquid state, the liquid salt would move upward because of the buoyant force. As a result, the melting rate in the upper portion of the tube was faster than that in the lower portion, so the solid/liquid interface was curved gradually. And the angle between the interface and horizontal plane was reduced accordingly. The velocity fields are also shown in Figs. 10 and 12. Because of the existence of metal foam, the buoyancy effect was weakened. It can be seen that the flow of liquid salt in metal foam was slower than that of pure salt, which was attributed to the effect of inertial resistance and viscous resistance. Figs. 11 and 13 show the comparisons of the temperature profiles for pure salt and metal foam/salt composites during heat retrieval. The temperature distribution in the entire melted salt became uniform at the freezing point, so the temperature difference in liquid salt disappeared at about 500 s for pure salt and 250 s for copper foam/salt composite. As a result, the natural convection driven by the temperature difference faded away gradually. Moreover, it can also be seen from Fig. 13 that the temperature of liquid salt became uniform quickly due to high thermal conductivity, i.e., the temperature difference in liquid salt quickly faded away during the initial freezing process. The natural

convection was almost negligible in the major part of heat retrieval process, and the sensible heat conduction dominated the heat transfer. The solid/liquid interfaces would disappear soon once the temperature of the salt decreased from the initial temperature of 260 °C to 220 °C. While the existence of solid/liquid interfaces would be maintained for a long time during heat storage because of the large temperature difference from the initial temperature of 10 °C to 220 °C, as shown in Figs. 10 and 12. In addition, the heat loss from the top of the LTES unit to the surroundings affected the heat storage process to some extent, which resulted in the existence of the solid/liquid interface at 4000 s. The heat transfer characteristics during melting and solidification were described by two-temperature energy equations. The temperature distributions in salt and metal foam showed that the temperature difference existed between the salt and metal foam, as shown in Fig. 14. Because of the large difference of thermal conductivity between salt and metal skeleton, the temperature difference was apparent when the molten salt was in solid state. And the temperature difference was also remarkable in the mushy zone of molten salt, which could also be seen in Fig. 12. The maximum temperature difference between the salt and copper skeleton during heat storage was 6.8 °C, while that between the salt and nickel skeleton was 4.4 °C. The reason was that the thermal non-equilibrium phenomenon was intensified by the latent heat of salt. In addition, the temperature difference was more distinct for the copper foam/salt composite than that of nickel foam/salt composite, which was due to the high thermal conductivity of copper skeleton. Such thermal non-equilibrium must be correctly taken into consideration in the heat transfer modeling, because the temperature distribution of the molten salt was significantly influenced by the presence of the metal foam in both heat storage and retrieval processes. In the present study, the time-durations of heat retrieval processes were determined from the experimental data when the temperatures of all the test points were below 35 °C, 75 °C and 115 °C, respectively, when the cooling temperatures were about 30 °C, 70 °C and 110 °C. Latent enthalpy change and sensible enthalpy change were estimated according to the mass of the salt filled in the LTES unit with and without metal foam. Then the heat storage and retrieval powers per volume were approximately estimated accordingly. The volumetric heat storage power in the LTES unit was in the range of 239.10–362.74 kW/m3, whereas the volumetric heat retrieval power from the LTES unit ranged from 102.13 kW/m3 to 255.55 kW/m3. A LTES system can be constructed

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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Tsalt (°C)

Tcopper (°C)

250 s

750 s

1250 s

250 s

750 s

1250 s

250 s

750 s

1250 s

(Ι-a) Tsalt (°C)

Tnickel (°C)

250 s

750 s

1250 s (Ι-b)

γ

γ

250 s

500 s (ΙΙ-a)

250 s

500 s (ΙΙ-b)

Fig. 13. Temperature profile (I) and solid/liquid interface (II) in metal foam/salt composites during heat retrieval (a) copper foam/salt composite (b) nickel foam/salt composite. (Tcooling = 30 °C).

Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004

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P. Zhang et al. / Applied Energy xxx (2014) xxx–xxx

(a)

tal information for performance evaluation of a LTES system, which can be very useful for heat transfer enhancement so as to realize high input and output powers.

270 240

o

Temperature ( C)

210 180

Num TB (salt)

150

Num TB (copper)

120

Num TC (salt)

90

Num TC (copper)

60

Num TD (salt)

30

Num TD (copper)

0

0

500

1000

1500

2000

5. Conclusions

2500

3000

Time (s)

o

Temperature ( C)

270 240

Num TB (salt)

210

Num TB (copper) Num TC (salt)

180

Num TC (copper)

150

Num TD (salt)

120

Num TD (copper)

90 60 30 0

0

500

1000

1500

2000

2500

3000

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(b)

270 240

o

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210 180

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120

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90

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60

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30

Num TD (nickel)

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210

(1) Natural convection was dominant for pure salt as the heat storage medium during heat storage, but it was weakened in the case of metal foam/salt composites as the heat storage medium due to the flow resistance of the metal foam. Heat retrieval process dominated by heat conduction was largely accelerated in the case of metal foam/salt composites due to the reason that the thermal conductivity was significantly enhanced, e.g., the time-durations of heat retrieval for copper foam/salt composite and nickel foam/salt composite showed 28.8% and 19.3% reduction, respectively, when the cooling temperature was 30 °C. (2) Heat transfer during heat storage and retrieval was described by considering thermal non-equilibrium between the salt and the skeleton of metal foam. Heat transfer investigations during heat storage and retrieval showed that the numerical results agreed reasonably with the experimental results, with a maximum deviation of about 18.0%. (3) The salt near the upper portion at the wall of the tube melted more quickly than that in the lower portion during the melting process, so the solid/liquid interface curved gradually. But the interface was almost perpendicular to the bottom surface of the tube during the freezing process, which also interpreted the heat transfer mechanism of molten salt profoundly. (4) The temperature difference between the salt and metal foam was distinct due to the high thermal conductivity of metal skeleton, e.g., the maximum temperature difference between the salt and copper skeleton during heat storage was 6.8 °C, while that between the salt and nickel skeleton was 4.4 °C. Thus such thermal non-equilibrium must be correctly taken into consideration in the heat transfer modeling.

Num TC (salt)

180

Num TC (nickel)

150

Acknowledgements

Num TD (salt)

120

Num TD (nickel)

This research is jointly supported by the Key Project of National Natural Science Foundation of China (No. U1137605) and the Innovation Foundation of Shanghai Academy of Space Technology (No. SAST201438).

90 60 30 0

In the present study, heat storage and retrieval characteristics of a LTES unit were experimentally and numerically investigated. The eutectic salt (50 wt% NaNO3, 50 wt% KNO3) with a phase change temperature of about 220 °C and metal foam/salt composites were used in the heat storage unit as the heat storage media. A three-dimensional model considering thermal non-equilibrium between the salt and metal foam was established to describe the heat transfer characteristics inside the LTES unit. The following conclusions can be drawn:

0

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References

Time (s) Fig. 14. Temperature evolutions of salt and metal skeleton for metal foam/salt composites during heat storage and retrieval. (a) copper foam/salt composite and (b) nickel foam/salt composite. (Theating = 260 °C, Tcooling = 30 °C). Several regions of the curves coincided because of the slight temperature difference among them.

by aligning many such LTES units in a heat storage tank with the high temperature oil as the HTF. The heat transfer performance of such LTES unit presented in the present study is the fundamen-

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Please cite this article in press as: Zhang P et al. Heat transfer characteristics of a molten-salt thermal energy storage unit with and without heat transfer enhancement. Appl Energy (2014), http://dx.doi.org/10.1016/j.apenergy.2014.10.004