A three-dimensional thermal resistance calculation method for vertical buried pipe heat exchanger

Abstract

The invention discloses a method for calculating the three-dimensional thermal resistance of a vertical ground pipe heat exchanger, comprising: obtaining the structure and thermophysical parameters of the ground pipe heat exchanger; performing dimensionless processing on the structure and thermophysical parameters of the ground pipe heat exchanger; calculating the borehole thermal resistance and the total internal thermal resistance of the ground pipe heat exchanger based on a pre-constructed three-dimensional thermal resistance correlation formula; the construction of the three-dimensional thermal resistance correlation formula comprises: constructing a three-dimensional heat transfer numerical model based on finite element simulation software; performing dimensionless processing on the structure and thermophysical parameters; establishing an orthogonal table; obtaining the borehole thermal resistance and the total internal thermal resistance under the structure and thermophysical parameters based on the orthogonal table; performing dimensionless processing on the borehole thermal resistance and the total internal thermal resistance; constructing a three-dimensional thermal resistance correlation formula based on the response surface method according to the dimensionless parameters of the structure and thermophysical parameters, the borehole thermal resistance and the total internal thermal resistance; the invention can accurately calculate the borehole thermal resistance and the total internal thermal resistance value of the ground pipe heat exchanger, thereby ensuring the reasonable and efficient operation of the ground source heat pump system.

Description

Technical Field

[0001] The invention relates to a three-dimensional thermal resistance calculation method for a vertical underground pipe heat exchanger, belonging to the technical field of underground heat exchangers. Background Art

[0002] The vertical buried pipe is the core component of the ground source heat pump system, and its heat transfer performance directly affects the operating efficiency of the ground source heat pump system. The thermal resistance of the buried pipe heat exchanger is an important factor in the design of the heat exchanger, and the drilling thermal resistance and total internal thermal resistance of the buried pipe heat exchanger need to be accurately calculated. At present, the calculation methods of the thermal resistance of the buried pipe heat exchanger mainly include: on-site thermal response test experimental method, analytical solution method and numerical calculation method. Compared with the on-site thermal response test experimental method and analytical solution method, the numerical calculation method has high calculation accuracy and is suitable for various complex situations. It can be used to accurately calculate the thermal resistance of the buried pipe heat exchanger in the ground source heat pump.

[0003] Although domestic and foreign scholars have conducted a relatively systematic analysis and research on the thermal resistance of buried pipe heat exchangers, there are still some urgent problems to be solved: 1. The influence of drilling depth on the thermal resistance of buried pipe heat exchangers is not considered. Most studies only obtain the thermal resistance value of a certain cross section of the buried pipe heat exchanger, but this thermal resistance is a two-dimensional concept and cannot reasonably reflect the influence of drilling depth on the thermal resistance of the buried pipe heat exchanger. In addition, this two-dimensional thermal resistance cannot describe the temperature distribution of the fluid in the pipe; 2. The influence of uneven borehole wall temperature on the thermal resistance of the buried pipe heat exchanger is not considered. Due to the temperature difference between the inlet pipe and the outlet pipe, the borehole wall temperature close to the inlet pipe is not equal to the borehole wall temperature close to the outlet pipe. Then, in most studies, a constant temperature is set on the borehole wall, which is bound to affect the accuracy of the thermal resistance of the buried pipe heat exchanger, especially when the distance between the pipe section and the borehole wall is small, the assumption of uniform borehole wall temperature will cause an error greater than the preset value in the thermal resistance of the tube heat exchanger. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a three-dimensional thermal resistance calculation method for a vertical buried pipe heat exchanger, which can accurately calculate the borehole thermal resistance and total internal thermal resistance of the buried pipe heat exchanger, thereby ensuring the reasonable and efficient operation of the ground source heat pump system.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0006] In a first aspect, the present invention provides a method for calculating three-dimensional thermal resistance of a vertical buried pipe heat exchanger, comprising:

[0007] Obtain the structure and thermophysical parameters of the ground pipe heat exchanger;

[0008] The structure and thermophysical parameters of the underground heat exchanger are dimensionlessly processed;

[0009] Based on the pre-built three-dimensional thermal resistance correlation, the borehole thermal resistance and total internal thermal resistance of the ground heat exchanger are calculated according to the dimensionless parameters of the structure and thermophysical parameters;

[0010] The construction of the three-dimensional thermal resistance correlation equation includes:

[0011] Based on finite element simulation software, a three-dimensional heat transfer numerical model of the buried pipe heat exchanger was constructed;

[0012] Non-dimensional processing of the structure and thermophysical parameters of the three-dimensional heat transfer numerical model;

[0013] An orthogonal table is established based on the Box-Behnken design according to the dimensionless parameters of the structure and thermophysical properties;

[0014] Based on the orthogonal table, the drilling thermal resistance and total internal thermal resistance of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger under the structural and thermophysical parameters are obtained;

[0015] The drilling thermal resistance and the total internal thermal resistance are dimensionless.

[0016] A three-dimensional thermal resistance correlation equation is constructed based on the response surface methodology according to the dimensionless parameters of the structural and thermophysical parameters, the drilling thermal resistance and the total internal thermal resistance.

[0017] Among them, the structural parameters of the buried pipe heat exchanger include drilling depth, drilling diameter, pipe diameter and pipe spacing; the thermal physical parameters of the buried pipe heat exchanger include soil thermal conductivity, backfill material thermal conductivity, pipe wall thermal conductivity and fluid velocity in the pipe.

[0018] Optionally, the dimensionless parameters of the structural and thermophysical property parameters are:

[0019]

[0020] In the formula, θ1, θ2, θ3, σ1, σ2, R e is the dimensionless parameter of the structure and thermophysical properties, X c is the tube spacing, d b is the drilling diameter, d po is the outer diameter of the tube, λ g is the thermal conductivity of the backfill material, λ s is the thermal conductivity of soil, λ p is the thermal conductivity of the tube wall, u is the fluid velocity in the tube, d pi is the inner diameter of the tube, u f is the dynamic viscosity of the fluid in the tube, ρ f is the density of the fluid in the pipe, and H is the drilling depth.

[0021] Optionally, the three-dimensional heat transfer numerical model includes, from the inside to the outside, the fluid in the tube, the wall of the single U-shaped tube, the backfill material in the borehole, the wall of the borehole and the soil, and the two ends of the single U-shaped tube are set as an inlet pipe and an outlet pipe; the structure and thermophysical parameters, calculation area, calculation time, boundary conditions and initial conditions of the three-dimensional heat transfer numerical model are set, and the inlet pipe orifice of the single U-shaped tube is set as the temperature and pressure inlet boundary of the three-dimensional heat transfer numerical model, and the outlet pipe orifice of the single U-shaped tube is set as the temperature and pressure outlet boundary of the three-dimensional heat transfer numerical model.

[0022] Optionally, the structure and thermophysical parameters of the three-dimensional heat transfer numerical model are the same as those of the ground pipe heat exchanger; the far boundary distance of the calculation area is set to a s is the thermal conductivity of soil; the calculation time is set to the time required for the heat transfer in the borehole to reach a quasi-steady state: t is the calculation time, r b is the drilling radius, a b is the thermal conductivity of the backfill material; the boundary condition is set as an adiabatic boundary condition; the initial condition is set as the initial temperature of the fluid in the pipe, the wall of the single U-shaped pipe, the backfill material in the borehole, the borehole wall and the soil is constant.

[0023] Optionally, obtaining the borehole thermal resistance and total internal thermal resistance of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger under the structure and thermophysical property parameters includes:

[0024] The free triangle mesh is used to mesh the calculation area of ​​the three-dimensional heat transfer numerical model, and the optimal number of meshes is determined by verifying the mesh independence of the meshes after meshing.

[0025] The finite element method is used to discretize and solve the fluid heat transfer differential equation and the solid heat transfer differential equation in the three-dimensional heat transfer numerical model to obtain the temperature field distribution of the three-dimensional heat transfer numerical model;

[0026] According to the temperature field distribution, the average temperature and heat transfer of the fluid in the water inlet and outlet pipes along the pipe length direction and the average temperature and heat transfer of the borehole wall near the water inlet and outlet pipes along the borehole depth direction in the three-dimensional heat transfer numerical model are calculated;

[0027] The borehole thermal resistance and total internal thermal resistance of the ground pipe heat exchanger are calculated based on the calculated average temperature and heat transfer based on the pre-built thermal resistance model.

[0028] Optionally, the use of free triangular grids to grid the calculation area of ​​the three-dimensional heat transfer numerical model includes sweeping along the depth direction to grid the three-dimensional heat transfer numerical model; wherein, grid encryption is performed on the fluid in the tube and the wall area of ​​the single U-shaped tube where the temperature gradient is greater than a preset value.

[0029] Optionally, the average temperature and heat transfer of the fluid in the water inlet pipe and the water outlet pipe along the pipe length direction are:

[0030]

[0031] Where, T f,m,1 and T f,m,2 are the average temperatures of the fluid in the inlet and outlet pipes along the pipe length, L is the length of the single U-shaped pipe, T f,1 (z) and T f,2 (z) are the temperatures of the fluid in the inlet pipe and the outlet pipe at depth z, respectively;

[0032]

[0033] In the formula, q f,m,1 and q f,m,2 are the average heat transfer of the fluid in the inlet pipe and the outlet pipe along the pipe length, q f,1 (z) and q f,2 (z) are the heat transfer values ​​of the fluid in the inlet pipe and the outlet pipe at depth z respectively;

[0034] The average temperature and heat transfer of the borehole wall near the water inlet pipe and the water outlet pipe along the depth direction of the borehole are:

[0035]

[0036] Where, T b,m,1 and T b,m,2 are the average temperatures of the borehole wall near the water inlet pipe and the water outlet pipe along the depth of the borehole, H is the depth of the borehole, T b,1 (z) and T b,2 (z) are the temperatures of the borehole wall at depth z near the inlet and outlet pipes, respectively;

[0037]

[0038] In the formula, q b,m,1 and q b,m,2 are the average heat transfer of the borehole wall near the water inlet pipe and the water outlet pipe along the depth direction of the borehole, q b,1 (z) and q b,2 (z) are the heat transfer of the borehole wall near the inlet pipe and outlet pipe at depth z respectively.

[0039] Optionally, the pre-built thermal resistance model is:

[0040]

[0041]

[0042]

[0043]

[0044] In the formula, R b,3D is the drilling thermal resistance of the buried pipe heat exchanger, R 12,3D is the thermal resistance between the inlet and outlet pipes, R b12,3D is the thermal resistance between the borehole walls near the inlet and outlet pipes, R a,3D is the total internal thermal resistance of the ground pipe heat exchanger; T f,m,1 and T f,m,2 are the average temperatures of the fluid in the inlet and outlet pipes along the length of the pipe, T b,m,1 and T b,m,2 are the average temperatures of the borehole wall near the water inlet pipe and the water outlet pipe along the depth of the borehole, q f,m,1 and q f,m,2 are the average heat transfer of the fluid in the inlet pipe and the outlet pipe along the pipe length, q b,m,1 and q b,m,2 They are the average heat transfer of the borehole wall close to the water inlet pipe and the water outlet pipe along the depth direction of the borehole.

[0045] Optionally, the dimensionless processing of the drilling thermal resistance and the total internal thermal resistance includes:

[0046]

[0047] in, and are dimensionless parameters of drilling thermal resistance and total internal thermal resistance, respectively, g is the thermal conductivity of the backfill material, R b,3D and R a,3D are the drilling thermal resistance and the total internal thermal resistance respectively.

[0048] Optionally, constructing a three-dimensional thermal resistance correlation equation based on the response surface method includes:

[0049] The multivariate quadratic regression equation is used to fit the dimensionless parameters of the drilling thermal resistance and the total internal thermal resistance with the structural and thermophysical parameters:

[0050]

[0051] Where Y is the dimensionless output response, or and are dimensionless parameters of drilling thermal resistance and total internal thermal resistance, β0 is a constant term, β i , β ii , β ij are the parameters of the linear, quadratic and interaction terms, respectively, X i and X jare the i-th and j-th dimensionless parameters of the structural and thermophysical property parameters, and n is the number of dimensionless parameters;

[0052] Using Matlab programming to obtain or When β0, β i , β ii , β ij Parameter value of

[0053] based on The corresponding β0, β i , β ii , β ij The parameter values ​​of are used to build the correlation between the structure and thermophysical parameters and the drilling thermal resistance:

[0054]

[0055] based on The corresponding β0, β i , β ii , β ij The parameter values ​​of are used to build the correlation between the structure and thermophysical parameters and the drilling thermal resistance and the total internal thermal resistance:

[0056]

[0057] Among them, R b,3D and R a,3D are the drilling thermal resistance and the total internal thermal resistance, λ g is the thermal conductivity of the backfill material.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The present invention provides a three-dimensional thermal resistance calculation method for a vertical buried pipe heat exchanger, which obtains the structure and thermophysical parameters of the buried pipe heat exchanger; performs dimensionless processing on the structure and thermophysical parameters of the buried pipe heat exchanger; calculates the borehole thermal resistance and total internal thermal resistance of the buried pipe heat exchanger according to the dimensionless parameters of the structure and thermophysical parameters based on a pre-constructed three-dimensional thermal resistance correlation formula; in the process of constructing the three-dimensional thermal resistance correlation formula, the temperature difference of the borehole wall is taken into account, and the calculated borehole thermal resistance and total internal thermal resistance values ​​of the buried pipe heat exchanger are more accurate, providing theoretical support for the precise design of the ground source heat pump system. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of a method for calculating three-dimensional thermal resistance of a vertical buried pipe heat exchanger provided by an embodiment of the present invention;

[0061] Figure 2 is a flow chart of a process for constructing a three-dimensional thermal resistance correlation formula provided by an embodiment of the present invention;

[0062] Figure 3 is a schematic diagram of a three-dimensional heat transfer numerical model of a ground pipe heat exchanger provided by an embodiment of the present invention;

[0063] Figure 4 is a schematic diagram of a thermal resistance model in a two-dimensional plane provided by an embodiment of the present invention;

[0064] Figure 5 is a schematic diagram showing the difference in drilling thermal resistance and total internal thermal resistance of a single U-shaped tube under different numbers of grids provided by an embodiment of the present invention;

[0065] Figure 6 It is a schematic diagram showing the simulated value and experimental value of the inlet and outlet fluid temperature of a single U-shaped tube provided by an embodiment of the present invention;

[0066] Figure 7 is a schematic diagram of an orthogonal table and dimensionless parameter values ​​corresponding to each operating condition provided by an embodiment of the present invention;

[0067] Figure 8 It is a schematic diagram of actual and predicted values ​​of the borehole thermal resistance and total internal thermal resistance of the buried pipe heat exchanger provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0069] Embodiment 1:

[0070] like Figure 1 As shown, an embodiment of the present invention provides a method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger, comprising the following steps:

[0071] 1. Obtain the structure and thermophysical parameters of the buried pipe heat exchanger.

[0072] The structural parameters of the buried pipe heat exchanger include drilling depth, drilling diameter, pipe diameter and pipe spacing; the thermal physical parameters of the buried pipe heat exchanger include soil thermal conductivity, backfill material thermal conductivity, pipe wall thermal conductivity and fluid velocity in the pipe.

[0073] 2. The structure and thermophysical parameters of the buried pipe heat exchanger are dimensionlessly processed.

[0074] By converting the eight factors of the structural and thermophysical parameters into six dimensionless parameters through dimensionless processing, the calculation cost can be effectively reduced and the operation efficiency can be improved. The dimensionless parameters of the structural and thermophysical parameters after processing are:

[0075]

[0076] In the formula, θ1, θ2, θ3, σ1, σ2, R e is the dimensionless parameter of the structure and thermophysical properties, X c is the tube spacing, d b is the drilling diameter, d po is the outer diameter of the tube, λ g is the thermal conductivity of the backfill material, λ s is the thermal conductivity of soil, λ p is the thermal conductivity of the tube wall, u is the fluid velocity in the tube, d pi is the inner diameter of the tube, u f is the dynamic viscosity of the fluid in the tube, ρ f is the density of the fluid in the pipe, and H is the drilling depth.

[0077] 3. Based on the pre-built three-dimensional thermal resistance correlation, the borehole thermal resistance and total internal thermal resistance of the buried pipe heat exchanger are calculated according to the dimensionless parameters of the structure and thermophysical parameters.

[0078] like Figure 2 As shown in Figure 1, the construction of the three-dimensional thermal resistance correlation equation includes the following steps:

[0079] S1. Construct a three-dimensional heat transfer numerical model of the ground pipe heat exchanger based on finite element simulation software;

[0080] Regarding the three-dimensional heat transfer numerical model, it specifically includes:

[0081] The three-dimensional heat transfer numerical model includes the fluid in the tube, the wall of the single U-shaped tube, the backfill material in the borehole, the borehole wall and the soil from the inside to the outside, and the two ends of the single U-shaped tube are set as the inlet pipe and the outlet pipe. The structure and thermophysical parameters, calculation area, calculation time, boundary conditions and initial conditions of the three-dimensional heat transfer numerical model are set, and the inlet pipe orifice of the single U-shaped tube is set as the temperature and pressure inlet boundary of the three-dimensional heat transfer numerical model, and the outlet pipe orifice of the single U-shaped tube is set as the temperature and pressure outlet boundary of the three-dimensional heat transfer numerical model.

[0082] The structure and thermophysical parameters of the three-dimensional heat transfer numerical model are the same as those of the ground pipe heat exchanger; the far boundary distance of the calculation area is set to a s is the thermal conductivity of soil; the calculation time is set to the time required for heat transfer in the borehole to reach a quasi-steady state: t is the calculation time, r b is the drilling radius, a b is the thermal conductivity of the backfill material; the boundary condition is set as an adiabatic boundary condition; the initial condition is set as the initial temperature of the fluid in the pipe, the wall of the single U-shaped pipe, the backfill material in the borehole, the borehole wall and the soil to be constant.

[0083] S2. Dimensionless processing is performed on the structure and thermophysical property parameters of the three-dimensional thermal resistance numerical model; the processing method is the same as that in step 2.

[0084] S3, establishing an orthogonal table based on the Box-Behnken (response surface method) design according to the dimensionless parameters of the structure and thermophysical parameters;

[0085] S4. Obtain the borehole thermal resistance and total internal thermal resistance of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger under the structural and thermophysical property parameters based on the orthogonal table;

[0086] S5. Dimensionless processing is performed on the drilling thermal resistance and the total internal thermal resistance;

[0087] S6. Construct a three-dimensional thermal resistance correlation equation based on the response surface methodology according to the structural and thermophysical parameters, the dimensionless parameters of the drilling thermal resistance and the total internal thermal resistance;

[0088] Among them, obtaining the drilling thermal resistance and total internal thermal resistance of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger under the structural and thermophysical parameters includes:

[0089] (1) The calculation area of ​​the three-dimensional heat transfer numerical model is meshed using a free triangle mesh, and the three-dimensional heat transfer numerical model is meshed by sweeping along the depth direction; the mesh is encrypted for the fluid in the tube and the wall area of ​​the single U-shaped tube where the temperature gradient is greater than the preset value. The optimal number of meshes is determined by verifying the mesh independence of the divided meshes.

[0090] The more grids there are in a three-dimensional heat transfer numerical model, the more accurate the calculation results will be, but at the same time, the longer the calculation time will be. Therefore, it is necessary to determine the optimal grid to reduce the calculation time while ensuring the accuracy of the calculation.

[0091] (2) The finite element method is used to discretize and solve the fluid heat transfer differential equation and the solid heat transfer differential equation in the three-dimensional heat transfer numerical model to obtain the temperature field distribution of the three-dimensional heat transfer numerical model;

[0092] The differential equation for heat transfer in fluids is used to describe heat transfer in fluids, and the differential equation for heat transfer in solids is used to describe heat transfer in pipe walls, backfill materials, and soil.

[0093] (3) According to the temperature field distribution, the average temperature and heat transfer of the fluid in the inlet and outlet pipes along the pipe length direction and the average temperature and heat transfer of the borehole wall near the inlet and outlet pipes along the borehole depth direction in the three-dimensional heat transfer numerical model are calculated;

[0094] The average temperature and heat transfer of the fluid in the inlet and outlet pipes along the pipe length are:

[0095]

[0096] Where, T f,m,1 and T f,m,2 are the average temperatures of the fluid in the inlet and outlet pipes along the pipe length, L is the length of the single U-shaped pipe, T f,1 (z) and T f,2 (z) are the temperatures of the fluid in the inlet pipe and the outlet pipe at depth z, respectively;

[0097]

[0098] In the formula, q f,m,1 and q f,m,2 are the average heat transfer of the fluid in the inlet pipe and the outlet pipe along the pipe length, q f,1 (z) and q f,2 (z) are the heat transfer values ​​of the fluid in the inlet pipe and the outlet pipe at depth z respectively;

[0099] The average temperature and heat transfer of the borehole wall near the water inlet and outlet pipes along the depth direction of the borehole are:

[0100]

[0101] Where, T b,m,1 and T b,m,2 are the average temperatures of the borehole wall near the water inlet pipe and the water outlet pipe along the depth of the borehole, H is the depth of the borehole, T b,1 (z) and T b,2 (z) are the temperatures of the borehole wall at depth z near the inlet and outlet pipes, respectively;

[0102]

[0103] In the formula, q b,m,1 and q b,m,2 are the average heat transfer of the borehole wall near the water inlet pipe and the water outlet pipe along the depth direction of the borehole, q b,1 (z) and q b,2 (z) are the heat transfer of the borehole wall near the inlet pipe and outlet pipe at depth z respectively.

[0104] (4) According to the calculated average temperature and heat transfer amount, the borehole thermal resistance and total internal thermal resistance of the buried pipe heat exchanger are calculated based on the pre-built thermal resistance model.

[0105] The pre-built thermal resistance models are:

[0106]

[0107]

[0108]

[0109]

[0110] In the formula, R b,3D is the drilling thermal resistance of the buried pipe heat exchanger, R 12,3D is the thermal resistance between the inlet and outlet pipes, R b12,3D is the thermal resistance between the borehole walls near the inlet and outlet pipes, R a,3D is the total internal thermal resistance of the ground pipe heat exchanger; T f,m,1 and T f,m,2 are the average temperatures of the fluid in the inlet and outlet pipes along the length of the pipe, T b,m,1 and T b,m,2 are the average temperatures of the borehole wall near the water inlet pipe and the water outlet pipe along the depth of the borehole, q f,m,1 and q f,m,2 are the average heat transfer of the fluid in the inlet pipe and the outlet pipe along the pipe length, q b,m,1 and q b,m,2 They are the average heat transfer of the borehole wall close to the water inlet pipe and the water outlet pipe along the depth direction of the borehole.

[0111] Optionally, dimensionless processing of the drilled thermal resistance and the total internal thermal resistance includes:

[0112]

[0113] in, and are dimensionless parameters of drilling thermal resistance and total internal thermal resistance, respectively, g is the thermal conductivity of the backfill material, R b,3D and R a,3D are the drilling thermal resistance and the total internal thermal resistance respectively.

[0114] The three-dimensional thermal resistance correlation equation based on the response surface method includes:

[0115] The multivariate quadratic regression equation is used to fit the dimensionless parameters of the drilling thermal resistance and the total internal thermal resistance with the structural and thermophysical parameters:

[0116]

[0117] Where Y is the dimensionless output response, or and are dimensionless parameters of drilling thermal resistance and total internal thermal resistance, β0 is a constant term, β i , β ii , β ij are the parameters of the linear, quadratic and interaction terms, respectively, X i and X jare the i-th and j-th dimensionless parameters of the structural and thermophysical property parameters, and n is the number of dimensionless parameters; in this embodiment, n=6.

[0118] Using Matlab programming to obtain or When β0, β i , β ii , β ij Parameter value of

[0119] based on The corresponding β0, β i , β ii , β ij The parameter values ​​of are used to build the correlation between the structure and thermophysical parameters and the drilling thermal resistance:

[0120]

[0121] based on The corresponding β0, β i , β ii , β ij The parameter values ​​of are used to build the correlation between the structure and thermophysical parameters and the drilling thermal resistance and the total internal thermal resistance:

[0122]

[0123] Among them, R b,3D and R a,3D are the drilling thermal resistance and the total internal thermal resistance, λ g is the thermal conductivity of the backfill material.

[0124] Experimental verification:

[0125] Three-dimensional heat transfer numerical model Figure 3 As shown, the input parameters of the three-dimensional heat transfer numerical model are shown in Tables 1 and 2:

[0126] Table 1 Thermophysical parameters of fluid, pipe wall, backfill material in borehole, and soil:

[0127] Thermophysical parameters unit fluid Pipe wall Backfill material soil λ <![CDATA[W.m -1 .K -1 ]]> 0.60 0.40 0.60 2.60 <![CDATA[C p ]]> <![CDATA[J.m -3 .K -1 ]]> <![CDATA[4.141×10 6 ]]> <![CDATA[1.820×10 6 ]]> <![CDATA[2.350×10 6 ]]> <![CDATA[1.704×10 6 ]]> μ kg / (ms) <![CDATA[8.7×10 -4 ]]>

[0128] Table 2 Geometric parameters inside and outside the drilling hole:

[0129] Geometric parameters unit value Geometric parameters unit value <![CDATA[d po ]]> m 0.025 XC m 0.075 <![CDATA[d pi ]]> m 0.0201 <![CDATA[r s ]]> m 4.10 <![CDATA[d b ]]> m 0.150 H m 50 u <![CDATA[m.s -1 ]]> 0.1

[0130] The values ​​of drilling depth, drilling diameter, pipe diameter, pipe spacing, soil thermal conductivity, backfill material thermal conductivity, pipe wall thermal conductivity and fluid velocity in the pipe vary under different working conditions (structure and thermophysical parameters of different three-dimensional heat transfer numerical models).

[0131] The initial conditions of the three-dimensional heat transfer numerical model are:

[0132] The simulation time of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger is determined according to the time required for the heat transfer in the borehole to reach a quasi-steady state. For the default working condition, t = 122.39h. Determine the far boundary distance r of the three-dimensional heat transfer numerical model of the ground heat exchanger according to the heat flow action distance s for For the default case, r s =4.10m. The initial temperatures of the fluid in the inner pipe, the wall of the single U-shaped pipe, the backfill material in the borehole, the borehole wall, and each soil layer in the model are set to 18.20℃.

[0133] The boundary conditions of the three-dimensional heat transfer numerical model are:

[0134] The top, side and bottom surfaces of the three-dimensional heat transfer numerical model of the ground pipe heat exchanger are set as adiabatic boundaries; the U-shaped buried pipe inlet pipe is set as the temperature and inlet boundary of the three-dimensional heat transfer numerical model of the ground pipe heat exchanger, and the inlet temperature is 35°C. For the default working condition, u=0.1ms-1. The U-shaped buried pipe outlet pipe is set as the pressure outlet boundary of the three-dimensional heat transfer numerical model of the ground pipe heat exchanger.

[0135] The free triangle mesh is used to mesh the surface calculation area of ​​the three-dimensional heat transfer numerical model of the buried pipe heat exchanger, and then it is swept every 0.5m along the depth direction. The mesh is encrypted for the fluid and wall areas in the pipe where the temperature gradient is greater than the preset value. The mesh independence of the divided grid is verified, and five numbers of grid units are determined: 261625, 495593, 753118, 1370759 and 2375380, which are labeled A, B, C, D and E respectively. Figure 4 The thermal resistance model is used to determine the drilling thermal resistance and total internal thermal resistance under different grid numbers. Figure 5 The differences in drilling thermal resistance and total internal thermal resistance under different numbers of grids are shown, and the optimal grid label is determined to be E, and the corresponding number of grids is 1370759.

[0136] The finite element method is used to discretize and solve the fluid heat transfer differential equation describing the heat transfer of the fluid in the three-dimensional heat transfer numerical model of the buried pipe heat exchanger and the solid heat transfer differential equation describing the heat transfer of the pipe wall, backfill material and soil. The simulated values ​​of the inlet and outlet fluid temperatures of the single U-tube are compared with the experimental values. Figure 6 As shown in the figure, it is found that the root mean square error and average relative error of the simulated value and the experimental value of the outlet fluid temperature are 0.29℃ and 0.67% respectively. The errors are within the allowable range and the numerical model is accurate. Therefore, the numerical model can be used to obtain the temperature field distribution of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger.

[0137] The average temperature and heat transfer of the fluid in the inlet and outlet pipes along the length of the pipe in the three-dimensional heat transfer numerical model of the buried pipe heat exchanger, as well as the average temperature and heat transfer of the borehole wall near the inlet and outlet pipes along the borehole depth direction, are obtained. The borehole thermal resistance and total internal thermal resistance of the single U-shaped buried pipe heat exchanger under the default working conditions and their dimensionless forms are obtained.

[0138] In order to reduce the calculation cost, the parameters are dimensionless, and the L-54 orthogonal table is established by Box-Behnken design to determine the drilling thermal resistance and total internal thermal resistance of the buried pipe heat exchanger under different structures and thermophysical parameters. The dimensionless parameters in the Box-Behnken design and the corresponding level numbers are shown in Table 3. The L-54 orthogonal design table and the dimensionless parameter values ​​corresponding to each working condition are shown in Figure 7 shown.

[0139] Table 3 Dimensionless parameters and corresponding number of levels in Box-Behnken design:

[0140]

[0141] Based on the response surface methodology, the borehole thermal resistance R of the buried pipe heat exchanger obtained under 54 working conditions is used. * b,3D And the total internal thermal resistance R * a,3D , using the multivariate quadratic regression equation to fit R * b,3D and R * a,3D Relationship with dimensionless factors:

[0142]

[0143] Where Y is the dimensionless output response, Y = R * b,3D / R * a,3D , β i , β ii and β ij The parameters of the linear, quadratic and interaction terms, respectively, X i and X j is a dimensionless input parameter, n is the number of dimensionless input parameters, n=6.

[0144] The dimensionless factors and responses are converted into dimensional parameters, and the drilling thermal resistance R of the buried pipe heat exchanger is obtained by Matlab programming. b,3D The correlation between the drilling depth, drilling diameter, pipe diameter, pipe spacing, soil thermal conductivity, backfill material thermal conductivity, pipe wall thermal conductivity and fluid velocity in the pipe is shown below:

[0145]

[0146] R b,3D The parameter values ​​of the linear, quadratic and interaction terms in the correlation equation are shown in Table 4:

[0147] Table 4 R b,3D Parameter values ​​for the linear, quadratic, and interaction terms in the correlation:

[0148]

[0149]

[0150] The dimensionless factors and responses are converted into dimensional parameters, and the total internal thermal resistance R of the buried pipe heat exchanger is obtained by Matlab programming. a,3D The relationship between the drilling depth, drilling diameter, pipe diameter, pipe spacing, soil thermal conductivity, backfill material thermal conductivity, pipe wall thermal conductivity and fluid velocity in the pipe is shown in the following formula:

[0151]

[0152] R a,3D The parameter values ​​of the linear, quadratic and interaction terms in the correlation equation are shown in Table 5:

[0153] Table 5 R a,3D Parameter values ​​for linear, quadratic, and interaction terms in the correlation

[0154]

[0155]

[0156] like Figure 8 As shown in the figure, the drilling thermal resistance R of the buried pipe heat exchanger is given. b,3D And the total internal thermal resistance R a,3D The difference between the actual value and the predicted value. As can be seen from the figure, most of the points are located near the diagonal line. b,3D and R a,3D The relative deviation between the actual value and the predicted value is almost within ±5%. In addition, the coefficient of determination R 2 , the adjusted regression model determination coefficient R 2 -adj, prediction coefficient R of regression model 2 -pred, P value and lack-of-fit value of the regression model are shown in Table 6. In general, R 2 It is an indicator for evaluating the goodness of fit of the regression equation. 2 The closer it is to 100%, the higher the quality of the regression equation, and the better the fit of the second-order polynomial. Similarly, R 2 -pred can represent the predictive ability of equations (14) and (15), R2 The closer -pred is to 100%, the more accurately and effectively the regression equation can predict the output response. In addition, the P value of the regression equation is much less than 0.05, indicating that the regression model has a high degree of fit. b,3D and R a,3D The lack-of-fit values ​​of the expressions are 0.512 and 0.904, respectively, which are much larger than 0.05, meaning that the lack-of-fit of the equation is not significant, which once again proves the accuracy of the second-order regression formula.

[0157] Table 6 R of the multivariate quadratic regression equation 2 ,R 2 -adj and R 2 -pred:

[0158]

[0159] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0160] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0161] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger, which is characterized in that it includes: Obtain the structure and thermophysical parameters of the ground pipe heat exchanger; The structure and thermophysical parameters of the underground heat exchanger are dimensionlessly processed; Based on the pre-built three-dimensional thermal resistance correlation, the borehole thermal resistance and total internal thermal resistance of the ground heat exchanger are calculated according to the dimensionless parameters of the structure and thermophysical parameters; The construction of the three-dimensional thermal resistance correlation equation includes: Based on finite element simulation software, a three-dimensional heat transfer numerical model of the buried pipe heat exchanger was constructed; Non-dimensional processing of the structure and thermophysical parameters of the three-dimensional heat transfer numerical model; An orthogonal table is established based on the Box-Behnken design according to the dimensionless parameters of the structure and thermophysical properties; Based on the orthogonal table, the drilling thermal resistance and total internal thermal resistance of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger under the structural and thermophysical parameters are obtained; The drilling thermal resistance and the total internal thermal resistance are dimensionless. A three-dimensional thermal resistance correlation equation is constructed based on the response surface methodology according to the dimensionless parameters of the structural and thermophysical parameters, the drilling thermal resistance and the total internal thermal resistance. The structural parameters of the buried pipe heat exchanger include drilling depth, drilling diameter, pipe diameter and pipe spacing; the thermal physical parameters of the buried pipe heat exchanger include soil thermal conductivity, backfill material thermal conductivity, pipe wall thermal conductivity and fluid velocity in the pipe; Wherein, the three-dimensional thermal resistance correlation equation constructed based on the response surface method includes: The multivariate quadratic regression equation is used to fit the dimensionless parameters of the drilling thermal resistance and the total internal thermal resistance with the structural and thermophysical parameters: Where Y is the dimensionless output response, or and are dimensionless parameters of drilling thermal resistance and total internal thermal resistance, β0 is a constant term, β i , β ii , β ij are the parameters of the linear, quadratic and interaction terms, respectively, X i and X j are the i-th and j-th dimensionless parameters of the structural and thermophysical property parameters, and n is the number of dimensionless parameters; Using Matlab programming to obtain or When β0, β i , β ii , β ij Parameter value of based on The corresponding β0, β i , β ii , β ij The parameter values ​​of are used to build the correlation between the structure and thermophysical parameters and the drilling thermal resistance: based on The corresponding β0, β i , β ii , β ij The parameter values ​​of are used to build the correlation between the structure and thermophysical parameters and the drilling thermal resistance and the total internal thermal resistance: Among them, R b，3D and R a，3D are respectively the drilling thermal resistance and the total internal thermal resistance, λ g is the thermal conductivity of the backfill material.

2. According to claim 1, a method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger is characterized in that the dimensionless parameters of the structural and thermal physical parameters are: In the formula, θ1, θ2, θ3, σ1, σ2, R e is the dimensionless parameter of the structure and thermophysical properties, X c is the tube spacing, d b is the drilling diameter, d po is the outer diameter of the tube, λ g is the thermal conductivity of the backfill material, λ s is the thermal conductivity of soil, λ p is the thermal conductivity of the tube wall, u is the fluid velocity in the tube, d pi is the inner diameter of the tube, u f is the dynamic viscosity of the fluid in the tube, ρ f is the density of the fluid in the pipe, and H is the drilling depth.

3. The method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger according to claim 1 is characterized in that: The three-dimensional heat transfer numerical model includes, from the inside to the outside, the fluid in the tube, the wall of the single U-shaped tube, the backfill material in the borehole, the borehole wall and the soil, and the two ends of the single U-shaped tube are set as a water inlet pipe and a water outlet pipe; The structure and thermophysical parameters, calculation area, calculation time, boundary conditions and initial conditions of the three-dimensional heat transfer numerical model are set, and the water inlet pipe orifice of the single U-shaped tube is set as the temperature and pressure inlet boundary of the three-dimensional heat transfer numerical model, and the water outlet pipe orifice of the single U-shaped tube is set as the temperature and pressure outlet boundary of the three-dimensional heat transfer numerical model.

4. A method for calculating the three-dimensional thermal resistance of a vertical ground pipe heat exchanger according to claim 3, wherein the structure and thermophysical parameters of the three-dimensional heat transfer numerical model are the same as those of the ground pipe heat exchanger; the far boundary distance of the calculation area is set to a s is the thermal conductivity of soil; the calculation time is set to the time required for the heat transfer in the borehole to reach a quasi-steady state: t is the calculation time, r b is the drilling radius, a b is the thermal conductivity of the backfill material; the boundary condition is set as an adiabatic boundary condition; the initial condition is set as the initial temperature of the fluid in the pipe, the wall of the single U-shaped pipe, the backfill material in the borehole, the borehole wall and the soil is constant.

5. The method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger according to claim 4 is characterized in that: The method of obtaining the borehole thermal resistance and the total internal thermal resistance of the three-dimensional heat transfer numerical model of the buried pipe heat exchanger under the structural and thermophysical property parameters includes: The free triangle mesh is used to mesh the calculation area of ​​the three-dimensional heat transfer numerical model, and the optimal number of meshes is determined by verifying the mesh independence of the meshes after meshing. The finite element method is used to discretize and solve the fluid heat transfer differential equation and the solid heat transfer differential equation in the three-dimensional heat transfer numerical model to obtain the temperature field distribution of the three-dimensional heat transfer numerical model; According to the temperature field distribution, the average temperature and heat transfer of the fluid in the water inlet and outlet pipes along the pipe length direction and the average temperature and heat transfer of the borehole wall near the water inlet and outlet pipes along the borehole depth direction in the three-dimensional heat transfer numerical model are calculated; The borehole thermal resistance and total internal thermal resistance of the ground pipe heat exchanger are calculated based on the calculated average temperature and heat transfer based on the pre-built thermal resistance model.

6. A method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger according to claim 5, wherein the method of using a free triangle grid to mesh the calculation area of ​​the three-dimensional heat transfer numerical model comprises sweeping along the depth direction to mesh the three-dimensional heat transfer numerical model; wherein, The mesh is encrypted for the fluid in the tube and the wall area of ​​the single U-tube where the temperature gradient is greater than the preset value.

7. The method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger according to claim 5 is characterized in that the average temperature and heat transfer of the fluid in the water inlet pipe and the water outlet pipe along the pipe length direction are: Where, T f，m，1 and T f，m，2 are the average temperatures of the fluid in the inlet and outlet pipes along the pipe length, L is the length of the single U-shaped pipe, T f，1 (z) and T f，2 (z) are the temperatures of the fluid in the inlet pipe and the outlet pipe at depth z, respectively; In the formula, q f , m, 1 and q f , m, 2 are the average heat transfer of the fluid in the inlet pipe and outlet pipe along the pipe length, q f , 1(z) and q f , 2(z) are the heat transfer of the fluid in the inlet pipe and the outlet pipe at depth z respectively; The average temperature and heat transfer of the borehole wall near the water inlet pipe and the water outlet pipe along the borehole depth direction are: Where, T b，m，1 and T b，m，2 are the average temperatures of the borehole wall near the water inlet pipe and the water outlet pipe along the depth of the borehole, H is the depth of the borehole, T b，1 (z) and T b，2 (z) are the temperatures of the borehole wall at depth z near the inlet and outlet pipes, respectively; In the formula, q b，m，1 and q b，m，2 are the average heat transfer of the borehole wall near the water inlet pipe and the water outlet pipe along the depth direction of the borehole, q b , 1(z) and q b , 2(z) are the heat transfer of the borehole wall near the inlet pipe and outlet pipe at depth z respectively.

8. The method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger according to claim 5, wherein the pre-constructed thermal resistance model is: In the formula, R b，3D is the drilling thermal resistance of the buried pipe heat exchanger, R 12，3D is the thermal resistance between the inlet and outlet pipes, R b12，3D is the thermal resistance between the borehole walls near the inlet and outlet pipes, R a，3D is the total internal thermal resistance of the ground pipe heat exchanger; T f，m，1 and T f，m，2 are the average temperatures of the fluid in the inlet and outlet pipes along the length of the pipe, T b，m，1 and T b，m，2 are the average temperatures of the borehole wall near the water inlet pipe and the water outlet pipe along the depth of the borehole, q f，m，1 and q f，m，2 are the average heat transfer of the fluid in the inlet pipe and the outlet pipe along the pipe length, q b，m，1 and q b，m，2 They are the average heat transfer of the borehole wall close to the water inlet pipe and the water outlet pipe along the depth direction of the borehole.

9. The method for calculating the three-dimensional thermal resistance of a vertical buried pipe heat exchanger according to claim 1 is characterized in that the dimensionless processing of the borehole thermal resistance and the total internal thermal resistance comprises: in, and are dimensionless parameters of drilling thermal resistance and total internal thermal resistance, respectively, g is the thermal conductivity of the backfill material, R b，3D and R a，3D are the drilling thermal resistance and the total internal thermal resistance respectively.

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