Experimental and numerical studies on molten salt migration in porous system with phase change

Experimental and numerical studies on molten salt migration in porous system with phase change

International Journal of Heat and Mass Transfer 129 (2019) 397–405 Contents lists available at ScienceDirect International Journal of Heat and Mass ...

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International Journal of Heat and Mass Transfer 129 (2019) 397–405

Contents lists available at ScienceDirect

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

Experimental and numerical studies on molten salt migration in porous system with phase change Yuanyuan Zhang, Jinqiao Wu, Weilong Wang, Jing Ding ⇑, Jianfeng Lu ⇑ School of Materials and Engineering, Sun Yat-Sen University, Guangzhou 510006, China

a r t i c l e

i n f o

Article history: Received 21 May 2018 Received in revised form 14 September 2018 Accepted 27 September 2018

Keywords: Molten salt Porous media Volume of fluid model Solidification

a b s t r a c t Molten salt is promising high temperature heat transfer fluid, and its transport in porous media is an important problem for molten salt application. In this paper, molten salt migration and phase change in cold porous system packed with sand particles is experimentally and numerically studied. Experimental results show that high temperature molten salt continuously migrates and a transparent liquid molten salt layer appears during discharge stage with molten salt pouring into porous bed, and then it solidifies as white opaque solid block during post-discharge stage. A transient axialsymmetrical flow and heat transfer model is developed using volume of fluid model and linear approximation in mushy zone, and the simulated results very well fit with experiment. After molten salt discharges and contacts with the cold surface, a thin solid layer quickly forms for solidification, and then it gradually expands and finally becomes a solid block. Since the earlier solid layer hinders molten salt vertical flow, liquid molten salt will flow across the outer boundary of solid layer, and then molten salt layer below the surface becomes thicker. After molten salt totally solidifies, an inner region with little molten salt will probably exist inside molten salt solid block. The maximum migration region for molten salt in cold porous system is affected by structural and operating parameters. For larger porosity and particle diameter or higher molten salt temperature, molten salt flow in porous system has less flow resistance, and then the maximum migration height can be increased, while the migration diameter is reduced. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Molten salt [1,2] as promising high temperature heat transfer fluid has various advantages as large density and heat capacity, high chemical stability, and low viscosity and vapor pressure, and it is widely used in kinds of industrial systems like solar power station. Molten salt is normally used in a very wide temperature range, so its variable properties play very important role in convective heat transfer. Liu et al. [3] studied turbulent heat transfer convection of molten salt in circular tube, and validated various empirical convective heat transfer correlations. Lu et al. [4,5] reported heat transfer correlations of molten salt in enhanced tubes including transversely and spirally grooved tube. Xiao et al. [6] experimentally reported Nusselt number of molten salt heat convection in helical annular duct. Qian et al. [7] established a tube-and-shell gas cooled molten salt heat exchanger, and obtained convective heat transfer data of molten salt in tube bun⇑ Corresponding authors at: School of Engineering, Sun Yat-Sen University, Guangzhou 510006, China (J. Lu). E-mail address: [email protected] (J. Lu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.122 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

dles. Du et al. [8] developed convective heat transfer correlation of molten salt inside shell-and-tube heat exchanger with segmental baffle. Chen et al. [9] measured laminar heat transfer convection of molten salt in concentric tube, and found that natural convection caused by buoyancy force can strengthen the heat transfer in laminar region. Lu et al. [10] numerically studied molten salt heat transfer in cold filling system. In recent years, molten salt flow and heat transfer in porous media have been also applied and studied. Pacheco et al. [11] developed molten salt thermocline thermal storage system constructed by packed bed with rocks, and measured the temperature distribution of molten salt in porous media. Yin et al. [12] studied thermocline performance of molten-salt in porous packed-bed tank. Xu et al. [13] established heat transfer model with liquid molten salt and solid porous media. Yang et al. [14] obtained performance improvement of a molten salt thermocline system with porous media fill with quartzite rock or silica sand. Abdulla and Reddy [15] considered operating parameter effect on molten salt packed-bed thermal energy storage system. Wu et al. [16] presented 1-D numerical model to analyze molten-salt packed-bed thermal energy storage system with phase change material

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Nomenclature A Amush C2 cp D f g H Hsl h k p Q R Sh Sm T t u u y

flow resistance (kg m2 s2) mushy zone constant (kg m3 s1) inertial loss coefficient (–) thermal capacity (J kg1 K1) diameter (m) content of solid or liquid phase (–) gravity acceleration (m s2) height, depth (m) latent heat (J/kg) heat transfer coefficient (W m2 K1) thermal conductivity (W m1 K1) pressure (Pa) flow rate (cm3 s1) radius (m) heat source (W m3) momentum source (kg m2 s2) temperature (°C) time (s) velocity (m/s) velocity vector (m/s) coordinate (m)

capsules. For heat and mass transfer in porous media as soil or sand, available researchers mainly focused on the transport of fluid, salt solution and contaminant in porous rock. Pia and Sanna [17] used an intermingled fractal unit model to predict permeability in porous media. Swami et al. [18] studied the behavior of reactive solute transport through stratified porous medium. Wu et al. [19] built a numerical model to simulate large-scale migration of nitrate in soil and groundwater. Since the freezing point of molten salt is remarkably higher than surrounding temperature, molten salt probably solidifies as its temperature dropping, and molten salt transport in porous media with phase change will be a critical problem. When molten salt thermocline thermal storage is initial filled or finally cooled down, molten salt in porous system will partially or totally solidify. In some extreme conditions like pipe/storage breakage in solar power station [20], molten salt is leaked, and then its migration in porous medium packed with soil or sand [21] will be a serious pollution problem. During some preparation of porous media as silicon carbide ceramics [22] and molten salt/expanded graphite composite phase change blocks [23], molten salt transport in porous media with phase change should be considered. The phenomena and mechanism of molten salt phase change have been further investigated in available literature. Pacheco and Dunkin [24] reported phase change phenomena of molten salt in the freezeup and recovery events of molten salt system. Liao et al. [25] simulated phase change of molten salt during cold filling of receiver tube by VOF model. Bergmann et al. [26] used two phase flow model to simulate the cooling and rapid solidification of molten metal droplets. Im et al. [27] conducted unified analysis on filling and solidification in casting with natural convection. Molten salt transport in porous media with phase change is an important problem for molten salt application, but associated experiment and mechanism have been seldom studied. In present article, molten salt migration in cold porous system is first experimentally and numerically studied, and special mechanism for molten salt flow and phase change is discovered. Molten salt migration and phase change phenomena in porous system are experimentally observed, and associated migration region is measured. Molten salt migration is further calculated by flow and heat

Greek symbols volume fraction, permeability (–) porosity (–) density (kg m3) small number (–) viscosity (kg m1 s1)

a e q c l

Subscripts ae average external thickness am average migration depth dis discharge process eff effective f fluid g gas in initial condition l liquid phase m molten salt mm maximum migration parameter p particle s solid phase, surrounding condition

transfer model with volume of fluid model and linear approximation in mushy zone. According to experimental and numerical results, molten salt migration characteristics in porous system with phase change are revealed, and then associated dynamic and thermal performance is reported under different conditions. 2. Experimental system and results 2.1. Experimental system According to Fig. 1, experimental system of molten salt migration in porous system mainly includes heating furnace, funnel, plate, quartz sand, thermometer, molten salt, and data acquisition system. Molten salt is heated by resistance furnace (SX-5-12, Tianjin City Taisite Instrument Co., Ltd.) to a prescribed temperature, and the furnace has a power of 5 kW and operating temperature

3

1

4

2

6

7

5 Fig. 1. Experimental system of high temperature molten salt migration in porous media. 1. Molten salt, 2. Funnel, 3. Thermometer, 4. Quartz sand, 5. Circular plate, 6. Thermocouple, 7. Data acquisition.

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of 0–1200 °C. High temperature molten salt is discharged from stainless steel funnel with diameter of 2 mm, and its height is 10–50 cm. The quartz sand as porous media is placed in the circular plate. Molten salt flow rate is calculated by quality change, density and discharge time. K-type thermocouples with uncertainty of 0.5 °C are placed inside the quartz sand, and the results are recorded by data acquisition system (FLUKE 2638A, Guangzhou Huiyuan Electronic Technology Co., Ltd.). The temperature of molten salt in funnel is directly measured by thermometer (Pro’s Kit MT1232, uncertainty of 1.0 °C). In the present experiments, the quartz sand with particle diameter 0.25–0.38 mm and porosity 0.468 and mixed nitrate SYSU-N1 are used, and their properties are described in Table 1 [4]. During solidification, parameters of molten salt are: solidus temperature Ts = 137 °C, liquidus temperature Tl = 140 °C, latent heat Hsl = 56.57 kJ/kg. Before experiment, the data acquisition system is open, and the funnel with molten salt is fixed above the center of plate. As the molten salt temperature drops to a prescribed temperature, the switch of funnel is open, and molten salt begins to flow down. During molten salt migration process, the photos of molten salt phase change phenomena are taken, and the temperatures of sand/molten salt are recorded. After the molten salt totally solidifies, the solid molten salt block is further measured. In present experiments, the discharge time is 90 s, and molten salt flow rate is 2.9 cm3 s1, while initial molten salt temperature is 200–300 °C. The initial temperature of quartz sand is equal to the surrounding temperature 27 °C. 2.2. Experimental results The molten salt solidification phenomena during the whole process are illustrated in Fig. 2, where molten salt flow rate Qm = 2.9 cm3 s1 and initial molten salt temperature Tin = 210 °C. When molten salt flows from the funnel into porous bed, it will first impact the sand, and a little hole forms below the funnel within a very short time. After that, molten salt migrates above and inside the sand. Before 90 s, high temperature molten salt continuously discharges and migrates, and a transparent liquid molten salt layer exists above the sand surface as Fig. 2a. After the discharge stage, molten salt gradually solidifies as opaque solid, and its color turns white. At 120 s, molten salt near outer boundary solidifies, because its temperature first decreases below freezing point. At 300 s, molten salt adjacent to the sand surface totally solidifies. After 600 s, molten salt in the center region gradually solidifies, and it becomes a solid block at 1200 s. In general, the molten salt migration region is mainly determined by the discharge process. The center temperature evolution is presented in Fig. 3, where Qm = 2.9 cm3 s1, Tin = 210 °C, 240 °C, 270 °C. In general, the center temperature evolution has similar tendency, and it totally drops as initial molten temperature decreasing. When molten salt discharges and contacts the surface, the center temperature will rapidly increase to a high temperature near the initial temperature, and then it gradually decreases because of heat loss. After 200– 300 s, the center temperature decreases to that near freezing point, and then it changes slowly for phase change.

Fig. 4 presents solid molten salt block after solidification process, where Qm = 2.9 cm3 s1, Tin = 210 °C. The solid molten salt block mainly includes two regions, and the region above sand surface only has solid molten salt with white and smooth section, while the region below the sand surface is a mixture of sand and molten salt with white and rough section. Because of the hole caused by impact and molten salt migration, a circular cone forms below the sand surface. The block has a little cave in the center of surface, because molten salt in this region finally solidifies as Fig. 2. The maximum diameter and central height of the block are respectively 17.6 cm and 4.1 cm. The height of block gradually decreases with the radius rising, and the height will be 1.6 cm with radius of 3 cm and 0.8 cm with radius of 6 cm. Table 2 further presents migration parameters of solid molten salt block under different initial molten salt temperature, where Qm = 2.9 cm3 s1, Tin = 210 °C, 240 °C and 270 °C. As the initial temperature rises, the viscosity of molten salt decreases, and the molten salt can migrate deeper, so the maximum depth and height increase, while the maximum migration diameter decreases. As initial molten salt temperature increases from 210 °C to 270 °C, the maximum migration height increases from 4.1 cm to 4.6 cm, while the maximum diameter decreases from 17.6 cm to 16.6 cm. 3. Physical model and validation 3.1. Physical model According to the experimental system, an axial symmetrical system as Fig. 5 is established to study the whole process. The simulation system includes the air region and porous region. The radius and height of porous region are R1 and H1, and the height of air region is H2, while the radius of molten salt inlet is R2. The hole impacted by molten salt flow is typically a circular cone with radius R3 and height H3. The bottom temperature is Ts, while the other boundaries have convective heat transfer with heat transfer coefficient of h and surrounding temperature of Ts. At beginning, molten salt with flow rate Qm and initial temperature Tin is discharged, and discharge time is tdis. The migration process will be calculated by volume of fluid model [28] and continuum surface force model [29]. For volume of fluid model, the tracking of the interface between two phases can be accomplished by the solution of equations for the volume fractions of phases. The volume fraction equations for two phase fluid are [28]:

@ am þ u  ram ¼ 0 @t

ð1aÞ

@ ag þ u  rag ¼ 0 @t

ð1bÞ

am þ ag ¼ 1

ð1cÞ

where am and ag mean contents of molten salt and gas, while u ¼ am um þ ag ug , um and ug mean superfacial velocities for molten salt and gas based on the total cross-sectional area of fluid and porous medium.

Table 1 Properties of materials. Material

SYSU-N1

Quartz sand

q (kgtm3)

2085–0.74T 1549–0.15T 0.697–0.000461T 31.59–0.1948T + 0.000425T2  0.0000003133T3

2212 871 1.35 + 0.0014T

cp (J kg1 K1) k (W m1 K1) l (mPas)

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(a) 90 s

(b) 120 s

(d) 600 s

(c) 300 s

(e) 900 s

(f) 1200 s

Fig. 2. Solidification phenomena of molten salt (Qm = 2.9 cm3 s1, Tin = 210 °C).

Table 2 Solid molten salt block parameters under different initial temperature.

o

T ( C)

300 250

Initial temperature

Maximum diameter

Maximum height

200

210 °C 240 °C 270 °C

17.6 cm 17.0 cm 16.6 cm

4.1 cm 4.3 cm 4.6 cm

150 o

210 C o 240 C o 270 C

100 50 0

0

100

200

y Molten salt

300

400

500

600

R2

H2

H3

t (s) Fig. 3. Center temperature evolution.

surface

R3

H2

R sand

Ts

R1

Fig. 5. Physical model of molten salt migration system.

solid salt

where e denotes sand porosity, and qf ¼ am qm þ ag qg . In the region above sand surface, e = 1. Momentum conservation equation is:

mixture of sand and salt

Fig. 4. Solid molten salt block (Qm = 2.9 cm3 s1, Tin = 210 °C).

@



  @ qf u @ ðetÞ

Continuity equation is:

eqf

@t



  þ r  qf u ¼ 0

ð2Þ



þ

r  qf uu

e

2

 ¼ rp þ r 

h

i

l f r u þ Sm  A  q f g

ð3Þ

where p, g, Sm and A respectively denote pressure, gravity acceleration, momentum source term in porous media and mushy zone. Momentum source term in porous media is:

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  l 1 ¼ ui þ C 2 qf jujui 2 a

200

where permeability a and inertial loss coefficient C2 can be calculated as [30]:

160 T (°C)

ð4Þ

Sm;i

120

D2p e3 150 ð1  eÞ2

ð5aÞ

3:5 ð1  eÞ C2 ¼ Dp e3

ð5bÞ

40

where e is porosity for porous media, and Dp is particle diameter. Momentum source term in mushy zone for molten salt can be calculated [28]:

0



A ¼ am

Amush ð1  f l Þ ðf l þ cÞ

2

3

ð6Þ

um

where Amush is mushy zone constant. In present simulation, c=0.001, Amush = 105 kg m3 s1. By using linear approximation in mushy zone, the content of liquid phase in molten salt fl can be described as:

f l ¼ 1 as T > T l fl ¼

T  Ts Tl  Ts

ð7aÞ

as T s 6 T 6 T l

f l ¼ 0 as T < T s h

ð7bÞ ð7cÞ

The energy balance equation is:

@ eqf cp;f T þ ð1  eÞqs cp;s T @t

i

    þ r  qf cp;f uT ¼ r keff rT þ Sh

ð8Þ

where effective thermal conductivity of porous medium keff and energy source term caused by latent heat Sh can be described as [14]:

keff ¼ ekf þ ð1  eÞks Sh ¼ am qm Hsl

@f l @t

ð9aÞ

80

Exp. r=0 cm, z=0 cm Exp. r=0 cm, z=-1.6 cm Sim. r=0 cm, z=0 cm Sim. r=0 cm, z=-1.6 cm

0

10 20 30 40 50 60 70 80 90 t (s)

Fig. 6. The temperature evolution from experiment and simulation (Qm = 2.9 cm3 s1, Tin = 210 °C).

validated. Fig. 6 presents the temperature evolution during the discharge process from experiment and simulation, where Qm = 2.9 cm3 s1 and Tin = 210 °C. When molten salt begins to flow down and impact the sand, the temperature below the funnel first rapidly increases to a high temperature within a short time, and then it gradually decreases because of heat loss to surrounding and sand. In general, the temperature evolution from simulation has a good agreement with experiment. Fig. 7 presents solid molten salt block after solidification process from simulation, where Qm = 2.9 cm3 s1, Tin = 210 °C. Compared with Fig. 4, the shape of solid molten salt block in simulation is similar to that in experiment. The solid block includes the upper region above the surface with salt and the lower region with a mixture of sand and molten salt, and a circular cone exists in the lower region. Because molten salt shrinks during solidification, there is a porous region with little molten salt in the center of block. The diameter and central height of the block are respectively 16.2 cm and 4.4 cm, and their differences between simulation and experiment are respectively less than 8.0% and 7.3%. As a conclusion, the simulated results fit with experiment, and the numerical model is reliable.

ð9bÞ

where kf and ks are thermal conductivities of fluid and solid, and Hsl is latent heat of molten salt. 3.2. Calculation conditions and validation In present experimental system, R1 = 15 cm, R2 = 0.1 cm, H1 = 10 cm, H2 = 15 cm, and properties of molten salt and sand are described in Table 2. According to the present experimental conditions and results, the dimensions for typical hole of circular cone are R3 = 3 cm and H3 = 1.2 cm. The surrounding temperature is Ts = 27 °C, and heat transfer coefficient is h = 5 W m2 K1. The gravity acceleration g is 9.8 m s2. Properties of air [31] are presented as: q=1.225 kg1 m3, cp = 1006 J kg1 K1, k = 0.0242 W m1 K1. l = 0.0000178 kg m1 s1. For typical molten salt discharge process, Qm = 2.9 cm3 s1, Tin = 210 °C, tdis = 90 s. The whole molten salt migration process is simulated by FLUENT 14.5 [28]. Since Reynolds number is larger than critical value of 2300, standard k-e model is applied. Pressure-velocity coupling scheme PISO and upwind scheme is used for calculation, and residual errors for velocity and energy are less than 104. The calculations with quad cell elements of 3828, 7656, 15,312 have similar results, and the difference of migration region is less than 2%, so grid with 3828 elements is used. Since molten salt migration region and solid block are mainly determined by the discharge stage, this stage will be further

4. Flow dynamics and heat transfer during discharge and postdischarge stages The whole molten salt migration process includes two stages: the discharge stage with molten salt pouring into porous bed and post-discharge stage with molten salt solidification. Molten salt distribution during discharge stage is presented in Fig. 8, where Qm = 2.9 cm3 s1, Tin = 210 °C, t = 1 s, 5 s, 10 s, 30 s, 60 s, 90 s. After molten salt flows down, molten salt spreads out around the initial hole. During 1–5 s, molten salt mostly flows inside the hole, and

sand surface

Fig. 7. Solid molten salt block from simulation (Qm = 2.9 cm3 s1, Tin = 210 °C).

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salt 0

7.5

15 cm

(a) 1 s

(b) 5 s

(c) 10 s

(d) 30 s

(e) 60 s

(f) 90 s

air

Fig. 8. Molten Tin = 210 °C).

salt

distribution

during

discharge

stage

(Qm = 2.9 cm3 s1,

o

27

63.6

100.2

(a) 1 s

136.8

173.4

(b) 10 s

C

210

(c) 90 s

Fig. 9. Temperature field distribution during discharge stage (Qm = 2.9 cm3 s1, Tin = 210 °C).

the rest begins to migrate into the sand. At 10 s, the molten salt covers the whole hole, and it also migrates below the hole. After that, molten salt spreads outside the hole, and the molten salt layer becomes larger and thicker. At 90 s, molten salt approaches to its far-end. Compared with molten salt layer above the surface, molten salt layer below the surface is thinner before 30 s, while it will be remarkably thicker after that.

During discharge stage, the temperature evolution is presented in Fig. 9, where Qm = 2.9 cm3 s1, Tin = 210 °C, t = 1 s, 10 s, 90 s. At 1 s, only the temperature of the region adjacent to the hole and axis above the surface increases, because the molten salt mostly flows inside the hole as Fig. 8. At 90 s, molten salt spreads out, and the region with high temperature remarkably expands. The molten salt flow from inlet to surface keeps very high temperature. As the molten salt spreads out, its temperature gradually decreases for heat loss. As a result, the temperature decreases from the axis with high temperature molten salt flow to the side, and it also decreases from surface region with molten salt layer to upper/ lower boundaries. Because of convection, the temperature of air above the surface will be higher than that below sand surface. Since the temperature of molten salt decreases along flow direction, it will solidify above and below the surface. The solidification phenomena during discharge stage is presented in Fig. 10, where Qm = 2.9 cm3 s1, Tin = 210 °C, t = 1 s, 15 s, 60 s, 90 s. In discharge stage, molten salt quickly freezes, and its solid phase gradually develops. At 1 s, the molten salt begins to solidify just after it touches the cold surface, and forms a thin solid layer in the bottom of hole. At 15 s, solid layer covers the bottom of hole. At 60 s, the solid layer has two regions inside and outside the hole. At 90 s, molten salt with solid layer expands to its far-end. At the end of discharge process, there is a small pool of liquid molten salt above the center of solid layer. Because the solid layer hinders molten salt vertical flow, a thin liquid molten salt layer adjacent to the solid layer flows across the outer boundary of solid layer as Fig. 10, and then the molten salt layer below the surface becomes thicker. In addition, solid molten salt block with solid molten salt above sand surface and a mixture of sand and molten salt below the sand surface can be further analyzed. Because cold porous media packed with sand has many pores, molten salt can migrate into it and then solidifies, and then the region below the sand surface is a mixture of sand and molten salt. Because the pervious solid layer limits molten salt vertical migration, some molten salt still exists above the sand surface. Fig. 11 describes flow field during discharge stage, where Qm = 2.9 cm3 s1, Tin = 210 °C, t = 10 s, 90 s. During the discharge

solid salt (a) 1 s

liquid salt

(b) 15 s

front region

air (c) 60 s

(d) 90 s

Fig. 10. Basic solidification phenomena during discharge stage (Qm = 2.9 cm3 s1, Tin = 210 °C).

0

0.1

(a) 10 s

0.2

0.3

0.4

(b) 90 s

Fig. 11. Velocity field during discharge stage (Qm = 2.9 cm3 s1, Tin = 210 °C).

>0.5 0.5 m/s

403

1.4

1.4

1.2

1.2

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0

40

80

120

160

Ham (cm)

0.0 200

t (s)

Dmm (cm)

Fig. 14. Average external thickness and migration depth (Qm = 2.9 cm3 s1, Tin = 210 °C).

16.4

5.2

16.2

5.0

16.0

4.8

Hmm (cm)

stage, the flow fields are mostly similar, and the region with high velocity gradually expands. Below the surface, the flow velocity is very low inside the porous media. In the region inside or near the vertical molten salt flow, the flow velocity increases from 0.5 m/s to 1.52 m/s as molten salt flowing down. The airflow above molten salt layer is induced by molten salt flow from top to side as Fig. 11a, and its flow velocity is also higher. In molten salt region above the surface, its flow velocity is not very high, because lower part of molten salt is solid and upper part has high viscosity with low temperature. Fig. 12 presents the vertical velocity distribution in molten salt layer during discharge stage, where Qm = 2.9 cm3 s1, Tin = 210 °C, y = 0.1 cm, t = 60 s, 90 s. In the inner region of molten salt layer (r < 7.2 cm at 60 s), the vertical velocity is very little, because molten salt flow in the vertical direction is restricted by the solid layer. In the front region of molten salt layer as Fig. 10, liquid molten salt has negative vertical velocity in this region (7.2 cm < r < 8.4 cm at 60 s) as Fig. 12, so liquid molten salt will flow across the outer boundary of solid layer to the underside of solid layer, and then the molten salt layer below the solid layer become thicker. Beyond the molten salt layer, high temperature air convection causes a small positive vertical velocity. After the discharge stage, the temperature of the whole system quickly drops without high temperature molten salt discharge, and molten salt will finally solidify as a solid block. Fig. 13 describes solidification process in post-discharge stage, where Qm = 2.9 cm3 s1, Tin = 210 °C, t = 240 s, 800 s, 1500 s. Above the solid layer, the liquid molten salt gradually solidifies, and it mostly finishes solidification at 800 s. In the lower part of molten salt layer, an inner region with little molten salt exists as shrinkage cavity in casting. After 800 s, the solid molten salt block has little variation.

Hae (cm)

Y. Zhang et al. / International Journal of Heat and Mass Transfer 129 (2019) 397–405

15.8

4.6

15.6

4.4

15.4 15.2

4.2

210 220 230 240 250 260 270 Tin (°C)

(a) Initial temperature (Qm=2.9 cm3s-1, Tin=210-270oC) 5.2

18

5.0 4.8

16

4.6

14

Hmm (cm)

Dmm (cm)

20

4.4 12

4.2

10 1

2

3

4

4.0

3

Qm (cm /s)

(b) Flow rate (Qm=1-4 cm3s-1, Tin=210oC) Fig. 12. Vertical velocity distribution in molten salt layer (Qm = 2.9 cm3 s1, Tin = 210 °C).

Fig. 15. Maximum molten salt migration diameter and height with different inlet conditions.

solid salt

liquid salt

air (a) 240 s

(b) 800 s

(c) 1500 s 3

1

Fig. 13. Solidification phenomena during post-discharge stage (Qm = 2.9 cm s

, Tin = 210 °C).

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5. Molten salt migration performance in cold porous system From Fig. 10, molten salt layer above and below surface quickly expands during discharge stage, and then it slowly changes during post-discharge stage. Fig. 14 describes average external thickness Hae and migration depth Ham related to maximum migration area, where Qm = 2.9 cm3 s1, Tin = 210 °C. Before 90 s, average external thickness and migration depth gradually rise, and then they almost keep constant as 0.7 cm and 1.2 cm after that. Compared with average external thickness, average migration depth is smaller before 30 s, while it will be larger after that. The initial temperature and flow rate remarkably affect molten salt migration process. Maximum migration diameter and migration height (sum of external thickness and migration depth) with different inlet conditions is presented in Fig. 15, where Qm = 1– 4 cm3 s1, Tin = 210–270 °C. When initial temperature increases from 210 °C to 270 °C in Fig. 15a, maximum migration diameter slowly decreases, while maximum migration height remarkably rises from 4.4 cm to 5.0 cm, and those very well fit with the experimental results in Table 2. When molten salt flow rate rises from 1 cm3 s1 to 4 cm3 s1 in Fig. 15b, maximum migration diameter increases from 9.6 cm to 19.2 cm, while maximum migration height decreases from 4.9 cm to 4.1 cm. For larger migration diameter, less liquid molten salt can flow across the front of molten salt layer as Fig. 10, so the migration height decreases.

17.2 4.6 16.8

4.2

16.0

Hmm (m)

Dmm (m)

4.4 16.4

4.0 15.6 3.8 15.2

0.35

0.40

0.45 ε (-)

0.50

0.55

(a) Porosity 5.2

17.2

5.0

16.8

The structure of porous media also affects molten salt migration process. Fig. 16 describes maximum migration diameter and height with different porosity and particle diameter, where Qm = 2.9 cm3 s1, Tin = 210 °C, e=0.35–0.55, Dp = 0.15–0.35 mm. As porosity is increased from 0.35 to 0.56, maximum migration height increases from 4.1 cm to 4.6 cm, while maximum migration diameter decreases from 16.8 cm to 15.4 cm. As particle diameter is increased from 0.15 to 0.35 mm, the maximum migration height increases from 4.1 cm to 5.1 cm, while maximum migration diameter decreases from 16.8 cm to 15.6 cm. Generally, small particle diameter and porosity can limit vertical migration, while horizontal migration scale increases. 6. Conclusions The present article experimentally and numerically studied molten salt migration in porous system with phase change, and conclusions can be given as follows. (1) The whole molten salt migration process in porous system with initial temperature below freezing point includes two stages: the discharge stage with molten salt pouring into porous bed and post-discharge stage. In discharge stage, high temperature molten salt continuously migrates inside and above porous media, and a transparent liquid molten salt layer exists above the surface. In post-discharge stage, molten salt solidifies as opaque solid. (2) The molten salt temperature decreases along flow direction above and below surface, and the system temperature decreases from the axis and surface with high temperature molten salt to the side. After high temperature molten salt touches cold porous media, it begins to solidify near the surface, and solid phase of molten salt gradually expands and finally it becomes a solid block. (3) Because the solid layer hinders molten salt flowing in vertical direction, liquid molten salt flows across the outer boundary of solid layer to the underside of solid layer, so the liquid molten salt in the front region has negative vertical velocity, and then the molten salt layer below the surface becomes thicker. (4) The maximum migration region is bounded by molten salt solidification, and maximum migration diameter and height gradually increase during discharge stage. For larger particle diameter and porosity, molten salt flow in porous system has less flow resistance, and maximum migration height will be increased because molten salt can migrate deeper caused by gravity force, while migration diameter is reduced. Conflict of interest

16.4

4.6

16.0

4.4

Hmm (m)

Dmm (m)

4.8

4.2 15.6 15.2 0.1

4.0 0.2

ε (-)

0.3

3.8 0.4

(b) Particle diameter Fig. 16. Maximum migration characteristics under different system structure (Qm = 2.9 cm3 s1, Tin = 210 °C).

The authors declared that there is no conflict of interest. Acknowledgement This paper is supported by National Natural Science Foundation of China (U1601215, 51476190), National Key Research and Development Program (2017YFB0603501) and Natural Science Foundation of Guangdong Province (2017B030308004). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.09.122.

Y. Zhang et al. / International Journal of Heat and Mass Transfer 129 (2019) 397–405

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