Geotemperature control performance of two-phase closed thermosyphons in the shady and sunny slopes of an embankment in a permafrost region

Applied Thermal Engineering 112 (2017) 986–998

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Geotemperature control performance of two-phase closed thermosyphons in the shady and sunny slopes of an embankment in a permafrost region Wansheng Pei a, Mingyi Zhang a,⇑, Shuangyang Li a, Yuanming Lai a, Long Jin b, Wei Zhai c, Fan Yu a, Jianguo Lu a a

State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China Key Laboratory of Highway Construction and Maintenance Technology in Permafrost Regions, Ministry of Transport, CCCC First Highway Consultants Co., LTD, Xi’an 710065, China c Gansu Earthquake Administration, Lanzhou 730000, China b

h i g h l i g h t s
A model describing the process of air-TPCT-soil coupled heat transfer and heat conduction with phase change is developed.
TPCTs can adjust the geotemperature under a permafrost embankment with shady-sunny effect.
The ambient solar energy can be transferred into the foundation soil by TPCTs in the cold seasons.
The working times and efficiency of TPCTs in the shady and sunny slopes are different.
A permafrost embankment with bilateral TPCTs is better able to reduce the shady-sunny slope effect.

a r t i c l e

i n f o

Article history: Received 15 April 2016 Revised 21 October 2016 Accepted 22 October 2016 Available online 24 October 2016 Keywords: Geotemperature adjustment Two-phase closed thermosyphon embankment Shady and sunny slopes Cold region Global warming

a b s t r a c t Heat pipes are a widely-used technology for energy exchange in the world. One of the important issues in the future is how ground heat control can meet the demands of the environmental and engineering stabilities in cold regions. In this paper, a low-temperature gravity assisted heat pipe (two-phase closed thermosyphon, TPCT) is innovatively installed in an embankment with shady and sunny slopes to adjust the geotemperature of the underlying permafrost stratum. The geothermal conditions for three cases—an embankment without TPCTs, an embankment with unilateral TPCTs (UTPCTs), and an embankment with bilateral TPCTs (BTPCTs)—are assessed based on a three-dimensional heat transfer model considering the global warming. The model includes coupled air-TPCT-soil heat transfer and conductive heat transfer with phase change. The numerical results show that: (1) both the UTPCTs and BTPCTs can cool the permafrost stratum, but the UTPCTs aggravate the asymmetric geotemperature caused by the shady-sunny slope effect; and (2) the BTPCTs are better to alleviate the asymmetric geotemperature by controlling the working time and efficiency of the TPCTs under the two slopes. Consequently, the BTPCTs are a more effective engineering measure for embankments affected by the shady-sunny slope effect. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Permafrost is soil or rock with a temperature below 0 °C for at least two consecutive years [1]. Permafrost includes perennial ground ice [1]. Permafrost regions constitute about 24% of the Earth’s exposed land surface (Fig. 1), and 22.4% of China’s land surface is permafrost regions [1,2]. Permafrost is, however, very sensitive to temperature changes caused by the existence of ground ice. ⇑ Corresponding author. E-mail address: [email protected] (M. Zhang). http://dx.doi.org/10.1016/j.applthermaleng.2016.10.143 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

Melting of ground ice in permafrost areas can produce uneven thaw settlement and can affect building stability [3,4]. One of the important future issues is how ground heat control can meet the demands of the environmental and engineering stability in cold regions. The Qinghai-Tibet Plateau (QTP), with an average elevation of over 4000 m above sea level and an area of about 2.5  106 km2 [4], contains the largest low-latitude permafrost region in the world, as shown in Fig. 1. Approximately 54.3% of the area of the QTP is permafrost [3]. Global mean temperatures have increased continuously since the industrial revolution according to the

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

987

Nomenclature h d L

l g C k Pr sn bn d

e g r y ln c bn V

m q q p t A

heat transfer coefficient (W/(m2°C)) diameter (m) length (m) dynamic viscosity (Pas) heat exchange efficiency volumetric heat capacity (J/m3°C) thermal conductivity (W/(m2°C)) Prandtl number fin space (m) fin height (m) fin thickness (m) dissipation rate of the turbulent kinetic energy gravitational acceleration (m/s2) radius y-direction napierian logarithm specific heat capacity (J/(kg°C)) fin height (m) wind speed (m/s) kinematic viscosity (m2/s) density (kg/m3) heat flux (W/m2) pressure (Pa) time (h) area (m2)

Fig. 1. Distribution of permafrost and ground ice in the Northern Hemisphere. ‘‘High (>20%)”, ‘‘Med (10–20%)”, and ‘‘Low (<10%)” refer to ice content, and ‘‘T (>5– 10 m)” and ‘‘t (<5–10 m)” refer to thick and thin overburden, respectively. QTP represents the Qinghai-Tibet Plateau. Source: Zhang et al. [2]; Image courtesy International Permafrost Association.

lt l R Re T x z k

dynamic viscosity of air (Pas) latent heat of working fluid (J/m3) thermal resistance (°C /W) Reynolds number temperature (°C) x-direction z-direction turbulent kinetic energy

Subscripts/superscripts H height ⁄ equivalent o outer c condenser e evaporator a adiabatic air air i in l liquid s soil f frozen u unfrozen sat saturation va vapor

Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4) and the Paris Climate Agreement of December 2015 [5]. However, a 4 °C warming will likely occur over the QTP over the next 100 years [4]. To date, many different engineering projects have traversed the permafrost areas of the QTP, e.g. the Qinghai–Tibet Railway (QTR), the Qinghai–Tibet Highway (QTH), and so on. Unfortunately, climate warming has accelerated the thawing of permafrost and has caused damage to engineering structures [3,7]. The two-phase closed thermosyphon (TPCT), as an active geothermal control technology, has been widely used in these engineering projects to cool the permafrost stratum and protect the permafrost from thawing. The TPCT is a wickless heat transfer device with highly efficient energy-transfer capacity, which requires no external power supply [8,9]. TPCTs have been widely used in many applications [8–11], e.g. the petrochemical industry [12], solar energy utilization [13– 16], nuclear power engineering [17], and cold regions engineering [18–21], due to their simple structure and eco-friendly advantages. Several studies have shown that TPCTs perform well in cooling permafrost embankments because the ground heat extracted from the soil by the TPCTs in cold seasons is much more than the ambient heat energy transferred into the soil in warm seasons [8,18,20]. TPCTs are usually inserted vertically into the shoulders of an embankment along the road direction, as depicted in Fig. 2a and b. On the QTP, the south-facing slope (sunny slope) often absorbs much more solar energy than the north-facing slope (shady slope) [22–25]. As a result, the transverse geotemperature distributions under the two slopes are asymmetric, which is called the ‘‘shady-sunny slope effect”. The difference in the geotemperatures under a permafrost embankment can cause uneven deformation and even longitudinal cracking [24,25]. To adjust the asymmetric geotemperatures under an embankment with shady and sunny slopes, both unilateral TPCT embankments (UTPCT embankments; Fig. 2a) and bilateral TPCT embankments (BTPCT

988

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

Fig. 2. Photos of TPCT embankments of the Qinghai-Tibet Highway (QTH) in the Qinghai-Tibet Plateau. (a) Unilateral TPCT embankment. (b) Bilateral TPCT embankment.

embankments; Fig. 2b) have been designed along the QTH. However, it remains unknown how the TPCTs can provide a desirable long-term cooling performance for embankments in permafrost regions, taking into account global warming [5,6,26]. In this study, we developed a three-dimensional numerical model to simulate the thermal conditions of TPCT embankments affected by the shady-sunny slope effect. Based on heat and mass transfer theories [9,18,27], the model included coupled air-TPCTsoil heat transfer and conductive heat transfer with phase change in the soil layers. To assess the geothermal control performance of TPCTs, the thermal conditions of three embankments—with UTPCTs, with BTPCTs, and without TPCTs—in a permafrost region of the QTP were simulated for 20 years. To simulate the influence of global warming, a global warming rate of 0.04 °C/year over the next 20 years was considered, based on the Paris Climate Agreement of December 2015 [6].

2. Mathematic model 2.1. The coupled air-TPCT-soil heat transfer model The thermal circuit between the TPCT, the air, and the soil is shown in Fig. 3a. There are three parts to the TPCT: evaporator, adiabatic, and condenser sections. The TPCT transfers heat energy from a heat source to a heat sink using the one-way heat transfer characteristic [9,10]. The working fluid in the evaporator section absorbs external heat energy and vaporizes under a small temperature difference. The vapor rises and passes through the adiabatic section toward the condenser section due to the vapor pressure gradient. In the condenser section, the vapor condenses and releases its latent heat. The condensate then returns to the evaporator under gravity. Large amounts of heat energy are transferred from the evaporator section to the condenser section because of the large amount of latent heat associated with the phase change process. Consequently, the heat energy of the underlying soil can be exchanged to the outside air when the air temperature is less than that of the surrounding soil, as long as the temperature difference between the air and the soil is beyond a critical temperature difference (the startup temperature difference); otherwise, the heat transfer between the air and the underlying soil would stop. Based on the schematic of the thermal resistance network shown in Fig. 3a and b, the equivalent thermal resistance for each section of the TPCT is presented in Table 1. In Table 1, Ac,1 is the area of the condenser section without fins; Ac,2 is the area with fins; Ac,3 is the total superficial area of the smooth condenser section; Lc is the length of the condenser section, n is the number of fins, d is the fin thickness, and r1 and r2 are the outside diameters of the fins and the smooth pipe, respectively. Re is the Reynolds number of the flow through the outside surface of condenser; V is the velocity; hoc is the coefficient of

Fig. 3. Thermal resistance network.

the convective heat transfer between the air and the outer wall of the condenser section; g is the heat exchange efficiency of the fins, and ha is the coefficient of the convective heat transfer of the smooth condenser section. Consequently, the total heat flow Q of the TPCT can be obtained as:

T air  T co T co  T ci T ci  T cl T cl  T el T el  T ei ¼ ¼ ¼ ¼ R1 R2 R3 R4 R5 T ei  T s T air  T s ¼ ¼ P R6 Ri

Q¼

ð1Þ

989

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998 Table 1 The equivalent thermal resistance of TPCT [9,18,21,28]. Section

Thermal resistance: R

Coefficient of the convective heat transfer: h

Condenser section

R1 between the air and the outer wall of the condenser: R1 ¼ Ac;31hoc

hoc ¼ ha

R2 for the tube wall of the condenser: R2 ¼

1 2pkLc

ln

 doc dic

R3 for the liquid film formed inner the condenser: R3 ¼ Aic1hic

Convective heat transfer area: A Ac;1 ¼ pdoc ðLc  ndÞ     Ac;2 ¼ p 2n r 22  r 21 þ 2nr2 d Ac;3 ¼ pLc doc

Ac;1 þgAc;2 ha Ac;3

¼ 0:1378 kdair Re0:718 Pr 1=3 oc where, Re ¼ Vdmoc  3 1=3 k q2 gl hic ¼ 0:925 ll q lLc

Aic ¼ pLc dic Lc

c



Adiabatic section

R4 ¼

0 þ1

the thermosyphon is in working state the thermosyphon is not in working state

R5 for the liquid film and liquid pool in the evaporator: R5 ¼ Aie1hie  R6 for the tube wall in the evaporator: R6 ¼ 2p1kLe ln ddocic

Evaporator section

Total thermal resistance:

P

 hie ¼ 0:32

kl0:3 q0:65 c0:7 g 0:2 q0:4 e l pl 0:25 l0:4 va

q

l

0:1 l



psat pair

1=3

Aie ¼ pdie Le

Ri ¼ R1 þ R2 þ R3 þ R4 þ R5 þ R6

Considering the thermal balance between the TPCT, the air, and the soil layers, the air-TPCT-soil coupled heat transfer process can be written as:

T air  T s @T P ¼ ks @n Ri

ð2Þ

pdoe Le

iteration ends if the normalized temperature change is less than 106 for every time interval [29]. 3. Numerical results and analyses 3.1. Computational model and parameters

where the subscripts f and u represent the frozen and unfrozen states, respectively; C and k are the volumetric heat capacity and thermal conductivity of the media, respectively; and l is the latent heat per unit volume.

In this study, we select an asphalt pavement embankment with an east–west direction in a permafrost region, located at an elevation of 4540 m in the QTP. The TPCT embankment computational domains are determined based on the practical embankment geometries and on the related Ref. [30]. The physical model is shown in Fig. 4. The computational domain of the embankment is shown in Fig. 4. The top width of the embankment is 10.0 m. The boundaries BHMM’H’B’ and CINN’I’C’ are the embankment fill layer surfaces and the boundary MM’N’N is the asphalt pavement surface. The longitudinal width is 2.0 m. There are three different layers of soil: the embankment fill layer, the subclay layer, and the strongly weathered stone layer. The thermal-physical parameters are listed in Table 2. TPCTs with ammonia as the working fluid are utilized at the shoulders of the embankment. The longitudinal spacing between two TPCTs is 2.0 m. The basic parameters of these TPCTs are given in Table 3. TPCTs #1 and #2 are installed in the shady and sunny slopes, respectively. Three cases are simulated according to the engineering entity of the QTH in China: an embankment without TPCTs, an embankment with UTPCTs, and an embankment with BTPCTs. The UTPCT embankment and the BTPCT embankment are designed to adjust the asymmetrical geotemperature distributions under the shady and sunny slopes of the embankment. For the UTPCT embankment, the TPCTs are vertically inserted at the sunny-slope shoulder of the embankment (only TPCT #2 is installed in this model, as shown in Fig. 4a). For the BTPCT embankment, the TPCTs are vertically installed in both the sunny-slope and shady-slope shoulders of the embankment (both TPCTs #1 and #2 are installed in the model, as shown in Fig. 4a).

2.3. Solution method

3.2. Boundary conditions and initial conditions

A numerical solution is employed since the governing equations are strongly nonlinear. The spatial and temporal discretization of Eq. (3) is carried out numerically by the ‘‘control volume integration method” [27]. The discrete equations are solved via a ‘‘successive under-relaxation method” for every time interval [27]. Each

3.2.1. Boundary conditions In a real situation, the thermal boundary conditions of natural ground surfaces and embankment surfaces can be influenced by numerous factors, e.g. solar radiation, air convection, rainfall, evaporation, and so on. To simplify the boundary conditions, the

2.2. The conductive heat transfer model for the soil layers Based on the assumption that heat conduction is 100–1000 times greater than convective heat transfer in the soil layers [29], the convective heat transfer in these layers can be ignored. Thus, only the heat conduction and phase change in the soil layers are considered, and the heat transfer process can be written as [18,25,29]:

C

      @T @ @T @ @T @ @T ¼ k þ k þ k @t @x @x @y @y @z @z

ð3Þ

We assume that the phase change of media occurs in a range of temperature (Tm ± DT). According to the theory of ‘‘sensible heat capacity”, the heat capacity and thermal conductivity of the media is constant when T is beyond phase-transition zone, otherwise, they change linearly with temperature in phase-transition zone. Thus, C⁄ and k⁄ can be expressed as [25]:

C ¼

k ¼

8 > < : 8 > < > :

T < T m  DT

Cf

l > 2DT

u þ C f þC 2

T m  DT 6 T 6 T m þ DT

ð4Þ

T > T m þ DT

Cu kf

T < T m  DT

kf þ k2u DkT f ½T  ðT m  DTÞ T m  DT 6 T 6 T m þ DT ku

ð5Þ

T > T m þ DT

990

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

Fig. 4. The computational model of the embankment with TPCTs. (Part I is the strongly weathered mudstone layer; Part II is the subclay layer; Part III is the embankment fill layer. In figure a, DD’ = 2.0 m, DE = 3.0 m, EF = 27.0 m. In figure b, the cross-section A”D”F”G” is in the middle section in figure a).

Table 2 Thermal-physical parameters of different materials in the computational model [21,32,33]. Physical variables

kf, W/(m°C)

Cf, J/(m3°C)

ku, W/(m°C)

Cu, J/(m3°C)

L, J/m3

Embankment fill Subclay Strongly weathered mudstone

1.980 1.351 1.824

1.913  106 1.879  106 1.846  106

1.919 1.125 1.474

2.227  106 2.357  106 2.099  106

2.04  107 6.03  107 3.77  107

Table 3 Basic parameters of TPCTs. Parameter

Value

Parameter

Value

Parameter

Value

Length of evaporator section, Le (m) Length of adiabatic section, La (m) Length of condenser section, Lc (m)

8 0 4

Inner diameter of pipe, di (m) Outer diameter of pipe, do (m) Thermal conductivity of pipe wall, k (W/(m°C))

0.073 0.083 48.00

Fin height, bn (m) Fin space, sn (m) Fin thickness, d (m)

0.025 0.010 0.0015

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998 Table 4 Temperature parameters of the slopes and natural ground surfaces [31]. Road trend

Variables

T0 (°C)

B (°C)

East–west trend

Ambient air Natural ground surfaces Asphalt pavement surface MM’N’N Sunny slope surfaces Shady slope surfaces

3.82 1.32 2.88

11.50 12.00 15.00

1.96 2.26

12.60 15.50

In Table 4, sunny slope includes surfaces BB’H’H and HH’M’M, and shady slope includes surfaces CC’I’I and II’N’N in Fig. 3.

temperature changes are directly applied to the air and natural ground surfaces [18,29,30]. Based on ‘‘adherent layer theory” and related references [31,32], simplified temperature variations are given in Eq. (6) and Table 4:



T ¼ T 0 þ B sin

2p p t h þ þ a0 8760 2



þ

DT th 8760

ð6Þ

where T0 is the mean annual temperature, B is the annual amplitude of temperature, th is the time in hours, a0 is the phase angle which is determined by the finishing time of embankment, and DT is the warming rate which is taken as 0.04 °C/year [4–6]. Based on the related field data [31], the mean annual air temperature is 3.82 °C. The ambient wind velocity outside the condenser section of the TPCTs can be expressed as [29]:

v 10 ¼ 3:64 þ 1:10 sin



2p 3 t h þ p þ a0 2 8760



ð7Þ

where v10 is the wind velocity at the height of 10 m. The wind velocity at a height of H from the natural ground surface can be calculated according to the following equation:

v H ¼ v 10



a H 10

ð8Þ

where a is the power law exponent, for which a value of a = 0.16 was taken in this study [33]. A constant heat flux of q = 0.06 W/m2 is applied to the bottom surface of the computational model. The lateral boundaries in Fig. 4a are assumed to be adiabatic. 3.2.2. Initial conditions In the simulation, we assumed that the embankment was constructed on July 15 (a0 = 0) since most of the heat energy transfer occurs in the warmest time of the year. The initial temperature fields of the subclay layer and strongly weathered mudstone layer (Parts II and I in Fig. 4) were obtained through a long-term transient solution without considering climate warming. The initial temperature fields of the embankment fill were determined by the air temperature at the construction time. 3.3. Results and analyses The geothermal conditions of the east–west trending embankments (three cases: embankment without TPCTs, UTPCT embankment, and BTPCT embankment) were simulated for 20 years after construction based on the same parameters and boundary conditions. The geothermal states of the middle cross-sections of these embankment models (Fig. 4b) were analyzed to assess the geothermal control performance of the TPCTs. 3.3.1. Embankment without TPCTs Fig. 5a–c shows the geotemperature distributions of the embankment without TPCTs on July 15, October 15, and January 15, in the 10th and 20th years after construction, respectively.

991

The dashed lines refer to the isotherms in the 20th year and the solid lines represent the isotherms in the 10th year. Fig. 5a shows the geotemperature distributions on July 15 in the 10th and 20th years. The geotemperature under the embankment is apparently higher than that under the natural ground surface due to the heat absorbed by the embankment. On this date, the temperature above 0 °C under the embankment is approximately symmetrically distributed. However, the 0.5 °C isotherm is clearly asymmetric due to the shady-sunny slope effect caused by the east–west trend of the embankment. Furthermore, the 0.5 °C isotherm on July 15 in the 20th year moves downwards because of global warming and the embankment construction. Fig. 5b shows that the temperature below the sunny slope is higher than that below the shady slope. A warm-temperature zone of 4.0 °C forms under the sunny slope; however, the 0.5 °C isotherm still exists under the shady slope. This asymmetrical distribution of temperature could make the embankment unstable because the mechanical characteristic of permafrost varies with temperature. The difference in the permafrost mechanics could cause uneven deformation of the embankment and even longitudinal cracking. On October 15, in the 10th and 20th years, the maximum thaw depth of the embankment occurs. The maximum depth of the 0 °C isotherm (permafrost table) under the natural ground surface is nearly Y = 1.71 m on October 15 in the 10th year, a depth that is 2.04 m higher than the permafrost table under the embankment (Y = 3.75 m). The downwards trend of the permafrost table indicates that the construction of the embankment has caused a rise in the geotemperature and resulted in permafrost degradation. The maximum permafrost table under the embankment moves downwards to Y = 5.0 m on October 15 in the 20th year due to climate warming and embankment construction. Meanwhile, the 0.5 °C isotherm also clearly moves downwards on October 15 in the 20th year. On January 15, in the 10th and 20th years (Fig. 5c), although a low-temperature region of 8 °C forms under the sunny slope, a 12 °C isotherm and a 16 °C isotherm appear under the shady slope. The whole embankment is almost frozen. However, there is a small zone of thawed interlayer under the embankment. The thawed interlayer exists close to the sunny slope. Furthermore, the thawed interlayer expands downwards 10 years later due to global warming. The geothermal states could cause problems with the embankment, e.g. uneven deformation of the embankment, cracking, and so on. 3.3.2. UTPCT embankment Figs. 6 and 7 show the thermal variation of a TPCT at the sunnyslope shoulder for the 20th year after construction. In these figures, Time = 0 refers to the beginning of December in the 19th year after construction. The variation of the outer-wall temperature of the evaporator section of the TPCT has three stages (Fig. 6). From the beginning of January to late March, the outer-wall temperature increases with the increasing air temperature. From the end of March to the end of September, the outer-wall temperature keeps increasing and the change rate of the outer-wall temperature slows down because the TPCT stops working during the warm season. After late September, the TPCT begins to work with the continued decrease of air temperature. The variation of the instantaneous heat flow at the outer wall of the evaporator of the TPCT is shown in Fig. 7. A positive heat flow indicates that the TPCT absorbs heat energy from the surrounding soil. It can be seen that the change process of the heat flow is consistent with the variation of the outer-wall temperature (Fig. 6). The heat flow reaches a maximum value (about 160 W/m2) at the end of December when the maximum temperature difference between the evaporator and air temperature occurs, and then decreases with the reduction of the temperature difference and

992

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

(a) July 15

(b) October 15

(c) January 15 Fig. 5. Geotemperature distributions of the embankment without TPCTs in the 10th and 20th years after construction: (a) July 15; (b) October 15; (c) January 15. (Unit: °C).

Fig. 6. Variation of outer-wall temperature at the evaporator section of the TPCT for the UTPCT embankment for the 20th year after construction.

Fig. 7. Variation of the instantaneous heat flow at the outer wall of the evaporator of the TPCT for the UTPCT embankment for the 20th year after construction.

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

993

Fig. 8. Variation of the ambient wind velocity at the height of 10.0 m in a year.

ambient wind velocity (Figs. 6 and 8). At the end of March, the TPCT stops working and the heat flow is 0 W/m2. The TPCT stops working during the warm season (from the end of March to the end of September) and then starts working with the decreasing air temperature and increasing wind velocity (Figs. 6 and 8). Fig. 8 shows the variation of ambient wind velocity at the height of 10.0 m. The wind velocity reaches a maximum value at the beginning of January which is similar with the variation of heat flow at the outer wall of the evaporator of TPCT. This occurs because the heat transfer efficiency increases with the increasing wind velocity. Fig. 9a–c shows the geotemperature distributions of the UTPCT embankment on July 15, October 15, and January 15, in the 10th and 20th years after construction. As in Fig. 5a–c, the dashed line represents the 20th year while the full line represents the 10th year. Similar to the embankment without TPCTs, the geotemperature under the embankment is higher than that under the natural ground surface on July 15 in the 10th and 20th year (Fig. 9a). However, the geotemperature is lower than that of the embankment without TPCTs (Fig. 5a). A low-temperature zone of 1.5 °C exists under the UTPCT embankment on July 15. The low-temperature zones under the embankment are also asymmetric, especially for the 1.5 °C isotherm. The geotemperature under the sunny slope is lower than that under the shady slope because the TPCTs are only inserted at the sunny-slope shoulder of the embankment. Furthermore, the 0.5 °C and 1.5 °C isotherms on July 15 in the 20th year are lower than those in the 10th year. These differences indicate that the geothermal control performance of the TPCTs reduces with global warming. On October 15, the TPCTs begin working, and the thaw depth of the embankment reaches its maximum value (Fig. 9b). The depth of the 0 °C isotherm (permafrost table) is Y = 1.78 m in the centerline of the embankment on October 15 in the 10th year, a depth that is about 0.1 m lower than the permafrost table under the natural ground surface (Y = 1.68 m). Consequently, the TPCTs of the UTPCT embankment can cool the embankment and reduce the thawing of the permafrost. Compared with the geotemperature distributions of the embankment without TPCTs (Fig. 5b), the warm-temperature zone of 4 °C under the embankment diminishes and moves toward the shady slope. However, the 1.5 °C isotherm only forms under the sunny slope due to the cooling performance of the TPCTs. The asymmetric geotemperature distribution could induce moisture redistribution under the embankment and could even cause uneven deformation of the

embankment. Furthermore, the permafrost table in the centerline of the embankment on October 15 in the 20th year still moves downwards because the cooling performance of the TPCTs reduces with global warming. The low-temperature 1.5 °C zone is also significantly diminished in the 20th year. Fig. 9c shows the geotemperature distribution of the UTPCT embankment on January 15 in the 10th and 20th years after construction. The heat flow at the outer wall of the evaporator is relatively high on this date. The soil around the TPCTs is cooled effectively, which can be seen in the existence of the 3 °C and 1.5 °C isotherms. The thawed interlayer under the embankment without TPCTs is eliminated by the geotemperature control of the UTPCTs. Although the embankment is cooled effectively by the TPCTs, the asymmetric geotemperatures could induce moisture redistribution around the TPCTs and could even induce uneven deformation of the embankment under the long-term freezethaw cycle. 3.3.3. BTPCT embankment Fig. 10 shows the air temperature and the outer-wall temperatures of the TPCTs in the 20th year after construction of the BTPCT embankment. The time axis Time = 0 refers to the beginning of December in the 19th year after construction. The variations of the outer-wall temperatures for the two types of TPCTs are similar. At the end of December, the outer-wall temperatures for the two types of TPCTs are the lowest when the ambient air reaches the coldest temperature, and then increase with the rising air temperature. During the warm season from March to September, the two types of TPCTs stop working. At the end of September, the two types of TPCTs start working with the decrease of the air temperature. However, the working time and working efficiency of the two types of TPCTs are different due to the shady-sunny slope effect. Since TPCT #1 is buried in the shady slope and TPCT #2 is buried in the sunny slope, the outer-wall temperature for TPCT #1 is lower than that for TPCT #2, especially when both types of TPCTs stop working. Fig. 11 shows the variations of the instantaneous heat flows of the two types of TPCTs for the 20th year after construction. The heat flow for the two types of TPCTs reaches a maximum value in late December: 146 W/m2 for TPCT #1 and 157 W/m2 for TPCT #2, respectively. The heat flows for the two types of TPCTs decrease with the rising air temperature and decreasing ambient wind velocity (Figs. 8 and 10). The heat flow of TPCT #1 in the shady slope decreases to 0 W/m2 and TPCT #1 stops working in early

994

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

(a) July 15

(b) October 15

(c) January 15 Fig. 9. Geotemperature distributions of the UTPCT embankment in the 10th and 20th years after construction: (a) July 15; (b) October 15; (c) January 15. (Unit: °C).

Fig. 10. Variations of the outer-wall temperatures at the evaporator section of the TPCTs for the BTPCT embankment for the 20th year after construction.

Fig. 11. Variations of the instantaneous heat flows at the outer walls of the evaporator of the TPCTs for the BTPCT embankment for the 20th year after construction.

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

March, while TPCT #2 in the sunny slope does not stop working until late March. Fig. 11 also illustrates that the working time and working efficiency for the two types of TPCTs are different due to the difference of the geotemperatures under the two slopes. In the cold season, the geotemperature under the sunny slope is higher than that under the shady slope (as shown in Fig. 5b and c). The temperature difference between the condenser and evaporator for TPCT #2 is greater than that for TPCT #1, and thus TPCT #2 in the sunny slope begins working a little earlier than TPCT #1 in the shady slope. Therefore, the BTPCTs cannot only cool the permafrost under the embankment, but can also decrease the geotemperature differences under the two slopes by controlling the working time and working efficiency of the two types of TPCTs. Fig. 12a–c shows the geotemperature distributions of the BTPCT embankment for the 10th and 20th years after construction. The geotemperature isotherms of the BTPCT embankment in Fig. 12 are clearly symmetric when compared with those in Figs. 5 and 9. The BTPCTs can also cool the embankment effectively, which can be seen in the existence of the 1.5 °C isotherm. Fig. 12a shows the geotemperature distributions of the BTPCT embankment on July 15 in the 10th and 20th years after

995

construction. The geotemperature under the embankment is lower than that under the natural ground surface. The 1.5 °C isotherm in the centerline of the embankment reaches Y = 1.9 m in the 10th year. Due to global warming, the cooling performance of the two types of TPCTs reduces over time. The downwards trend of the geotemperature isotherms, especially the 0.5 °C and 1.5 °C isotherms, indicates that the geotemperature rises slightly on July 15 in the 20th year. On October 15 in Fig. 12b, the TPCTs in the two slopes have started to work. The permafrost table in the centerline of the embankment is at Y = 1.29 m in the 10th year and Y = 1.45 m in the 20th year, respectively. The thawed depth under the natural ground surface is relatively deep, with the permafrost table at Y = 1.71 m in the 10th year and Y = 1.79 m in the 20th year. On October 15 in the 20th year, the 1.5 °C isotherm diminishes compared with that in the 10th year due to global warming and heat absorption by the pavement. The zone for the 4 °C isotherm is also smaller than that in the UTPCT embankment (Fig. 9b). The geotemperature distributions on October 15 show that the BTPCT embankment can adjust the geotemperature effectively and can reduce the asymmetry caused by the shady-sunny slope effect.

(a) July 15

(b) October 15

(c) January 15 Fig. 12. Geotemperature distributions of the BTPCT embankment in the 10th and 20th years after construction: (a) July 15; (b) October 15; (c) January 15. (Unit: °C).

996

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

On January 15, the two types of TPCTs are both in efficient working condition. The geotemperatures under the two slopes are very low because of the performance of the BTPCTs. The 3 °C isotherm forms around both types of TPCTs. Under the effect of global warming, the cooling performance of the TPCTs reduces and the 3 °C isotherm narrows in the 20th year compared with that in the 10th year. The foundation soil for the embankment is frozen and no thawed interlayer exists. Furthermore, the geotemperatures under both the sunny slope and the shady slope are approximately symmetric. The geotemperature distribution can prevent the embankment problems caused by the shady-sunny slope effect in permafrost regions. Although the BTPCTs can adjust the geotemperature differences under the two slopes, the vertically buried TPCTs cannot completely remove the asymmetric geotemperature distribution, which can be seen in the existence of the 12 oC isotherm below the shady slope. Furthermore, the geotemperatures around the two types of TPCTs are cooled two much in cold winters (Fig. 12c). As a result, uneven transverse frost heave might appear, which could also affect the stability of the embankment.

Fig. 13. Variations of the geotemperatures along LL’ and RR’ for the three embankments on October 15 in the 20th year after construction.

To differentiate the geothermal control performance of the TPCTs in the embankment, the geotemperature along line LL’ under the sunny slope toe and line RR’ under the shady slope toe (as shown in Fig. 4b) on October 15 in the 20th year are given in Fig. 13, for the UTPCT embankment, the BTPCT embankment, and the embankment without TPCTs. For the embankment without TPCTs, the geotemperature along line RR’ is lower than that along line LL’, and the permafrost table (0 °C isotherm) under the sunny slope toe is about 0.6 m deeper than that under the shady slope toe. The maximum geotemperature difference above the permafrost table is 1.56 °C, and that under the permafrost table is 0.28 °C. For the UTPCT embankment, the geotemperature under the shady slope toe (RR’) is still lower than that of the sunny slope toe (LL’) above the permafrost table, but the maximum temperature difference decreases to 0.91 °C. However, the geotemperature at the shady slope toe line (RR’) is higher than that at the sunny slope toe line (LL’) under the permafrost table due to the cooling performance of the TPCTs buried in the sunny slope. The maximum geotemperature difference under the permafrost table reaches 0.38 °C. When the embankment is designed with BTPCTs, the geotemperatures for the two slope toe lines are very low although the geotemperature at the shady slope toe is lower than that at the sunny slope toe. The minimum difference between the two toe lines under the permafrost table is 0.21 °C. The geotemperature difference is the smallest when compared with those for the UTPCT embankment and the embankment without TPCTs. Fig. 14 shows the variations of the permafrost tables in the centerlines of the three embankments over the 20 years since their construction. The depth of the permafrost table also represents the maximum thawed depth, which occurs on October 15 each year. In Fig. 14, the downward trend of the permafrost table represents the degeneration of the permafrost under the embankment. For the embankment without TPCTs, the permafrost table continues to move downwards at a rate of about 0.13 m/year. Therefore, engineering construction and climate warming disturb the thermal condition under the original natural ground surface and cause degeneration of the permafrost stratum under the embankment. For the UTPCT embankment, the permafrost table moves downwards slightly in the first year due to the thermal disturbance of the embankment construction (on July 15). It rises under the cooling performance of the TPCTs, but then begins to move downwards again with climate warming after the 6th year after construction. However, the degeneration rate of the permafrost table (nearly

Fig. 14. Variations of the permafrost tables with time under the embankment centerlines over the 20 years after construction.

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

0.05 m/year) is slower than that under the embankment without TPCTs. For the BTPCT embankment, the BTPCTs can effectively ease the permafrost degeneration. The TPCTs in the two shoulders perform well in cooling of the foundation soil during the first three years. The maximum thawed depth (permafrost table) remains stable from the 3rd year to the 9th year, and it then gradually moves downwards at a rate of about 0.02 m/year. However, the maximum thawed depth is Y = 1.48 m in the 20th year, which is shallower than the initial maximum thawed depth. 4. Conclusions and suggestions In this paper, we simulated the geotemperature control performance of a two-phase closed thermosyphon (TPCT) embankment with shady and sunny slopes in a permafrost region of the Qinghai-Tibet Plateau, based on a coupled air-TPCT-soil heat transfer model. The geotemperature states for three cases—an embankment with unilateral TPCTs (UTPCTs), an embankment with bilateral TPCTs (BTPCTs), and an embankment without TPCTs— were simulated to assess the geothermal controlling performance of TPCTs for an embankment affected by the shady-sunny slope effect, in the context of global warming. On the basis of the simulations, the following conclusions can be drawn: (1) The geotemperature of the foundation soil under the embankment with an east–west trend is highly asymmetric due to the shady-sunny slope effect. The asymmetric geotemperature distribution under the embankment could cause uneven deformation of the embankment in a permafrost region, especially under the context of global warming. (2) TPCTs buried in the sunny shoulder of a UTPCT embankment can effectively ease the permafrost degeneration and cool the foundation soil under the sunny slope. However, this kind of TPCT embankment aggravates the asymmetric geotemperature distribution of the foundation soil. (3) In contrast, the BTPCT embankment is better able to cool the geotemperature of the foundation soil under the embankment by adjusting the working time and efficiency of the two types of TPCTs under the two slopes. Thus, the BTPCT embankment could enhance the stability because the BTPCT embankment cannot only prevent the foundation soil from degenerating but also alleviate the asymmetric geotemperature distribution. (4) However, the BTPCT embankment cannot completely remove the asymmetric geotemperature distribution caused by the shady-sunny slope effect in a permafrost region. Our future work will focus on other control structures, and we will extend the application of TPCTs to wider high-grade highways, considering the installation position and spacing, the embedding depth, the inclination angle, and so on. Acknowledgements This research was supported by the National Natural Science Foundation of China (Grant No. 41471063, 41672315); the 100Talent Program of the Chinese Academy of Sciences (Granted to Dr. Mingyi Zhang); the Key Research Program of Frontier Sciences of Chinese Academy of Sciences (QYZDY-SSW-DQC015); the Program of the State Key Laboratory of Frozen Soil Engineering (Nos. SKLFSE-ZQ-38 and SKLFSE-ZT-26); the STS Program of the Chinese Academy of Sciences (Grant No. HHS-TSS-STS-1502); and the Youth Innovation Promotion Association, Chinese Academy of Sciences (Grant No. 2012300 to Dr. Mingyi Zhang).

997

References [1] P. Subcommittee, Glossary of Permafrost and Related Ground-Ice Terms, Associate Committee on Geotechnical Research, National Research Council of Canada, Ottawa, 1988, p. 156. [2] T.J. Zhang, R.G. Barry, K. Knowles, et al., Statistics and characteristics of permafrost and ground-ice distribution in the Northern Hemisphere, Polar Geogr. 31 (1–2) (2008) 47–68. [3] G.D. Cheng, Permafrost studies in the Qinghai-Tibet plateau for road construction, J. Cold Reg. Eng. 19 (1) (2005) 19–29. [4] S.C. Kang, Y.W. Xu, Q.L. You, W.A. Flügel, N. Pepin, T.D. Yao, Review of climate and cryospheric change in the Tibetan Plateau, Environ. Res. Lett. 5 (1) (2010) 015101. [5] Climate Change 2007-The Physical Science Basis: Working Group I Contribution to the Fourth Assessment Report of the IPCC, Cambridge University Press, 2007. [6] D.H. Qin, The Comprehensive Evaluating Report on the Environment Evolvement in West China, Science Press, Beijing, 2002. [7] W. Ma, G.D. Cheng, Q.B. Wu, Construction on permafrost foundations: lessons learned from the Qinghai-Tibet railroad, Cold Reg. Sci. Technol. 59 (1) (2009) 3–11. [8] M.Y. Zhang, Y.M. Lai, W.S. Pei, L. Jin, Effect of inclination angle on the heat transfer performance of a two-phase closed thermosyphon under lowtemperature conditions, J. Cold Reg. Eng. 28 (4) (2014) 04014007. [9] E.G. Jung, J.H. Boo, Thermal numerical model of a high temperature heat pipe heat exchanger under radiation, Appl. Energy 135 (2014) 586– 596. [10] A. Alizadehdakhel, M. Rahimi, A.A. Alsairafi, CFD modeling of flow and heat transfer in a thermosyphon, Int. Commun. Heat Mass Transfer 37 (3) (2010) 312–318. [11] J. Danielewicz, M.A. Sayegh, B. S´niechowska, M. Szulgowska-Zgrzywa, H. Jouhara, Experimental and analytical performance investigation of air to air two phase closed thermosyphon based heat exchangers, Energy 77 (2014) 82– 87. [12] M. Shanbedi, S.Z. Heris, A. Amiri, A. Sadegh, A. Mohsen, B. Majid, Optimization of the thermal efficiency of a two-phase closed thermosyphon using active learning on the human algorithm interaction, Numer. Heat Transfer Part A: Appl. 66 (8) (2014) 947–962. [13] S.A. Nada, H.H. El-Ghetany, H.M.S. Hussein, Performance of a two-phase closed thermosyphon solar collector with a shell and tube heat exchanger, Appl. Therm. Eng. 24 (13) (2004) 1959–1968. [14] H.M.S. Hussein, Optimization of a natural circulation two phase closed thermosyphon flat plate solar water heater, Energy Convers. Manage. 44 (14) (2003) 2341–2352. [15] H.M.S. Hussein, Transient investigation of a two phase closed thermosyphon flat plate solar water heater, Energy Convers. Manage. 43 (18) (2002) 2479– 2492. [16] X.X. Zhang, X.D. Zhao, J.H. Xu, X.T. Yu, Characterization of a solar photovoltaic/ loop-heat-pipe heat pump water heating system, Appl. Energy 102 (2013) 1229–1245. [17] M. Mochizuki, R. Singh, T. Nguyen, T. Nguyen, Heat pipe based passive emergency core cooling system for safe shutdown of nuclear power reactor, Appl. Therm. Eng. 73 (1) (2014) 697–704. [18] M.Y. Zhang, Y.M. Lai, J.M. Zhang, Z.Z. Sun, Numerical study on cooling characteristics of two-phase closed thermosyphon embankment in permafrost regions, Cold Reg. Sci. Technol. 65 (2011) 203–210. [19] L. Guo, Q.H. Yu, Y.H. You, X.B. Wang, X.X. Li, C. Yuan, Cooling effects of thermosyphons in tower foundation soils in permafrost regions along the Qinghai-Tibet Power Transmission Line from Golmud, Qinghai Province to Lhasa, Tibet Autonomous Region, China, Cold Reg. Sci. Technol. 121 (2016) 196–204. [20] F. Yu, J.L. Qi, M.Y. Zhang, Y.M. Lai, X.L. Yao, Y.Z. Liu, G.L. Wu, Cooling performance of two-phase closed thermosyphons installed at a highway embankment in permafrost regions, Appl. Therm. Eng. 98 (2016) 220–227. [21] K. Bakirci, Evaluation of the performance of a ground-source heat-pump system with series GHE (ground heat exchanger) in the cold climate region, Energy 35 (7) (2010) 3088–3096. [22] T. Pan, S.H. Wu, E.F. Dai, Y.J. Liu, Estimating the daily global solar radiation spatial distribution from diurnal temperature ranges over the Tibetan Plateau in China, Appl. Energy 107 (2013) 384–393. [23] H.X. Zang, Q.S. Xu, H.H. Bian, Generation of typical solar radiation data for different climates of China, Energy 38 (1) (2012) 236–248. [24] Y.L. Chou, Y. Sheng, Z.M. Wei, W. Ma, Calculation of temperature differences between the sunny slopes and the shady slopes along railways in permafrost regions on Qinghai-Tibet Plateau, Cold Reg. Sci. Technol. 53 (3) (2008) 346– 354. [25] Y.M. Lai, S.J. Zhang, L.X. Zhang, J.Z. Xiao, Adjusting temperature distribution under the south and north slopes of embankment in permafrost regions by the ripped-rock revetment, Cold Reg. Sci. Technol. 39 (1) (2004) 67–79. [26] Y.P. Fang, Y.Q. Wei, Climate change adaptation on the Qinghai-Tibetan Plateau: the importance of solar energy utilization for rural household, Renew. Sust. Energy Rev. 18 (2013) 508–518. [27] S. Patankar, Numerical Heat Transfer and Fluid Flow, CRC Press, 1980.

998

W. Pei et al. / Applied Thermal Engineering 112 (2017) 986–998

[28] J. Zhuang, H. Zhang, Heat Pipe Technology and Engineering Application, China Industry Press, Beijing, 2000. [29] M.Y. Zhang, X.Y. Zhang, S.Y. Li, D.Y. Wu, W.S. Pei, Y.M. Lai, Evaluating the cooling performance of crushed-rock interlayer embankments with unperforated and perforated ventilation ducts in permafrost regions, Energy 93 (2015) 874–881. [30] M.Y. Zhang, W.S. Pei, X.Y. Zhang, J.G. Lu, Lateral thermal disturbance of embankments in the permafrost regions of the Qinghai-Tibet Engineering Corridor, Nat. Hazards 78 (3) (2015) 2121–2142.

[31] G.D. Cheng, H. Jiang, K.L. Wang, Q.B. Wu, Thawing index and freezing index on the embankment surface in permafrost regions, J. Glaciol. Geocryol. 25 (6) (2003) 603–607. [32] L.N. Zhu, Study of the adherent layer on different types of ground in permafrost regions on the Qinghai-Xizang Plateau, J. Glaciol. Geocryol. 10 (1) (1988) 8–14. [33] M.Y. Zhang, Y.M. Lai, Z.H. Gao, W.B. Yu, Influence of boundary conditions on the cooling effect of crushed-rock embankment in permafrost regions of Qinghai-Tibetan Plateau, Cold Reg. Sci. Technol. 44 (3) (2006) 225–239.