Design and Analysis of a Photovoltaic Anti-Freezing System for Shallow Water Source Wells in Alpine Areas Compatible With Solar Water Lifting Project

. In order to solve the problem that shallow water source wells in northern pastoral areas are prone to freezing in winter, which brings inconvenience to drinking water for local residents. shallow water source wells are taken as the research object. Through field experiments 、 indoor and software simulations, the key factors to prevent freezing of water source wells are discovered by obtained temperature distribution pattern of water source wells,A photovoltaic heating system compatible with existing solar water extraction systems in pastoral areas is designed. It is found that the temperature distribution of water source wells is "steep-slow-slow " in the field and extreme conditions. The steep-rising areas are located at 0.0-1.3m, 0.0-0.8m away from the wellhead, and the temperature rising rates in the steep-rising areas are 10.58 C/m and 15.75 C/m, respectively. Increasing the temperature of "steep rise zone" is very important to improve the water surface temperature of water source wells. The ANSYS software was used to simulate the temperature field of the water source well under extreme conditions (-40℃), and compared with the indoor simulation results to verify its accuracy. A photovoltaic heating system compatible with the existing solar water lifting system in the pastoral area was designed which can generate 1659.52J heat a day larger than 412.2J heat dissipation per day under extreme conditions which is calculated by software model. Theoretically this system can meet antifreeze requirements. An indoor anti-freezing experiment of solar heating for a freezing period (3 months) was carried out. It was found that the temperature at the water surface of the water source well was about 0℃, which verified the feasibility of the solar heating system.


Introduction
The pastoral areas in northern China affected by the Siberian cold current in winter because it's high altitude and .The cold wave drops very frequently, resulting in a cold and long winter in the pastoral areas. It's cold season in most areas lasts for 3~4 months, and the lowest temperature in some areas reaches minus 40℃. Shallow water source wells are the main water supply source for some pastoral areas. In winter, they are often frozen due to low temperature and lack of reliable and effective anti-freezing facilities, bringing great inconvenience and safety risks to local residents and livestock drinking water.
At present, there are few researches on antifreezing of shallow water source wells. The traditional passive anti-freezing measures for shallow water source wells in pastoral areas are mainly adopted, that is, the passive anti-freezing measures are carried out by shrinking the well head, capping the well head, wrapping the thermal insulation anti-freezing materials and cattle and sheep dung around the well head, etc. According to the actual investigation, the above passive insulation measures are adopted. In the long and cold winter, especially in the extreme conditions (-40℃), the water source well will still freeze and lose its water supply function.
Chen Quchang measured the winter temperature field distribution in the water source well of Abaga Banner experiment in Xilin Gol League in the 1980s, but due to the limitation of meteorological conditions, the expected extreme temperature condition (-40℃) was not reached, and no laboratory simulation test analysis was conducted [1] . Other researches on well temperature field mainly focus on mine [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] . Although they are different from the objects of this paper, they provide certain inspiration and reference for the research of this paper. Chen zhiyu et al. made a comprehensive and systematic study on the development law of inclined shaft freezing temperature field by using a physical simulation test with a certain geometric contraction ratio, and obtained the distribution law of inclined shaft freezing temperature field along the axis [2] . Chen honglei et al. analyzed the weak boundary number of temperature field under the actual hole position of the freezing hole at three horizontal positions of the world's first deep frozen wellbore with ANSYS in view of the weak interface of temperature field in the deep frozen wellbore [3] . Ren yanlong et al. studied the expansion and distribution of freezing temperature field and optimized freezing scheme by numerical simulation of transient temperature field on freezing wall of single-ring hole and primary and secondary double-ring hole freezing schemes [4] . Zhou shengquan et al through field measurement and other means, studied the freeze-thaw law of deep shaft wall [5] .Gong youchang et al analyzed expansion law of the freezing temperature field in deep frozen shaft by using the finite element software [6] .Li yong et al studied the influence factors of temperature stress field through basing on the relevant theories of heat transfer and elastoplastic mechanics,in combination with the actual sealing conditions of cement sheath [7] .
In this paper, the temperature field data of water source well at -26℃ was obtained through field experiments. In order to obtain the temperature field data of water source well under extreme conditions (-40℃), indoor simulation method was needed. This paper carried out the following research: (1)Carry out indoor simulation research based on field conditions (temperature)、compare and analyze with measured data to verify the correctness and accuracy of indoor simulation method (2) The distribution law of temperature field of water source well under extreme conditions (-40℃) was obtained by indoor simulation; (3) The rationality of software simulation was verified by comparing ANSYS simulation and indoor simulation methods, and the parameters of solar heating antifreezing system were designed based on the data of software simulation (4) The feasibility of anti-freezing of the solar heating system in extreme conditions (-40℃) was verified through laboratory tests

Overview of the study area
The average annual temperature is 2.5℃, and the average annual wind speed is 4.5m/s. The zonal soil is chestnut soil with rough texture. The soil layer is generally 30cm thick, and the calcium accumulation layer under it is generally 30-50cm thick.
A typical water source well in Xilamuren grassland was studied. The depth of the test water source well is 7.8m, with a static water level of 3.4m and a diameter of 1.5m. The structure of the water source well is formed by the accumulation of cement rings, as shown in Figure 1.

Field test research methods
The field experiment was conducted on a bobbin well in Xilamuren Grassland, Baotou City, Inner Mongolia, from October 2016 to February 2017. The measurement method was a positioning steel wire placed at the bottom of the water source well. A Pt100 temperature probe was set every 0.5m in height, and another probe was set for temperature measurement. The temperature distribution inside the water source well was measured.

Test results
January 22, 2017 is selected as the representative day, and the temperature distribution inside the water source well is shown in Figure 2. It can be seen from Figure 2 that during the test period, the temperature of the water source well increased with the increase of the well depth. According to the temperature rise rate (), the temperature change in the well can be roughly divided into three stages. The first stage is the "steep rise zone", from 0.0m to 1.3m away from the wellhead. The temperature in this stage rises faster, from -15.7℃ to -1.9℃, with a temperature increase of 13.5℃ and a temperature rise rate of 10.58℃/m. The second stage is the "slow rise zone", from 1.3m to 1.8m away from the wellhead, the temperature rise rate in this stage is slow, from -1.9℃ to -1.1℃, the temperature increased by 0.8℃ The third stage is from 1.8m to 7.8m from the wellhead. During this stage, the temperature rise rate changes very little. The temperature rises from -1.1℃ to 1.8℃, the distance increases 6m, and the temperature rises only 2.9℃.
According to the field meteorological data, the local minimum temperature during the test period was -26℃, which did not reach the extreme temperature condition expected in the test (-40℃). Therefore, it is necessary to conduct indoor simulation to study the distribution law of the temperature field in the water source well under extreme conditions.

Model making
According to the similarity theory. Select the same materials as field test conditions and make similar models. The soil layer of the field test soil -chestnut soil,That is to say, prototype materials are used in the simulation test, in which, Density reduction ratio: Reduction of thermal conductivity: Specific heat capacity shrinkage ratio: Latent heat shrinkage ratio of water to ice: ρandρ' are the material density of engineering prototype and test model respectively, kg/m 3 ;λ and λ' are the thermal conductivity of engineering prototype and test model materials, respectively, W/(m·℃);C and C' are the specific heat capacity of engineering prototype and test model, kJ/(kgꞏ℃), respectively. ψ、ψ' are the latent heat released by engineering prototype and experimental model respectively, kJ /m 3 .
Geometric reduction. Considering the test conditions, the processing of the model and the feasibility of the test, in order to meet the requirements of the test scale and test accuracy, the geometric reduction ratio was selected as 9.3 according to the similarity criterion. Through calculation, the height of the model water source well is 839mm and the diameter is 161mm. The model water source well uses cement pipe, which is consistent with the material of the test water source well.
Temperature reduction C t . According to Kosovich's criterion: According to(1)-(4) ， Equation (6) is taken into equation (5) to obtain Where, t and t' are the temperature of engineering prototype and test model respectively, ℃.According to(1)-(4)、(6)、(7) According to C t =1, the temperature at the corresponding point of the engineering prototype and the test model is the same.
Time reduction. According to Fourier's criterion: Where, τ and τ' are the time of engineering prototype and test model respectively, s; r is the length of the engineering prototype, m; r' is the thermal conductivity of the material for the length time of the test model, W/(mꞏ℃). According to(9)-(11) C λ C τ /(C r 2 C ρ ) =1， according to(1)、 (2): C τ = C r 2 =86.5， C τ is the time reduction; C r is the geometric contraction.
The test water source well model is shown in Figure  3.

Design of indoor simulation scheme
The laboratory test was conducted in a low-temperature chamber (Shanghai Tianfeng: TF-LK40-4000LA). The temperature in the cryogenic chamber ranges from 40℃ to -44℃.
The boundary conditions are similar. According to C t =1, the temperature in the simulation test should be the same as that in the actual project. Therefore, insulation materials should be used around and at the bottom of the soil layer under test to ensure the consistency of temperature boundary conditions. For this reason, rubber and plastic insulation materials are wrapped around and at the bottom of the test water source well, and heating resistance wires are laid in the sand at the bottom of the water source well to ensure the consistency of the bottom boundary conditions. Temperature probes are placed around the water source well to measure the temperature of the soil layer around and under the test water source well. The design diagram of the indoor test scheme is shown in Figure 4, and the test layout is shown in Figure  5. Through observation and comparison, the boundary temperature of test water source well is consistent with field condition under the same temperature condition.  Install a positioning iron wire inside the water source well to measure the temperature inside the well. In order to compare with the field test data, it needs to be installed at the same location. After calculation, a total of 8 locations are located 0cm, 3.2cm, 8.6cm, 4.7cm, 35.5cm, 46.2cm, and 84cm away from the wellhead (relative to the field 0.0m, 0.3m, 0.8m, 1.3m, 2.3m, 3.3m, 4.3m, and 7.8m).

Comparative analysis
The temperature distribution of the water source well on a typical day of the field test is selected. Combined with the indoor simulated temperature distribution under the same conditions, the data of the two are analyzed and compared. After analysis, the data of the two are basically the same, which proves that the size and boundary conditions of the test water source well are consistent with the field test, and proves the reliability of the indoor simulation.

ANSYS simulation research
Using ANSYS to simulate the convective heat transfer model of a water source well, several assumptions were made: ① the temperature at the bottom of the water source well is a constant temperature field; ② Neglecting the heat conduction between the water source well and the surrounding soil, i.e. ignoring the heat loss along the horizontal axis of the water source well, and only considering the heat loss in the vertical direction of the water source well; ③ Use the measured boundary and bottom temperature in the field as the boundary conditions for ANSYS simulation.

Simulation Model
According to the geometric dimension of the actual well, the numerical computational geometry model is established by UG, as shown in Figure 6: The diameter of the water well is 1.5m; Light blue represents air, with a height of 3.4m; Dark blue represents the area of water, with a height of 4.4m;The gray color represents the cement well wall surface, with a total height of 7.8m;There is a 2cm thick iron manhole cover above the cement well wall. Because the actual well structure is symmetrical, the temperature distribution can be considered as symmetrical distribution, and half of the actual structure is taken for calculation.

Initial and boundary conditions of the model
According to the temperature settings under extreme indoor conditions, set the initial temperature to 1 ℃ and the ambient temperature to extreme temperature conditions (-40 ℃). There is natural convective heat transfer between the external air manhole cover and the exposed cement pipeline, and the convective heat transfer coefficient is set to 4.752Wm ℃ according to literature. The outer surface of the cement buried underground is set as a temperature boundary. Based on actual field measurement data, the upper part of the temperature is set to vary along the depth, the bottom is set to a constant temperature of 0.8 ℃ according to indoor simulation results, and the other contact surfaces are isothermal interfaces, which means that the temperature at the interface between the air temperature inside the pipe and the inner pipe wall is considered equal. The temperature setting of the outer wall of the upper part of the well is shown in Figure 7.

Calculation results
The temperature field after 12 hours of reaching the thermal equilibrium state (steady-state) was calculated, and the water temperature value in the water source well is shown in Figure 8.

Comparative analysis
The comparison between ANSYS simulated values and indoor simulated measured values is shown in Figure 9. From the above figure, it can be seen that the simulation results using ANSYS are basically similar to the field measured data and change trends, and the overall consistency is good. Among them, at a distance of 0.3m from the wellhead, the simulated temperature is -17.0 ℃, and the measured temperature is -14.8 ℃, with an error of 2.2 ℃; At a distance of 0.8m from the wellhead, the simulated temperature is -9.5 ℃, while the measured temperature is -8.5 ℃, with an error of 1.0 ℃; At a distance of 1.3m from the wellhead, the simulated temperature is -5.5 ℃, while the measured temperature is -4.8 ℃, with an error of 0.7 ℃; At a distance of 2.3m from the wellhead, the simulated temperature is -2.2 ℃, while the measured temperature is 0.1 ℃, with an error of 2.3 ℃; At a distance of 3.3m from the wellhead, the simulated temperature is 1.3 ℃, while the measured temperature is 0.9 ℃, with an error of 0.4 ℃; At a distance of 4.3m from the wellhead, the simulated temperature is 1.9 ℃, while the measured temperature is 0.9 ℃, with an error of 1.0 ℃; At the bottom of the well, the simulated temperature is 2.0 ℃, while the measured temperature is 0.9 ℃, with an error of 1.1 ℃.
Analysis of error reasons: ① Due to the fact that the outdoor temperature did not reach extreme conditions (-40 ℃), there is no data on the distribution of temperature fields at the boundary of the water source well under extreme conditions, namely the soil temperature at the wellhead edge and the temperature at the bottom of the well. When setting boundary conditions using ANSYS, data obtained from field measurements are used as boundary conditions, which are lower than the boundary values under extreme conditions, resulting in errors between simulation results and measured values The freezing of water source wells is mainly affected by temperature, but temperature is an unstable and irregular process of change, making it difficult to simulate temperature similarity conditions during the simulation process During the freezing process of the water source well, the water source not only conducts thermal convection with the air in the well, but also conducts thermal conduction with the surrounding soil. When using ANSYS for simulation, the heat transfer model was simplified, ignoring the heat exchange between water sources and surrounding soil, and only considering the heat exchange process between water and air. Therefore, it caused an error between the simulated and measured values. From the above, it can be seen that the ANSYS simulation results have a high similarity with the indoor simulation results, which can be used as a reference basis.

Heat dissipation calculation
Using ANSYS to calculate the heat dissipated by the water source well within 24 hours is 412.2J. Therefore, in order to ensure the stability of the water source temperature, the designed solar heating system needs to generate at least 412.2J of heat per day.

Design of Solar Heating System
From the previous analysis of the temperature field of the water source well, it can be seen that under extreme conditions, the temperature change of the water source well can be divided into three stages. Among them, the first stage has the fastest temperature rise, which is located 0.0-0.8m away from the wellhead. Therefore, how to effectively increase the temperature of this stage is of great significance for improving the water surface temperature of the water source well and preventing the freezing of the water source well.
This article uses spiral shaped thermoelectric resistance wires to drive the resistance wires to generate heat through solar direct current (without converting AC power), thereby increasing the air temperature in this section. At the same time, in order to prevent hot air from flowing up and losing due to its lower density compared to cold air, this article designs an insulation cover similar to a "pot cover" to prevent the loss of hot air, forming an insulation layer above the inside of the water source well, By increasing the temperature of the water source well during this stage, it can also reduce the heat exchange between the water source and the external air, thereby preventing a significant decrease in water surface temperature and achieving the goal of preventing water source freezing.Place the resistance wire and insulation cover 0.06m away from the wellhead. The outer edge of the insulation cover is made of iron, and the inner edge is filled with rubber plastic insulation material, with a thickness of 5mm. The diameter is the same as the diameter of the water source well, with a diameter of 16.1cm and a height of 6cm, as shown in Figure 10.

System parameter determination
The experimental photovoltaic panel adopts 110W, with a heating resistance wire of 30 Ω. The photovoltaic panel is a fixed type, facing due south, and the test site is located in Xilamuren Grassland, Baotou City. The heat output of the resistance wire was measured on site from 6:00 to 17:30 on October 28, 2018, as shown in Figure 11. ,The heating system composed of 110W photovoltaic panels and 30 Ω has a daily heating capacity of 1659.52J, which is much greater than the heat dissipation capacity of 412.2J. Therefore, theoretically, this system can meet the antifreeze requirements of water source wells.

Experimental steps
The following experimental conditions were adopted in this article: a freezing period of 3 months (from November to February of the following year). Observe the temperature changes of the water source well during the entire freezing period on a daily basis. Within a day (from 8:00 am to 8:00 am the next day), the heating period is 8 hours (from 8:00 am to 16:00 am in winter), and the freezing period is 16 hours (from 16:00 am to 8:00 am the next day).
The scale of this water source well model is 1:9.3. According to the Kosovitch criterion, C τ= Cr2=86.5, which means the ratio of experimental time to actual time is 1:86.5. After calculation, the experimental duration of the entire freezing period is 25 hours. Therefore, the experimental operation steps are: place the water source well in a low-temperature box (-40 ℃), start the solar heating system in the first step, run for 6 minutes, then turn off the heating system and freeze for 12 minutes. Repeat this cycle for 25 hours to observe if the water surface of the water source well has frozen.

Experimental results
The low-temperature box starts working at 10:30, and the initial temperature of the environment is -40 ℃. At this time, the temperature at the wellhead is 1.8 ℃, and the temperature at the water surface is 6.2 ℃,the temperature at the bottom of the well is 7.8 ℃. The temperature field inside the water source well is shown in Figure 12. After 25 hours of operation simulation, the temperature inside the water source well is shown in Figure 13. It can be seen that after a freezing period, under the operation of the heating system, the temperature at 3.3m was -0.1 ℃, and the temperature at the water surface was about 0 ℃. No freezing occurred, achieving the expected goal of the experiment. Compared to before freezing, the temperature curve of the water source well has flattened, especially the temperature difference between 0.0m and 0.3m has increased from 1.7 ℃ before heating to 0.2 ℃. The main reason is that some of the heat loss is compensated for by the heat generated by the heating system, which reduces the temperature drop in the area and also reduces the temperature drop in the rest of the water source well, thereby preventing the freezing of the water source well.

Conclusion
1. The temperature field of the water source well exhibits a three-stage distribution of "steep gentle gentle" under field conditions. The "steep rise zone" is located 0.0m to 1.3m away from the wellhead, with a temperature increase rate of 10.58 ℃/m from -15.7 ℃ to -1.9 ℃; The "slow rise zone" is located 1.3m-1.8m away from the wellhead, with a gradual temperature increase rate of 1.0 ℃/m; The third stage is located 1.8m to 7.8m away from the wellhead, with a temperature rise rate of 0.48 ℃/m.
2. The temperature field of the water source well is located in the "steep rise zone" under extreme conditions (-40 ℃) at a distance of 0.0m to 0.8m from the wellhead, with a temperature rise rate of 15.75 ℃/m; The second stage is the "slow rise zone", with a temperature rise rate of 2.4 ℃/m from 0.8m to 1.8m from the wellhead; The third stage is from 1.8m to 7.8m away from the wellhead, with a temperature rise rate of 0.43 ℃/m. 3. After a simulation of a freezing period (3 months), it was found that the temperature field inside the wellbore significantly decreased. However, under the operation of the heating system, the temperature drop at 0.0m decreased slightly. The temperature difference between 0.0m and 0.3m increased from 1.7 ℃ before heating to 0.2 ℃, and the temperature at the water surface was about 0.0 ℃. The water surface did not freeze.