Single factor sensitivity analysis of vertical single U-shaped buried tube heat exchanger
Abstract: Based on the thermal-permeability coupled heat transfer model of vertical single U-shaped buried tube heat exchanger, the thermal conductivity of rock and soil, volumetric heat capacity of rock and soil, porosity of rock and soil, original ground temperature, groundwater seepage velocity and buried pipe depth are analyzed. The influence of factors such as fluid flow in the pipe, inlet water temperature of the buried pipe and operation mode on the heat transfer performance of the buried pipe heat exchanger. Univariate regression analysis was carried out, and the regression equations of the unit well depth heat transfer and the outlet water temperature of the buried pipe and various parameters were obtained. Key words: buried pipe heat exchanger unit well deep heat exchange volume outlet water temperature influence factor regression 0 Preface The unit well depth heat exchange and the buried pipe outlet water temperature are important indicators reflecting the performance of the buried pipe heat exchanger. The unit well depth heat transfer directly affects the design capacity and operation effect of the buried pipe; the buried pipe outlet water temperature to the ground source heat pump The operating efficiency of the unit has a great influence. In summer cooling, the higher the outlet water temperature of the buried pipe is, the lower the operating efficiency is. When the heating is performed in winter, the lower the outlet water temperature of the buried pipe is, the lower the operating efficiency is. Therefore, it is necessary to study the effects of various factors on the heat flux of the unit well and the water temperature at the outlet of the buried pipe. The heat transfer process of the vertical buried heat exchanger is very complicated, and it is subject to hydrogeological conditions (such as groundwater level, different geological layers and groundwater flow) and buried pipe parameters (such as pipe, pipe diameter and pipe spacing) within the drilling depth range. The influence of factors such as fluid parameters in the tube and the operating mode of the heat pump. At present, the research on buried tube heat exchangers is mainly carried out from two aspects: actual measurement [1-2] and numerical simulation [3-5]. Due to the wide variety of hydrogeological conditions, the measured data is difficult to guide the underground burial in other areas. Tube heat exchanger design; and numerical simulation is difficult to use for practical engineering due to the long calculation time. Therefore, based on the thermal-permeability coupled heat transfer model of the buried tube heat exchanger, a large number of numerical simulations are carried out on the operating characteristics of the system in summer. By regression analysis of the simulation results, a vertical single U is obtained. The relationship between the depth of heat exchange and the water temperature at the outlet of the buried pipe heat exchanger in the summer working condition and the influence parameters are convenient for engineering applications. 1. Heat-induced coupled heat transfer model [6] 1.1·Simplified assumptions The heat transfer of the buried tube heat exchanger is a complex unsteady process, which usually requires a long time operation, and the geometric and physical conditions involved in the process are also complicated, so in order to facilitate the analysis, the following is required. The necessary simplification: 2 Single factor sensitivity analysis 2.1 Parameter value study There are many factors affecting the performance of vertical buried heat exchangers, which can be divided into geotechnical and groundwater parameters, buried pipe heat exchanger parameters, circulating fluid parameters and operating modes. This paper mainly selects the geothermal conductivity, geothermal heat capacity, geotechnical porosity, original geothermal temperature, groundwater seepage velocity, buried pipe depth, pipe fluid flow, inlet temperature and operation mode, etc., according to engineering practice and related literature. [8-10] The reference value and variation range of each influencing factor are determined, as shown in Table 1, for the following simulation calculation. 2.2 Single factor impact analysis 2.2.1 Thermal conductivity of geotechnical Figure 1 reflects the influence of the thermal conductivity of geotechnical soil on the heat flux per unit well and the water temperature at the outlet of the buried pipe. When the thermal conductivity of rock and soil increases, the heat exchange rate per unit well increases linearly, and the water temperature at the outlet of the buried pipe decreases linearly. When the thermal conductivity of the soil increased from 0. 75 W/(m·°C) to 2.25 W/(m·°C), the heat exchange per unit well increased by 85.47%, and the outlet water temperature of the buried pipe decreased by 8.91%. The reduction of the outlet water temperature of the buried pipe is beneficial to the improvement of the cooling efficiency of the heat pump unit. The volumetric heat capacity of rock and soil is a parameter to characterize the heat storage capacity of rock and soil. The larger the volumetric heat capacity, the greater the heat that can be provided per unit volume of rock and soil, so the smaller the range that can be affected by the buried heat exchanger. The smaller the heat impact radius. The thermophysical parameters of geotechnical are a function of its mineral content, porosity and saturation. Among them, porosity is the most important influence parameter, which is determined by the formation mechanism and nature of geotechnical soil. Figure 3 shows the variation of the heat flux per unit well and the outlet water temperature of the buried pipe with the porosity of the rock. It can be seen from Fig. 3 that as the porosity increases, the heat exchange capacity per unit well decreases gradually, and the outlet water temperature increases slightly. For unsaturated geotechnical soils, the large porosity means that the volume of air between the particles increases, and the contact area between the particles decreases, resulting in a decrease in thermal conductivity of the rock and a decrease in heat exchange capacity. For saturated geotechnical soil, the pores in the geotechnical soil are filled with liquid water, and the thermal conductivity of water is smaller than that of geotechnical soil. Therefore, the increase of porosity of saturated geotechnical soil will also reduce the comprehensive thermal conductivity and reduce the heat exchange capacity, but this It is obtained without considering the increase of the hydraulic conductivity of the rock and soil caused by the increase of the porosity. The relationship between porosity and geotechnical hydraulic conductivity needs further study. Figure 4 shows the variation of the heat flux per unit well and the outlet water temperature of the buried pipe with the original ground temperature. It can be seen from Fig. 4 that with the increase of the original ground temperature, the heat exchange rate per unit well decreases linearly, and the water temperature at the outlet of the buried pipe rises linearly. Therefore, the higher the original ground temperature, the more unfavorable the summer cooling conditions of the ground source heat pump system. 2.2.5 Groundwater seepage velocity Figures 5 and 6 reflect the effect of groundwater seepage velocity on the heat flux per unit well and the outlet water temperature of the buried pipe. On the one hand, the increase of groundwater seepage velocity enhances the convective heat transfer between the buried pipe and the rock, increases the heat exchange capacity per unit well, and reduces the outlet water temperature, based on the operational data of the 10th day, when the seepage velocity When increasing from 0.01 m/d to 0.66 m/d, the heat flux per unit depth increased by 47.5%, and the outlet water temperature decreased from 32 °C to 30.27 °C (see Figure 5). On the other hand, the groundwater seepage velocity increased. Large, greatly shortening the time when the heat exchange in the underground buried pipe area is stable. When the groundwater seepage velocity reaches 0.66 m/d, the heat exchange per unit well depth no longer decreases with the running time, and basically stabilizes at 58.69 W/m (see Figure 6). It can be seen that the existence of groundwater seepage greatly enhances the heat transfer capacity of the geothermal soil in the buried pipe area and shortens the time for the system to reach stable operation. Therefore, in the design process of the ground source heat pump system, the groundwater in the construction area is determined. The rate of seepage is very important. 2.2.6 Buried pipe depth Figure 7 shows the variation of the heat flux per unit well and the outlet water temperature of the buried pipe with the depth of the buried pipe. It can be seen from Fig. 7 that the depth of the buried pipe increases, the heat exchange amount per unit well decreases, and the outlet water temperature decreases. The reason is that as the depth of the buried pipe increases, the temperature difference between the coil and the rock becomes smaller, resulting in a weakening of the heat exchange capacity between the coil and the rock. In addition, as the depth of the buried pipe increases, the water temperature at the outlet of the buried pipe decreases (summer conditions), which improves the cooling efficiency of the unit. When the depth of the buried pipe increased from 5m to 150m, the outlet water temperature of the buried pipe dropped from 33.45 °C to 30.15 °C, a decrease of 9.87%. Figure 8 shows the variation of the heat flux per unit well and the water temperature at the outlet of the buried pipe with the fluid flow in the pipe. It can be seen from Fig. 8 that when the fluid flow in the pipe increases, the heat flux per unit well and the outlet water temperature of the buried pipe increase. When the flow rate increases from 0.6 m3/h to 2 m3/h, the heat exchange per unit well increases. 26.4%, the outlet water temperature increased from 27.81 ° C to 32.94 ° C. Therefore, the increase of flow rate is beneficial to increase the heat exchange capacity per unit well, but it will cause the water temperature at the outlet of the buried pipe to rise, which will cause the cooling efficiency of the unit to decrease. At the same time, the increase of the flow rate will increase the operating cost of the pump. Therefore, it is necessary to optimize the flow in the pipe, not only to limit the minimum flow, so that the fluid in the pipe is in a turbulent state, but also to prevent the water temperature at the outlet of the buried pipe from being too high due to the increase of the flow rate, and also to consider the running power consumption of the pump. 2.2.8 Underground pipe inlet water temperature Since the ground source heat pump system operates under dynamic load, the outlet water temperature of the condenser of the heat pump unit, that is, the inlet water temperature of the buried pipe is also constantly changing. Figure 9 shows the variation of the heat flux per unit well and the outlet water temperature of the buried pipe with the inlet water temperature. It can be seen from Fig. 9 that the inlet water temperature of the buried pipe increases, the heat exchange amount per unit well increases, and the outlet water temperature increases. When the inlet water temperature is raised from 30 °C to 40 °C, the heat exchange capacity per unit well is increased by 76.9%, and the outlet water temperature of the buried pipe is raised from 27.81 °C to 35.93 °C. Because the inlet water temperature rises, the heat exchange temperature difference between the fluid and the rock in the pipe increases, which directly leads to an increase in the heat exchange amount. However, it is necessary to pay attention to the increase of the inlet water temperature, which may also cause the water temperature at the outlet of the buried pipe to rise. The efficiency of the heat pump unit is reduced. When the temperature of the local buried pipe outlet exceeds the maximum allowable inlet water temperature of the heat pump unit, the unit will be shut down. Figure 10 shows the variation of the average unit well depth heat transfer on the 10th day and the outlet water temperature at the end of the operation for 10 days of continuous operation of the buried tube heat exchanger under different daily operating conditions. When the running time increased from 6 h/d to 16 h/d, the heat exchange reached a steady state, the heat exchange per unit well decreased by 30.6%, and the outlet water temperature increased by 2.5%. Therefore, when selecting a ground source heat pump system, the operating mode of the system must be considered. If it is used in a residential building, 24 hours of operation will adversely affect the temperature recovery of the large-area buried area. Therefore, careful consideration should be given to the system load and the area of ​​the buried pipe, or other auxiliary cold and heat sources should be used. To ensure the long-term and efficient operation of the system, this part of the research needs to be further developed. 3 single factor regression analysis In the simulation calculation, the value of the research parameters is changed, and the other parameters are taken as the reference value. The results obtained by the simulation are processed and analyzed by the statistical analysis software SPSS, and the unit well depth heat exchange amount ql and the buried pipe outlet water temperature tout are obtained. With the regression equations for each parameter, see Table 2, all regression equations and regression coefficients passed the significance test. It can be seen that the unit heat transfer rate and the outlet water temperature of the buried pipe are linearly related to the thermal conductivity of the rock, the volumetric heat capacity of the rock, the inlet water temperature, the original ground temperature and the depth of the buried pipe, and the porosity of the rock and the seepage velocity of the groundwater. It has a second power relationship and is exponentially related to the fluid flow in the tube, and has a logarithmic relationship with the daily running time. Under the summer heat exhaust conditions, the following conclusions were obtained. references: [1] Wang Yong, Liu Xianying, Fu Xiangyu.Experimental Study of Ground Source Heat Pump and Underground Energy Storage System[J].Journal Heating Ventilating and Airconditioning, 2003, 33(5):21-23
1) The soil is a uniform, rigid, isotropic porous medium, ignoring its mass force, radiation heat transfer and viscous dissipation; 2) the soil is saturated, that is, the soil pores are all filled with water; 3) soil heat Physical properties do not change with temperature; 4) fluids and solids in the soil instantaneously reach local thermal equilibrium, ie tf(x, y, Ï„) = ts(x, y, Ï„) = t(x, y, Ï„), where subscript f And s represent fluid and solid, respectively, Ï„ is time; 5) groundwater flow only in the horizontal direction, ignoring the flow in the vertical direction; 6) the vertical U-shaped tube is equivalent to an equivalent diameter round tube; 7) the internal fluid The temperature and velocity distribution at the same section are uniform.
1.2 Control equations In non-isothermal seepage, a material system or space volume contains both solid and fluid parts. When studying actual non-isothermal seepage, the two should be combined to form a unified energy equation, and when it is on the soil, the wall, When the fluids in the tube are respectively solved by the energy equation, the boundary conditions at each interface include two conditions: temperature and heat flux. The thermal boundary condition is determined dynamically by the heat transfer process and cannot be predetermined. For this coupled heat transfer problem [7], in order to avoid repeated iterative calculations, the whole field discrete and whole field solution method is adopted. The unsteady general control equation of the buried tube heat exchanger is obtained [6].
The subscripts i in equations (1) to (4) are s, f1, p, which represent geotechnical, intra-tube fluids and coils respectively; when i is s, σi is the total geotechnical (including geotechnical framework and groundwater fraction) and The ratio of the volumetric heat capacity of groundwater, when i is f1 and p, σi=1; ti is temperature, °C; ui is the groundwater seepage velocity or fluid velocity inside the pipe, m/a or m/s; αi is the total thermal diffusivity, M2/s;qi is the internal heat source, W/m; Ï is the density, kgm3; cp is the specific pressure heat capacity, J/(kg·K); t0 is the original ground temperature, °C; tin is the inlet water temperature of the coil, °C. According to the complexity of the physical model of the buried tube heat exchanger, the unstructured grid is used to divide and the finite volume method is used to solve the equation discrete and Gauss-Seidel point iterative method.
2.2.2 Geothermal volumetric heat capacity
Figure 2 reflects the effect of the volumetric heat capacity of the geotechnical volume on the heat flux of the unit well and the water temperature at the outlet of the buried pipe. As the volumetric heat capacity of the rock increases, the heat flux per unit well increases linearly. When the volumetric heat capacity of the rock increases from 1 270 kJ/(m3·°C) to 2 754 kJ/(m3·°C), the unit well is exchanged. The heat increased by 5.7% and the outlet water temperature dropped by 0.6%. It can be seen that the influence of the volumetric heat capacity of the rock on the outlet water temperature is not significant.
2.2.3 Geotechnical porosity
2.2.4 Original ground temperature
2.2.7 Fluid flow in the tube
2.2.9 Operating mode
4 Conclusion
1) The unit heat transfer rate and the outlet water temperature of the buried pipe are linear with the thermal conductivity of the rock, the volumetric heat capacity of the rock, the original ground temperature, the inlet temperature of the fluid in the pipe and the depth of the buried pipe, and the porosity of the rock and the seepage velocity of the groundwater are The second power relationship is exponentially related to the fluid flow in the tube and is logarithmically related to the daily running time.
2) The heat exchange capacity per unit well decreases with the increase of rock porosity, original ground temperature, buried pipe depth and daily running time, with thermal conductivity of rock and soil, volumetric heat capacity of rock and soil, fluid inlet temperature in pipeline, groundwater seepage velocity and in-tube The fluid flow increases and increases.
3) The outlet water temperature of the buried pipe decreases with the increase of the thermal conductivity of the rock, the volumetric heat capacity of the rock, the seepage velocity of the groundwater and the depth of the buried pipe. With the porosity of the rock, the original ground temperature, the inlet temperature of the fluid in the pipe, the fluid flow in the pipe and the day The increase in running time increases.
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