Analytical Model Solving Method for Determining Heat Transfer Performance of Buried Tube Heat Exchangers in Underground Engineering Structures

Abstract

The present invention discloses an analytical model solving method for determining the heat transfer performance of buried tube heat exchangers in underground engineering structures. The method includes: simplifying the arched cross-section of the entrance passage of the protective engineering into an equivalent circular cross-section, which is a two-dimensional model; equivalent the radius where the discrete line heat source is located to a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylindrical heat transfer calculation model with an internal heat source; taking the cylindrical surface where the buried tube heat exchanger in the underground engineering structure is located as the boundary, and re-dividing and analyzing the heat transfer process of the entrance passage, including the following three parts: heat transfer between the circulating water and the lining, heat transfer between the lining and the air, and heat transfer between the lining and the surrounding rock; optimizing the semi-infinite cylindrical heat transfer calculation model with an internal heat source to obtain the surrounding rock side heat conduction model, that is, the analytical model; solving the analytical model.

Description

Technical Field

[0001] The present invention relates to the technical field of heat transfer in underground engineering, and particularly to an analytical model solving method for determining the heat transfer performance of buried tube heat exchangers in underground engineering structures. Background Art

[0002] Deep underground in protective engineering, whether the heat can be discharged smoothly is a key issue related to the smooth operation of the project. Imitating the heat transfer form of the buried tubes in the lining of the portal passage of the energy tunnel well overcomes the disadvantages of the cooling tower being easily exposed, the limited heat capacity of the reservoir, and the high construction cost and difficulty of the ground source heat pump system, and improves the protection ability of the project, as Figure 1 shown.

[0003] In the lining at a certain length from the entrance, serpentine heat exchange tubes are uniformly arranged along the axial direction. The circulating medium in the tubes 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 project heat to the environment. In this process, heat is transferred among the air in the passage, 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 mode will affect the ventilation volume, and the ventilation volume will in turn affect the convective heat transfer coefficient, and finally determine the distribution ratio of the heat entering the air and the heat entering the surrounding rock. The heat transfer process of the surrounding rock has a time lag, and the coupled heat transfer with the buried tube heat exchanger in the lining is a non-steady 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 tube heat exchanger in the portal passage of the protective engineering, it is necessary to establish a model for simulation calculation. The analytical model has attracted the research interest of many scholars due to its convenient calculation. Most of the existing studies focus on borehole heat exchangers and pile heat exchangers. However, due to the special structure of the buried tubes in the tunnel lining, their geometric distribution and boundary conditions are very different from those of pile heat exchangers. There are two-way heat exchanges in the energy tunnel, one is with the air in the tunnel, and the other is with the surrounding rock. The traditional cylindrical heat source and linear heat source models are not applicable here. The current solution is to simplify the lining surface as 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 transfer. Simply limiting the heat diffusion within the plane transfer direction range does not conform to the actual situation. Summary of the Invention

[0005] The purpose of the present invention is to provide an analytical model solving method for determining the heat transfer performance of buried tube heat exchangers in underground engineering structures in view of the problems existing in the above-mentioned prior art, establish an analytical solution model for the curved surface of the buried tube heat exchanger in the lining, compare it with the one-dimensional plane model, and finally use this model to analyze the influence of air flow in the passage on the heat transfer performance, providing a theoretical basis for optimizing the heat transfer characteristics of the passage.

[0006] The technical solution for achieving the object of the present invention is: an analytical model solving method for determining the heat transfer performance of the buried tube heat exchanger in the underground engineering structure, the method comprising:

[0007] Step 1, during the heat transfer process, the heat source is the circulating hot water in the buried tube heat exchanger, and the arched cross-section of the entrance passage of the protective engineering is simplified into an equivalent circular cross-section, which is a two-dimensional model;

[0008] Step 2, the radius where the discrete line heat source is located is equivalent to a surface heat source, and thus the two-dimensional model is simplified into a semi-infinite cylindrical heat transfer calculation model with an internal heat source;

[0009] Step 3, taking the cylindrical surface where the buried tube heat exchanger in the underground engineering structure is located as the boundary, re-divide and analyze the heat transfer process of the entrance passage, including the following three parts: the heat transfer between the circulating water and the lining, the heat transfer between the lining and the air, and the heat transfer between the lining and the surrounding rock;

[0010] Step 4, based on the heat transfer process re-divided in Step 3, optimize the semi-infinite cylindrical heat transfer calculation model with an internal heat source to obtain the surrounding rock side heat conduction model, that is, the analytical model;

[0011] Step 5, solve the analytical model.

[0012] Further, in Step 2, simplifying the two-dimensional model into a semi-infinite cylindrical heat transfer calculation model with an internal heat source specifically includes:

[0013] According to Fourier's law and the first law of thermodynamics, establish a differential equation for thermal conductivity:

[0014] ;

[0015] Initial condition:

[0016] ;

[0017] Boundary condition:

[0018] ;

[0019] In the formula, is the temperature of the surrounding rock at the radius r, with the unit of ; is the thermal diffusivity of the surrounding rock, with the unit of ;

[0020] is the thermal conductivity of the surrounding rock, with the unit of ; is the density of the surrounding rock, with the unit of ; is the specific heat capacity of the surrounding rock under constant pressure, with the unit of ; is the heat released per unit volume of the buried pipe heat exchanger, with the unit of ; is the equivalent radius of the inlet channel, with the unit of m; is the temperature of the far boundary of the surrounding rock, with the unit of ; is the convective heat transfer coefficient between the air in the orifice channel and the lining surface, with the unit of ; is the temperature of the air in the orifice channel, with the unit of , represents time.

[0021] Furthermore, the relationship among 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, which is expressed as:

[0022] ;

[0023] In the formula, is the total heat flux released by the heat exchange tube per unit channel length, with the unit of ; is the heat flux released from the heat exchange tube per unit channel length to the air, with the unit of ; is the heat flux transferred from the heat exchange tube per unit channel length to the surrounding rock, with the unit of .

[0024] Furthermore, according to the heat flux, , are defined as:

[0025] ;

[0026] Among them,

[0027] ;

[0028] In the formula, is the average temperature of the circulating water in the underground heat exchanger, with the unit of ; is the air temperature in the orifice channel, with the unit of ; is the temperature of the contact surface between the lining and the surrounding rock, with the unit of ; is the temperature of the circulating water entering the buried pipe heat exchanger, with the unit of ; is the temperature of the circulating water at the outlet of the buried pipe heat exchanger , is the thermal resistance between the circulating water in the buried tube heat exchanger and the air in the orifice passage, with the unit of ; is the thermal resistance between the circulating water and the surrounding rock, with the unit of .

[0029] Furthermore, the calculation formulas for the thermal resistances and are respectively:

[0030] ;

[0031] In the formula, is the convective heat transfer coefficient of the air between the inlet passage and the lining surface, with the unit of ; D is the diameter of the inlet passage, with the unit of m; is the thermal conductivity of the lining material, with the unit of ; is the distance between the laying surface of the buried tube heat exchanger and the inner surface of the lining, with the unit of m; is the lining thickness, with the unit of m; is the convective heat transfer coefficient of the circulating water in the buried tube heat exchanger, with the unit of , and the calculation formula is:

[0032] ;

[0033] In the formula, , is the average flow velocity in the buried tube heat exchanger; is a dimensionless constant; is the thermal conductivity of the circulating water, with the unit of ; d is the inner diameter of the buried tube heat exchanger, with the unit of mm; is the kinematic viscosity of water, with the unit of , is the Nusselt number, which is a dimensionless number.

[0034] Furthermore, step 4 specifically includes:

[0035] Rewriting the semi-infinite cylindrical heat transfer calculation model with an internal heat source into the differential equation of heat conduction on the side of the surrounding rock, that is, the heat conduction model on the side of the surrounding rock, where is used as the boundary condition for the buried tube heat exchanger in the underground engineering structure to release heat to the surrounding rock, specifically expressed as:

[0036] ;

[0037] Initial condition:

[0038] ;

[0039] Boundary conditions:

[0040] ;

[0041] In the formula, is the distance from the ground to the center of the tunnel.

[0042] Furthermore, step 5 solves the analytical model, specifically including:

[0043] Step 5-1, solve the analytical model to obtain the surrounding rock temperature at the radius along the central axis of the semi-infinite cylinder at time r , and the surrounding rock temperature at the interface between the lining and the surrounding rock ;

[0044] Step 5-2, introduce the ratio of the actual occupied area of the buried pipe to the area of the cylinder to correct the heat exchange between the circulating water and the lining;

[0045] Step 5-3, based on the results of step 3 and steps 5-1 and 5-3, solve to obtain the solution of the analytical model.

[0046] Furthermore, in step 5-1, the heat conduction model on the side of the surrounding rock is solved by integral transformation, and the surrounding rock temperature at the radius r along the central axis of the semi-infinite cylinder at time is:

[0047] ;

[0048] In the formula, is the zero-order Bessel function of the first kind, is the first-order Bessel function of the second kind, and u is a variable with no actual meaning;

[0049] Let , and obtain the surrounding rock temperature at the interface between the lining and the surrounding rock as:

[0050] ;

[0051] In the formula, is the surrounding rock temperature at the interface between the lining and the surrounding rock at time

[0052] Furthermore, in step 5-2, the ratio of the actual occupied area of the buried pipe to the area of the cylinder is introduced to correct the heat exchange between the circulating water and the lining, specifically as:

[0053] ;

[0054] In the formula, The total heat flux released by the heat exchange tube per unit channel length is the constant pressure specific heat capacity of the circulating water, with the unit of ; is the density of the circulating water, with the unit of ; is the flow velocity of the circulating water in the buried pipe, with the unit of ; S is the cross-sectional area of the buried pipe heat exchanger, with the unit of ; is the temperature of the circulating water entering the buried pipe heat exchanger, with the unit of ; is the temperature of the circulating water at the outlet of the buried pipe heat exchanger, with the unit of ; is the length of the buried pipe heat exchanger laid along the channel, with the unit of m; k is the ratio of the actual occupied area of the buried pipe to the cylindrical area.

[0055] Furthermore, step 5-3 solves to obtain the solution of the analytical model based on the results of step 3 and steps 5-1 and 5-3, specifically as follows:

[0056] Let:

[0057] ;

[0058] Then:

[0059] .

[0060] Compared with the prior art, the remarkable advantages of the present invention are:

[0061] (1) For the transient heat transfer problem of a non-uniform composite medium cylinder containing discrete internal heat sources, a mathematical model of the heat transfer process of the lined buried pipe heat exchanger is established. The solution process avoids the traditional method of making the problem homogeneous by using the linear superposition principle. Instead, it takes a different approach and simplifies the model from the perspective of the heat transfer process. Taking the cylindrical surface where the buried pipe heat exchanger is located as the boundary, the heat transfer process is decomposed into the heat transfer between the circulating water and the lining, the heat transfer between the lining and the air, and the heat transfer between the lining and the surrounding rock, thereby transforming the original non-homogeneous, non-steady-state, non-linear second-order differential equation into a directly solvable model.

[0062] (2) For the above-mentioned analytical model of the heat transfer process of the lined buried pipe heat exchanger, the system of equations is solved to obtain explicit expressions for parameters such as the outlet water temperature, the contact surface temperature, the heat transferred into the air, the heat transferred into the surrounding rock, and the total heat transfer. Through the existing experimental data, it is verified that the model can reproduce the heat transfer process under the condition of continuous heat release in a circular channel.

[0063] The present invention will be further described in detail below with reference to the accompanying drawings. Description of the Drawings

[0064] Figure 1 It is a schematic diagram of the laying of the buried tube heat exchanger in the lining of the access tunnel at the entrance of the protective engineering. Figure 1 In (a) and (b) of , they are respectively the three-dimensional schematic diagram and cross-sectional view of the laying of the buried tube heat exchanger in the lining of the access tunnel at the entrance of the protective engineering.

[0065] Figure 2 It is a schematic diagram of the one-dimensional heat transfer simplified model of the buried tube heat exchanger in the lining.

[0066] Figure 3 It is a flow chart of the solution method of the analytical model for determining the heat transfer performance of the buried tube heat exchanger in the underground engineering structure of the present invention.

[0067] Figure 4 It is a schematic diagram of the solution of the present invention in an embodiment.

[0068] Figure 5 It is a comparison result diagram of the analytical solution value and the experimental value in the literature in an embodiment, where Figure 5 In (a) and (b) of , they are respectively the comparison results of the first group of experimental data and the second group of experimental data. Specific embodiments

[0069] In order to make the purpose, technical solutions and advantages of the present application clearer, the following further details the present application 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.

[0070] 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 for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the fact that those skilled in the art can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0071] In an embodiment, in combination with Figure 3 and Figure 4 , a solution method for an analytical model for determining the heat transfer performance of a buried tube heat exchanger in an underground engineering structure is provided, and the method includes the following steps:

[0072] Step 1, during the heat transfer process, the heat source is the circulating hot water in the buried tube heat exchanger, and the arched section of the access tunnel of the protective engineering is simplified into an equivalent circular section, which is a two-dimensional model.

[0073] Step 2, since the buried pipe spacing is small, the radius where the discrete line heat source is located can be equivalent to a surface heat source, and the two-dimensional model can be further simplified to a semi-infinite cylindrical heat transfer calculation model with an internal heat source, as Figure 2 shown.

[0074] 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, a differential equation for thermal conductivity is established:

[0075]

[0076] Initial condition:

[0077] ;

[0078] Boundary condition:

[0079] ;

[0080] In the formula, is the temperature of the surrounding rock at radius r, with the unit of ; is the thermal diffusivity of the surrounding rock, with the unit of ;

[0081] is the thermal conductivity of the surrounding rock, with the unit of ; is the density of the surrounding rock, with the unit of ; is the specific heat capacity of the surrounding rock at constant pressure, with the unit of ; is the heat released per unit volume of the buried pipe heat exchanger, with the unit of ; is the equivalent radius of the inlet channel, with the unit of m; is the far boundary temperature of the surrounding rock, with the unit of ; is the convective heat transfer coefficient between the air in the inlet channel and the lining surface, with the unit of ; is the temperature of the air in the inlet channel, with the unit of , represents time.

[0082] 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 unsteady nonlinear differential equation. There are many methods to solve this problem. Most of them focus on the research of volume heat sources and do not involve the heat transfer calculation of surface heat sources. If the existing methods are directly applied, the linear superposition principle needs to be used to transform the problem into a homogeneous one. The solution is divided into two parts. One part is the solution of the non-uniform steady-state heat conduction problem, and the other part is the solution of the uniform transient heat conduction problem. The calculation method is complex and inefficient.

[0083] Step 3. To simplify this problem, taking the cylindrical surface where the buried pipe heat exchanger is located as the boundary, re-analyze the heat transfer process of the orifice channel, which mainly includes the following three parts: the heat transfer between the circulating water and the lining, the heat transfer between the lining and the air, and the heat transfer between the lining and the surrounding rock. The relationship among these three parts 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 the surrounding rock. The expression is as follows:

[0084]

[0085] In the formula, is the total heat flux released by the heat exchange tube per unit channel length, with the unit of ; is the heat flux released from the heat exchange tube per unit channel length to the air, with the unit of ; is the heat flux transferred from the heat exchange tube per unit channel length to the surrounding rock, with the unit of . Among them, can be used as the boundary condition for the heat released by the buried pipe heat exchanger to the surrounding rock. Equations (1-1)-(1-4) can be rewritten as the heat conduction differential equation on the side surface of the surrounding rock:

[0086]

[0087] Initial condition:

[0088]

[0089] Boundary condition:

[0090]

[0091] Step 4. Solve equations (1-6)-(1-9) through integral transformation to obtain the temperature of the surrounding rock at the radius r along the central axis of the cylinder at the moment in equation (1-10).

[0092]

[0093] In the formula, is the zero-order Bessel function of the first kind, is the second kind of first-order Bessel function, u and the variable has no actual meaning.

[0094] Step 5, when calculate the surrounding rock temperature at the interface between the lining and the surrounding rock :

[0095]

[0096] Step 6, since the heat released into the air and the heat released into the surrounding rock are both provided by the buried tube heat exchanger. When the surface where the buried tube heat exchanger is located is equivalent to a heat source surface, the smaller the pipe spacing, the more accurate the model equivalence. In fact, there is impossible to have no spacing between pipes. To eliminate the difference between the equivalent cylindrical surface heat source and the actual line heat source with spacing, the ratio k of the actual occupied area of the buried tube to the cylindrical area is introduced. Therefore, the total heat per unit channel length is:

[0097]

[0098] In the formula, is the total heat flux released by the heat exchange tubes per unit channel length, is the constant pressure specific heat capacity of the circulating water, with the unit of ; is the density of the circulating water, with the unit of ; is the flow velocity of the circulating water in the buried tube, with the unit of ; S is the cross-sectional area of the buried tube heat exchanger, with the unit of ; is the temperature of the circulating water entering the buried tube heat exchanger, with the unit of ; is the temperature of the circulating water at the outlet of the buried tube heat exchanger, with the unit of ; is the length of the buried tube heat exchanger laid along the channel, with the unit of m; k is the ratio of the actual occupied area of the buried tube to the cylindrical area.

[0099] Step 7, according to the definition of heat flux,

[0100]

[0101] Among them, is the average temperature of the circulating water in the underground heat exchanger, with the unit of ; is the air temperature in the mouth channel, with the unit of ; is the temperature of the contact surface between the lining and the surrounding rock, with the unit of , obtained from Equation (1-11); is the temperature of the circulating water entering the buried tube heat exchanger, with the unit of ; is the temperature of the circulating water at the outlet of the buried tube heat exchanger, with the unit of , is the thermal resistance between the circulating water in the buried tube heat exchanger and the air in the orifice channel, with the unit of ; is the thermal resistance between the circulating water and the surrounding rock, with the unit of .

[0102] Step 8, according to the calculation formula for heat conduction in a cylindrical wall under the third boundary condition:

[0103]

[0104] where is the convective heat transfer coefficient of the air between the inlet channel and the lining surface, with the unit of ; D is the diameter of the inlet channel, with the unit of m; is the thermal conductivity of the lining material, with the unit of ; is the distance between the laying surface of the buried tube heat exchanger and the inner surface of the lining, with the unit of m; is the lining thickness, with the unit of m; is the convective heat transfer coefficient of the circulating water in the buried tube heat exchanger, with the unit of , calculated from Equation (1-18):

[0105] ;

[0106] In the formula, , is the average flow velocity in the buried tube heat exchanger; is a dimensionless constant, generally taken as ; is the thermal conductivity of the circulating water, with the unit of ; d is the inner diameter of the buried tube heat exchanger, with the unit of mm; is the kinematic viscosity of water, with the unit of , is the Nusselt number, which is a dimensionless number.

[0107] Step 9, obtain the relationship between from Equations (1-11)-(1-18). Let:

[0108]

[0109] Then:

[0110]

[0111] Equations (1-21)-(1-26) are the inlet water temperatures and the explicit analytical solutions of each physical quantity when they are known.

[0112] Furthermore, the method further includes:

[0113] Step 10, verifying the above analytical model.

[0114] Exemplarily, two existing sets of test data are used for comparison. The model setting parameters and the test parameters are the same, as shown in Table 1.

[0115]

[0116] The simulation calculation time is 50 hours, and the outlet fluid temperature calculated by the analytical model is compared with the test results as Figure 5 shown. As can be seen from the figure, as the operation time increases, the deviation between the model calculation result and the measured data gradually decreases. It can be inferred that the analytical model can reasonably reproduce the transient heat transfer process within 50 hours of continuous cooling of the buried pipe in the circular channel.

[0117] In one embodiment, an analytical model solving system for determining the heat transfer performance of a buried tube heat exchanger in an underground engineering structure is provided. The system includes:

[0118] The first module is used to simplify the arched cross-section of the portal channel of the protective engineering into an equivalent circular cross-section, which is a two-dimensional model;

[0119] The second module is used to equivalently replace the radius where the discrete line heat source is located with a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylindrical heat transfer calculation model with an internal heat source;

[0120] The third module is used to re-divide the heat transfer process of the portal channel with the cylindrical surface where the buried tube heat exchanger in the underground engineering structure is located as the boundary, including the following three parts: the heat transfer between the circulating water and the lining, the heat transfer between the lining and the air, and the heat transfer between the lining and the surrounding rock;

[0121] The fourth module is used to optimize the semi-infinite cylindrical heat transfer calculation model with an internal heat source based on the heat transfer process re-divided by the third module to obtain a surrounding rock side heat conduction model, that is, an analytical model;

[0122] The fifth module is used to solve the analytical model.

[0123] Furthermore, the system further includes:

[0124] The sixth module is used to verify the analytical model.

[0125] For the specific limitations of the analytical model solving system for determining the heat transfer performance of the buried tube heat exchanger in the underground engineering structure, reference can be made to the limitations of the analytical model solving method for determining the heat transfer performance of the buried tube heat exchanger in the underground engineering structure in the above text, which will not be elaborated here. Each module in the above-mentioned analytical model solving system for determining the heat transfer performance of the buried tube heat exchanger in the underground engineering structure can be implemented in whole or in part through software, hardware, and their combinations. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or stored in the memory of the computer device in the form of software, so as to facilitate the processor to call and execute the operations corresponding to each of the above modules.

[0126] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the following is implemented:

[0127] Step 1, during the heat transfer process, the heat source is the circulating hot water in the buried tube heat exchanger. The arched cross-section of the portal passage of the protective engineering is simplified into an equivalent circular cross-section, which is a two-dimensional model.

[0128] Step 2, the radius where the discrete line heat source is located is equivalent to a surface heat source, and thus the two-dimensional model is simplified into a semi-infinite cylindrical heat transfer calculation model with an internal heat source.

[0129] Step 3, taking the cylindrical surface where the buried tube heat exchanger in the underground engineering structure is located as the boundary, re-divide and analyze the heat transfer process of the portal passage, including the following three parts: heat transfer between the circulating water and the lining, heat transfer between the lining and the air, and heat transfer between the lining and the surrounding rock.

[0130] Step 4, based on the heat transfer process re-divided in Step 3, optimize the semi-infinite cylindrical heat transfer calculation model with an internal heat source to obtain the surrounding rock side heat conduction model, that is, the analytical model.

[0131] Step 5, solve the analytical model.

[0132] Step 6, verify the analytical model.

[0133] For the specific limitations of each step, reference can be made to the limitations of the analytical model solving method for determining the heat transfer performance of the buried tube heat exchanger in the underground engineering structure in the above text, which will not be elaborated here.

[0134] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the following is implemented:

[0135] Step 1, during the heat transfer process, the heat source is the circulating hot water in the buried tube heat exchanger. The arched cross-section of the portal passage of the protective engineering is simplified into an equivalent circular cross-section, which is a two-dimensional model.

[0136] Step 2: Equivalent the radius where the discrete line heat source is located to a surface heat source, thereby simplifying the two-dimensional model into a semi-infinite cylindrical heat transfer calculation model with an internal heat source;

[0137] Step 3: Take the cylindrical surface where the buried tube heat exchanger in the underground engineering structure is located as the boundary, and re-divide and analyze the heat transfer process of the orifice channel, including the following three parts: heat transfer between the circulating water and the lining, heat transfer between the lining and the air, and heat transfer between the lining and the surrounding rock;

[0138] Step 4: Based on the heat transfer process re-divided in Step 3, optimize the semi-infinite cylindrical heat transfer calculation model with an internal heat source to obtain the surrounding rock side heat conduction model, i.e., the analytical model;

[0139] Step 5: Solve the analytical model.

[0140] Step 6: Verify the analytical model.

[0141] For the specific limitations of each step, reference can be made to the limitations of the analytical model solving method for determining the heat transfer performance of the buried tube heat exchanger in the underground engineering structure in the above text, which will not be elaborated here.

[0142] 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. What is described in the above embodiments and the specification only illustrates the principle of the present invention. Without departing from the spirit and scope of the present invention, any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within 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, the heat exchange process of the mouth channel is re-divided and analyzed, 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; the relationship between the three parts 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 ; 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 ; 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 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.

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 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.

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 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.

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 5, 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.

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 6, 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.

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 3 or 7, 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: 。 9. An analytical model solving system for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure based on the method according to any one of claims 1 to 8, characterized in that: The system comprises: 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.

10. The analytical model solving system for determining the heat transfer performance of a buried heat exchanger in an underground engineering structure according to claim 9, characterized in that: The system further comprises: The sixth module is used to verify the analytical model.

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