Hybrid scheme for borehole heat exchanger based on spatially split physical coupling

Abstract

The application discloses a mixed format algorithm of a borehole heat exchanger based on a spatial separation physical coupling idea, and comprises the following steps: a grid division method is designed to establish a radial one-dimensional Nr node non-steady-state diffusion numerical model of a backfill material in a hole and a rock-soil area outside the hole of an underground heat exchanger; a grid division method is designed to establish a one-dimensional 2Nf node non-steady-state convection diffusion numerical model of fluid along a flow direction, and a radial one-dimensional two-node heat conduction numerical model of a pipe wall; a kind of implicit and explicit hybrid numerical format is designed to realize the coupling calculation of non-steady-state heat transfer of fluid+PE pipe and backfill material+rock-soil; a kind of two-fold iteration algorithm is designed for the numerical model of step S2 to realize simultaneous solution of fluid temperature in the PE pipe and pipe inner wall temperature at each time step; based on the implicit and explicit hybrid numerical format, an algorithm is designed to realize the sequential simulation of "receiving import temperature→calculating fluid temperature along the way and pipe wall temperature→calculating pipe outer wall heat exchange amount→calculating pipe outer solid area temperature".

Description

Technical Field

[0001] This invention relates to the field of ground source heat pump heat exchange technology, and in particular to a global unsteady one-dimensional implicit-explicit hybrid numerical model and algorithm for a vertically buried U-shaped tube borehole heat exchanger with the inlet temperature as a known condition. Background Technology

[0002] Ground source heat pumps are a type of air conditioning system that utilizes shallow, renewable geothermal energy and has advantages such as high efficiency, energy saving, and environmental protection. They are widely used both domestically and internationally.

[0003] The components of a ground source heat pump system include: (1) terminal air handling equipment and fans, responsible for cooling or heating indoor air; (2) load-side circulating water pumps, responsible for distributing the hot and cold water generated by the heat pump unit to the terminal equipment; (3) heat pump units, which realize cooling and heating. It includes four major components: evaporator, condenser, compressor and expansion device, as well as other auxiliary and control components; (5) source-side water pumps, responsible for realizing water circulation between the heat pump and the underground heat exchanger; (6) underground heat exchanger, which serves as a heat sink in summer and a heat source in winter. Among them, the underground heat exchanger is the key component that distinguishes the ground source heat pump air conditioning system from the conventional air conditioning system. The vertically buried U-shaped tube underground heat exchanger is the most widely used form. Whether its design is reasonable or not is related to the cost of the ground source heat pump project and the safety and reliability of long-term operation. Scientific design of underground heat exchangers requires accurate heat transfer models and heat property parameters inside and outside the heat exchanger holes. The heat property parameters inside and outside the vertically buried U-shaped tube underground heat exchanger holes are also obtained by inverting the heat transfer model based on the thermal response test data. It is evident that the heat transfer model of the underground heat exchanger is the basis for the design and performance calculation of the ground source heat pump system.

[0004] Vertically buried U-tube underground heat exchangers have large structural dimensions, and their loads change dynamically hourly, resulting in heat transfer characteristics such as non-steady-state operation and long time spans. Life-cycle performance calculations require dynamic calculations over one year or even 30 years. Meanwhile, thermal response test sampling intervals are less than 10 minutes, or even as short as 30 seconds, necessitating accurate short-step calculations for the inversion of heat exchanger thermophysical parameters. Therefore, model accuracy and speed are crucial considerations.

[0005] While existing general-purpose full 3D numerical heat transfer simulation software can be used for simulation research of underground heat exchangers in ground source heat pumps, the computational cost is too high, and its practicality in engineering design calculations is weak. Simplified 1D linear or column heat source analytical models mostly adopt the assumption of steady-state heat transfer within the borehole, resulting in significant short-time step calculation errors; moreover, analytical models are often derived based on constant heat flow conditions, making them unsuitable for direct application to calculations under hourly load variations. "Geothermal Star" uses an approximate analytical model, calculating based on the building's average monthly load and peak load, without performing hourly calculations. Patents "CN 104732111 A" and "CN 110147639 A" each present a 1D numerical model that can be directly used for rapid calculations under dynamic loads, but still employ the assumption of quasi-steady-state heat transfer within the borehole, resulting in significant short-time step calculation errors. The TRNSYS underground heat exchanger model does not consider the unsteady-state heat transfer processes of the pipe wall and backfill material; thermal response test data verification shows that short-time step calculation errors are also significant. Summary of the Invention

[0006] The purpose of this invention is to provide a hybrid format algorithm for borehole heat exchangers based on the concept of spatial separation and physical coupling, addressing the aforementioned shortcomings. This solves the problem that while existing general-purpose full three-dimensional numerical heat transfer simulation software can be used for simulation research of underground heat exchangers for ground source heat pumps, its computational cost is too high and its practicality in engineering design calculations is weak.

[0007] This solution considers the accuracy and speed requirements of short-time step and long-cycle calculations for underground heat exchange using vertically buried U-tubes in ground source heat pumps. It proposes a global unsteady one-dimensional implicit-explicit hybrid numerical model and algorithm for U-tube borehole heat exchangers, based on the concept of spatial separation and physical coupling, with inlet temperature as input. Given the heat exchanger's structural parameters (including borehole depth, borehole diameter, tube spacing, inner tube diameter, outer tube diameter, and hole spacing) and physical properties (including the thermal conductivity and volumetric specific heat of the soil, backfill material, and PE pipe), and inputting the original ground temperature, flow rate, and U-tube inlet temperature, the algorithm can calculate the outlet temperature, ground temperature changes, and heat exchange rate.

[0008] This invention is achieved through the following scheme: The hybrid scheme algorithm for borehole heat exchangers based on the concept of spatial separation and physical coupling includes the following steps: Step S1: Design a mesh generation method to establish a radial one-dimensional Nr node unsteady diffusion numerical model of the soil and rock region outside the pore backfill of the underground heat exchanger. Step S2: Design a mesh generation method to establish a one-dimensional 2N mesh along the flow direction. f A numerical model of unsteady convection and diffusion at nodes was developed, and a one-dimensional two-node unsteady heat conduction numerical model of the radial direction of the pipe wall was established. Step S3: Design a hybrid numerical scheme that combines implicit and explicit representations to achieve coupled calculation of unsteady heat transfer between fluid + PE pipe and backfill + soil. Step S4: Design a two-fold iterative algorithm for the numerical model in step S2 to solve the fluid temperature inside the PE pipe and the inner wall temperature at each time step. Step S5: Design an algorithm based on the implicit and explicit hybrid numerical format to realize the sequential simulation of "receiving inlet temperature → calculating fluid friction temperature and pipe wall temperature → calculating heat transfer on the outer wall of the pipe → calculating the temperature of the solid region outside the pipe".

[0009] Step S1 specifically includes the following steps: The backfill material inside the borehole and the soil and rock outside the borehole are divided into the following radial directions: Two units are fixedly installed for the backfill material inside the hole, and after the third unit ( The borehole is a geotechnical unit. The first unit at the borehole center is a solid cylinder of height L, and the remaining units are annular cylinders. The center coordinates of the second unit of the backfill material are set at the center of the PE pipe. The interface between the second unit and the first unit is set in... At this location, the interface between the second and third units is set at the hole wall r= The geotechnical unit interface is located at the center of the two nodes; for a single hole, the radius of the far boundary can be 10m or 20m, and for a group of holes, the radius of the far boundary can be 1 / 2 of the hole spacing; the boundary conditions are set as follows: the upper, lower and far boundaries of the heat exchanger calculation area are considered as adiabatic boundaries; internal heat source: the internal heat source is only set in the second unit of the backfill material. According to the innovative idea of ​​"spatial separation and physical coupling", the single / double U-shaped vertical buried pipe is abstracted as 2 / 4 of the linear heat sources without shape and volume; the heat generation of the internal heat source of the backfill material unit 2 is equal to the heat of the outer wall of the pipe.

[0010] Step S2 specifically includes the following steps: The inlet and outlet branches of the U-shaped tube are respectively installed along the flow direction. There are 1 node, and 1 group of U-shaped tubes. The fluid node, the first Units are evenly distributed, j=1 and The unit is a control body of 0; The PE pipe wall is divided into sections corresponding to fluid nodes in the flow direction. Each section is insulated from the others; each section of PE pipe has two nodes fixed radially on its wall, one on the inner wall and one on the outer wall; the heat from the outer wall of the pipe is used as the internal heat source for the backfill unit 2; the temperature of the outer wall node is set to be equal to the temperature of the backfill unit 2.

[0011] The numerical model of backfill + soil in step S3 was obtained in the following way: all nodes of backfill inside the borehole and soil outside the borehole ( The unsteady-state thermal conductivity explicit numerical discrete equation is established using the finite volume method to calculate the radial temperature of backfill and soil. When establishing the numerical equation for the temperature of the second unit of the backfill in the borehole, the single / double U-shaped vertical buried pipe is simplified to 2 / 4 of the line heat source, without considering its shape and volume, and its internal heat source is set to be equal to the heat released / absorbed by the outer wall of the U-shaped pipe. The nodal temperature calculation formula is established using an explicit format.

[0012] The numerical model of fluid + PE pipe in step S3 is obtained in the following way: the temperature of fluid nodes inside PE pipe of vertical buried U-shaped tube underground heat exchanger is solved by establishing discrete equations using fully implicit QUICK scheme, and the temperature of node 1 on the inner wall of PE pipe is solved by establishing discrete equations using implicit and explicit hybrid scheme. The inlet temperature of the inlet branch pipe is known, and the outlet node j=Nf is the outflow boundary; the inlet temperature of the outlet branch pipe is equal to the outlet temperature of the inlet branch, and its outlet node j=1 is the outflow boundary.

[0013] In step S3, the model coupling method is as follows: When establishing the numerical equations for the fluid and inner wall temperature of the PE pipe, the fluid and inner wall temperatures are taken at the same moment, and the outer wall temperature is set to be equal to the temperature of the backfill unit 2 in the hole at the previous moment; the inner wall node and the fluid node have an implicit relationship, and a simultaneous iterative solution is used to ensure convergence; the inner wall node and the outer wall node have an explicit relationship, realizing the separate solution of the PE pipe and the outer region. Heat exchange on the inner wall of the tube Based on Newton's law of cooling, the current temperature of the inner wall nodes is used. With the corresponding fluid node temperature Calculations are performed; the convective heat transfer coefficient of the pipe is calculated using the classical Dittus correlation in heat transfer; the outer wall of the pipe... Heat absorption / release is measured using the current temperature of the inner wall nodes. and the temperature of the outer wall node at the previous moment calculate.

[0014] Step S4 specifically includes the following steps: Step S41: Receive drilling depth L and PE pipe outer diameter d o and inner diameter d i and mesh parameters; Step S42: Receive the thermal conductivity λ of the PE pipe p and specific heat of volume ρ p c p Fluid thermophysical parameters; Step S43: Receive the inlet temperature T of the U-tube in Flow rate F, initial temperature of soil and rock Initial temperature of the fluid Initial temperature of the inner wall of the pipe Parameters; Step S44: Receive the convective heat transfer coefficient h of the tube wall; Step S45: Assume the inner wall temperature of the PE pipe ; Step S46: Calculate the coefficients of the discrete equations for the fluid element using the QUICK scheme; Step S47: Solve for the temperature of the fluid element using relaxation iteration. ; Step S48: Based on fluid element temperature And the temperature of the outer wall of the tube at the previous moment. Calculate the inner wall temperature of the PE pipe ; Step S49: Based on step S45 ; and in step S48 Update the PE pipe inner wall temperature with a relaxation factor of 0.5. ; Step S410: Calculate the temperature error of the inner wall of the PE pipe. ; Step S411: If the maximum error If the precision is greater than the set value eps=0.001, use... Alternative Proceed to step S46; otherwise, end the iteration and proceed to step S412. Step S412: Determine the fluid temperature at the current moment. Inner wall temperature Calculate the heat exchange of the inner wall of the pipe ; Step S413: Determine the current inner wall temperature The temperature of the outer wall at the previous moment Calculate the heat released / absorbed by the outer wall of the tube. ; Step S414: The fluid inlet temperature Tin and outlet temperature... Calculate the total heat of the heat exchanger .

[0015] Step S5 specifically includes the following steps: Step S51: Receive the borehole diameter Db, the spacing between U-shaped tubes in the borehole Dp, the borehole depth L, the borehole spacing D, the outer diameter do and inner diameter di of the PE pipe, and the grid parameters; Step S52: Receive the thermal conductivity λs and volumetric specific heat ρscs of the soil and rock, the thermal conductivity λb and volumetric specific heat ρbcb of the borehole backfill, the thermal conductivity λp and volumetric specific heat ρpcp of the PE pipe, and the fluid thermal properties. Step S53: Receive the current temperature Tin, flow rate F, and initial temperature of the soil and rock at the U-shaped pipe inlet. Initial temperature of pipe wall Initial temperature of the fluid Parameters; Step S54: Calculate the tube wall convective heat transfer coefficient at the current moment using the Dittus convective heat transfer correlation in the tube; Step S55: Apply the "two-iteration algorithm" to solve for the fluid friction temperature distribution T at the current moment. f and the temperature of the inner wall of the PE pipe And calculate the total heat capacity Q of the heat exchanger. f Heat Q of the inner wall of PE pipe fp and the heat Q of the outer wall pb ; Step S56: Based on the heat exchange rate Q of the PE pipe outer wall in step S55 pb and the initial temperature of the soil and rock The temperature T of the solid region outside the pipe at the current moment is calculated using the "backfill + explicit numerical model of soil and rock". Step S57: Utilize the current soil and rock temperature T and the current fluid temperature T f and the current pipe wall temperature Update the initial temperature of the soil and rock respectively Initial temperature of the fluid Initial temperature of pipe wall Proceed to step S53 to begin the calculation for the next time step, until all time steps have been calculated.

[0016] In step S3, the temperature calculation formula for borehole center unit i=1 is:

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] in This represents the current borehole center temperature. The borehole center temperature at the previous moment. The temperature of the second element node at the previous time step. The specific heat of the backfill material is the volumetric heat. The thermal conductivity of the backfill material. For the volume of unit 1, The radius of the location of unit 2. Let L be the radius of the interface between element 1 and element 2, and L be the drilling depth. The diameter of the borehole. For pipe spacing, The outer diameter of the PE pipe; The formula for calculating the temperature of the i=2nd unit inside the hole is:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] in This represents the current temperature of the second drilling unit. This represents the temperature of the second drilling unit at the previous moment. The temperature of the third element node at the previous time step. For the volume of unit 2, The radius of the interface between element 2 and element 3 is the radius of the hole wall. The total heat released / absorbed by the outer wall of the PE pipe. The equivalent thermal conductivity at the borehole wall is obtained by averaging the thermal conductivity of the backfill material and the thermal conductivity of the soil and rock. The temperature calculation formula for the i=3rd unit is:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] in The temperature of the third unit at the current moment. This refers to the temperature of the third unit at the previous moment. The temperature of the 4th unit node at the previous moment. For the volume of unit 3, Let be the radius of the interface between element 3 and element 4. The equivalent thermal conductivity at the borehole wall is obtained by averaging the thermal conductivity of the backfill material and the thermal conductivity of the soil and rock. The thermal conductivity of the soil and rock is... Specific heat of rock and soil by volume: No. The temperature calculation formula for each unit is:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] in Let i be the temperature of the i-th unit at the current moment. Let i be the temperature of the i-th unit at the previous time step. The temperature of the (i+1)th cell node at the previous time step. Let i be the volume of element i. Let be the radius of the interface position between element i and element i+1; No. The temperature calculation formula for each unit is:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] in Let i be the temperature of the i-th unit at the current moment. Let i be the temperature of the i-th unit at the previous time step. Let i be the volume of element i. Let be the radius at the position of element node i.

[0049] In step S3, the numerical discrete equations for the fluid and the temperature of the joints on the inner wall of the PE pipe, and the heat calculation formulas are as follows: Inlet branch fluid node j=1, ; The numerical discretization equation for the second fluid node j=2 at the inlet branch is:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] in Let J be the temperature of the j-th fluid element at the current moment. Let j be the temperature of the j-th fluid element at the previous moment. The temperature of the upstream fluid unit at the current moment. The temperature of the downstream fluid unit at the current moment. The temperature of the PE pipe inner wall corresponding to fluid element j at the current moment is... Let j be the length of the fluid element. The distance between unit node j and upstream node j-1, Let P be the distance between node j and downstream node j+1, P be the perimeter of the pipe cross-section, A be the cross-sectional area of ​​the pipe, and u be the current flow velocity in the pipe. Specific heat of fluid volume Let h be the thermal conductivity of the fluid and h be the heat transfer coefficient of the inner wall surface of the pipe. The calculation is performed using the classical Dittus correlation in heat transfer.

[0058]

[0059]

[0060] in Where is the fluid viscosity, Nu is the Nusselt number, Pr is the Prandtl number, and Re is the Reynolds number. For fluid density, The specific heat of the fluid is given by n, which is 0.4 when the fluid is heated and 0.3 when the fluid is cooled. Import support node The numerical discrete equation is:

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] in Let J be the temperature of the j-th fluid element at the current moment. Let j be the temperature of the j-th fluid element at the previous moment. The temperature of the upstream fluid unit at the current moment. The temperature of the downstream fluid unit at the current moment. The temperature of the PE pipe inner wall corresponding to fluid element j at the current moment is... Let j be the length of the fluid element. The distance between unit node j and upstream node j-1, Let be the distance between element node j and downstream node j+1, h be the heat transfer coefficient of the inner wall of the pipe, P be the perimeter of the inner wall of the pipe cross-section, A be the cross-sectional area of ​​the pipe, and u be the current flow velocity inside the pipe. Specific heat of fluid volume The fluid's thermal conductivity; Imported support The temperature of a node is obtained by fitting a quadratic curve to the temperature values ​​of the three upstream nodes and extrapolating it. Export support Each node has a temperature equal to the outlet temperature of the inlet branch; Export support The numerical discrete equation for each node is the same as the equation for the second node of the inlet support. Export support The numerical discrete equations of the nodes and the import support are related to the first node. The equations for all nodes are the same; Export support The temperature of a node is obtained by fitting a quadratic curve to the temperature values ​​of the three upstream nodes and extrapolating it. With fluid nodes The temperature discretization equation for the corresponding PE pipe inner wall node is as follows:

[0070]

[0071]

[0072]

[0073]

[0074] in Let J be the temperature of the inner wall of the j-th fluid element at the current moment. Let be the pipe wall temperature corresponding to the j-th fluid unit at the previous moment. Let J be the temperature of the j-th fluid element at the current moment. The temperature of the outer wall of the pipe corresponding to the j-th fluid unit at the previous moment is... , Let be the length of fluid element j, h be the heat transfer coefficient of the inner wall surface of the pipe, P be the perimeter of the inner wall of the pipe cross-section, and A be the cross-sectional area of ​​the pipe. For the volumetric specific heat of PE, The thermal conductivity of PE is... Let be the volume of the inner wall unit of the PE pipe corresponding to the j-th fluid unit; where the inner wall node has an implicit relationship with the fluid node and an explicit relationship with the outer wall node; The heat exchange rate of each axial unit of the PE pipe is:

[0075] The heat exchange rate of each axial unit of the PE pipe is:

[0076] The total heat exchange capacity provided by the temperature difference between the inlet and outlet of the U-shaped tube is:

[0077] Where G is the mass flow rate. For the inlet temperature, This refers to the outlet temperature.

[0078] In summary, due to the adoption of the above technical solution, the beneficial effects of this solution are: 1) High accuracy: This method abandons the assumption of steady-state heat transfer inside the borehole of the vertically buried U-shaped tube borehole heat exchanger. It establishes an unsteady-state heat transfer model for the entire domain of fluid, pipe wall, borehole backfill and external soil, which is more in line with the actual physical situation and the short-time step simulation calculation is more accurate. Figure 4 The results were verified using thermal response experimental data. The same data was input for calculation. The results showed that the outlet temperature calculated by the internationally renowned software trnsys type557a was generally higher than expected in the first 10 hours, with a maximum deviation of 2.6℃ and a root mean square deviation of 0.45℃. The new model was consistent with the measured values ​​throughout the process, with a maximum deviation of 0.5℃ and a root mean square deviation of 0.05℃.

[0079] 2) Fast calculation speed: Since the fluid, pipe wall, and solid regions inside and outside the hole all adopt special one-dimensional models and adopt a hidden and explicit hybrid format, and the water temperature of PE pipe and the temperature of backfill + soil solid region are calculated in sequence, the calculation speed is more than 90% faster than general full three-dimensional numerical calculation software.

[0080] 3) Wide Application Scope: Due to its accurate short-step calculation and fast calculation speed, this method can be used to develop dedicated calculation software for inverting four thermophysical property parameters—thermal conductivity, volumetric specific heat, etc.—of the backfill material inside the borehole and the surrounding soil and rock in the thermal response test of underground heat exchangers in ground source heat pump systems. The unsteady-state numerical model of this invention can also be extended to simulation calculations using the dynamic load of the heat pump unit as input, enabling the development of dedicated software for simulating the dynamic performance of ground source heat pump systems throughout the year, used for the full life-cycle performance evaluation of design schemes. Attached Figure Description

[0081] Figure 1 This is a schematic diagram illustrating the concept of "spatial separation and physical coupling" in a U-tube heat exchanger. Figure 2 Mesh diagram for calculating the one-dimensional thermal conductivity numerical model of the U-tube heat exchanger backfill and the soil-rock region; Figure 3 Mesh diagram for numerical model calculation of one-dimensional axial convection diffusion and one-dimensional radial heat conduction of the U-tube heat exchanger; Figure 4 Schematic diagram for verification of a one-dimensional implicit-explicit hybrid format numerical model of a U-tube heat exchanger Detailed Implementation All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0082] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0083] In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a predetermined orientation, or be constructed and operated in a predetermined orientation. Therefore, they should not be construed as limitations on this invention.

[0084] Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature.

[0085] Example 1 like Figures 1-4 As shown, the present invention provides a technical solution: The hybrid scheme algorithm for borehole heat exchangers based on the concept of spatial separation and physical coupling includes the following steps: Step S1: Design a mesh generation method to establish a radial one-dimensional Nr node unsteady diffusion (heat conduction) numerical model (Model 1) of the soil and rock region outside the pore backfill of the underground heat exchanger. Step S2: Design a mesh generation method to establish a one-dimensional 2Nf node unsteady convection-diffusion numerical model of the fluid along the flow direction (Model 2.1), and establish a one-dimensional two-node unsteady heat conduction numerical model of the pipe wall radial direction (Model 2.2). Step S3: Design a hybrid numerical scheme that combines explicit and implicit calculations to achieve coupled calculation of unsteady heat transfer between (fluid + pipe wall) and (backfill + soil). Step S4: Design a two-fold iterative algorithm for Model 2 to solve the fluid temperature inside the PE pipe and the pipe wall temperature simultaneously at each time step. Step S5: Design an algorithm based on the implicit and explicit hybrid numerical format to realize the sequential simulation of "receiving inlet temperature → calculating fluid friction temperature and pipe wall temperature → calculating heat transfer on the outer wall of the pipe → calculating the temperature of the solid region outside the pipe".

[0086] The core concept of this scheme is "spatial separation and physical coupling," meaning that the U-shaped tube perforated heat exchanger is spatially separated into two large, independent regions: (backfill + soil) and (fluid + tube wall). Separate models are created for each region, while ensuring coordinated coupling of temperature and thermal parameters at the interface between the two regions, as shown in the attached diagram. Figure 1 As shown.

[0087] Step S1 specifically includes the following steps: A mesh generation method is designed to establish a radial one-dimensional Nr node numerical calculation model for the backfill material inside the borehole and the soil and rock region outside the borehole of a vertically buried U-tube heat exchanger (referred to as Model 1, see Model 1). Figure 2): The backfill material inside the borehole and the soil and rock outside the borehole are divided into the following radial directions: Two units are fixedly installed for the backfill material inside the hole, and after the third unit ( The borehole is a geotechnical unit. The first unit at the borehole center is a solid cylinder of height L, and the remaining units are annular cylinders. The center coordinates of the second unit of the backfill material are set at the center of the PE pipe. The interface between the second unit and the first unit is set in... At this location, the interface between the second and third units is set at the hole wall r= The interface between the geotechnical units is located at the center of the two nodes. For a single borehole, the radius of the far boundary can be 10m or 20m; for a group of boreholes, the radius of the far boundary can be half the distance between boreholes.

[0088] The boundary conditions are set as follows: the upper, lower, and far boundaries of the heat exchanger calculation region are considered as adiabatic boundaries.

[0089] Internal heat source: The internal heat source is only set in the second unit of the backfill. Based on the innovative idea of ​​"spatial separation and physical coupling", the single / double U-shaped vertical buried pipe is abstracted as 2 / 4 of the linear heat sources without shape and volume; the heat generation of the internal heat source of the backfill unit 2 is equal to the heat of the outer wall of the pipe.

[0090] The effect of Unit 2 on the pipeline: The average temperature of Unit 2 is used as the outer wall temperature of the pipeline.

[0091] Step S2 specifically includes the following steps: Design a special mesh generation method to establish Model 2 (see Figure 3 This includes a one-dimensional 2Nf node numerical model for the fluid axis (Model 2.1) and a one-dimensional two-node numerical model for the pipe wall radial direction (Model 2.2): The inlet and outlet branches of the U-shaped tube are respectively installed along the flow direction. There are 1 node, and 1 group of U-shaped tubes. The fluid node, the first Units are evenly distributed, j=1 and The unit is a control body of 0; The PE pipe wall is divided into sections corresponding to fluid nodes in the flow direction. Each PE pipe segment is insulated from the others. Two nodes are fixed radially on each segment's wall: one on the inner wall and one on the outer wall. The heat from the outer wall serves as the internal heat source for the backfill unit 2; the temperature of the outer wall nodes is set equal to the temperature of the backfill unit 2.

[0092] Step S3 specifically includes the following steps: Designing a special hybrid numerical scheme that combines implicit and explicit representations to achieve unsteady-state heat transfer coupling calculations between (fluid + PE pipe) and (backfill + soil): Numerical Model 1 (Backfill + Soil): All nodes of backfill material inside the borehole and soil outside the borehole ( An explicit numerical discretization equation for unsteady thermal conduction was established using the finite volume method to calculate the radial temperature of the backfill material and soil. When establishing the numerical equation for the temperature of the second unit of the in-hole backfill material, single / double U-shaped vertical buried pipes were simplified to equivalent to 2 / 4 of a line heat source, disregarding their shape and volume, and their internal heat source was set to equal the heat released / absorbed by the outer wall of the U-shaped pipe. An explicit scheme was used to establish the nodal temperature calculation formula to improve the overall solution speed.

[0093] The formulas for calculating the temperature at each node are as follows: (1) The temperature calculation formula for borehole center unit i=1 is:

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] in This represents the current borehole center temperature. The borehole center temperature at the previous moment. The temperature of the second element node at the previous time step. The specific heat of the backfill material is the volumetric heat. The thermal conductivity of the backfill material. For the volume of unit 1, The radius of the location of unit 2. Let L be the radius of the interface between element 1 and element 2, and L be the drilling depth. The diameter of the borehole. For pipe spacing, This refers to the outer diameter of the PE pipe.

[0101] (2) The formula for calculating the temperature of the i=2th unit inside the hole is:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] in This represents the current temperature of the second drilling unit. This represents the temperature of the second drilling unit at the previous moment. The temperature of the third element node at the previous time step. For the volume of unit 2, The radius of the interface between element 2 and element 3 is the radius of the hole wall. The total heat released / absorbed by the outer wall of the PE pipe. The equivalent thermal conductivity at the borehole wall is obtained by averaging the thermal conductivity of the backfill material and the thermal conductivity of the soil and rock.

[0109] (3) The temperature calculation formula for the i=3rd unit is:

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] in The temperature of the third unit at the current moment. This refers to the temperature of the third unit at the previous moment. The temperature of the 4th unit node at the previous moment. For the volume of unit 3, Let be the radius of the interface between element 3 and element 4. The equivalent thermal conductivity at the borehole wall is obtained by averaging the thermal conductivity of the backfill material and the thermal conductivity of the soil and rock. The thermal conductivity of the soil and rock is... It is the volumetric specific heat of rock and soil.

[0116] (4) No. The temperature calculation formula for each unit is:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] in Let i be the temperature of the i-th unit at the current moment. Let i be the temperature of the i-th unit at the previous time step. The temperature of the (i+1)th cell node at the previous time step. Let i be the volume of element i. Let be the radius of the interface position between element i and element i+1.

[0123] (5) No. The temperature calculation formula for each unit is:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] in Let i be the temperature of the i-th unit at the current moment. Let i be the temperature of the i-th unit at the previous time step. Let i be the volume of element i. Let be the radius at the position of element node i.

[0130] 2. (Fluid + PE pipe) Numerical Model 2: The temperature of the fluid node inside the PE pipe of the vertically buried U-shaped underground heat exchanger is solved by establishing a discrete equation using the fully implicit QUICK scheme, and the temperature of node 1 on the inner wall of the PE pipe is solved by establishing a discrete equation using the implicit-explicit hybrid scheme.

[0131] The inlet temperature of the inlet branch pipe is known, and the outlet node j=Nf is the outflow boundary. The inlet temperature of the outlet branch pipe is equal to the outlet temperature of the inlet branch, and its outlet node j=1 is the outflow boundary.

[0132] Model coupling method: When establishing the numerical equations for the fluid and inner wall temperature in the PE pipe, the fluid and inner wall temperatures are taken at the same moment, while the outer wall temperature is set to be equal to the temperature of the backfill unit 2 in the hole at the previous moment. The inner wall nodes and fluid nodes have an implicit relationship, which is solved using simultaneous iterative solutions to ensure convergence. The inner wall nodes and outer wall nodes have an explicit relationship, realizing the separate solution of the PE pipe and the external region, thus improving the overall calculation speed.

[0133] Heat exchange on the inner wall of the tube Based on Newton's law of cooling, the current temperature of the inner wall nodes is used. With the corresponding fluid node temperature Calculations are performed. The convective heat transfer coefficient of the pipe is calculated using the classical Dittus correlation in heat transfer. (Pipe outer wall...) Heat absorption / release is measured using the current temperature of the inner wall nodes. and the temperature of the outer wall node at the previous moment calculate.

[0134] The numerical discrete equations for the fluid and the temperature at the joints on the inner wall of the PE pipe, as well as the heat calculation formulas, are as follows: (1) The inlet branch node j=1, (Known); (2) The second fluid node j=2 at the inlet branch has the following numerical discretization equation:

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] in Let J be the temperature of the j-th fluid element at the current moment. Let j be the temperature of the j-th fluid element at the previous moment. The temperature of the upstream fluid unit at the current moment. The temperature of the downstream fluid unit at the current moment. The temperature of the PE pipe inner wall corresponding to fluid element j at the current moment is... Let j be the length of the fluid element. The distance between unit node j and upstream node j-1, Let P be the distance between node j and downstream node j+1, P be the perimeter of the pipe cross-section, A be the cross-sectional area of ​​the pipe, and u be the current flow velocity in the pipe. Specific heat of fluid volume Let h be the thermal conductivity of the fluid and h be the heat transfer coefficient of the inner wall surface of the pipe. The calculation is performed using the classical Dittus correlation in heat transfer.

[0143]

[0144]

[0145] in Where is the fluid viscosity, Nu is the Nusselt number, Pr is the Prandtl number, and Re is the Reynolds number. For fluid density, The specific heat of the fluid is n, which is 0.4 when the fluid is heated and 0.3 when the fluid is cooled.

[0146] (3) Import support node The numerical discrete equation is:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154]

[0155] in Let J be the temperature of the j-th fluid element at the current moment. Let j be the temperature of the j-th fluid element at the previous moment. The temperature of the upstream fluid unit at the current moment. The temperature of the downstream fluid unit at the current moment. The temperature of the PE pipe inner wall corresponding to fluid element j at the current moment is... Let j be the length of the fluid element. The distance between unit node j and upstream node j-1, Let be the distance between element node j and downstream node j+1, h be the heat transfer coefficient of the inner wall of the pipe, P be the perimeter of the inner wall of the pipe cross-section, A be the cross-sectional area of ​​the pipe, and u be the current flow velocity inside the pipe. Specific heat of fluid volume is the thermal conductivity of the fluid.

[0156] (4) Import support The temperature of a node is obtained by fitting the temperature values ​​of the three upstream nodes to a quadratic curve and extrapolating it.

[0157] (5) Export support Each node has a temperature equal to the outlet temperature of the inlet branch.

[0158] (6) Export support The numerical discrete equation for the first node is the same as that for the second node of the inlet support.

[0159] (7) Export support The numerical discrete equations of the nodes and the import support are related to the first node. The equations for each node are the same.

[0160] (8) Export support The temperature of a node is obtained by fitting the temperature values ​​of the three upstream nodes to a quadratic curve and extrapolating it.

[0161] (9) With fluid nodes The temperature discretization equation for the corresponding PE pipe inner wall node is as follows:

[0162]

[0163]

[0164]

[0165]

[0166] in Let J be the temperature of the inner wall of the j-th fluid element at the current moment. Let be the pipe wall temperature corresponding to the j-th fluid unit at the previous moment. Let J be the temperature of the j-th fluid element at the current moment. The temperature of the outer wall of the pipe corresponding to the j-th fluid unit at the previous moment is... , Let be the length of fluid element j, h be the heat transfer coefficient of the inner wall surface of the pipe, P be the perimeter of the inner wall of the pipe cross-section, and A be the cross-sectional area of ​​the pipe. For the volumetric specific heat of PE, The thermal conductivity of PE is... Let be the volume of the inner wall unit of the PE pipe corresponding to the j-th fluid unit. The relationship between the inner wall nodes and the fluid nodes is implicit, while the relationship with the outer wall nodes is explicit.

[0167] (10) The heat exchange capacity of the inner wall of each axial unit of the PE pipe is:

[0168] (11) The heat exchange of the outer wall of each axial unit of the PE pipe is:

[0169] (12) The total heat exchange capacity provided by the temperature difference between the inlet and outlet of the U-shaped tube is:

[0170] Where G is the mass flow rate. For the inlet temperature, This refers to the outlet temperature.

[0171] Step S4 specifically includes the following steps: designing a special "double iteration" algorithm to simultaneously solve for the fluid temperature inside the PE pipe and the pipe wall temperature at each time step; based on the above numerical model, the solution steps include: Step S41: Receive the drilling depth (L), PE pipe outer diameter (do) and inner diameter (di), and grid parameters; Step S42: Receive the thermal conductivity (λp) and volumetric specific heat (ρpcp) of the PE pipe, as well as the fluid's thermophysical properties (including density (ρf), specific heat (cf), viscosity (μf), etc.). Step S43: Receive the inlet temperature (Tin), flow rate (F), and initial soil temperature of the U-tube. ), initial fluid temperature ), initial temperature of the inner wall of the pipe ( ) and other parameters; Step S44: Receive the convective heat transfer coefficient h of the tube wall; Step S45: Assume the inner wall temperature of the PE pipe ; Step S46: Calculate the coefficients of the discrete equations for the fluid element using the QUICK scheme; Step S47: Solve for the fluid element temperature using relaxation iteration (relaxation factor = 0.5). ; Step S48: Based on fluid element temperature And the temperature of the outer wall of the tube at the previous moment. Calculate the inner wall temperature of the PE pipe ; Step S49: Based on step S45 ; and in step eight Update the PE pipe inner wall temperature with a relaxation factor of 0.5. ; Step S410: Calculate the temperature error of the inner wall of the PE pipe. ; Step S411: If the maximum error If the precision is greater than the set value eps=0.001, use... Alternative Proceed to step S46; otherwise, end the iteration and proceed to step S412. Step S412: Determine the fluid temperature at the current moment. Inner wall temperature Calculate the heat exchange of the inner wall of the pipe ; Step S413: Determine the current inner wall temperature The temperature of the outer wall at the previous moment Calculate the heat released / absorbed by the outer wall of the tube. ; Step S414: The fluid inlet temperature Tin and outlet temperature... Calculate the total heat of the heat exchanger .

[0172] Steps S45 to S411 constitute the first external iteration, which is used to solve for the inner wall temperature of the pipe. Step S47 constitutes the second internal iteration, which is used to solve for the fluid temperature. The two iterations bring the fluid temperature and the inner wall temperature of the pipe closer together.

[0173] Step S5 specifically includes the following steps: Design a special algorithm to realize the sequential simulation of "receiving inlet temperature → calculating fluid friction temperature and pipe wall temperature → calculating heat transfer on the outer wall of the pipe → calculating the temperature of the solid region outside the pipe". The basis for the sequential algorithm is that the inner wall nodes and outer wall nodes of the PE pipe are explicitly related. The steps include: Step S51: Receive the borehole diameter (D) b ), the spacing between the U-shaped tubes inside the hole (D) p ), Drilling depth (L), Drilling spacing (D), PE pipe outer diameter (d) o ) and inner diameter (d) i ), mesh parameters; Step S52: Receive the thermal conductivity (λ) of the soil and rock. s ) and volumetric specific heat (ρ s c s ), thermal conductivity of borehole backfill (λ) b ) and volumetric specific heat (ρ b c b ), thermal conductivity of PE pipe (λ) p ) and volumetric specific heat (ρp c p ), fluid thermophysical parameters (including density (ρ) f ), specific heat (c f Viscosity (μ) f )wait); Step S53: Receive the current temperature (T) at the inlet of the U-tube. in ), flow rate (F), initial temperature of soil and rock ( ), initial temperature of pipe wall ( ), initial fluid temperature ) and other parameters; Step S54: Calculate the tube wall convective heat transfer coefficient at the current moment using the Dittus convective heat transfer correlation in the tube; Step S55: Apply the "two-iteration algorithm" to solve for the fluid friction temperature distribution T at the current moment. f and the temperature of the inner wall of the PE pipe ( ), and calculate the total heat capacity Q of the heat exchanger. f Heat Q of the inner wall of PE pipe fp and the heat Q of the outer wall pb ; Step S56: Based on the heat exchange rate Q of the PE pipe outer wall in step S55 pb and the initial temperature of the soil and rock ( The temperature T of the solid region outside the pipe at the current moment is calculated using the "backfill + explicit numerical model of soil and rock". Step S57: Utilize the current soil and rock temperature T, the current fluid temperature Tf, and the current pipe wall temperature ( ), respectively update the initial temperature of the soil and rock ( ), initial fluid temperature ), initial temperature of pipe wall ( Proceed to step S53 to begin the calculation of the next time step, until all time steps have been calculated.

[0174] exist Figure 4 (Input data: sampling interval 30s, original ground temperature 19℃, flow rate 1.2m³ / h, electric heater power 6kW, hole depth 120m, hole diameter 0.17m, pipe spacing 0.1m, pipe outer diameter 0.032m, pipe inner diameter 0.025m, pipe thermal conductivity 0.4W / (m·K), pipe volumetric specific heat 2MJ / (m³·K), backfill thermal conductivity 1.87W / (m·K), backfill volumetric specific heat 0.3MJ / (m³·K), soil thermal conductivity 1.94W / (m·K), soil volumetric specific heat 0.7MJ / (m³·K)).

[0175] The core of this plan is: A special method for numerical calculation mesh generation of the in-hole backfill material and the external soil and rock area was adopted. Figure 2 The backfill material and soil in the borehole are divided into the following categories along the radial direction: The borehole backfill material consists of two fixed units, followed by soil and rock units. The first unit at the borehole center is a solid cylinder of height L, while the remaining units are annular cylinders. The center coordinates of the second unit of the borehole backfill material are set at the center of the PE pipe (r= The interface between the second unit and the first unit is set in... The interface between the second and third units is set at the hole wall, r= .

[0176] A special U-shaped pipe fluid and pipe wall numerical calculation mesh generation method was also adopted. Figure 3 ): The inlet and outlet branches of the U-shaped tube are respectively installed along the flow direction. There are several nodes. The PE pipe wall is divided into several sections in the flow direction. Each section of the PE pipe is insulated from the others. Two nodes are fixed radially on each section of the PE pipe wall: one node on the inner wall and one node on the outer wall.

[0177] It also employs a special numerical scheme that combines fluid, pipe wall, backfill material, and soil / rock sedimentation. (1) One-dimensional backfill material + soil numerical model 1: Backfill material inside the borehole and all joints of soil and rock outside the borehole ( The finite volume method was used to establish an explicit numerical discrete equation for unsteady heat conduction, enabling the calculation of radial temperature of backfill material and soil. When establishing the numerical calculation equation for the temperature of the second unit of the in-hole backfill material, the innovative concept of "spatial separation and physical coupling" was proposed. That is, single / double U-shaped vertical buried pipes are equivalently simplified to 2 / 4 of a line heat source, without considering the influence of their shape and volume. The internal heat source is set to be equal to the heat released / absorbed by the outer wall of the U-shaped pipe; and it is assumed that the temperature of the second unit of the in-hole backfill material is equal to the temperature of the outer wall of the pipe.

[0178] (2) Numerical model of one-dimensional fluid + PE pipe wall: A one-dimensional unsteady convection-diffusion implicit numerical model is established using the QUICK scheme for the fluid nodes. The inlet temperature of the inlet branch pipe is known, and the outlet node j=Nf is the outflow boundary. The inlet temperature of the outlet branch pipe is equal to the outlet temperature of the inlet branch, and its outlet node j=1 is the outflow boundary. For node 1 on the inner wall of the PE pipe, a mixed implicit-explicit scheme numerical discretization equation for unsteady thermal conduction is established using the finite volume method. It is assumed that the outer wall temperature of the pipe is equal to the temperature of the second element of the backfill material inside the hole.

[0179] (3) Model coupling method: When establishing the numerical equations for the fluid and inner wall temperature in the PE pipe, the fluid and inner wall temperatures are taken at the same moment, while the outer wall temperature is set to be equal to the temperature of the backfill element 2 in the hole at the previous moment. The inner wall nodes and fluid nodes have an implicit relationship, which is solved using a simultaneous iterative method to ensure convergence. The inner wall nodes and outer wall nodes have an explicit relationship, realizing the separate solution of the PE pipe and the external region, thus improving the overall calculation speed.

[0180] Heat exchange on the inner wall of the tube Based on Newton's law of cooling, the current temperature of the inner wall nodes is used. With the corresponding fluid node temperature Calculations are performed. The convective heat transfer coefficient of the pipe is calculated using the Dittus correlation. (Pipe outer wall...) Heat absorption / release is measured using the current temperature of the inner wall nodes. and the temperature of the outer wall node at the previous moment calculate.

[0181] A special "double iteration" algorithm for solving fluid and pipe wall temperatures was also adopted: the first external iteration solves the pipe inner wall temperature with a relaxation factor of 0.5; the second internal iteration solves the fluid temperature with a relaxation factor of 0.5.

[0182] It also employs a special sequential simulation algorithm: "receive inlet temperature → calculate fluid friction temperature and pipe wall temperature → calculate heat transfer on the outer wall of the pipe → calculate temperature of the solid region outside the pipe".

[0183] Example 2 This solution can also provide a system, which includes a user interface program, a numerical calculation mesh generation program for U-tube heat exchangers, a (fluid + pipe wall) - (backfill + soil) coupling program, and a system based on... Figure 2 The numerical grid and "backfill + soil numerical model 1" were used to design a "backfill + soil temperature calculation program" based on Figure 3 Based on the numerical grid and the "fluid + PE pipe wall numerical model 2", a "fluid + PE pipe wall temperature calculation program" was designed.

[0184] The main functions of the user interface program are: (1) Receive the structural parameters of the U-tube heat exchanger, including depth, borehole diameter, tube spacing, tube inner diameter, tube outer diameter, hole spacing or single hole far boundary diameter; (2) Receive the thermal conductivity and volumetric specific heat of the backfill material, the thermal conductivity and volumetric specific heat of the soil and rock, and the thermal conductivity and volumetric specific heat of the PE pipe; (3) Receive fluid property parameters; (3) Receive the initial temperature of the fluid, the initial temperature of the pipe wall, the initial temperature of the backfill, and the initial temperature of the soil and rock; (4) Receive the number of simulation steps and the time step; (5) Receive inlet temperature; (6) Receive traffic; (7) Call the “Numerical Calculation Mesh Generation Program for U-tube Heat Exchangers”; (8) Call the “(fluid + pipe wall) - (backfill + soil) coupling program”; (9) Process the calculation results data, draw charts, etc.

[0185] based on Figure 2 , Figure 3 The main functions of the "Numerical Calculation Mesh Generation Program for U-tube Heat Exchangers" are as follows: (1) Receive heat exchanger structural parameters, including depth, borehole diameter, tube spacing, tube inner diameter, tube outer diameter, hole spacing or single hole far boundary diameter; (2) Set the total number of radial nodes, and calculate the coordinates of each node in the backfill and soil area, as well as the boundary coordinates of each unit.

[0186] (3) Set the total number of vertical nodes in the pipeline, and calculate the coordinates of the fluid nodes and the upstream and downstream coordinates of each unit.

[0187] The "(fluid + pipe wall) - (backfill + soil) coupling program" has the following main functions: (1) Receive heat exchanger structural parameters, including depth, borehole diameter, tube spacing, tube inner diameter, tube outer diameter, hole spacing or single hole far boundary diameter; (2) The thermal conductivity and volumetric specific heat of the receiving backfill material, and the thermal conductivity and volumetric specific heat of the soil and rock; (3) Receive fluid physical property parameters and pipe wall physical property parameters; (4) Receive the initial temperature of the fluid, the initial temperature of the pipe wall, the initial temperature of the backfill, and the initial temperature of the soil and rock; (5) Receive the number of simulation steps and the time step; (6) Receive inlet temperature; (7) Receive traffic; (8) Implement a time-step loop, and implement the following functions at each time step: (1) Call the "Fluid + PE Pipe Wall Temperature Calculation Program"; (2) Call the "Backfill Material + Soil Temperature Calculation Program"; based on Figure 2 Based on the numerical grid and the "backfill + soil numerical model 1", a "backfill + soil temperature calculation program" was designed, whose main functions are: (1) Receive the radial node coordinates and unit boundary coordinates of "backfill + soil"; (2) The thermal conductivity and volumetric specific heat of the receiving backfill material, and the thermal conductivity and volumetric specific heat of the soil and rock; (3) Receive the initial temperature of the backfill material and the soil-rock joint; (4) Reception time step; (5) Receive the total heat released / absorbed by the outer wall of the U-shaped tube; (6) Calculate the explicit equation coefficients for each node, where the total heat released / absorbed by the outer wall of the U-shaped tube is applied to the second unit; (7) Calculate the temperature of each node at the current time; (8) Output the current temperature of each node.

[0188] based on Figure 3 Based on the numerical grid and the "Fluid + PE Pipe Wall Numerical Model 2", a "Fluid + PE Pipe Wall Temperature Calculation Program" was designed, whose main functions are: (1) Receive vertical fluid node coordinates, upstream and downstream boundary coordinates, and pipe diameter; (2) Receive the temperature of the fluid, pipe wall, and backfill at the previous moment; (3) Receive fluid property parameters and PE pipe property parameters; (4) Receive traffic; (5) Reception time step; (6) Calculate the convective heat transfer coefficient of the inner surface; (7) Design an external iterative program to calculate the pipe wall temperature. Its functions include: 1) Calculate the coefficients of the fully implicit QUICK scheme equations for fluid nodes; 2) Iteratively solve for the fluid node temperature (internal iteration); 3) Calculate the equation coefficients of the nodes on the inner wall of the PE pipe; 4) Iteratively solve for the node temperature on the inner wall of the PE pipe; Calculate the heat transfer on the inner and outer walls of the PE pipe; The total heat is calculated from the inlet and outlet temperatures of the U-shaped tube; Output fluid node temperature, pipe wall temperature, heat on the inner wall of the pipe, heat on the outer wall of the pipe, and total heat.

[0189] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A hybrid format algorithm for borehole heat exchangers based on the concept of spatial separation and physical coupling, characterized in that, Includes the following steps: Step S1: Design a mesh generation method to establish a radial one-dimensional Nr node unsteady diffusion numerical model of the soil and rock region outside the pore backfill of the underground heat exchanger. Step S2: Design a mesh generation method to establish a one-dimensional 2N mesh along the flow direction. f A numerical model of unsteady convection and diffusion at nodes was developed, and a one-dimensional two-node unsteady heat conduction numerical model of the radial direction of the pipe wall was established. Step S3: Design a hybrid numerical scheme that combines implicit and explicit representations to achieve coupled calculation of unsteady heat transfer between fluid + PE pipe and backfill + soil. Step S4: Design a two-fold iterative algorithm for the numerical model in step S2 to solve the fluid temperature inside the PE pipe and the inner wall temperature at each time step. Step S5: Design an algorithm based on the implicit and explicit hybrid numerical format to realize the sequential simulation of "receiving inlet temperature → calculating fluid friction temperature and pipe wall temperature → calculating heat transfer on the outer wall of the pipe → calculating the temperature of the solid region outside the pipe".

2. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 1, characterized in that: Step S1 specifically includes the following steps: The backfill material inside the borehole and the soil and rock outside the borehole are divided into the following radial directions: Two units are fixedly installed for the backfill material inside the hole, and after the third unit ( The borehole is a geotechnical unit. The first unit at the borehole center is a solid cylinder of height L, and the remaining units are annular cylinders. The center coordinates of the second unit of the backfill material are set at the center of the PE pipe. The interface between the second unit and the first unit is set in... At this location, the interface between the second and third units is set at the hole wall r= The geotechnical unit interface is located at the center of the two nodes; for a single hole, the radius of the far boundary can be 10m or 20m, and for a group of holes, the radius of the far boundary can be 1 / 2 of the hole spacing; the boundary conditions are set as follows: the upper, lower and far boundaries of the heat exchanger calculation area are considered as adiabatic boundaries; internal heat source: the internal heat source is only set in the second unit of the backfill material. According to the innovative idea of ​​"spatial separation and physical coupling", the single / double U-shaped vertical buried pipe is abstracted as 2 / 4 of the linear heat sources without shape and volume; the heat generation of the internal heat source of the backfill material unit 2 is equal to the heat of the outer wall of the pipe.

3. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 1, characterized in that: Step S2 specifically includes the following steps: The inlet and outlet branches of the U-shaped tube are respectively installed along the flow direction. There are 1 node, and 1 group of U-shaped tubes. The fluid node, the first Units are evenly distributed, j=1 and The unit is a control body of 0; The PE pipe wall is divided into sections corresponding to fluid nodes in the flow direction. Each section is insulated from the others; each section of PE pipe has two nodes fixed radially on its wall, one on the inner wall and one on the outer wall; the heat from the outer wall of the pipe is used as the internal heat source for the backfill unit 2; the temperature of the outer wall node is set to be equal to the temperature of the backfill unit 2.

4. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 1, characterized in that: The numerical model of backfill + soil in step S3 was obtained in the following way: all nodes of backfill inside the borehole and soil outside the borehole ( The unsteady-state thermal conductivity explicit numerical discrete equation is established using the finite volume method to calculate the radial temperature of backfill and soil. When establishing the numerical equation for the temperature of the second unit of the backfill in the borehole, the single / double U-shaped vertical buried pipe is simplified to 2 / 4 of the line heat source, without considering its shape and volume, and its internal heat source is set to be equal to the heat released / absorbed by the outer wall of the U-shaped pipe. The nodal temperature calculation formula is established using an explicit format.

5. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 1, characterized in that: The numerical model of fluid + PE pipe in step S3 is obtained in the following way: the temperature of fluid nodes inside PE pipe of vertical buried U-shaped tube underground heat exchanger is solved by establishing discrete equations using fully implicit QUICK scheme, and the temperature of node 1 on the inner wall of PE pipe is solved by establishing discrete equations using implicit and explicit hybrid scheme. The inlet temperature of the inlet branch pipe is known, and the outlet node j=N f The outlet node j=1 is the outflow boundary; the inlet temperature of the outlet branch pipe is equal to the outlet temperature of the inlet branch, and its outlet node j=1 is the outflow boundary.

6. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 1, characterized in that: In step S3, the model coupling method is as follows: When establishing the numerical equations for the fluid and inner wall temperature of the PE pipe, the fluid and inner wall temperatures are taken at the same moment, and the outer wall temperature is set to be equal to the temperature of the backfill unit 2 in the hole at the previous moment; the inner wall node and the fluid node have an implicit relationship, and a simultaneous iterative solution is used to ensure convergence; the inner wall node and the outer wall node have an explicit relationship, realizing the separate solution of the PE pipe and the outer region. Heat exchange on the inner wall of the tube Based on Newton's law of cooling, the current temperature of the inner wall nodes is used. With the corresponding fluid node temperature Calculations are performed; the convective heat transfer coefficient of the pipe is calculated using the classical Dittus correlation in heat transfer; the outer wall of the pipe... Heat absorption / release is measured using the current temperature of the inner wall nodes. and the temperature of the outer wall node at the previous moment calculate.

7. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 1, characterized in that: Step S4 Specifically, the following steps are included: Step S41: Receive drilling depth L and PE pipe outer diameter d o and inner diameter d i and mesh parameters; Step S42: Receive the thermal conductivity λ of the PE pipe p and specific heat of volume ρ p c p Fluid thermophysical parameters; Step S43: Receive the inlet temperature T of the U-tube in Flow rate F, initial temperature of soil and rock Initial temperature of the fluid Initial temperature of the inner wall of the pipe Parameters; Step S44: Receive the convective heat transfer coefficient h of the tube wall; Step S45: Assume the inner wall temperature of the PE pipe ; Step S46: Calculate the coefficients of the discrete equations for the fluid element using the QUICK scheme; Step S47: Solve for the temperature of the fluid element using relaxation iteration. ; Step S48: Based on fluid element temperature And the temperature of the outer wall of the tube at the previous moment. Calculate the inner wall temperature of the PE pipe ; Step S49: Based on step S45 ; and in step S48 Update the PE pipe inner wall temperature with a relaxation factor of 0.

5. ; Step S410: Calculate the temperature error of the inner wall of the PE pipe. ; Step S411: If the maximum error If the precision is greater than the set value eps=0.001, use... Alternative Proceed to step S46; otherwise, end the iteration and proceed to step S412. Step S412: Determine the fluid temperature at the current moment. Inner wall temperature Calculate the heat exchange of the inner wall of the pipe ; Step S413: Determine the current inner wall temperature The temperature of the outer wall at the previous moment Calculate the heat released / absorbed by the outer wall of the tube. ; Step S414: The fluid inlet temperature Tin and outlet temperature... Calculate the total heat of the heat exchanger .

8. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 1, characterized in that: Step S5 specifically includes the following steps: Step S51: Receive borehole diameter D b , Spacing D of U-shaped tubes inside the hole p Drilling depth L, drilling spacing D, PE pipe outer diameter d o and inner diameter d i Mesh parameters; Step S52: Receive the thermal conductivity λ of the soil and rock. s and specific heat of volume ρ s c s Thermal conductivity λ of borehole backfill b and specific heat of volume ρ b c b PE pipe thermal conductivity λ p and specific heat of volume ρ p c p Fluid thermophysical parameters; Step S53: Receive the current temperature T at the inlet of the U-tube. in Flow rate F, initial temperature of soil and rock Initial temperature of pipe wall Initial temperature of the fluid Parameters; Step S54: Calculate the tube wall convective heat transfer coefficient at the current moment using the Dittus convective heat transfer correlation in the tube; Step S55: Apply the "two-iteration algorithm" to solve for the fluid friction temperature distribution Tf at the current moment, and the PE pipe inner wall temperature. And calculate the total heat capacity Q of the heat exchanger. f Heat Q of the inner wall of PE pipe fp and the heat Q of the outer wall pb ; Step S56: Based on the heat exchange rate Q of the PE pipe outer wall in step S55 pb and the initial temperature of the soil and rock The temperature T of the solid region outside the pipe at the current moment is calculated using the "backfill + explicit numerical model of soil and rock". Step S57: Utilize the current soil and rock temperature T, the current fluid temperature Tf, and the current pipe wall temperature. Update the initial temperature of the soil and rock respectively Initial temperature of the fluid Initial temperature of pipe wall Proceed to step S53 to begin the calculation for the next time step, until all time steps have been calculated.

9. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 3, characterized in that: The formula for calculating the temperature of borehole center element i=1 is: in This represents the current borehole center temperature. The borehole center temperature at the previous moment. The temperature of the second element node at the previous time step. The specific heat of the backfill material is the volumetric heat. The thermal conductivity of the backfill material. For the volume of unit 1, The radius of the location of unit 2. Let L be the radius of the interface between element 1 and element 2, and L be the drilling depth. The diameter of the borehole. For pipe spacing, The outer diameter of the PE pipe; The formula for calculating the temperature of the i=2nd unit inside the hole is: in This represents the current temperature of the second drilling unit. This represents the temperature of the second drilling unit at the previous moment. The temperature of the third element node at the previous time step. For the volume of unit 2, The radius of the interface between element 2 and element 3 is the radius of the hole wall. The total heat released / absorbed by the outer wall of the PE pipe. The equivalent thermal conductivity at the borehole wall is obtained by averaging the thermal conductivity of the backfill material and the thermal conductivity of the soil and rock. The temperature calculation formula for the i=3rd unit is: in The temperature of the third unit at the current moment. This refers to the temperature of the third unit at the previous moment. The temperature of the 4th unit node at the previous moment. For the volume of unit 3, Let be the radius of the interface between element 3 and element 4. The equivalent thermal conductivity at the borehole wall is obtained by averaging the thermal conductivity of the backfill material and the thermal conductivity of the soil and rock. The thermal conductivity of the soil and rock is... Specific heat of rock and soil by volume: No. The temperature calculation formula for each unit is: in Let i be the temperature of the i-th unit at the current moment. Let i be the temperature of the i-th unit at the previous time step. The temperature of the (i+1)th cell node at the previous time step. Let i be the volume of element i. Let be the radius of the interface position between element i and element i+1; No. The temperature calculation formula for each unit is: in Let i be the temperature of the i-th unit at the current moment. Let i be the temperature of the i-th unit at the previous time step. Let i be the volume of element i. Let be the radius at the position of element node i.

10. The hybrid format algorithm for borehole heat exchangers based on the spatial separation and physical coupling concept as described in claim 4, characterized in that: The numerical discrete equations for the fluid and the temperature at the joints on the inner wall of the PE pipe, as well as the heat calculation formulas, are as follows: Inlet branch fluid node j=1, ; The numerical discretization equation for the second fluid node j=2 at the inlet branch is: in Let J be the temperature of the j-th fluid element at the current moment. Let j be the temperature of the j-th fluid element at the previous moment. The temperature of the upstream fluid unit at the current moment. The temperature of the downstream fluid unit at the current moment. The temperature of the PE pipe inner wall corresponding to fluid element j at the current moment is... Let j be the length of the fluid element. The distance between unit node j and upstream node j-1, Let P be the distance between node j and downstream node j+1, P be the perimeter of the pipe cross-section, A be the cross-sectional area of ​​the pipe, and u be the current flow velocity in the pipe. Specific heat of fluid volume Let h be the thermal conductivity of the fluid and h be the heat transfer coefficient of the inner wall surface of the pipe. The calculation is performed using the classical Dittus correlation in heat transfer. in Where is the fluid viscosity, Nu is the Nusselt number, Pr is the Prandtl number, and Re is the Reynolds number. For fluid density, The specific heat of the fluid is given by n, which is 0.4 when the fluid is heated and 0.3 when the fluid is cooled. Import support node The numerical discrete equation is: in Let J be the temperature of the j-th fluid element at the current moment. Let j be the temperature of the j-th fluid element at the previous moment. The temperature of the upstream fluid unit at the current moment. The temperature of the downstream fluid unit at the current moment. The temperature of the PE pipe inner wall corresponding to fluid element j at the current moment is... Let j be the length of the fluid element. The distance between unit node j and upstream node j-1, Let be the distance between element node j and downstream node j+1, h be the heat transfer coefficient of the inner wall of the pipe, P be the perimeter of the inner wall of the pipe cross-section, A be the cross-sectional area of ​​the pipe, and u be the current flow velocity inside the pipe. Specific heat of fluid volume The fluid's thermal conductivity; Imported support The temperature of a node is obtained by fitting a quadratic curve to the temperature values ​​of the three upstream nodes and extrapolating it. Export support Each node has a temperature equal to the outlet temperature of the inlet branch; Export support The numerical discrete equation for each node is the same as the equation for the second node of the inlet support. Export support The numerical discrete equations of the nodes and the import support are related to the first node. The equations for all nodes are the same; Export support The temperature of a node is obtained by fitting a quadratic curve to the temperature values ​​of the three upstream nodes and extrapolating it. With fluid nodes The temperature discretization equation for the corresponding PE pipe inner wall node is as follows: in Let J be the temperature of the inner wall of the j-th fluid element at the current moment. Let be the pipe wall temperature corresponding to the j-th fluid unit at the previous moment. Let J be the temperature of the j-th fluid element at the current moment. The temperature of the outer wall of the pipe corresponding to the j-th fluid unit at the previous moment is... , Let be the length of fluid element j, h be the heat transfer coefficient of the inner wall surface of the pipe, P be the perimeter of the inner wall of the pipe cross-section, and A be the cross-sectional area of ​​the pipe. For the volumetric specific heat of PE, The thermal conductivity of PE is... Let be the volume of the inner wall unit of the PE pipe corresponding to the j-th fluid unit; where the inner wall node has an implicit relationship with the fluid node and an explicit relationship with the outer wall node; The heat exchange rate of each axial unit of the PE pipe is: The heat exchange rate of each axial unit of the PE pipe is: The total heat exchange capacity provided by the temperature difference between the inlet and outlet of the U-shaped tube is: Where G is the mass flow rate. For the inlet temperature, This refers to the outlet temperature.

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