Analytic model solving method for determining heat exchange performance of buried pipe heat exchanger in underground engineering structure

Abstract

The invention discloses an analytical model solving method for determining the heat exchange performance of a buried pipe heat exchanger in an underground engineering structure, and the method comprises the steps: simplifying an arched section of a protective engineering mouth channel into an equivalent circular section, which is a two-dimensional model; the radius where the discrete linear heat source is located is equivalent to a surface heat source, and therefore the two-dimensional model is simplified into a semi-infinite cylindrical heat transfer calculation model with an internal heat source; the cylindrical surface where the buried pipe heat exchanger in the underground engineering structure is located serves as the boundary, the heat exchange process of an opening channel is re-divided and analyzed, and the heat exchange process comprises the following three parts of heat exchange of circulating water and a lining, heat exchange of the lining and air and heat exchange of the lining and surrounding rock; optimizing the semi-infinite cylindrical heat transfer calculation model with the internal heat source to obtain a surrounding rock side heat transfer model, namely an analytical model; and solving the analytical model.

Description

Technical Field

[0001] The present invention relates to the field of underground engineering heat transfer technology, and in particular to an analytical model solving method for determining the heat transfer performance of a buried pipe heat exchanger in an underground engineering structure. Background Art

[0002] The protection project is deep underground, and whether its heat can be discharged smoothly is a key issue for the smooth operation of the project. The heat exchange form of the buried pipe in the lining of the mouth channel of the energy tunnel has overcome the disadvantages of easy exposure of the cooling tower, limited thermal capacity of the reservoir, and difficult and expensive construction of the ground source heat pump system, thus improving the protection capacity of the project. Figure 1 shown.

[0003] In the lining at a certain distance from the entrance, serpentine heat exchange tubes are evenly arranged along the axial direction. The circulating medium in the tube absorbs the heat from the condenser of the chiller, and then exchanges heat with the air and surrounding rock outside the lining, so as to achieve the purpose of transferring the engineering heat to the environment. In this process, heat is transferred between the air in the channel, the circulating water in the pipeline and the surrounding rock through heat conduction, convection and radiation, which is a coupled heat transfer process. The ventilation method will affect the ventilation volume, and the ventilation volume will affect the convective heat transfer coefficient, which ultimately determines the distribution ratio of the heat entering the air to the heat entering the surrounding rock. The heat exchange process of the surrounding rock has a time lag, and the coupled heat exchange with the buried pipe heat exchanger in the lining is a non-steady-state process. There is no ready-made model for reference for this multi-parameter coupled heat transfer process.

[0004] In order to obtain the heat transfer law of the buried heat exchanger in the mouth channel of the protection project, it is necessary to establish a model for simulation calculation. The analytical model has attracted the research interest of many scholars because of its convenient calculation. Most existing studies focus on bored heat exchangers and pile heat exchangers. However, due to the special structure of the buried pipe in the tunnel lining, its geometric distribution and boundary conditions are very different from those of the pile heat exchanger. There are two directions of heat exchange in the energy tunnel, one is heat exchange with the air in the tunnel, and the other is heat exchange with the surrounding rock. The traditional cylindrical heat source and linear heat source model are not applicable here. The current solution is to simplify the lining surface into a surface heat source and establish a one-dimensional plane heat transfer model. However, the top surface of the tunnel is actually a curved surface, which is different from plane heat exchange. Simply limiting the heat diffusion to the plane transfer direction does not conform to the actual situation. Summary of the invention

[0005] The purpose of the present invention is to provide a method for solving an analytical model for determining the heat transfer performance of a buried pipe heat exchanger in an underground engineering structure in response to the problems existing in the above-mentioned prior art. An analytical solution model of the surface of a buried pipe heat exchanger in a lining is established and compared with a one-dimensional plane model. Finally, the model is used to analyze the influence of air flow in the channel on the heat transfer performance, providing a theoretical basis for optimizing the heat transfer characteristics of the channel.

[0006] The technical solution to achieve the purpose of the present invention is: a method for solving an analytical model for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure, the method comprising: Step 1: During the heat exchange process, the heat source is the circulating hot water in the buried pipe heat exchanger. The arched section of the mouth passage of the protection project is simplified to an equivalent circular section. This is a two-dimensional model. Step 2, the radius where the discrete line heat source is located is equivalent to a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylinder heat transfer calculation model with an internal heat source; Step 3, taking the cylindrical surface where the buried heat exchanger in the underground engineering structure is located as the boundary, re-dividing and analyzing the heat exchange process of the mouth channel, including the following three parts: heat exchange between circulating water and lining, heat exchange between lining and air, and heat exchange between lining and surrounding rock; Step 4, based on the heat exchange process re-divided in step 3, the heat transfer calculation model of the semi-infinite cylinder with an internal heat source is optimized to obtain a heat conduction model of the surrounding rock side, i.e., an analytical model; Step 5: solving the analytical model.

[0007] Furthermore, in step 2, the two-dimensional model is simplified into a semi-infinite cylindrical heat transfer calculation model with an internal heat source, specifically including: According to Fourier's law and the first law of thermodynamics, the differential equation of thermal conductivity is established: ; Initial conditions: ; Boundary conditions: ; In the formula, is the temperature of the surrounding rock at radius r, in units of ; is the thermal diffusivity of the surrounding rock, in units of ; is the thermal conductivity of the surrounding rock, in units of ; is the surrounding rock density, in ; is the specific heat capacity of surrounding rock at constant pressure, in units of ; is the heat released per unit volume of the buried pipe heat exchanger, in units of ; is the equivalent radius of the entrance channel, in m; is the far boundary temperature of the surrounding rock, in units of ; is the convective heat transfer coefficient between the air in the mouth channel and the lining surface, in units of ; is the temperature of the air in the mouth passage, in , express time.

[0008] Furthermore, the relationship between the three parts in step 3 follows the law of conservation of energy, that is, the heat transferred from the circulating water to the lining is equal to the sum of the heat transferred from the lining to the air and to the surrounding rock, expressed as: ; In the formula, is the total heat flux released by the heat exchange tube per unit channel length, in units of ; is the heat flux released to the air per unit channel length of the heat exchange tube, in units of ; is the heat flux transferred from the heat exchange tube to the surrounding rock per unit channel length, in units of .

[0009] Furthermore, according to the heat flow, , for: ; in, ; In the formula, is the average temperature of the circulating water in the underground heat exchanger, in ; is the air temperature in the mouth passage, in ; is the contact surface temperature between lining and surrounding rock, in units of ; is the circulating water temperature entering the underground heat exchanger, in units of ; is the temperature of circulating water at the outlet of the buried heat exchanger, in units of , is the thermal resistance between the circulating water in the ground heat exchanger and the air in the mouth channel, in units of ; is the thermal resistance between the circulating water and the surrounding rock, in units of .

[0010] Furthermore, the thermal resistance , The calculation formulas are: ; In the formula, is the convective heat transfer coefficient of air between the inlet channel and the lining surface, in units of ; D is the diameter of the inlet channel, in m; is the thermal conductivity of the lining material, in units of ; It is the distance between the laying surface of the buried pipe heat exchanger and the inner surface of the lining, in meters; is the lining thickness, in m; is the convection heat transfer coefficient of circulating water in the buried pipe heat exchanger, in units of , the calculation formula is: ; In the formula, , is the average flow velocity in the borehole heat exchanger; is a dimensionless constant; is the thermal conductivity of the circulating water in units of ; d is the inner diameter of the buried heat exchanger, in mm; is the kinematic viscosity of water, in , is the Nusselt number, which is a dimensionless number.

[0011] Furthermore, step 4 specifically includes: The heat transfer calculation model of the semi-infinite cylinder with internal heat source is rewritten as the heat conduction differential equation of the surrounding rock side, that is, the heat conduction model of the surrounding rock side, in which As the boundary condition for the buried heat exchanger in the underground engineering structure to release heat to the surrounding rock, it is specifically expressed as: ; Initial conditions: ; Boundary conditions: ; In the formula, is the distance from the ground to the center of the tunnel.

[0012] Furthermore, step 5 solves the analytical model, specifically including: Step 5-1, solve the analytical model to obtain the surrounding rock temperature at the radius r along the central axis of the semi-infinite cylinder , and the surrounding rock temperature at the junction of the lining and the surrounding rock ; Step 5-2: Introduce the ratio of the actual area occupied by the buried pipe to the cylindrical area , correct the heat exchange between circulating water and lining; Step 5-3, based on the results of step 3 and steps 5-1 and 5-3, obtain the solution of the analytical model.

[0013] Furthermore, in step 5-1, the heat conduction model of the surrounding rock side is solved by integral transformation to obtain the radius r along the central axis of the semi-infinite cylinder. Surrounding rock temperature at the moment for: ; In the formula, is the zero-order Bessel function of the first kind, It is the second kind of first-order Bessel function, and u is a variable with no actual meaning; make , obtain the surrounding rock temperature at the junction of lining and surrounding rock for: ; In the formula, for The surrounding rock temperature at the junction of the lining and the surrounding rock at all times.

[0014] Furthermore, the ratio of the actual occupied area of ​​the buried pipe introduced in step 5-2 to the cylindrical area is , correct the heat exchange between circulating water and lining, specifically: ; In the formula, is the total heat flux released by the heat exchange tube per unit channel length, is the constant pressure specific heat capacity of circulating water, in units of ; is the circulating water density, in units of ; is the flow rate of circulating water in the buried pipe, in units of ; S is the cross-sectional area of ​​the buried pipe heat exchanger, in units ; is the circulating water temperature entering the underground heat exchanger, in units of ; is the temperature of circulating water at the outlet of the buried heat exchanger, in units of ; is the length of the buried pipe heat exchanger laid along the channel, in meters; k is the ratio of the actual occupied area of ​​the buried pipe to the cylindrical area.

[0015] Further, step 5-3 is based on the results of step 3 and steps 5-1 and 5-3 to obtain the solution of the analytical model, which is specifically: make: ; but: .

[0016] Compared with the prior art, the present invention has the following significant advantages: (1) Aiming at the transient heat transfer problem of a non-uniform composite medium cylinder with a discrete internal heat source, a mathematical model of the heat transfer process of a lined buried heat exchanger was established. The solution process avoids the traditional method of using the linear superposition principle to make the problem homogeneous, but takes a different approach to simplify the model from the perspective of the heat transfer process. Taking the cylindrical surface where the buried heat exchanger is located as the boundary, the heat transfer process is decomposed into the heat exchange between circulating water and lining, the heat exchange between lining and air, and the heat exchange between lining and surrounding rock, thereby converting the original non-homogeneous, non-steady-state, nonlinear second-order differential equation into a model that can be directly solved.

[0017] (2) Based on the analytical model of the heat transfer process of the buried lined heat exchanger, the equations were solved to obtain explicit expressions for parameters such as outlet water temperature, contact surface temperature, incoming air heat, incoming surrounding rock heat, and total heat transfer. The existing experimental data verified that the model can reproduce the heat transfer process under the condition of continuous heat release in a circular channel.

[0018] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a schematic diagram of laying the buried pipe heat exchanger in the lining of the entrance channel of the protection project. Figure 1 (a) and (b) are respectively a three-dimensional schematic diagram and a cross-sectional diagram of the laying of the buried pipe heat exchanger in the lining of the mouth channel of the protection project.

[0020] Figure 2 Schematic diagram of the simplified one-dimensional heat transfer model of the lined buried tube heat exchanger.

[0021] Figure 3 The present invention is a flow chart of the analytical model solving method for determining the heat transfer performance of the buried pipe heat exchanger in the underground engineering structure.

[0022] Figure 4 It is a schematic diagram of solving the present invention in one embodiment.

[0023] Figure 5 The figure is a comparison result of the analytical solution value and the experimental value in the literature in an embodiment, where Figure 5 (a) and (b) are the comparison results of the first and second sets of experimental data, respectively. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0025] It should be noted that if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0026] In one embodiment, in combination Figure 3 and Figure 4 , provides a method for solving an analytical model for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure, the method comprising the following steps: Step 1: During the heat exchange process, the heat source is the circulating hot water in the buried pipe heat exchanger. The arched section of the mouth channel of the protection project is simplified to an equivalent circular section. This is a two-dimensional model.

[0027] Step 2: Due to the small spacing between buried pipes, the radius where the discrete linear heat source is located can be equivalent to a surface heat source. The two-dimensional model can be further simplified into a semi-infinite cylindrical heat transfer calculation model with an internal heat source, such as Figure 2 shown.

[0028] This model can be regarded as a heat transfer problem of a semi-infinite hollow cylinder with an internal heat source. According to Fourier's law and the first law of thermodynamics, the differential equation of thermal conductivity is established:

[0029] Initial conditions: ; Boundary conditions: ; In the formula, is the temperature of the surrounding rock at radius r, in units of ; is the thermal diffusivity of the surrounding rock, in units of ; is the thermal conductivity of the surrounding rock, in units of ; is the surrounding rock density, in ; is the specific heat capacity of surrounding rock at constant pressure, in units of ; is the heat released per unit volume of the buried pipe heat exchanger, in units of ; is the equivalent radius of the entrance channel, in m; is the far boundary temperature of the surrounding rock, in units of ; is the convective heat transfer coefficient between the air in the mouth channel and the lining surface, in units of ; is the temperature of the air in the mouth passage, in , express time.

[0030] The model established by equations (1-1)-(1-4) belongs to the transient heat transfer problem of a non-uniform composite medium cylinder with an internal heat source. Equation (1-1) is a second-order non-homogeneous non-steady-state nonlinear differential equation. There are many ways to solve this problem, most of which are studies on body heat sources and do not involve heat transfer calculations of surface heat sources. If the existing methods are directly applied, it is necessary to use the linear superposition principle to transform the problem into a homogeneous one. The solution is divided into two parts, one is the solution of the non-uniform steady-state heat conduction problem, and the other is the solution of the uniform transient heat conduction problem. The calculation method is complex and inefficient.

[0031] Step 3, in order to simplify this problem, the cylindrical surface where the ground heat exchanger is located is used as the boundary to re-analyze the heat exchange process of the mouth channel, which mainly includes the following three parts: heat exchange between circulating water and lining, heat exchange between lining and air, and heat exchange between lining and surrounding rock. The relationship between these three parts follows the law of conservation of energy, that is, the heat transferred from circulating water to lining is equal to the sum of the heat transferred from lining to air and to surrounding rock. The expression is as follows:

[0032] In the formula, is the total heat flux released by the heat exchange tube per unit channel length, in units of ; is the heat flux released to the air per unit channel length of the heat exchange tube, in units of ; is the heat flux transferred from the heat exchange tube to the surrounding rock per unit channel length, in units of .in, It can be used as the boundary condition for the buried pipe heat exchanger to release heat to the surrounding rock. Equations (1-1)-(1-4) can be rewritten as the differential equation of heat conduction on the side of the surrounding rock:

[0033] Initial conditions:

[0034] Boundary conditions:

[0035] Step 4: Solve equations (1-6)-(1-9) by integral transformation to obtain the value along the radius r of the central axis of the cylinder in equation (1-10): The surrounding rock temperature at that moment.

[0036]

[0037] In the formula, is the zero-order Bessel function of the first kind, is the first-order Bessel function of the second kind, u The variable has no actual meaning.

[0038] Step 5, when When the calculated temperature is the surrounding rock temperature at the junction of the lining and the surrounding rock :

[0039]

[0040] Step 6, due to the heat released into the air and the heat released into the surrounding rock All are provided by the buried heat exchanger. When the surface where the buried heat exchanger is located is equivalent to the heat source surface, the smaller the pipe spacing, the more accurate the model equivalence. In fact, it is impossible for there to be no spacing between the pipes. In order to eliminate the difference between the equivalent cylindrical surface heat source and the actual linear heat source with spacing, the ratio k of the actual occupied area of ​​the buried pipe to the cylindrical area is introduced, so the total heat per unit channel length is for:

[0041] In the formula, is the total heat flux released by the heat exchange tube per unit channel length, is the constant pressure specific heat capacity of circulating water, in units of ; is the circulating water density, in units of ; is the flow rate of circulating water in the buried pipe, in units of ; S is the cross-sectional area of ​​the buried pipe heat exchanger, in units ; is the circulating water temperature entering the underground heat exchanger, in units of ; is the temperature of circulating water at the outlet of the buried heat exchanger, in units of ; is the length of the buried pipe heat exchanger laid along the channel, in meters; k is the ratio of the actual occupied area of ​​the buried pipe to the cylindrical area.

[0042] Step 7, according to the heat flow definition,

[0043] in, is the average temperature of the circulating water in the underground heat exchanger, in ; is the air temperature in the mouth passage, in ; is the contact surface temperature between lining and surrounding rock, in units of , obtained by formula (1-11); is the circulating water temperature entering the underground heat exchanger, in units of ; is the temperature of circulating water at the outlet of the buried heat exchanger, in units of , is the thermal resistance between the circulating water in the ground heat exchanger and the air in the mouth channel, in units of ; is the thermal resistance between the circulating water and the surrounding rock, in units of .

[0044] Step 8, according to the calculation formula of the heat conduction of the cylindrical wall under the third boundary condition:

[0045] in, is the convective heat transfer coefficient of air between the inlet channel and the lining surface, in units of ; D is the diameter of the inlet channel, in m; is the thermal conductivity of the lining material, in units of ; It is the distance between the laying surface of the buried pipe heat exchanger and the inner surface of the lining, in meters; is the lining thickness, in m; is the convection heat transfer coefficient of circulating water in the buried pipe heat exchanger, in units of , calculated by formula (1-18): ; In the formula, , is the average flow velocity in the borehole heat exchanger; is a dimensionless constant, usually taken as ; is the thermal conductivity of the circulating water in units of ; d is the inner diameter of the buried heat exchanger, in mm; is the kinematic viscosity of water, in , is the Nusselt number, which is a dimensionless number.

[0046] Step 9, from equations (1-11)-(1-18) we get The relationship between . Order:

[0047] but:

[0048] Formula (1-21)-(1-26) is the inlet water temperature Explicit analytical solutions for each physical quantity when ρ is known.

[0049] Furthermore, the method further comprises: Step 10: Verify the above analytical model.

[0050] For example, two groups of existing test data are used for comparison. The model setting parameters are the same as the test parameters, as shown in Table 1.

[0051]

[0052] The simulation time is 50 hours, and the outlet fluid temperature calculated by the analytical model is Compared with the test results Figure 5 As shown in the figure, as the running time increases, the deviation between the model calculation results and the measured data gradually decreases. It can be inferred that the analytical model can reasonably reproduce the transient heat transfer process of the circular channel buried pipe during continuous cooling for 50 hours.

[0053] In one embodiment, a system for solving an analytical model for determining heat transfer performance of a buried heat exchanger in an underground engineering structure is provided, the system comprising: The first module is used to simplify the arched section of the entrance passage of the protection project into an equivalent circular section. This is a two-dimensional model. The second module is used to treat the radius where the discrete line heat source is located as equivalent to a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylinder heat transfer calculation model with an internal heat source; The third module is used to re-divide and analyze the heat transfer process of the mouth channel with the cylindrical surface where the buried pipe heat exchanger in the underground engineering structure is located as the boundary, including the following three parts: heat transfer between circulating water and lining, heat transfer between lining and air, and heat transfer between lining and surrounding rock; The fourth module is used to optimize the heat transfer calculation model of the semi-infinite cylinder with an internal heat source based on the heat exchange process re-divided in the third module, and obtain a heat conduction model of the surrounding rock side, that is, an analytical model; The fifth module is used to solve the analytical model.

[0054] Furthermore, the system further comprises: The sixth module is used to verify the analytical model.

[0055] Regarding the specific limitations of the analytical model solution system for determining the heat transfer performance of buried pipe heat exchangers in underground engineering structures, please refer to the limitations of the analytical model solution method for determining the heat transfer performance of buried pipe heat exchangers in underground engineering structures mentioned above, which will not be repeated here. Each module in the above-mentioned analytical model solution system for determining the heat transfer performance of buried pipe heat exchangers in underground engineering structures can be implemented in whole or in part through software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0056] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the following is achieved: Step 1: During the heat exchange process, the heat source is the circulating hot water in the buried pipe heat exchanger. The arched section of the mouth passage of the protection project is simplified to an equivalent circular section. This is a two-dimensional model. Step 2, the radius where the discrete line heat source is located is equivalent to a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylinder heat transfer calculation model with an internal heat source; Step 3, taking the cylindrical surface where the buried heat exchanger in the underground engineering structure is located as the boundary, re-dividing and analyzing the heat exchange process of the mouth channel, including the following three parts: heat exchange between circulating water and lining, heat exchange between lining and air, and heat exchange between lining and surrounding rock; Step 4, based on the heat exchange process re-divided in step 3, the heat transfer calculation model of the semi-infinite cylinder with an internal heat source is optimized to obtain a heat conduction model of the surrounding rock side, i.e., an analytical model; Step 5: solving the analytical model.

[0057] Step 6: verify the analytical model.

[0058] The specific limitations of each step can be found in the above limitations on the analytical model solution method for determining the heat transfer performance of the buried pipe heat exchanger in the underground engineering structure, which will not be repeated here.

[0059] In one embodiment, a computer readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the computer program implements: Step 1: During the heat exchange process, the heat source is the circulating hot water in the buried pipe heat exchanger. The arched section of the mouth passage of the protection project is simplified to an equivalent circular section. This is a two-dimensional model. Step 2, the radius where the discrete line heat source is located is equivalent to a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylinder heat transfer calculation model with an internal heat source; Step 3, taking the cylindrical surface where the buried heat exchanger in the underground engineering structure is located as the boundary, re-dividing and analyzing the heat exchange process of the mouth channel, including the following three parts: heat exchange between circulating water and lining, heat exchange between lining and air, and heat exchange between lining and surrounding rock; Step 4, based on the heat exchange process re-divided in step 3, the heat transfer calculation model of the semi-infinite cylinder with an internal heat source is optimized to obtain a heat conduction model of the surrounding rock side, i.e., an analytical model; Step 5: solving the analytical model.

[0060] Step 6: verify the analytical model.

[0061] The specific limitations of each step can be found in the above limitations on the analytical model solution method for determining the heat transfer performance of the buried pipe heat exchanger in the underground engineering structure, which will not be repeated here.

[0062] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for solving an analytical model for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure, characterized in that: The method comprises: Step 1: During the heat exchange process, the heat source is the circulating hot water in the buried pipe heat exchanger. The arched section of the mouth passage of the protection project is simplified to an equivalent circular section. This is a two-dimensional model. Step 2, the radius where the discrete line heat source is located is equivalent to a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylinder heat transfer calculation model with an internal heat source; Step 3, taking the cylindrical surface where the buried heat exchanger in the underground engineering structure is located as the boundary, re-dividing and analyzing the heat exchange process of the mouth channel, including the following three parts: heat exchange between circulating water and lining, heat exchange between lining and air, and heat exchange between lining and surrounding rock; Step 4, based on the heat exchange process re-divided in step 3, the heat transfer calculation model of the semi-infinite cylinder with an internal heat source is optimized to obtain a heat conduction model of the surrounding rock side, i.e., an analytical model; Step 5: solving the analytical model.

2. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 1, characterized in that: In step 2, the two-dimensional model is simplified into a semi-infinite cylindrical heat transfer calculation model with an internal heat source, which specifically includes: According to Fourier's law and the first law of thermodynamics, the differential equation of thermal conductivity is established: ； Initial conditions: ； Boundary conditions: ； In the formula, is the temperature of the surrounding rock at radius r, in units of ; is the thermal diffusivity of the surrounding rock, in ; is the thermal conductivity of the surrounding rock, in units of ; is the surrounding rock density, in ; is the specific heat capacity of surrounding rock at constant pressure, in units of ; is the heat released per unit volume of the buried pipe heat exchanger, in units of ; is the equivalent radius of the entrance channel, in m; is the far boundary temperature of the surrounding rock, in units of ; is the convective heat transfer coefficient between the air in the mouth channel and the lining surface, in units of ; is the temperature of the air in the mouth passage, in , express time.

3. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 1, characterized in that: The relationship between the three parts in step 3 follows the law of conservation of energy, that is, the heat transferred from the circulating water to the lining is equal to the sum of the heat transferred from the lining to the air and to the surrounding rock, expressed as: ； In the formula, is the total heat flux released by the heat exchange tube per unit channel length, in units of ; is the heat flux released to the air per unit channel length of the heat exchange tube, in units of ; is the heat flux transferred from the heat exchange tube to the surrounding rock per unit channel length, in units of .

4. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 3, characterized in that: According to the heat flow, , for: ； in, ； In the formula, is the average temperature of the circulating water in the underground heat exchanger, in ; is the air temperature in the mouth passage, in ; is the contact surface temperature between lining and surrounding rock, in units of ; is the circulating water temperature entering the underground heat exchanger, in units of ; is the temperature of circulating water at the outlet of the buried heat exchanger, in units of , is the thermal resistance between the circulating water in the ground heat exchanger and the air in the mouth channel, in units of ; is the thermal resistance between the circulating water and the surrounding rock, in units of .

5. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 4, characterized in that: The thermal resistance , The calculation formulas are: ； In the formula, is the convective heat transfer coefficient of air between the inlet channel and the lining surface, in units of ; D is the diameter of the inlet channel, in m; is the thermal conductivity of the lining material, in units of ; It is the distance between the laying surface of the buried pipe heat exchanger and the inner surface of the lining, in meters; is the lining thickness, in m; is the convection heat transfer coefficient of circulating water in the buried pipe heat exchanger, in units of , the calculation formula is: ； In the formula, , is the average flow velocity in the borehole heat exchanger; is a dimensionless constant; is the thermal conductivity of the circulating water in units of ; d is the inner diameter of the buried heat exchanger, in mm; is the kinematic viscosity of water, in , is the Nusselt number, which is a dimensionless number.

6. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 2 or 3, characterized in that: Step 4 specifically includes: The heat transfer calculation model of the semi-infinite cylinder with internal heat source is rewritten as the heat conduction differential equation of the surrounding rock side, that is, the heat conduction model of the surrounding rock side, in which As the boundary condition for the buried heat exchanger in the underground engineering structure to release heat to the surrounding rock, it is specifically expressed as: ； Initial conditions: ； Boundary conditions: ； In the formula, is the distance from the ground to the center of the tunnel.

7. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 1, characterized in that: Step 5 solves the analytical model, specifically including: Step 5-1, solve the analytical model to obtain the surrounding rock temperature at the radius r along the central axis of the semi-infinite cylinder , and the surrounding rock temperature at the junction of the lining and the surrounding rock ; Step 5-2: Introduce the ratio of the actual area occupied by the buried pipe to the cylindrical area , correct the heat exchange between circulating water and lining; Step 5-3, based on the results of step 3 and steps 5-1 and 5-3, obtain the solution of the analytical model.

8. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 7, characterized in that: In step 5-1, the heat conduction model of the surrounding rock side is solved by integral transformation, and the radius r along the central axis of the semi-infinite cylinder is obtained. Surrounding rock temperature at the moment for: ； In the formula, is the zero-order Bessel function of the first kind, It is the second kind of first-order Bessel function, and u is a variable with no actual meaning; make , obtain the surrounding rock temperature at the junction of lining and surrounding rock for: ； In the formula, for The surrounding rock temperature at the junction of the lining and the surrounding rock at all times.

9. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 8, characterized in that: The ratio of the actual occupied area of ​​the buried pipe introduced in step 5-2 to the cylindrical area , correct the heat exchange between circulating water and lining, specifically: ； In the formula, is the total heat flux released by the heat exchange tube per unit channel length, is the constant pressure specific heat capacity of circulating water, in units of ; is the circulating water density, in units of ; is the flow rate of circulating water in the buried pipe, in units of ; S is the cross-sectional area of ​​the buried pipe heat exchanger, in units ; is the circulating water temperature entering the underground heat exchanger, in units of ; is the temperature of circulating water at the outlet of the buried heat exchanger, in units of ; is the length of the buried pipe heat exchanger laid along the channel, in meters; k is the ratio of the actual occupied area of ​​the buried pipe to the cylindrical area.

10. The analytical model solving method for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 5 or 9, characterized in that: Step 5-3: Based on the results of step 3 and steps 5-1 and 5-3, the solution of the analytical model is obtained, which is: make: ； but: 。

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