Temperature Field and Optimal Design of Duct-Ventilated Tower Foundation in Permafrost Regions

-e bearing capacity and deformation characteristics of a tower foundation are seriously affected by its temperature status in permafrost regions. It is very important to maintain the tower foundation at a lower temperature status. In this paper, a ventilation duct is introduced into the tower foundation to decline the temperature around the tower footing. A 3D numerical heat transfer model is established to investigate the cooling effectiveness of a duct-ventilated tower foundation. Several cases with different parameters (e.g., diameters and buried depths) are calculated to compare the temperature distribution around the tower foundation during the cold season.-e results show a significant cooling effect of the foundation near the ventilation duct, and an optimized case is found. In the warm season, the adjustable shutter is employed in the duct-ventilated tower foundation to prevent heat in the tower foundation. It is established that an adjustable shutter installed in the ventilation duct can keep the tower foundation in a frozen state in the warm season.


Introduction
e construction of the Qinghai-Tibet Power Transmission Line (QTPTL), running from Golmud (Qinghai Province) to Lhasa (Tibet Autonomous regions), began in July 2010 and was completed in October 2011.It is 550 km in length, located in permafrost regions and interspersed with 1207 towers.More than 70% of the towers are established by precast or cast-in-place footings with embedding depths ranging from 3.7 to 6.0 m [1,2].Due to the characteristic design of the transmission tower, a substantial heave force threatens the stability of the shallow foundation [3,4].Since temperature is an important influencing factor, keeping a lower temperature is the key to guaranteeing the thermal stability of the tower foundation.
ermosyphons are widely used to maintain thermal stability in the QTPTL based on their outstanding cooling effect.In the late 1960s, thermosyphons were adopted to improve the thermal stability of foundations in the cold regions of Canada and America.ermosyphons have been used in the Qinghai-Tibet Highway in China since 1989 and have made an outstanding contribution.
e cooling mechanism of thermosyphons [5,6], the distribution of thermosyphons, the temperature distribution of the foundation [2,7], the long-term cooling effect, and the stress of the thermosyphons were researched around the QTPTL [3,8].It was determined that the thermosyphons could keep the foundation soil at a lower temperature but resulted in a frost jacking risk in the foundations and thermosyphons-induced longitudinal cracks.
e previously mentioned phenomena threatened the stability of the tower foundation and embankment [3,8,9].In addition, the cost of thermosyphons is high and the condensate needs to be added at intervals.us, another active measure is proposed to use in the tower's foundation-duct-ventilated tower foundation.
e investigations showed that the ventilation duct can keep the subgrade at a lower temperature for up to 50 years [24,25]; additionally, combined measures expressed the cooling effect better than the single ventilation duct, e.g., selfadjusting windward vents and chimneys clearly improve the cooling efficiency [26].Furthermore, the cooling effect and mechanism were analysed by comparing the temperature and wind velocity in the duct and the temperature field surrounding the foundation [27].e above studies provide a study basis for ventilation ducts applied in tower foundations, and the application effect should be further studied.
In this paper, the temperature field around the ductventilated tower foundation is analysed via numerical simulations.First, the temperature in the duct is compared to confirm the heat release status.Second, the pipe diameter, depth, and the diameter of the duct-ventilated tower foundation are analysed.e author hopes to find an optimal design for a duct-ventilated tower foundation.

Numerical Model
To guarantee the thermal stability of the tower, the thermal stability of every foot should be considered.For better simulating the boundary of the tower footing, one footing is chosen for calculation.e computational area extends 15 m from the footing centreline and 20 m vertically from the natural ground surface.e diameter of the ventilatedduct tower foundation is D, the diameter of the ventilation duct is d, and the buried depth of the duct-ventilated tower foundation is H. Figure 1 shows the profile map of the duct-ventilated tower foundation.
e column of the foundation soil is divided into backfills and weathered mudstone based on the construction method, with thicknesses of 5 m and 15 m, respectively.e footing has a cone-shaped pile with a height of 4.1 m in the upper part and a cylinder base in the lower part 0.6 m in height and 1.5 m in radius.e influence on the temperature distribution under different buried depths and diameters of the duct-ventilated tower foundation and the diameter of the ventilation duct are considered.Because diameters of thermosyphons are 76 mm, the calculated diameters of the ventilation duct are 8 cm, 12 cm, 16 cm, and 20 cm. e depth of the duct-ventilated tower foundation is based on the depth of the footing, so the calculated buried depths of the duct-ventilated tower foundation are 4.3 m, 4.5 m, and 4.7 m. e diameter of the duct-ventilated tower foundation is 4 m, 4.5 m, and 5 m. e details of the cases are shown in Table 1, and the thermal parameters are shown in Table 2.

Heat Transfer Model for the Air-Ventilated Duct-Soil
System.
e analysis system is CFX in workbench 14.5.A 3D numerical model is constructed to analysis the temperature distribution of the ventilation duct.Four ventilation ducts are distributed symmetrically.e assumption is that the air has constant physical properties and can be treated as an incompressible fluid.
Considering the conduction and phase change problem, the heat transfer process can be written as [ where C s and λ s are the effective volumetric heat capacity and effective thermal conductivity, respectively.e phase change of the media in the tower foundation occurs in a range of temperatures (T m ± ΔT).C sf and λ sf are volumetric heat capacity and thermal conductivity of the media in the frozen area, respectively.C su and λ su are volumetric heat capacity and thermal conductivity of the media in the unfrozen area, respectively.L s is the latent heat per unit volume.C s and λ s are expressed as [30] C s �

Boundary and Initial
Conditions. e mean annual ground temperature is approximately −1∼−2 °C, the mean annual air temperature is approximately −4.0∼−5 °C, and the mean annual wind velocity is approximately 3.0∼5.0m/s [31,32].According to available research and the situ observations, the thermal boundary condition can be written as follows [32,33]: e air temperature: e natural ground surface temperature: e geothermal heat flux at the bottom boundary is 0.06 W/ m 2 , and the lateral boundaries are assumed to be adiabatic.
According to the investigation for wind in the Qinghai-Tibet Plateau, the wind velocity 10 m above the ground surface is changed based on the following equation [27]: Advances in Materials Science and Engineering It is assumed that the initial temperature of the ground surface is -1.0 °C, the air temperature is -4 °C, and the wind velocity is 4 m/s.e calculation begins from July 15, and the time step is 365 h (calculated 48 times per year).e initial temperature boundary condition on July 15 was obtained through a long-term transient solution with the mentioned boundaries.

Results and Discussion
e cooling effect of the duct-ventilated tower foundation is validated by comparing the mean annual temperature in the ventilation duct and temperature on the inner wall and axis of the duct.

Temperature and Wind Velocity in the Ventilated
Duct. e detailed parameters of the ventilated ducts are listed in Table 1 (C1 and C5). e calculation is performed based on the above parameters and the initial and boundary conditions.To check the reliability of the computational model and method in this study, the axial wind velocities changing along the radial direction in the middle crosssection of the duct on January 15 and July 15 are shown in  Table 2: ermal parameters [28]. of the wind on those two dates has the same distribution form as Figure 7 in Zhang et al. [27].e distribution of the annual mean temperature in the lateral duct (from D to L in Figure 3) is similar to Figure 5 in Zhang et al. [27].erefore, the computational model and method in this paper are reliable.
e velocity of the wind in the duct has a maximum value near the axial, and the velocity near the inner wall is the minimum value (Figure 2).ese kinds of distributions are consistent with the usual form of turbulent pipe ow.Furthermore, the mean velocities are 2.7 m/s and 1.5 m/s on January 15 and July 15, respectively (Figure 4).It can therefore fully develop turbulent ow [27].
To demonstrate the cooling e ect of the ventilation duct, Figure 3 displays a comparison of the calculated mean annual temperatures in the axis of the duct, inner wall of the duct, and the virtual duct.e virtual duct is from C 1, which is calculated without the ventilation duct.In detail, the mean annual temperature in the inner wall of the duct (-3.4 °C) is higher than the temperature in the axis of the duct (-3.75 °C), and the mean annual temperature in the axis of the duct (-3.75 °C) is higher than the outside air (-4 °C). is illustrates that the annual heat release of the ventilated duct is larger than the annual heat absorption.Furthermore, the mean annual temperature in the virtual duct (-1.3 °C) is higher than the temperature (-3.4 °C) in the duct. is obviously means that the ventilation ducts can cool the soil around them. e above results show that the ventilation duct has a good cooling e ect.
However, the duct-ventilated tower foundation is different from the duct-ventilated embankment.e ventilated    ducts in the tower foundation have a vertical section.e distributions of the temperature and the velocity are also significantly different.e temperature in the inlet is larger than in the bottom of the duct, which is the same as the velocity.Meanwhile, the temperature in the inlet is slightly higher than the outlet, but the velocity in the inlet is lower than that in the outlet.

Temperature Distribution.
In the permafrost region, the temperature is the most important determined factor that controls construction stability.For a duct-ventilated tower foundation, different parameters can affect the temperature distribution of the surrounding foundation soils.To find the influence of the parameters on the temperature distributions of the tower foundation, the temperature distribution of the duct-ventilated tower foundation is analysed for 5 years.

Influence of the Pipe Diameter.
e detailed parameters of the operating conditions, which have different diameters, are shown in Table 1 (C2, C3, C4, and C5). Figure 5 shows the temperature distributions of the tower foundation.Figure 5 Advances in Materials Science and Engineering temperature near the bottom of the duct is lower than the temperature of the bottom of the tower footing, with the minimum value appearing in Figure 6(d).
Figure 7 is the temperature at a depth of −4.7 m after 5 years of construction on January 15. e in uence of the ventilation duct reaches to 10 m from the footing centreline.
e lowest temperature is approximately −8 °C in the footing centreline, and the lowest temperature is approximately −14 °C at the bottom of the ventilated duct.As far as the present comparison is concerned, d 20 cm has the best cooling e ect.

In uence of the Buried Depth.
e detail parameters of the operating cases, which have di erent buried depths (−4.3 m, −4.5 m, and −4.6 m), are shown in Table 1 (C5, C6, and C7).Figures 8(a  e cooling e ect is better than others in the footing centreline.At 8 m and 10 m, there is no di erence, which is that the in uence range is 8 m from the centreline.In Figure 10, with the cooling e ect of the ventilation duct, the temperature obviously declines, but the depth has little in uence on the cooling e ect.

In uence of the Duct-Ventilated Tower Foundation
Diameter.
e detailed parameters of the operating conditions, which have di erent lateral distances (4 m, 4.5 m, and 5 m), are shown in Table 1 (C5, C8, and C9).Figures 11(a)-11(c) are the temperature distributions of the tower foundation with di erent lateral distances on January 15 after 5 years of construction.ey display that the isotherms are very intensively around the ventilated duct at a depth of 0 m to 5 m.
In Figure 12, when H −11.6 m, the temperature does not have a large wave. is means that the soil stays in a thermally stable state.When H −7.9 m, the temperature has a wave. is means that lateral distance of the duct has an in uence in the lateral direction.When H −6.7 m, the 6 Advances in Materials Science and Engineering temperature near the duct and tower footing is much lower than the temperature of other places as shown in Figure 12 and the temperature on the bottom of the duct is lower than the bottom of the tower footing [34].Figure 13 is the temperature at a depth of −4.7 m on January 15. e lowest temperature is approximately −8 °C in the footing centreline, and the lowest temperature is approximately −14.3 °C at the bottom of the ventilated duct.

Parameter Optimization.
Figure 14 shows the mean annual temperatures of all cases.It is shown that d 0.2 m always has a lower temperature than the other 3 diameters and the lowest temperature (−2.6 °C) appears in the bottom of the footing in the Figure 14(a).It can be seen from Figure 14(b) that H −4.7 m has a lower temperature than other buried depths.It can also be seen from Figure 14(c) that L 4 m always has a lower temperature than the other two conditions and the lowest temperature (−2.6 °C) appears in the bottom of the footing.Obviously, C5 has the best cooling e ect in the above conditions.e instantaneous temperatures of C5 are displayed in Figure 14(d) at four time nodes (Jan 15, Apr 15, Jul 15, and Oct 15).It is regrettable that the temperature in the depth of −4.7 m is higher than 0 °C, as that would melt in the bottom of the tower footing.Our aim is to keep the tower footing stable at all times.In other words, the temperature under the bottom of the tower footing must under 0 °C.erefore, 0      Advances in Materials Science and Engineering it is against our original intention.is problem should be solved.

Duct-Ventilated Tower Foundation with an Adjustable
Shutter.To reduce the temperature under the footing bottom on July 15, the duct-ventilated tower foundation with an adjustable shutter is proposed.In the warm season (the temperature above 0 °C), the duct is kept close; in the cold season (the temperature under 0 °C), the duct is kept open.e detailed work time is shown in Figure 15, and the detailed operating conditions are shown in Table 1 (C5 and C10).e only difference between the two cases is that C10 is kept close in the warm season and C5 is kept open in the warm season.
Based on the ventilation duct, a large thermal gradient quite clearly develops around the ventilation duct and foundation soils.On July 15, the temperatures on the bottom of the footing with the ventilation duct are −2 °C and 0 °C in the two operating conditions, respectively (Figures 16(a) and 16(b)).In the shallow foundation soils, the depth of the thaw is 1 m in Figure 16(a) and 3 m in Figure 16(b), and the 0 °C isothermal line around the footing is 4 m higher than that in Figure 16(b).Due to the ventilated duct and good heat transfer through the concrete footing, the soil temperature near the duct and footing has a much greater difference.e temperature around the duct and footing in Figure 16(a) is almost under −2 °C, which illustrates that the soils in this region stay frozen, but the temperatures around the duct and footing in Figure 16(b) are all above 0 °C. is demonstrates that the duct-ventilated tower footing with a self-adjusting windward switch can keep the soil frozen on July 15. Figure 16(c) shows the temperature distribution without a ventilated-duct tower foundation.e 0 °C isothermal line around the footing is 2 m lower than that in Figure 16(a).
is satisfies the requirement of keeping the tower footing stable all the time.

Conclusions
is paper presents a potential method to cool down the tower foundation temperature in permafrost regions.e temperature distribution of the ventilated-duct tower foundation is simulated and discussed based on the monitoring dates from QTPTL.e contributions are as follows: (1) e ventilated duct around the tower foundation can effectively reduce the temperature of the tower foundation during the cold season (2) A ventilated-duct tower foundation with a good cooling effect can be obtained by an optimized analysis (3) In the warm season, the foundation can stay at a lower temperature by employing an adjustable shutter in the ventilation duct It should be noted that the potential method could be used in other places with other geological parameters.

Table 1 : 7
Numerical simulation cases.Case D (m) D (cm) Yes Note.D: diameter of the duct-ventilated tower foundation; d: diameter of the ventilation duct; H: buried depth of the duct-ventilated tower foundation.

Figure 2 :
Figure 2: Radial wind velocity distribution inside the duct on January 15 and July 15.
wall of the virtual duct Axis of the duct Inner wall of the duct

Figure 3 :
Figure 3: Annual mean temperature at the axis and inner wall of the duct (virtual duct).

Figure 4 :
Figure 4: Instantaneous temperatures at the axis and inner wall of the duct on January 15 and July 15.
)-8(c) are the temperature distributions of the tower foundation with di erent buried depths on January 15 after 5 years of construction.ey show that the isotherms are very intensively around the ventilation duct.It can be seen that H −4.3 m has the smallest range of the −1.0 °C isotherm and H −4.7 m has the largest range of the −1.0 °C isotherm.

Figures 9 (
Figures 9(a)-9(c) are the temperatures at di erent distances from the footing centreline.e cooling e ect is better than others in the footing centreline.At 8 m and 10 m, there is no di erence, which is that the in uence range is 8 m from the centreline.In Figure10, with the cooling e ect of the ventilation duct, the temperature obviously declines, but the depth has little in uence on the cooling e ect.

Figure 7 :
Figure 7: Annual mean temperature in footing centrelines on January 15.