Migration and phase change phenomena and characteristics of molten salt leaked into soil porous system

Migration and phase change phenomena and characteristics of molten salt leaked into soil porous system

International Journal of Heat and Mass Transfer 111 (2017) 312–320 Contents lists available at ScienceDirect International Journal of Heat and Mass ...

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International Journal of Heat and Mass Transfer 111 (2017) 312–320

Contents lists available at ScienceDirect

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

Migration and phase change phenomena and characteristics of molten salt leaked into soil porous system Jinqiao Wu, Jing Ding, Jianfeng Lu ⇑, Weilong Wang School of Engineering, Sun Yat-Sen University, Guangzhou 510006, China

a r t i c l e

i n f o

Article history: Received 22 July 2016 Received in revised form 31 March 2017 Accepted 1 April 2017

Keywords: Molten salt Environmental pollution Leakage Solidification Volume of fluid model

a b s t r a c t Molten salt is important heat transfer and storage medium in various high temperature industrial systems, but its leakage and pollution have been seldom investigated. In this paper, migration and phase change phenomena and characteristics of molten salt leaked into soil porous system are numerically investigated using volume of fluid model. During the leakage stage, molten salt expands above the soil, migrates inside the soil and begins to solidify, and finally it solidifies as a solid layer during the postleakage stage. The vertical velocity of molten salt inside the soil linearly decreases near the surface during the leakage stage, so molten salt gradually migrates into the soil, while the whole flow velocity rapidly approaches to zero after leakage. The temperature and heat flux in the soil near the surface both increase during the leakage stage, and then they decrease during the post-leakage stage. Because of solidification, there exist maximum migration radius and migration depth, so the environment pollution can be limited. As the inlet temperature rises, the maximum migration radius and migration depth both increase for low viscosity of molten salt, while the inlet velocity increment only increases the maximum migration radius. As the soil porosity or particle diameter increases, the maximum migration radius decreases, while the maximum migration depth increases. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Molten salt [1,2] is widely used as heat transfer and storage medium in solar thermal power and other industrial systems. Molten salt is generally composed of two or more inorganic salts, and it has many advantages such as large heat capacity, low melting point, low viscosity and chemical stability at high temperature. The environmental pollution caused by molten salt is also an important problem for its application, and it mainly includes the release of nitrogen oxides under high temperature condition [3,4] and molten salt migration in the soil/groundwater after leakage [5]. In some extreme conditions like pipe/storage breakage, molten salt is leaked into the soil, and molten salt pollution in the soil and groundwater will be a serious problem. The leaked molten salt will flow above and into the soil, and the molten salt and air both play an important role in flow dynamic and heat transfer, so the molten salt leakage process is an unsteady multiphase flow. Various numerical methods [6,7] including VOF (Volume of fluid), CSF (continuum surface force model), and phase field method have been

⇑ Corresponding author. E-mail address: [email protected] (J. Lu). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.04.002 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

applied to investigate these kinds of multiphase processes. Tseng et al. [8] calculated the fluid filling into micro-fabricated reservoirs by VOF and CSF. Lu et al. [9] simulated the dynamic and thermal performance of filled molten salt by VOF. Dawson et al. [10] used the moving boundary model to simulate the growth of crystalline deposits from undetected leakages of industrial process liquors. As the molten salt is leaked into the soil, the temperature of molten salt will drop below the freezing point, so phase change phenomena such as solidification play important roles in the molten salt leakage process. Researchers have investigated the phase change of molten salt during filling process. Pacheco and Dunkin [11] studied the freeze-up and recovery events of a molten salt receiver, and reported the phase change phenomena of molten salt. Lu et al. [12] numerically studied the solidification and melting behaviors and characteristics of molten salt in cold filling pipe. Liao et al. [13] simulated phase change of molten salt during the cold filling of a receiver tube. The phase change of molten salt/metal during its preparation process has been also studied. Bergmann et al. [14] proposed a standard two phase flow simulation model to investigate the cooling and rapid solidification of molten metal droplets. Im et al. [15] analyzed the solidification phenomena in casting. When the leaked molten salt is dissolved by the rain or other water flow, it will migrate into the soil and groundwater. Available

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Nomenclature A Amush C2 cp Dp f g H Hsl h k P q R Sh Sm T t tw u u y

flow resistance (kg m2 s2) mushy zone constant (kg m3 s1) inertial loss coefficient (–) thermal capacity (J kg1 K1) particle diameter (m) content of solid or liquid phase (–) gravity acceleration (ms2) depth (m) latent heat (J/kg) heat transfer coefficient (W m2 K1) thermal conductivity (W m1 K1) pressure (Pa) heat flux (W m2) radius (m) heat source (W m3) momentum source (kg m2 s2) temperature (°C) time (s) the whole leakage time (s) velocity (m/s) velocity vector (m/s) coordinate (m)

researchers have studied the migration of nitrate. Crevoisier et al. [16] simulated the water and nitrogen transfer under furrow irrigation. Wang et al. [17] detected the leaching of nitrate under heavy rainfall, high irrigation rate in growing season and with different amounts of initial accumulated Peng et al. [18] investigated nitrate migration with waters due to nitrogen fertilizer transformation in paddy soils. Ramos et al. [19] successfully simulated water and solute transport in soils, in which water with different salinity and nitrogen concentrations was used. Available articles have respectively studied the phase change of molten salt and migration of salt as solute, but the migration and phase change of molten salt leaked into soil porous system have been seldom studied. Hence, numerical model is proposed to investigate the dynamic behaviors and thermal characteristics of molten salt leaked into soil in present article. The multiphase flow process is simulated using volume of fluid model, and the solid and liquid phases of molten salt during phase change are calculated by considering mushy zone, while the soil is assumed as homogeneous porous medium. The basic migration and solidification phenomena of molten salt during the leakage and post-leakage stages are first described, and then associated dynamic and thermal performances including the flow field, temperature and heat flux are reported. In addition, the maximum migration radius and migration depth are further analyzed under different operating conditions and structural parameters, and the environmental pollution of molten salt under dry condition can be estimated.

2. Physical and mathematical model In order to investigate the migration and phase change phenomena of molten salt leaked into the soil, an axial symmetrical system will be studied. As illustrated in Fig. 1, the whole system is a cylinder, and it mainly includes the soil region and the air region above the soil. The radius of the cylinder is R1, and the heights of the air region and soil region are respectively H1 and H2. The inlet with radius of R2 is set in the top of cylinder. Convection exists in the air boundary, and the heat transfer coefficient and surrounding temperature are respectively h and Ts. The tempera-

Greek symbols volume fraction, permeability (–) porosity (–) density (kg m3) interface tension (N/m) small number (–) viscosity (kg m1 s1)

a e q r c l

Subscripts 0 inlet condition aet average external thickness amd average migration depth eff effective f fluid g gas in inlet l liquid phase m molten salt mmd maximum migration depth mmr maximum migration radius n natural convection s solid phase, surrounding condition

air

inlet, u0

y R2

molten salt

H1

0

R R1

H2 soil Fig. 1. The physical model of molten salt leakage system.

ture of the soil bottom is equal to the surrounding temperature Ts. At the initial time, the molten salt with temperature Tin and velocity uin is leaked from the inlet, and the whole leakage time is tw. After molten salt is leaked, it first drops from the inlet to the soil, then expands above the soil and migrates inside the soil, and it gradually solidifies with its temperature decreasing. Since the leakage process is a multiphase problem, it is simulated using volume of fluid (VOF) model [20], and the interface between molten salt and gas is calculated by the continuum surface force (CSF) model [21]. The continuity equations for the molten salt and gas phases are [20]:

@ am ! Sa þ u ram ¼ m @t qm

ð1aÞ

Sa @ ag ! þ u rag ¼ g @t qg

ð1bÞ

where am and ag denote the contents of the molten salt and gas, and ! ! ! ! ! am þ ag ¼ 1, u ¼ am um þag ug , um and ug denote the velocities of the molten salt and gas, Sam and Sag denote source terms for the contents of molten salt and gas.

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The molten salt with solid and liquid phases can be described as:

f l ¼ 1 as T > T l fl ¼

T  Ts Tl  Ts

ð2aÞ

as T s 6 T 6 T l

ð2bÞ

f l ¼ 0 as T < T s

ð2cÞ

where fl and fs = 1  fl denote the contents of solid and liquid phases in the molten salt zone. The molten salt and gas both act as fluid phase, and the whole system includes the soil porous region and air region. The continuity equation is:

@ðeqf Þ ! þ rðqf u Þ ¼ 0 @t

ð3Þ

where e denotes the porosity of soil, qf ¼ am qm þ ag qg . For air region, e = 1. The momentum equation is: !

! !

! @ðqf u Þ r  ðqf u u Þ ! ! þ ¼ erp þ r½lf r u  þ e Sm eA  eqf g @t e

ð4Þ

!

!

where g denotes the gravity acceleration, Sm is the momentum source term, and A means the momentum sink in the mushy zone of molten salt. The momentum source term including the viscous loss term and inertial loss term can be calculated as: !

Sm ¼ 

lf ! C 2 ! ! u  qf j u j u a 2

ð5Þ

where the permeability a and inertial loss coefficient C2 in each component direction can be identified as [22]:



D2p e3 150 ð1  eÞ2

ð6aÞ

3:5 ð1  eÞ Dp e3

ð6bÞ

C2 ¼

where e and Dp are respectively the porosity and particle diameter of soil. The momentum sink in the mushy zone of molten salt is [20]:

A ¼ am

2

Amush ð1  f l Þ ðf l þ cÞ

3

!

ð7Þ

um

where Amush means the mushy zone constant, c is a small number (0.001) to prevent division by zero. The mushy zone constant measures the amplitude of the damping: the higher this value, the steeper the transition of the molten salt velocity to zero as it solidifies. The energy balance equation is:

h i @ eqf cp;f T þ ð1  eÞqs cp;s T @t ¼ r  ðkeff rTÞ þ Sh

!

þ r  ðqf cp;f u TÞ ð8Þ

where Sh is the energy source term caused by molten salt phase change. The effective thermal conductivity of the porous medium keff is calculated by [20]:

keff ¼ ekf þ ð1  eÞks

ð9Þ

where kf ¼ am km þ ag kg means the thermal conductivity of fluid, and ks means the thermal conductivity of solid medium. The heat generation Sh in Eq. (8) is:

Sh ¼ am qm eHsl

@f l @t

ð10Þ

where Hsl means the latent heat caused by the molten salt phase change. The properties of the molten salt [23], air [24] and soil are illustrated in Table 1. Other important parameters of molten salt during the solidification and melting process are described as following, Ts = 137 °C, Tl = 140 °C, H = 59 kJ/kg, Amush = 105 kg m3 s1. For a typical leakage system in this article, R1 = 10 m, R2 = 0.1 m, H1 = 0.2 m, H2 = 1.3 m. As a porous media of soil (sand), e = 0.468, and Dp = 0.25 mm. The surrounding temperature is 27 °C, and the heat transfer coefficient of the natural convection is 5 W m2 K1. The interface tension of molten salt is r = 0.149–5.56  105T N/ m [12]. The gravity acceleration g is 9.8 ms2. In addition, uin = 3 m/s, Tin = 300 °C, tw = 120 s, and the standard k-e model is proposed to simulate this problem. The simulations are performed using the commercial software FLUENT 14.5 [20]. The present numerical model is a combined model of multiphase flow with molten salt phase change and molten salt transport in porous media, and it can not been directly validated against experimental data due to lack of accurate/available data. However, the numerical model of multiphase flow with molten salt phase change has been developed and validated in our previous article [9,12], and the numerical model of molten salt transport in porous media was validated in available article [25]. As a conclusion, the individual aspects of the current model have been validated, and the modeling approach is expected to be valid. The computational domain is discretized into finite volumes, and the variables are stored in the centre of the mesh cells. The Pressure-Implicit with Splitting of Operators (PISO) pressurevelocity coupling scheme is used to derive the approximate relation between the corrections for pressure and velocity. The explicit interface capturing scheme with VOF model is used. Upwind scheme is used to discretize the momentum and energy equation, and the residual errors of velocity and energy are less than 104. In present investigation, 2-D axial symmetric model is used, and the computational domain including the air and soil zone is comprised by quad cells. According to Table 2, calculations with different elements of 3100, 6200, 12,400, 18,600 and 24,800 yield similar results, and the differences of maximum migration radius and migration depth for last four grids are less than 1%, so grid with 6200 elements is used. The dynamic time-stepping approach is used as Dt = 0.005 s (t  120 s) and Dt = 0.02 s (t > 120 s). 3. Basic dynamic characteristics 3.1. The leakage stage The whole dynamical process mainly includes two stages: the leakage stage and post-leakage stage. During the leakage stage, molten salt is continuously leaked from the inlet to the soil, and then expands above the soil and migrates inside the soil. During the post-leakage stage, molten salt migrates into the soil, and gradually solidifies as solid layer. Fig. 2 presents the molten salt distribution during the leakage stage, where Tin = 300 °C, uin = 3.0 m/s, t = 0.07 s, 0.1 s, 10 s, 30 s, 60 s, 120 s. After the molten salt is leaked from the inlet, molten salt spreads out. As the molten salt flows along the soil, its temperature gradually drops to the freezing point, and the flow velocity of molten salt will drop to zero, so the front of molten salt will stop at a certain point. At 0.07 s, the molten salt flowing from the inlet contacts with the soil surface, then it slightly spreads at 0.1 s, and there are few splashing droplets. At 33 s, the molten salt spreads to the far-end of 6.85 m. Before 97 s, molten salt mainly concentrates near the inlet and the far-end, and molten salt in

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J. Wu et al. / International Journal of Heat and Mass Transfer 111 (2017) 312–320 Table 1 Properties of molten salt, air and steel in present simulation. Properties

Molten salt

Air

Soil

q (kg

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

1.225 1006 0.0242 0.0000178

2212 871 1.35  0.0014T

1

3

m ) cp (J kg1 K1) 1 1 k (W m K ) l (kg m1 s1)

Table 2 Simulation results with different grids. Number of grid element

Maximum migration radius (Rmmr) (m)

Maximum migration depth (Hmmd) (m)

3100 6200 12,400 18,600 24,800

6.97 6.95 6.95 6.96 6.96

0.238 0.248 0.249 0.248 0.247

molten salt mostly keeps high during the leakage stage. In the region above molten salt, the temperature of air is also very high because of heat convection, while the temperature in the region below molten salt drops very quickly. As the molten salt continuously leaks, the high temperature region expands. 3.2. The post-leakage stage

the middle region is a very thin layer. After that, a continuous thick molten salt layer forms. In general, the system has three regions including inlet region, far-end region and middle region. In the inlet region, when molten salt drops from the inlet, it first accumulates just below the inlet, and then it migrates into the soil with high vertical velocity, so the height of molten salt layer above soil surface will rapidly decrease for spreading radius increment and migration inside soil. In far-end region, the flow velocity of molten salt decreases to zero for solidification, so it accumulates as thick layer. In the middle region, molten salt spreads with high horizontal velocity, and most of molten salt transfers from inlet region to far-end region, so only a very thin layer exists. During the leaking process, the molten salt continuously migrates into the soil especially in inlet region and far-end region. Fig. 3 presents the radial velocity field during the leakage stage, where Tin = 300 °C, uin = 3.0 m/s, t = 30 s, 120 s. In general, the flow fields at different times are very similar, and the whole system can be divided into three regions as molten salt region, region above molten salt, and other region. In the molten salt region, the radial velocity is positive because molten salt flows from the centre to boundary, and its maximum velocity is 2.14 m/s at 30 s. In the region above molten salt, the radial velocity is positive in the region adjacent to molten salt layer, because air is droved by the spreading molten salt, while it will be opposite in higher region for the back-flow effect. In the other region, the radial velocity is about zero. At 120 s, the region with high velocity is less than that at 30 s, because molten salt near the far-end is almost stable. Fig. 4 presents the temperature field during the leakage stage, where Tin = 300 °C, uin = 3.0 m/s, t = 30 s, 120 s. In general, the temperature fields at different times are very similar, and the temperature decreases from the centre to boundary. The temperature of

After the molten salt is leaked from the inlet, its temperature drops along the flow direction, and the solidification phenomena appear as the temperature of molten salt is below the freezing point. Fig. 5 typically presents the basic solidification phenomena during the whole process, where Tin = 300 °C, uin = 3.0 m/s. At 75 s, the molten salt begins to freeze in the front region near 6.8 m. At 90 s, the solid phase of molten salt slowly expands. At 121 s, the molten salt leakage finishes, and the solid phase is a very thin layer with the thickness of 0.019 m. At 360 s, the thickness and length of the solid phase respectively increase to 0.028 m and 0.85 m. At 800 s, the length of the solid layer obviously increases along the radial direction, and only the region near the centre has little solid phase. At 2000 s, the molten salt totally changes as solid phase, and a circular solid layer forms. After the molten salt leakage finishes, the solidification process dominates the whole system, so the flow velocity rapidly approaches to zero. Fig. 6 presents the temperature field during the post-leakage stage, where Tin = 300 °C, uin = 3.0 m/s, t = 360 s, 2000 s. As the time goes on, the highest temperature remarkably drops, while the region with high temperature expands. At 360 s, the highest temperature drops to 172 °C, and the depth of the soil with high temperature is about 0.6 m. At 2000 s, the highest temperature remarkably drops to the freezing point. 4. Dynamical and thermal performance evolution 4.1. Flow dynamical performance evolution Fig. 7 presents the radial velocity distribution at the soil surface during the whole process, where Tin = 300 °C, uin = 3.0 m/s, y = 0, t = 30 s, 60 s, 120 s, 121 s. During the leakage stage, the radial velocity distributions at different times are very similar. Near the

salt 0

(a) 0.07 s

10 m

(b) 0.1 s

(c) 10 s

(d) 30 s

(e) 60 s

(f) 120 s

air

Fig. 2. Molten salt distribution during the leakage stage.

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m/s -1.16 -0.94 -0.72 -0.60 -0.28 -0.06 0.16 0.38 0.60 0.82 1.04 1.28 1.48 1.70 1.92

(a) 30 s

2.14

(b) 120 s

Fig. 3. Radial velocity field during the leakage stage.

o

27

82

136

191

(a) 30 s

245

C

300

(b) 120 s

Fig. 4. Temperature field during the leakage stage.

solid salt (a) 80 s

(b) 90 s

(c) 121 s

(d) 360 s

(e) 800 s

(f) 2000 s

liquid salt

air

Fig. 5. Solidification phenomena during the whole process.

o

C

27

56

85

(a) 360 s

124

143

172

(b) 2000s

Fig. 6. Temperature field during the post-leakage stage.

centre R < 0.2 m, the radial velocity rapidly increases to 1.42 m/s. In the middle region, the radial velocity gradually decreases, and the molten salt will be a very thin layer for high velocity as shown in Fig. 2. In the outer region, the radial velocity first remarkably drops to about 0.03–0.06 m/s, and gradually decreases to zero. Since the radial velocity in the outer region is very low, molten salt layer becomes thick. During the leakage stage, the thick molten salt layer in the outer region expands. After the leakage stage, the radial velocity remarkably drops to near zero, and the maximum radial velocity at 121 s is only 0.02 m/s. Fig. 8 presents the vertical velocity distribution inside the soil during the whole process, where Tin = 300 °C, uin = 3.0 m/s, R = 1.0 m. During the whole leakage stage, the vertical velocity inside the soil is similar at different times. As the soil depth y rises, the vertical velocity first linearly decreases from about 0.0085 m/s at the soil surface to about 0.0004 m/s at 0.05 m, so the molten salt gradually migrates into the soil. As the soil depth y is larger than

0.05 m, the vertical velocity is very low. Compared with radial velocity in Fig. 7, the vertical velocity is very little. After the leakage stage finishes, the vertical velocity remarkably decreases during 120–123 s, but it still linearly decreases with the soil depth in the range of 0–0.05 m. After 123 s, the vertical velocity is less than 0.00009 m/s. 4.2. Temperature and heat flux distributions and evolutions During the whole process, the distributions of temperature and heat flux quickly change with the migration and phase change process. Fig. 9 presents the temperature distribution of soil surface during the whole process, where Tin = 300 °C, uin = 3.0 m/s, t = 30 s, 60 s, 120 s, 360 s, 800 s and 2000 s. During the leakage stage, the temperature gradually increases, and the temperature reaches its maximum at the end of leakage stage 120 s. As the radius rises, the temperature quickly drops from 300 °C near

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J. Wu et al. / International Journal of Heat and Mass Transfer 111 (2017) 312–320

30 s

1.4

60 s 1.2

120 s

uR (m/s)

1.0

121 s

0.8 0.6 0.4 0.2 0.0

0

1

2

3

4

5

6

7

R (m) Fig. 7. Radial velocity distribution at the soil surface (y = 0).

30 s

0.008

120 s 121 s

0.006

uy (m/s)

2000 s, the temperature of soil surface is totally below the freezing point. Fig. 10 presents the temperature evolution of the soil along the axial direction, where Tin = 300 °C, uin = 3.0 m/s, t = 30 s, 60 s, 120 s, 360 s, 800 s and 2000 s. During the leakage stage, the soil temperature gradually increases, because the hot molten salt continuously heats the soil. As the soil depth increases, the temperature gradually drops. After the leakage stage finishes, the soil temperature near the soil surface gradually decreases, while the soil temperature away from the soil surface slowly increases because of the heat transfer from soil surface to bottom. At 800 s, the temperature at y = 1.2 is still near the surrounding temperature, so the heat transfer in the soil is slow. Fig. 11 illustrates the heat flux distribution evolution inside the soil, where Tin = 300 °C, uin = 3.0 m/s, y = 0.20 m, t = 30 s, 60 s, 120 s, 360 s and 800 s. In general, the heat flux inside the soil gradually increases during the leakage stage, and then decreases during the post-leakage stage. In the leakage stage, the heat flux quickly drops near the centre for the inlet molten salt effect, then it gradually decreases in the middle region, and it almost linearly drops to zero in the outer region with radius 5–7 m. In the post-leakage stage, the heat flux slightly changes in the region with radius 0– 5 m, and then it almost linearly decreases to zero in the outer region.

121.5 s 123 s

0.004

300

0.002

30 s 60 s

250

120 s 200

0.05

0.10

0.15

0.20

o

y (m)

T ( C)

0.000 0.00

360 s 800 s

150

2000 s

Fig. 8. Vertical velocity distribution inside the soil (R = 1.0 m).

100 50 300

30 s 60 s 120 s 360 s 800 s 2000 s

250

o

T ( C)

200

0

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

y (m) Fig. 10. Temperature evolution of the soil along the axial direction (R = 0).

150

1200

30 s

100

1000

60 s 120 s

800 2

4

6

8

R (m) Fig. 9. Temperature distribution of soil surface during the whole process (y = 0).

the centre, and then it gradually decreases to the freezing point. In the region with radius 6–7 m, the temperature is below the freezing point, so the molten salt will quickly solidify. After the leakage stage finishes, the temperature quickly decreases. At 800 s, the temperature in the region R < 4.75 m is equal to the freezing point, and the phase change plays the primary role in this stage. After

360 s

2

0

qs (W/m )

50

600

800 s

400 200 0

0

1

2

3

4

5

6

R (m) Fig. 11. The heat flux distribution inside the soil (y = 0.20 m).

7

318

J. Wu et al. / International Journal of Heat and Mass Transfer 111 (2017) 312–320

4.3. Molten salt migration performances Fig. 12 presents the average external thickness Haet and average migration depth Hamd evolutions for molten salt during the whole process, where Tin = 300 °C, uin = 3.0 m/s. In general, the average external thickness for molten salt above the surface and the average migration depth below the surface both gradually increase during the leakage stage. Before 32 s, the average external thickness is larger than average migration depth, because the molten salt inside the soil migrates more slowly. Between 32 and 120 s, the average external thickness is less than average migration depth. After 120 s, the average external thickness and migration depth for molten salt change very little, and they are respectively 0.033 m and 0.083 m. The maximum migration radius Rmmr and maximum migration depth Hmmd for molten salt play the critical important role in the environment pollution caused by molten salt leakage. Fig. 13 pre-

sents the maximum migration radius and migration depth evolutions for molten salt during the whole process, where Tin = 300 °C, uin = 3.0 m/s. In general, the maximum migration radius is remarkably larger than the maximum migration depth, and they both gradually increase during the leakage stage. After the leakage stage, the maximum migration radius and migration depth almost keep constant, and they are respectively 6.95 m and 0.248 m. 5. Migration characteristics under different conditions According to flow dynamic and heat transfer of the leakage process, the operating conditions and structural parameters are expected to play an important role in the migration and phase change process. Fig. 14 presents final solidification profiles under different inlet temperatures, where Tin = 300 °C, 400 °C, 400 °C and 565 °C, uin = 3.0 m/s. Similar to Figs. 2 and 5, the final solidifi-

0.10

Haet 9.0

Rmmr (m)

0.04

8.0

0.32

7.5 0.28

0.02

0.00

0.36

8.5

0.06

7.0

0

50

100

150

200

6.5

250

300

350

400

500

550

0.24

Tin ( C)

(a) Inlet temperature

Fig. 12. Average external thickness and migration depth evolutions for molten salt.

0.32

9.0

8

0.25 8.5

7

0.10

3

Hmmd (m)

0.15

4

2 0.05

0.28

8.0 7.5

0.24 7.0 6.5

1 1

0

50

100

150

200

Hmmd (m)

5

Rmmr (m)

0.20

6

Rmmr (m)

450 o

t (s)

0

Hmmd (m)

H (m)

0.40

Hamd

0.08

2

3

0.00 250

4

5

6

0.20

uin (m/s)

t (s)

(b) Inlet flow velocity

Fig. 13. Maximum migration radius and migration depth evolutions for molten salt.

Fig. 15. Maximum characteristics under different operating conditions.

solid salt liquid salt air

(a) 300oC

(b) 400 oC

(c) 500oC

(d) 565 oC

Fig. 14. Final solidification profiles under different inlet temperatures.

J. Wu et al. / International Journal of Heat and Mass Transfer 111 (2017) 312–320

cation profile has three regions including inlet region, far-end region and middle region. As the inlet temperature of molten salt increases, the flow resistance decreases with viscosity dropping, and maximum migration radius and maximum migration depth both increase. When the distance between inlet region and farend region is large enough under high inlet temperature, the solidification layer in the middle region is too thin to be observed, and the inlet region and far-end region almost separate with each other. Fig. 15a presents the maximum migration radius and migration depth for molten salt under different inlet temperatures, where Tin = 300–565 °C, uin = 3.0 m/s. As the temperature increases from 300 °C to 565 °C, the maximum migration radius increases from 6.95 m to 9.18 m, while the maximum migration depth increases from 0.248 m to 0.379 m. As a result, the inlet temperature increment will remarkably increase the environment pollution, because the molten salt can flow further and deeper for low viscosity. Fig. 15b presents the maximum migration radius and migration depth for molten salt under different inlet flow velocities (uintw = 360 m), where Tin = 300 °C, uin = 1.5–6.0 m/s (tw = 60–240 s). As the inlet flow velocity increases, the maximum migration radius significantly increases, while the maximum migration depth changes very little. Fig. 16 presents the maximum migration radius and migration depth for molten salt under different soil porosities and particle diameters, where Tin = 300 °C, uin = 3.0 m/s. As the soil porosity increases from 0.38 to 0.54, the maximum migration radius decreases from 8.23 m to 6.47 m, while the maximum migration depth increases from 0.147 m to 0.34 m. As the particle diameter 8.4 0.35 8.1 0.30

7.5

0.25

7.2 0.20

6.9 6.6

Hmmd (m)

Rmmr (m)

7.8

0.15

6.3 0.35

0.40

0.45

0.50

0.55

(-)

(a) Soil porosity 0.5

7.4

0.4

7.0 0.3 6.8 0.2

6.6 6.4

0.2

0.3

0.4

0.5

0.1

dm (mm)

(b) Particle diameter Fig. 16. Maximum characteristics under different soil structures.

Hmmd (m)

Rmmr (m)

7.2

319

increases from 0.18 mm to 0.55 mm, the maximum migration radius decreases from 7.24 m to 6.42 m, while the maximum migration depth increases from 0.168 m to 0.445 m. In general, small particle diameter and soil porosity will reduce the molten salt migration in the vertical direction, while the maximum migration radius increases. 6. Conclusions The present article numerically investigated the migration and phase change phenomena and characteristics of molten salt leaked into the soil porous system, and several conclusions can be given as follow: (1) The whole dynamical process of molten salt leakage includes two stages: the leakage stage and post-leakage stage. During the leakage stage, the molten salt expands above the soil and migrates inside the soil, and it began to solidify as a thin layer. During the post-leakage stage, molten salt totally solidifies as solid layer. (2) During the leakage stage, the radial velocity of molten salt rapidly increases near the centre, then it gradually decreases in the middle region with a thin layer, and it rapidly drops in the outer region. The vertical velocity is remarkably less than the radial velocity, and it linearly decreases near the surface, so molten salt gradually migrates into the soil. During the post-leakage stage, the velocity quickly approaches to zero. (3) During the leakage stage, the soil temperature gradually increases, because the hot molten salt continuously heats the soil. After the leakage stage finishes, the soil temperature near the soil surface gradually decreases, while the soil temperature away from the soil surface slowly increases. In addition, the heat flux inside the soil gradually increases during the leakage stage, and then decreases during the post-leakage stage. (4) Because of molten salt solidification, the maximum migration radius and migration depth exist, and then the environment pollution can be limited. The maximum migration radius and migration depth both gradually increase during the leakage stage and change very little during the postleakage stage. (5) The operating conditions and structural parameters play an important role in the migration process. The inlet temperature increment remarkably increases the environment pollution by the increases of maximum migration radius and migration depth, while the inlet velocity increment only increases the maximum migration radius. As the soil porosity or particle diameter increases, the maximum migration radius decreases, while the maximum migration depth increases.

Acknowledgement This paper is supported by National Natural Science Foundation of China (U1601215, 51476190), National Key Technology Support Program (2014BAA01B01), Natural Science Foundation of Guangdong Province (1714050000074), and the Fundamental Research Funds for the Central Universities. References [1] U. Herrmann, B. Kelly, H. Price, Two-tank molten salt storage for parabolic trough solar power plants, Energy 29 (2004) 883–893. [2] G.J. Janz, Molten Salts Handbook, Academic Publisher, New York, 1967.

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[3] R.I. Olivares, The thermal stability of molten nitrite/nitrates salt for solar thermal energy storage in different atmospheres, Sol. Energy 86 (2012) 2576– 2583. [4] X.L. Wei, M. Song, Q. Peng, J.P. Yang, X.X. Yang, J. Ding, NOx emissions and NO2formation in thermal energy storage process of binary molten nitrate salts, Energy 74 (2014) 215–221. [5] L.W. Canter, Nitrates in Groundwater, CRC Press, Boca Raton, FL, 1997. [6] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39 (1981) 201–225. [7] T. Biben, Phase-field models for free-boundary problems, Eur. J. Phys. 26 (2005) S47–S55. [8] F.G. Tseng, I.D. Yang, K.H. Lin, K.T. Ma, M.C. Lu, Y.T. Tseng, C.C. Chieng, Fluid filling into micro-fabricated reservoirs, Sens. Actuat. A 98 (2002) 131–138. [9] J.F. Lu, J. Ding, Dynamical and thermal performance of molten salt pipe during filling process, Int. J. Heat Mass Transfer 52 (2009) 3576–3584. [10] M. Dawson, D. Borman, R.B. Hammond, D. Lesnic, D. Rhodes, Moving boundary models for the growth of crystalline deposits from undetected leakages of industrial process liquors, Comput. Chem. Eng. 71 (2014) 331–346. [11] J.E. Pacheco, S.R. Dunkin, Assessment of molten-salt solar central-receiver freeze-up and recovery events, in: International Solar Energy Conference, 1996, pp. 85–90. [12] J.F. Lu, J. Ding, J.P. Yang, Solidification and melting behaviors and characteristics of molten salt in cold filling pipe, Int. J. Heat Mass Transfer 53 (2010) 1628–1635. [13] Z.R. Liao, X. Li, Z.F. Wang, C. Chang, C. Xu, Phase change of molten salt during the cold filling of a receiver tube, Sol. Energy 101 (2014) 254–264. [14] D. Bergmann, U. Fritsching, K. Bauckhage, A mathematical model for cooling and rapid solidification of molten metal droplets, Int. J. Therm. Sci. 39 (2000) 53–62.

[15] I.T. Im, W.S. Kim, K.S. Lee, A unified analysis of filling and solidification in casting with natural convection, Int. J. Heat Mass Transfer 44 (2001) 1507– 1515. [16] D. Crevoisier, Z. Popova, J.C. Mailhol, P. Ruelle, Assessment and simulation of water and nitrogen transfer under furrow irrigation, J. Agric. Water Manage. 95 (2008) 354–366. [17] H. Wang, X. Ju, Y. Wei, B. Li, K. Hu, Simulation of bromide and nitrate leaching under heavy rainfall and high-intensity irrigation rates in North China Plain, J. Agric. Water Manage. 97 (2010) 1646–1654. [18] S.Z. Peng, S.H. Yang, J.Z. Xu, Y.F. Luo, H.J. Hou, Nitrate migration with waters due to nitrogen fertilizer transformation in paddy soils, Paddy Water Environ, 9 (2011) 333–342. [19] T.B. Ramos, J. Simunek, M.C. Goncalves, J.C. Martins, A. Prazeres, N.L. Castanheira, L.S. Pereira, Field evaluation of a multicomponent solute transport model in soils irrigated with saline waters, J. Hydrol. 407 (2011) 129–144. [20] FLUENT 6.1 Documentation. . [21] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100 (1992) 335–354. [22] S. Ergun, Fluid flow through packed columns, Chem. Eng. Prog. 48 (1952) 89– 94. [23] J.F. Lu, X.Y. Shen, J. Ding, Q. Peng, Y.L. Wen, Convective heat transfer of high temperature molten salt in transversely grooved tube, Appl. Therm. Eng. 61 (2013) 157–162. [24] J.H. Lienhard IV, V.J.H. Lienhard, A Heat Transfer Textbook, Phlogiston Press, Cambridge, Massachusetts, U.S.A., 2002. [25] C. Xu, Z. Wang, Y. He, X. Li, F. Bai, Sensitivity analysis of the numerical study on the thermal performance of a packed-bed molten salt thermocline thermal storage system, Appl. Energy 92 (2012) 65–75.