Underground building ventilation system and numerical heat transfer model thereof

Abstract

The application discloses an underground building ventilation system, comprising a ventilation channel, the ventilation channel is formed in a buried pipeline buried in underground soil, the inlet of the ventilation channel is located on the ground surface, and the outlet is located in an underground building, characterized in that a layer of equal-thickness phase change material is arranged on the outer surface of the ventilation channel, the phase change material layer is filled with a shaped phase change material, and the shell of the phase change material layer forms a containment structure and is buried and coated in the underground soil. The numerical heat transfer model of the system is also disclosed. The underground building ventilation system improves the heat exchange efficiency of the ventilation channel and the soil, better reduces the temperature control energy consumption of the underground building, and achieves the effect of energy saving and emission reduction. Meanwhile, the numerical heat transfer model of the system is designed, and better guarantee is provided for the reliability of the design and implementation of the ventilation system.

Description

Technical Field

[0001] This invention relates to the field of ventilation technology for underground buildings, specifically to an underground building ventilation system and its numerical heat transfer model. Background Technology

[0002] Air conditioning is a major contributor to building energy consumption, and the rational development and utilization of renewable energy is an important way to reduce building energy consumption. When designing and constructing underground buildings, it is common practice to introduce fresh air from the surface to the underground for ventilation. Simultaneously, during ventilation, due to the soil's characteristic of being warm in winter and cool in summer, the soil around the ventilation duct exchanges heat with the airflow within the duct, acting as a natural heat exchanger and further reducing the energy consumption for temperature control in underground buildings.

[0003] Taking subway stations as an example, the energy consumption of the subway environmental control system accounts for a large proportion of the total energy consumption of the subway, and there is considerable room for energy saving. Subway stations are generally buried at great depths, and in summer, they rely on the coldness of the soil around the ventilation ducts to form abundant and usable natural cold sources. The subway's fresh air ducts connect the interior of the subway station with the outdoor atmosphere, acting as a natural soil-air heat exchanger. However, in ordinary ventilation duct systems, the ducts directly contact the soil for heat exchange, easily causing a cold and heat accumulation effect in the shallow soil, resulting in limited efficiency in utilizing the soil's coldness. At the same time, in the design process of existing underground building ventilation ducts, the heat transfer control model is usually calculated using a simple air heat balance equation model. This is only applicable to calculations of simple heat exchange between soil and air, and cannot be applied to calculations of more complex heat exchange methods involving phase change heat storage and release processes. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is: how to provide an underground building ventilation system and its numerical heat transfer model that can better utilize the cold (heat) energy of underground soil, improve the heat exchange efficiency of ventilation ducts and soil, and better reduce the energy consumption of underground building temperature control, so that the heat transfer model is more targeted and can be applied to the calculation of ventilation duct heat exchange mode containing phase change heat storage and release process, and provide better guarantee for the reliability of ventilation duct design.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] An underground building ventilation system includes a ventilation duct formed within a buried pipe embedded in the underground soil. The ventilation duct inlet is located at the surface, and the outlet is located within the underground building. The system is characterized in that the outer surface of the ventilation duct is covered with a layer of phase change material of equal thickness, and the phase change material layer is filled with a solid-liquid phase change material (preferably a shape-fixed phase change material). The outer shell of the phase change material layer forms an enclosure structure and is buried and covered within the underground soil.

[0007] In this way, by wrapping the ventilation duct with a layer of phase change material, the phase change material can store the cold energy from the cool air at night in summer and the cold energy inside the soil, and release it during the day, realizing the spatial and temporal transfer of cold energy. During the summer daytime, hot outdoor air flows in through the ventilation duct inlet, is cooled by the phase change material layer, and becomes cool air before entering the underground structure. Therefore, it can better utilize the cold (heat) energy of the underground soil, improve the heat exchange efficiency of the ventilation duct and the soil, and better reduce the energy consumption for temperature control in underground structures.

[0008] Furthermore, the underground structure is a subway station, and the ventilation duct entrance is a fresh air pavilion for the subway station.

[0009] Subway stations are usually located deep underground, making them more suitable for applying the solution of this invention to reduce temperature control energy consumption by utilizing the coldness of the underground soil.

[0010] Furthermore, a porous, shaped phase change material is prepared by using a binary composite phase change material of decanoic acid and palmitic acid with a mass ratio of 97:3 as the phase change heat storage core material and expanded graphite accounting for 10% of the core material mass as the substrate.

[0011] This was achieved through a comprehensive comparison of phase change materials in terms of phase change temperature range, structural stability, thermal conductivity, and supercooling, followed by laboratory testing. The results showed that this composite phase change material has good thermal conductivity and can be better integrated with building envelope structures.

[0012] This invention also discloses a numerical heat transfer model for the aforementioned underground building ventilation system. Its key feature is that the ventilation duct, along with the external phase change material and the soil layer (i.e., the area within the far boundary of the hot zone) within a certain thickness range (typically 4-6m), is considered as the computational domain of the system model. The physical structure of the computational domain includes an air layer, a phase change layer, and a soil layer from the inside out. The model is segmented along the airflow direction, with the air within each segment of the ventilation duct considered as a whole. The heat transfer of the three different material components is theoretically analyzed using the air heat balance equation, the phase change material heat transfer control equation, and the soil heat transfer control equation. The equivalent heat capacity method is used to handle the phase change heat transfer process, and the finite difference method is used to discretize the aforementioned heat transfer control equations. Then, the solution process is achieved using the CHASE pursuit method (a current algorithm for solving linear equations) based on the algebraic equations, resulting in the numerical calculation model.

[0013] Thus, this model fully considers the heat storage form and heat absorption / release effect of the phase change material layer located between the ventilation duct and the soil layer. It also simplifies the heat transfer process of the incoming air within the ventilation duct, simplifying the calculation process and improving computational efficiency while ensuring accurate results. The applicant compared test data from an experimental platform with the simulation results of this model, verifying its reliability and correctness. Furthermore, response surface methodology was used for multi-factor analysis, and based on this theoretical foundation, more accurate and reliable engineering design recommendations can be provided for ventilation systems applied in subway station fresh air ducts.

[0014] Specifically, establishing the numerical heat transfer model includes the following steps:

[0015] Step 1: Perform phase change layer heat transfer calculations. The calculations are based on the equivalent heat capacity method to analyze the phase change heat transfer process. (The equivalent heat capacity method treats the latent heat of phase change as a large sensible heat capacity within a certain temperature range including the phase change temperature. Through this simplified equivalent treatment, the complex nonlinear phase change heat transfer process can be effectively simplified to a pure conduction heat transfer process, thus greatly reducing the computational difficulty.) Based on the energy conservation equation and the equivalent heat capacity method, the heat transfer differential equation for the phase change material heat transfer process is as follows:

[0016] Energy conservation equation:

[0017] (Equation 1)

[0018] Equivalent heat capacity equation:

[0019] (Equation 2)

[0020] (Equation 3)

[0021] In the formula: —Equivalent heat capacity of phase change materials, ;

[0022] —Equivalent thermal conductivity of phase change materials ;

[0023] —Latent heat of phase change in phase change materials ;

[0024] —Specific heat capacity of phase change materials before melting ;

[0025] —Specific heat capacity of phase change materials after melting. ;

[0026] —The melting point temperature of phase change materials ;

[0027] —The melting point of phase change materials ;

[0028] —The thermal conductivity of the phase change material before melting. ;

[0029] —The thermal conductivity of the phase change material after melting. ;

[0030] T—Current temperature of the phase change material ;

[0031] Based on the definitions of equivalent heat capacity and equivalent thermal conductivity using the equivalent heat capacity method, the equivalent heat capacity and thermal conductivity of phase change materials are linearized. The resulting calculation formulas are as follows:

[0032] (Equation 4)

[0033] The phase transition temperature range of the decanoic acid-palmitic acid binary composite phase change material is 28.16 ℃ to 32.68 ℃, therefore =28.16 ℃ =32.68 ℃. The equivalent specific heat capacity has a peak value in the phase transition temperature range. For ease of calculation, the temperature corresponding to this value is introduced as... =32.06 ℃;

[0034] Therefore, we obtain

[0035] (Equation 5);

[0036] Step 2: Establish the heat transfer control equations for the model;

[0037] First, establish the basic settings, setting the underground building ventilation system to be located in a dry soil layer without direct sunlight, and make the following settings for the system's heat transfer process:

[0038] ① Air is incompressible, the airflow velocity and state parameters are uniformly distributed across the same cross section, and the influence of changes in air humidity on heat transfer performance is ignored.

[0039] ② The phase change material is equivalent to an isotropic homogeneous solid medium, whose density and specific heat remain unchanged within the temperature range discussed in this method. The effect of heat convection on the heat transfer of the phase change material is ignored, and only heat conduction is considered.

[0040] ③ Soil is considered to be an isotropic homogeneous solid material with constant thermal properties. Due to the small axial temperature gradient, heat conduction along the axial direction is negligible.

[0041] ④ The contact between the various substances within the system is good, and the contact thermal resistance between materials is not considered;

[0042] ⑤ Buried pipelines typically use impermeable pipe materials and have limited lengths of heat exchange systems. Therefore, the latent heat exchange process of water evaporation and condensation inside the pipe is not considered. Only the sensible heat exchange between the air and the phase change material in the system is considered.

[0043] ⑥ Because the pipe wall thickness in actual engineering is relatively small when in contact with air, the thermal impact of the pipe material on the system is ignored;

[0044] Then, heat transfer control equations for different material layers are established separately; (The physical structure of the model includes an air layer, a phase change layer, and a soil layer from the inside out; heat transfer control equations for the air layer, the phase change material layer, and the soil layer are established respectively using basic heat transfer theory methods;)

[0045] (1) Establish the heat transfer control equation for the air layer:

[0046] Based on the basic heat transfer equation, the general form of the governing equations for mass conservation, momentum conservation, and energy conservation that describe all flow and heat transfer phenomena is shown in Equation 6. It consists of four terms: from left to right, they are the unsteady-state term, the convection term, the diffusion term, and the source term.

[0047] (Equation 6)

[0048] (Considering the high temperatures in summer, latent heat transfer is ignored. When sensible heat exchange occurs between the air and the wall, the air energy is only reflected in the air temperature, so the diffusion term can be ignored simultaneously. At this time, the air layer is considered as a whole, and its heat exchange process is divided into two parts: one part is the internal heat transfer of the air along the flow direction of the channel, and the other part is the convective heat exchange between the flowing air and the boundary of the phase change material layer.) The heat transfer control equation of the air layer is derived from Equation 6 as follows:

[0049] (Equation 7)

[0050] In the formula: π — Pi (the mathematical constant of a circle);

[0051] —Equivalent radius of the tunnel, ;

[0052] —Air density, ;

[0053] —Specific heat capacity of air, ;

[0054] —Air temperature, °C;

[0055] —Airflow speed, ;

[0056] —The source term for heat and mass transfer from the phase change layer wall to the air.

[0057] Among them, It can be expressed by the following formula:

[0058] (Equation 8)

[0059] In the formula:

[0060] —Temperature of the phase change layer immediately adjacent to the air passage, °C;

[0061] —The convective heat transfer coefficient of the air wall. ;

[0062] The convective heat transfer coefficient h can be calculated by the following formula:

[0063] (Equation 9)

[0064] In the formula:

[0065] —The thermal conductivity of air, ;

[0066] D – Equivalent diameter of the air tunnel ;

[0067] —Reynolds criterion number:

[0068] (Equation 10)

[0069] In the formula, —The dynamic viscosity of air, .

[0070] (2) Establish the heat transfer control equations for the phase change layer:

[0071] Similarly, according to Equation 6, and based on the fundamental assumption that the phase change material is an isotropic homogeneous solid medium, the convection term on the left side and the diffusion term on the right side of the governing equation are ignored during axial flow. Therefore, the basic heat and mass transfer equations for the phase change layer are:

[0072] (Equation 11)

[0073] In the formula:

[0074] —Calculate the base area of ​​the unit, in square meters;

[0075] —Density of phase change materials, ;

[0076] Specific heat capacity of phase change materials ;

[0077] —The phase change material in this unit is subject to heat exchange sources from other adjacent contact surface materials;

[0078] The source term S of the phase change layer energy control equation can be divided into three cases based on heat transfer. The first case is a single phase change layer adjacent to the air layer, where the heat exchange in the source term mainly involves convective heat exchange between the flowing air and the phase change layer, and heat conduction between adjacent phase change units. The second case is a single phase change layer inside the phase change layer, where the heat exchange mainly considers the heat conduction between the phase change materials on both sides. The third case is a single phase change layer adjacent to the soil layer, where the heat exchange mainly involves heat conduction with the phase change material on one side and heat conduction with the soil on the other side. Therefore, the source term S of the phase change layer heat transfer control equation is divided into the following three categories:

[0079] (Equation 12)

[0080] In the formula:

[0081] —Calculate the perimeter of the cell, in meters;

[0082] — Thermal conductivity of the rock mass ;

[0083] —The thermal conductivity of phase change materials, ;

[0084] T p1 —Temperature of the phase change material layer adjacent to the air, °C;

[0085] T p2 —Temperature of the phase change material adjacent to the soil, °C.

[0086] (3) Establish the heat transfer control equation for the soil layer:

[0087] Regarding heat conduction in the soil layer, based on the above assumptions, the cross-section of the ventilation tunnel is approximated as a cylinder. Ignoring the convection and diffusion terms in the soil heat transfer control equation, the left side of the equation represents the unsteady-state term of the soil itself, and the right side represents the heat conduction source term between the soil and adjacent soil in the radial direction. Therefore, the soil control equation for the internal retaining structure of the buried pipeline is:

[0088] (Equation 13)

[0089] in:

[0090] —Calculation radius of the soil layer, in meters;

[0091] — Soil thermal diffusivity, m 2 / s.

[0092] The formula for calculating the soil thermal diffusivity is as follows:

[0093] (Equation 14)

[0094] In the formula:

[0095] Soil density, ;

[0096] Specific heat capacity of soil ;

[0097] Step 3: Discretize the heat transfer control equations established in Step 2;

[0098] First, the computational domain of the system is divided into a two-dimensional mesh;

[0099] In the axial direction, the computational domain of the system is defined by a thickness of... The thin sheet is discretely divided into Z / Each thin slice computational unit is represented by a subscript from 1 to z, indicating the specific axial position of each thin slice computational unit within the computational domain.

[0100] In the radial direction, each radial slice of the system is divided into three large control units:

[0101] ① The central region is the radius Air computing domain control unit;

[0102] ② The mezzanine area is of length Phase change computational domain control unit;

[0103] ③ The outer region is the length The rock mass computational domain control unit;

[0104] In terms of time processing, use The time discrete unit is represented by the superscript n, which indicates the current calculation time, 0 is the initial time, and N is the calculation end time. When the time calculation step is one day, the unit of n is day; when the calculation time step is hours, the unit of n is hour.

[0105] (Because the heat exchange medium in the system includes air, phase change material, and soil, the discrete analysis of the governing equations mainly considers the heat exchange between these three; the model is cylindrical and axisymmetric along the centerline, so it is simplified to a two-dimensional model during the discretization process.) The system model is divided into z layers in the axial direction of airflow and j+4 layers in the radial direction from bottom to top, including j layers of soil; air, phase change material, and soil are distributed sequentially in the radial direction.

[0106] (Because the specific heat distribution inside the air is not considered in this scheme) the entire air section is divided into only one grid along the radial direction, and the grid length is... This indicates that (this is also where the computational speed advantage of this model lies.)

[0107] (The model established in this invention is mainly used for rapid calculations in the engineering field. Mechanistic parameters such as the liquid phase ratio within the phase change layer are not the primary research focus. To ensure calculation speed, considering the heat transfer of the phase change material and different contact surfaces,) the entire phase change material is uniformly divided into three grid layers: PCM1, PCM2, and PCM3, along the radial direction. The first layer, PCM1, is the outer boundary of the phase change material, adjacent to the air layer, and is used to represent the convective heat transfer between the phase change layer and the air layer. The second layer, PCM2, is the inner grid of the phase change layer, enclosed by the inner and outer phase change layers, and is used to represent the liquid phase ratio conversion within the phase change material. The third layer, PCM3, is the inner boundary of the phase change layer, adjacent to the soil layer, and is used to represent the heat conduction between the phase change material and the soil. The total length of the phase change layer grid is... The grid is divided into three equal parts, and the unit phase transition grid is used. express, ;

[0108] For the final soil layer mesh, (to facilitate the discretization of the subsequent heat transfer control equations), the first soil layer in the radial direction, adjacent to PCM3, is defined as the SS layer. Subsequent soil layer meshes are sequentially designated as S1 to S... j-1 To represent the second soil grid layer to the far boundary of the soil grid; the length of the entire soil layer is represented by... This indicates that the mesh is divided into j layers, and the cell mesh length is expressed as... To indicate;

[0109] Then, the heat transfer control equations established in step 2 are discretized;

[0110] For the discretization of the heat transfer control equations in the air layer, the unsteady-state terms are discretized using the classical first-order backward difference method, with a fully implicit scheme for time. The convective terms of the air layer heat transfer control equations, specifically the temperature derivative with respect to length, are discretized using a second-order upwind scheme. For the phase change layer, heat transfer control equations are established for different phase change layers based on the mesh division, and these three equations are discretized. The unsteady-state terms in the heat balance equations at the soil wall are discretized using the first-order backward difference method, approximating the source terms as one-dimensional single-layer flat-wall heat conduction. (Due to the stable thermal properties and high thermal inertia of the soil itself, coupled with the uniform distribution of the soil layer mesh and the small temperature difference between adjacent soil meshes in this model, the central difference method is a relatively reasonable choice for discretization.)

[0111] (1) Discretize the air layer heat transfer control equations:

[0112] (Equation 15)

[0113] For ease of subsequent calculations, Equation 15 can be combined and categorized, and written in the following form:

[0114] (Equation 16)

[0115] In the formula:

[0116] G—Buried pipeline ventilation mass flow rate, unit kg / h;

[0117] L a —Perimeter of the ventilation section of the buried pipeline, in meters;

[0118] Throughout the discretization process (which requires initial calculations due to parameter shortages), the following approximations are performed: For the unsteady-state terms in the air layer heat transfer control equations, when n=1, This term should be the air temperature value at time 0, which is uniformly replaced by the ambient air temperature in this method; for the convection term in the air layer heat transfer control equation, when i=1, (because there are not enough parameters for the second-order backward difference, so only) the first-order backward difference method is used at this node, and the discrete form of the air layer heat transfer control equation at this node is as follows:

[0119] (Equation 17)

[0120] Similarly, after merging, the form is as follows:

[0121] (Equation 18)

[0122] (2) Discretize the heat transfer control equations of the phase change layer:

[0123] (To ensure consistency in model application, the following settings are made for the phase change layer material in the model beforehand: the density of the phase change material in this model is determined to be a constant value; the shaped phase change material selected in this model is uniformly encapsulated and is not affected by gravity to deform.)

[0124] Based on the phase change layer heat transfer control equation, equations 11 and 12 are discretized for three different heat exchange scenarios; in the unsteady-state term of equation 11, the specific heat capacity and thermal conductivity depend on the temperature range of the material, and are sequentially represented by C according to the mesh. p1 C p2 C p3 and The specific heat capacity and thermal conductivity of different phase change layers are represented by the specific parameters determined by the properties of the phase change material itself (see Table 4); where A represents the bottom area of ​​the current calculation unit. Since the geometry of this model is a concentric cylinder, the expression for the bottom area of ​​each grid unit is also different. The specific expression is shown in Equations 19-24 below.

[0125] (Equation 12 is the source term of the equation. Due to the different contact and interaction objects, according to the current meshing method of the phase change layer, it corresponds to the source term expressions of the PCM1, PCM2, and PCM3 phase change material layers respectively; therefore,) by combining Equations 11 and 12, the phase change material is divided into three different heat transfer control equations according to the current meshing method to accurately describe its heat exchange situation, and mathematical discretization is performed; the results are as follows:

[0126] ① Phase transition first layer PCM1 layer

[0127] Heat transfer control equation:

[0128] (Equation 19)

[0129] Discrete equations:

[0130] (Equation 20)

[0131] ② Phase transition second layer PCM2 layer

[0132] Heat transfer control equation:

[0133] (Equation 21)

[0134] Discrete equations:

[0135] (Equation 22)

[0136] ③ Phase transition third layer PCM3 layer

[0137] Heat transfer control equation:

[0138] (Equation 23)

[0139] Discrete equations:

[0140] (Equation 24)

[0141] In the formula:

[0142] —The base area of ​​the i-th phase transition computation unit, m 2 ;

[0143] —The perimeter of the i-th phase transition calculation unit, in meters;

[0144] —Specific heat capacity of the i-th phase change material ;

[0145] —The thermal conductivity of phase change materials, ;

[0146] —Thickness of a single-layer phase change material, in meters (m).

[0147] (3) Discretization of the heat transfer control equations of the SS layer at the wall

[0148] (To distinguish it from the stable heat conduction within the soil layer, this paper separately divides the soil layer near the phase change material (PCM) wall into an SS layer during mesh generation. Because the various thermophysical parameters of the PCM change material change drastically with temperature fluctuations, heat exchange in the soil layer near the PCM wall is unstable. For the sake of consistency in the discrete difference scheme, this section will discuss the heat balance equations for the soil wall layer separately.)

[0149] Similarly, according to the conservation equation 6 of the heat transfer control equation, since the soil is a solid, the flow and diffusion terms in the heat transfer control equation are ignored. Therefore, (similar to the heat transfer control equation of the phase change layer mentioned above), the heat transfer control equation of the SS layer consists of the unsteady terms of the soil itself and the boundary heat exchange source terms in contact with it. The heat exchange with the soil in the SS layer is mainly caused by the thermal conduction of the phase change layer of P3 and the soil of S1.

[0150] Therefore, the heat transfer control equation for the soil SS layer is as follows:

[0151] (Equation 25)

[0152] The unsteady-state terms of the heat transfer control equation 25 above are discretized using the first-order backward difference method. The source term can be approximated as a one-dimensional single-layer flat-wall heat conduction. The discretization results are as follows:

[0153] (Equation 26)

[0154] (4) Discretization of the heat transfer control equation of the soil layer

[0155] (Regarding the soil heat transfer control equations established in step 2, this section will discuss how to discretize the soil flow equations for the unit thin sheet. Because the soil itself has stable thermal properties and relatively high thermal inertia, and because the soil layer grids in this model are uniformly distributed and the temperature difference between adjacent soil grids is very small, it is relatively reasonable to use the central difference method for discretization.)

[0156] Discretizing Equation 13 using the finite difference method yields...

[0157] (Equation 27)

[0158] The formula introduces Fo—the Fourier number—as a dimensionless quantity describing unsteady-state heat conduction and molecular diffusion. The expression is:

[0159] (Equation 28)

[0160] Step 4: Calculation and Solution Methods and Model Establishment

[0161] Based on the mesh generation and discrete equation results in step 3, the internal heat transfer problem of the system is analyzed and calculated. This model adopts a time-by-time calculation model, and the calculation and solution process is mainly carried out in the following three steps.

[0162] The first step is to initialize and define various calculation parameters, including the geometric dimensions of the buried pipeline, the thermal properties of air, phase change material, and soil, as well as the inlet flow rate and inlet wind speed.

[0163] The second step is boundary condition assignment and mesh generation. Boundary conditions include the outdoor air input parameters at the system inlet and the temperature distribution of the soil at the far boundary. The air input parameters at the inlet are obtained based on typical meteorological data of the project site. The soil temperature distribution at the far boundary is determined based on the temperature disturbance depth of the soil at the project site to determine the model's far boundary range and axial temperature distribution. The outdoor air input parameters at the inlet and the soil temperature distribution at the far boundary are compiled into a "boundary input file" and added to the model calculation folder in chronological order. Then, the model is meshed and verified. The reliability of the time step is determined and verified through pre-run.

[0164] The third step is to proceed with numerical calculations. Each horizontal row in the radial direction is considered a calculation slice. Starting from the first slice position (i=1) at the air inlet of the system, the temperature parameters and heat flux density components of the air, phase change material, and soil in each grid slice are calculated sequentially along the axial direction. After the calculation of the last slice at the end of the air channel is completed, the program moves to the next time step and starts iterating again from the air channel inlet to calculate the parameters of the previous round. When all time steps are completed, the program calculation ends.

[0165] When calculating the interior of each thin sheet, the basic principle is to establish a linear equation system using the heat transfer control equation of the air layer, the heat transfer control equation of the phase change material phase change layer, and the heat balance equation inside the soil. After mathematical processing of the above discrete equations, the linear equation system is constructed into a tridiagonal matrix that is easy to calculate, as shown in Equation 29.

[0166] (Equation 29)

[0167] This allows us to further obtain the system of linear equations at each level:

[0168]

[0169] (Formula 30)

[0170] The linear equations in Equation 30 above constitute the numerical heat transfer model of the underground building ventilation system. Specifically, during the calculation, the linear equations form a tridiagonal equation system based on three cases: the air wall heat balance equation, the phase change material heat transfer control equation, and the soil heat transfer control equation. Therefore, when calculating the model, each grid on the radial thin plate can be treated as an unknown quantity to be solved, and a tridiagonal matrix with j+4 rows can be written out. The solution calculation can be completed by using the triangular decomposition method.

[0171] Therefore, the underground building ventilation system of this invention can better utilize the cold (heat) energy of the underground soil, improve the heat exchange efficiency of ventilation ducts and soil, and better reduce the energy consumption of underground building temperature control, thus achieving energy saving and emission reduction. At the same time, a numerical heat transfer model for this system is designed, which can be used more accurately and reliably for the design calculation of the ventilation system parameters, providing better assurance for the reliability of the ventilation system design and implementation. Attached Figure Description

[0172] Figure 1 This is a schematic diagram of the cross-sectional structure of the ventilation system in an underground building, as shown in a specific implementation.

[0173] Figure 2 This is a schematic diagram of the DSC curve of the phase change material in a specific implementation.

[0174] Figure 3This refers to the equivalent heat capacity of the phase change material in the specific implementation.

[0175] Figure 4 The value represents the thermal conductivity of the phase change material in the specific implementation.

[0176] Figure 5 This is a schematic diagram of the computational domain grid partitioning in a specific implementation method.

[0177] Figure 6 This is a discrete node diagram of the air layer, phase change material layer, and soil layer in a specific implementation.

[0178] Figure 7 The flowchart of the heat transfer numerical model calculation program of the present invention.

[0179] Figure 8 This document provides a reference table for determining the PCM length and thickness values ​​in the actual design and application of the EAHE-PCHS system, illustrating specific implementation methods.

[0180] Figure 9 This is a schematic diagram comparing experimental and simulated temperatures.

[0181] Figure 10 This diagram illustrates the comparison of air temperature between ventilation systems containing and without phase change material layers in Chongqing Metro stations, based on a survey and analysis.

[0182] Figure 11 This diagram illustrates the comparison of cooling energy efficiency ratios of ventilation systems with and without phase change material layers in Chongqing Metro stations, based on a survey and analysis.

[0183] Figure 12 This diagram illustrates the comparison of the average daily cooling capacity of ventilation systems with and without phase change material layers in Chongqing Metro stations, based on a survey and analysis. Detailed Implementation

[0184] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0185] Detailed implementation: A ventilation system for underground buildings, see [link / reference] Figure 1 It includes a ventilation duct 1, which is formed in a buried pipe 2 buried in the underground soil. The ventilation duct inlet is located at the ground surface and the outlet is located in the underground building. Its feature is that the outer surface of the ventilation duct 1 is wrapped with a layer of phase change material 3 of equal thickness. The phase change material layer 3 is filled with solid-liquid phase change material. The outer shell 4 of the phase change material layer forms an enclosure structure and is buried and covered in the underground soil 5.

[0186] In this way, by wrapping the ventilation duct with a layer of phase change material, the phase change material can store the cold energy from the cool air at night in summer and the cold energy inside the soil, and release it during the day, realizing the spatial and temporal transfer of cold energy. During the summer daytime, hot outdoor air flows in through the ventilation duct inlet, is cooled by the phase change material layer, and becomes cool air before entering the underground structure. Therefore, it can better utilize the cold (heat) energy of the underground soil, improve the heat exchange efficiency of the ventilation duct and the soil, and better reduce the energy consumption for temperature control in underground structures.

[0187] The underground structure is a subway station, and the ventilation duct entrance is the subway station's fresh air pavilion.

[0188] Subway stations are usually located deep underground, making them more suitable for applying the solution of this invention to reduce temperature control energy consumption by utilizing the coldness of the underground soil.

[0189] Among them, the phase change material layer uses a binary composite phase change material of decanoic acid and palmitic acid with a mass ratio of 97:3 as the phase change heat storage core material, and uses expanded graphite accounting for 10% of the core material mass as the substrate to make a porous shaped phase change material.

[0190] This approach involves a comprehensive comparison of phase change materials (PCMs) based on their phase change temperature range, structural stability, thermal conductivity, and supercooling. Laboratory tests further confirm that this composite PCM has good thermal conductivity, allowing for better integration with building envelope structures. In practice, differential scanning calorimetry (DSC) was used to measure the changes in specific heat capacity and thermal conductivity during the phase change process of the material samples. The DSC curves are shown below. Figure 2 As shown. Further, based on the definitions of equivalent heat capacity and equivalent thermal conductivity in Equations 2 and 3, the curves showing the variation of the equivalent heat capacity and equivalent thermal conductivity of the phase change material used in the model with temperature can be obtained, as shown below. Figure 3 , Figure 4 As shown.

[0191] This invention also discloses a numerical heat transfer model for the aforementioned underground building ventilation system. Its key feature is that the ventilation duct, along with the external phase change material and the soil layer (i.e., the area within the far boundary of the hot zone) within a certain thickness range (typically 4-6m), is considered as the computational domain of the system model. The physical structure of the computational domain includes an air layer, a phase change layer, and a soil layer from the inside out. The model is segmented along the airflow direction, with the air within each segment of the ventilation duct considered as a whole. The heat transfer of the three different material components is theoretically analyzed using the air heat balance equation, the phase change material heat transfer control equation, and the soil heat transfer control equation. The equivalent heat capacity method is used to handle the phase change heat transfer process, and the finite difference method is used to discretize the aforementioned heat transfer control equations. Then, the solution process is achieved using the CHASE pursuit method (a current algorithm for solving linear equations) based on the algebraic equations, resulting in the numerical calculation model.

[0192] Thus, this model fully considers the heat storage form and heat absorption / release effect of the phase change material layer located between the ventilation duct and the soil layer. It also simplifies the heat transfer process of the incoming air within the ventilation duct, simplifying the calculation process and improving computational efficiency while ensuring accurate results. The applicant compared test data from an experimental platform with the simulation results of this model, verifying its reliability and correctness. Furthermore, response surface methodology was used for multi-factor analysis, and based on this theoretical foundation, more accurate and reliable engineering design recommendations can be provided for ventilation systems applied in subway station fresh air ducts.

[0193] Specifically, establishing the numerical heat transfer model includes the following steps:

[0194] Step 1: Perform phase change layer heat transfer calculations. The calculations are based on the equivalent heat capacity method to analyze the phase change heat transfer process. This method treats the latent heat of phase change as a large sensible heat capacity within a certain temperature range encompassing the phase change temperature. Through this simplified equivalent treatment, the complex nonlinear phase change heat transfer process can be effectively simplified to a pure conduction heat transfer process, thus greatly reducing the computational difficulty. Based on the energy conservation equation and the equivalent heat capacity method, the heat transfer differential equation for the phase change material heat transfer process is as follows:

[0195] Energy conservation equation:

[0196] (Equation 1)

[0197] Equivalent heat capacity equation:

[0198] (Equation 2)

[0199] (Equation 3)

[0200] In the formula: —Equivalent heat capacity of phase change materials, ;

[0201] —Equivalent thermal conductivity of phase change materials ;

[0202] —Latent heat of phase change in phase change materials ;

[0203] —Specific heat capacity of phase change materials before melting ;

[0204] —Specific heat capacity of phase change materials after melting. ;

[0205] —The melting point temperature of phase change materials ;

[0206] —The melting point of phase change materials ;

[0207] —The thermal conductivity of the phase change material before melting. ;

[0208] —The thermal conductivity of the phase change material after melting. ;

[0209] T—Current temperature of the phase change material ;

[0210] Based on the definitions of equivalent heat capacity and equivalent thermal conductivity using the equivalent heat capacity method, the variation curves of the equivalent heat capacity and thermal conductivity of the shaped phase change material in this method within the phase change temperature range are as follows: Figure 3 , Figure 4 As shown, the equivalent heat capacity and thermal conductivity of the phase change material are linearized, and the actual calculation formula after the linearization is as follows:

[0211] (Equation 4)

[0212] The phase transition temperature range of the decanoic acid-palmitic acid binary composite phase change material is 28.16 ℃ to 32.68 ℃, therefore =28.16 ℃ =32.68 ℃. The equivalent specific heat capacity has a peak value in the phase transition temperature range. For ease of calculation, the temperature corresponding to this value is introduced as... =32.06 ℃;

[0213] Therefore, we obtain

[0214] (Equation 5);

[0215] Step 2: Establish the heat transfer control equations for the model;

[0216] First, establish the basic settings, setting the underground building ventilation system to be located in a dry soil layer without direct sunlight, and make the following settings for the system's heat transfer process:

[0217] ① Air is incompressible, the airflow velocity and state parameters are uniformly distributed across the same cross section, and the influence of changes in air humidity on heat transfer performance is ignored.

[0218] ② The phase change material is equivalent to an isotropic homogeneous solid medium, whose density and specific heat remain unchanged within the temperature range discussed in this method. The effect of heat convection on the heat transfer of the phase change material is ignored, and only heat conduction is considered.

[0219] ③ Soil is considered to be an isotropic homogeneous solid material with constant thermal properties. Due to the small axial temperature gradient, heat conduction along the axial direction is negligible.

[0220] ④ The contact between the various substances within the system is good, and the contact thermal resistance between materials is not considered;

[0221] ⑤ Buried pipelines typically use impermeable pipe materials and have limited lengths of heat exchange systems. Therefore, the latent heat exchange process of water evaporation and condensation inside the pipe is not considered. Only the sensible heat exchange between the air and the phase change material in the system is considered.

[0222] ⑥ Because the pipe wall thickness in actual engineering is relatively small when in contact with air, the thermal impact of the pipe material on the system is ignored;

[0223] Then, heat transfer control equations for different material layers are established separately; the physical structure of the model includes an air layer, a phase change layer, and a soil layer from the inside out; heat transfer control equations for the air layer, the phase change material layer, and the soil layer are established respectively based on the basic methods of heat transfer theory.

[0224] (1) Establish the heat transfer control equation for the air layer:

[0225] Based on the basic heat transfer equation, the general form of the governing equations for mass conservation, momentum conservation, and energy conservation that describe all flow and heat transfer phenomena is shown in Equation 6. It consists of four terms: from left to right, they are the unsteady-state term, the convection term, the diffusion term, and the source term.

[0226] (Equation 6)

[0227] Considering the high temperatures in summer, latent heat transfer is ignored. When sensible heat exchange occurs between the air and the wall, the air energy is only reflected in the air temperature, so the diffusion term can also be ignored. In this case, the air layer is considered as a whole, and its heat exchange process is divided into two parts: one part is the internal heat transfer of the air along the flow direction of the channel, and the other part is the convective heat exchange between the flowing air and the boundary of the phase change material layer. Based on Equation 6, the heat transfer control equation for the air layer is derived as follows:

[0228] (Equation 7)

[0229] In the formula: π — Pi (the mathematical constant of a circle);

[0230] —Equivalent radius of the tunnel, ;

[0231] —Air density, ;

[0232] —Specific heat capacity of air, ;

[0233] —Air temperature, °C;

[0234] —Airflow speed, ;

[0235] —The source term for heat and mass transfer from the phase change layer wall to the air via convection.

[0236] Among them, It can be expressed by the following formula:

[0237] (Equation 8)

[0238] In the formula:

[0239] —Temperature of the phase change layer immediately adjacent to the air passage, °C;

[0240] —The convective heat transfer coefficient of the air wall. ;

[0241] The convective heat transfer coefficient h can be calculated by the following formula:

[0242] (Equation 9)

[0243] In the formula:

[0244] —The thermal conductivity of air, ;

[0245] D – Equivalent diameter of the air tunnel ;

[0246] —Reynolds criterion number:

[0247] (Equation 10)

[0248] In the formula, —The dynamic viscosity of air, .

[0249] (2) Establish the heat transfer control equations for the phase change layer:

[0250] Similarly, according to Equation 6, and based on the fundamental assumption that the phase change material is an isotropic homogeneous solid medium, the convection term on the left side and the diffusion term on the right side of the governing equation are ignored during axial flow. Therefore, the basic heat and mass transfer equations for the phase change layer are:

[0251] (Equation 11)

[0252] In the formula:

[0253] —Calculate the base area of ​​the unit, in square meters;

[0254] —Density of phase change materials, ;

[0255] Specific heat capacity of phase change materials ;

[0256] —The phase change material in this unit is subject to heat exchange sources from other adjacent contact surface materials;

[0257] The source term S of the phase change layer energy control equation can be divided into three cases based on heat transfer. The first case is a single phase change layer adjacent to the air layer, where the heat exchange in the source term mainly involves convective heat exchange between the flowing air and the phase change layer, and heat conduction between adjacent phase change units. The second case is a single phase change layer inside the phase change layer, where the heat exchange mainly considers the heat conduction between the phase change materials on both sides. The third case is a single phase change layer adjacent to the soil layer, where the heat exchange mainly involves heat conduction with the phase change material on one side and heat conduction with the soil on the other side. Therefore, the source term S of the phase change layer heat transfer control equation is divided into the following three categories:

[0258] (Equation 12)

[0259] In the formula:

[0260] —Calculate the perimeter of the cell, in meters;

[0261] — Thermal conductivity of the rock mass ;

[0262] —The thermal conductivity of phase change materials, ;

[0263] T p1 —Temperature of the phase change material layer adjacent to the air, °C;

[0264] T p2 —Temperature of the phase change material adjacent to the soil, °C.

[0265] (3) Establish the soil heat transfer control equation:

[0266] Regarding heat conduction in the soil layer, based on the above assumptions, the cross-section of the ventilation tunnel is approximated as a cylinder. Ignoring the convection and diffusion terms in the soil heat transfer control equation, the left side of the equation represents the unsteady-state term of the soil itself, and the right side represents the heat conduction source term between the soil and adjacent soil in the radial direction. Therefore, the soil control equation for the internal retaining structure of the buried pipeline is:

[0267] (Equation 13)

[0268] in:

[0269] —Calculation radius of the soil layer, in meters;

[0270] — Soil thermal diffusivity, m 2 / s.

[0271] The formula for calculating the soil thermal diffusivity is as follows:

[0272] (Equation 14)

[0273] In the formula:

[0274] Soil density, ;

[0275] Specific heat capacity of soil ;

[0276] Step 3: Discretize the heat transfer control equations established in Step 2;

[0277] First, the computational domain of the system is divided into a two-dimensional mesh; a schematic diagram of the two-dimensional mesh division of the system's computational domain is shown below. Figure 5 .

[0278] In the axial direction, the computational domain of the system is defined by a thickness of... The thin sheet is discretely divided into Z / Each thin slice computational unit is represented by a subscript from 1 to z, indicating the specific axial position of each thin slice computational unit within the computational domain.

[0279] In the radial direction, each radial slice of the system is divided into three large control units:

[0280] ① The central region is the radius Air computing domain control unit;

[0281] ② The interlayer area is of length Phase change computational domain control unit;

[0282] ③ The outer region is the length The rock mass computational domain control unit;

[0283] In terms of time processing, use The time discrete unit is represented by the superscript n, which indicates the current calculation time, 0 is the initial time, and N is the calculation end time. When the time calculation step is one day, the unit of n is day; when the calculation time step is hours, the unit of n is hour.

[0284] Because the heat exchange medium in the system includes air, phase change material, and soil, the discrete analysis of the governing equations mainly considers the heat exchange between these three components. The model is cylindrical and axisymmetric along its centerline, so it is simplified to a two-dimensional model during discretization. Based on the above analysis, the discrete nodes of the control volumes for air, phase change material, and soil in the EAHE-PCHS system model are as follows: Figure 6 As shown in the node diagram, the system model is divided into z layers in the axial direction of airflow and j+4 layers in the radial direction from bottom to top, including j layers of soil; air, phase change material, and soil are distributed sequentially in the radial direction.

[0285] Because this scheme does not consider the specific heat distribution inside the air, the entire air section is divided into only one grid along the radial direction, and the grid length is used as... This indicates that the computational speed advantage of this calculation model lies in its speed.

[0286] The model established in this invention is mainly used for rapid calculations in engineering fields. The specific heat transfer within the phase change layer, such as mechanistic parameters like liquid phase fraction, is not the primary focus. To ensure calculation speed, considering the heat transfer of the phase change material and different contact surfaces, the entire phase change material is uniformly divided into three grid layers—PCM1, PCM2, and PCM3—radially. The first layer, PCM1, represents the outer boundary of the phase change material, adjacent to the air layer, and is used to represent the convective heat transfer between the phase change layer and the air layer. The second layer, PCM2, is the internal grid of the phase change layer, enclosed by the inner and outer phase change layers, and is used to represent the liquid phase fraction conversion within the phase change material. The third layer, PCM3, represents the inner boundary of the phase change layer, adjacent to the soil layer, and is used to represent the heat conduction between the phase change material and the soil. The total length of the phase change layer grid is... The grid is divided into three equal parts, and the unit phase transition grid is used. express, ;

[0287] For the final soil layer mesh, to facilitate the discretization of the subsequent heat transfer control equations, the first soil layer in the radial direction, adjacent to PCM3, is defined as the SS layer. Subsequent soil layer meshes are sequentially designated as S1 to S2. j-1To represent the second soil grid layer to the far boundary of the soil grid; the length of the entire soil layer is represented by... This indicates that the mesh is divided into j layers, and the cell mesh length is expressed as... To indicate;

[0288] Then, the heat transfer control equations established in step 2 are discretized;

[0289] For the discretization of the heat transfer control equations in the air layer, the unsteady-state terms are discretized using the classical first-order backward difference method, with a fully implicit scheme for time. The convective terms of the air layer heat transfer control equations, specifically the temperature derivative with respect to length, are discretized using a second-order upwind scheme. For the phase change layer, heat transfer control equations are established for different phase change layers based on the grid division, and the three equations are discretized. The unsteady-state terms in the heat balance equations at the soil wall are discretized using the first-order backward difference method, approximating the source terms as one-dimensional single-layer flat-wall heat conduction. Since the soil itself has stable thermal properties and relatively high thermal inertia, and given the uniform distribution of the soil layer grids and the small temperature difference between adjacent soil grids in this model, the central difference method is a relatively reasonable choice for discretization.

[0290] (1) Discretize the air layer heat transfer control equations:

[0291] (Equation 15)

[0292] For ease of subsequent calculations, Equation 15 can be combined and categorized, and written in the following form:

[0293] (Equation 16)

[0294] In the formula:

[0295] G—Buried pipeline ventilation mass flow rate, unit kg / h;

[0296] L a —Perimeter of the ventilation section of the buried pipeline, in meters;

[0297] During the entire discretization process, the initial calculation process requires the following approximation due to the lack of parameters; for the unsteady-state term in the air layer heat transfer control equation, when n=1, This term should be the air temperature value at time 0, which is uniformly replaced by the ambient air temperature in this method. For the convection term in the air layer heat transfer control equation, when i=1, since there are not enough parameters for the second-order backward difference, the first-order backward difference method is only used at this node. The discretized form of the air layer heat transfer control equation at this node is as follows:

[0298] (Equation 17)

[0299] Similarly, after merging, the form is as follows:

[0300] (Equation 18)

[0301] (2) Discretize the heat transfer control equations of the phase change layer:

[0302] To ensure consistency in model application, the following settings are made for the phase change layer material in the model beforehand: the density of the phase change material in this model is determined to be a constant value; the shape-fixed phase change material selected in this model is uniformly encapsulated and is not affected by gravity to undergo deformation.

[0303] According to the phase change layer heat transfer control equations 11, 12 and... Figure 6 Equations 11 and 12 are discretized for three different heat exchange scenarios; in the unsteady-state term of equation 11, the specific heat capacity and thermal conductivity depend on the temperature range of the material, and are sequentially represented by C according to the mesh. p1 C p2 C p3 and The specific heat capacity and thermal conductivity of different phase change layers are represented by the specific parameters determined by the properties of the phase change material itself (see Table 4); where A represents the bottom area of ​​the current calculation unit. Since the geometry of this model is a concentric cylinder, the expression for the bottom area of ​​each grid unit is also different. The specific expression is shown in Equations 19-24 below.

[0304] Equation 12 is the source term of the equation. Due to the different contact and interaction objects, according to the current meshing method of the phase change layer, it corresponds to the source term expressions of the PCM1, PCM2, and PCM3 phase change material layers respectively. Therefore, by combining Equations 11 and 12, the phase change material is divided into three different heat transfer control equations according to the current meshing method to accurately describe its heat exchange situation, and mathematical discretization is performed. The results are as follows:

[0305] ① Phase transition first layer PCM1 layer

[0306] Heat transfer control equation:

[0307] (Equation 19)

[0308] Discrete equations:

[0309] (Equation 20)

[0310] ② Phase transition second layer PCM2 layer

[0311] Heat transfer control equation:

[0312] (Equation 21)

[0313] Discrete equations:

[0314] (Equation 22)

[0315] ③ Phase transition third layer PCM3 layer

[0316] Heat transfer control equation:

[0317] (Equation 23)

[0318] Discrete equations:

[0319] (Equation 24)

[0320] In the formula:

[0321] —The base area of ​​the i-th phase transition computation unit, m 2 ;

[0322] —The perimeter of the i-th phase transition calculation unit, in meters;

[0323] —Specific heat capacity of the i-th phase change material ;

[0324] —The thermal conductivity of phase change materials, ;

[0325] —Thickness of a single-layer phase change material, in meters;

[0326] (3) Discretization of the heat transfer control equations of the SS layer at the wall

[0327] To distinguish it from the stable heat conduction within the soil layer, this paper separately divides the soil layer near the phase change material (PCM) wall into an SS layer during mesh generation. Because the various thermophysical parameters of the PCM change material change drastically with temperature fluctuations, heat exchange in the soil layer near the PCM wall is unstable. For the sake of consistency in the discrete difference scheme, this section will discuss the heat balance equations for the soil wall layer separately.

[0328] Similarly, according to the conservation equation 6 of the heat transfer control equation, since the soil is a solid, the flow and diffusion terms in the heat transfer control equation are ignored. Therefore, similar to the heat transfer control equation of the phase change layer mentioned above, the heat transfer control equation of the SS layer consists of the unsteady term of the soil itself and the boundary heat exchange source term in contact with it. The heat exchange with the soil in the SS layer is mainly caused by the heat conduction of the phase change layer of P3 and the soil of S1.

[0329] Therefore, the heat transfer control equation for the soil SS layer is as follows:

[0330] (Equation 25)

[0331] The unsteady-state terms of the heat transfer control equation 25 above are discretized using the first-order backward difference method. The source term can be approximated as a one-dimensional single-layer flat-wall heat conduction. The discretization results are as follows:

[0332] (Equation 26)

[0333] (4) Discretization of the heat transfer control equation of the soil layer

[0334] Regarding the soil heat transfer control equations established in step 2, this section will discuss how to discretize the soil flow equations for the unit thin sheet. Because the soil itself has stable thermal properties and relatively high thermal inertia, and given the uniform distribution of the soil layer grids and the small temperature difference between adjacent soil grids in this model, the central difference method is a relatively reasonable choice for discretization.

[0335] Discretizing Equation 13 using the finite difference method yields...

[0336] (Equation 27)

[0337] The formula introduces Fo—the Fourier number—as a dimensionless quantity describing unsteady-state heat conduction and molecular diffusion. The expression is:

[0338] (Equation 28)

[0339] Step 4: Calculation and Solution Methods and Model Establishment

[0340] Based on the mesh generation and discrete equation results in step 3, the internal heat transfer problem of the system is analyzed and calculated. This model adopts a time-by-time calculation model, and the calculation and solution process is mainly carried out in the following three steps.

[0341] The first step is to initialize and define various calculation parameters, including the geometric dimensions of the buried pipeline, the thermal properties of air, phase change material, and soil, as well as the inlet flow rate and inlet wind speed.

[0342] The second step is boundary condition assignment and mesh generation. Boundary conditions include the outdoor air input parameters at the system inlet and the temperature distribution of the soil at the far boundary. The air input parameters at the inlet are obtained based on typical meteorological data of the project site. The soil temperature distribution at the far boundary is determined based on the temperature disturbance depth of the soil at the project site to determine the model's far boundary range and axial temperature distribution. The outdoor air input parameters at the inlet and the soil temperature distribution at the far boundary are compiled into a "boundary input file" and added to the model calculation folder in chronological order. Then, the model is meshed and verified. The reliability of the time step is determined and verified through pre-run.

[0343] The third step is to proceed with numerical calculations. Each horizontal row in the radial direction is considered a calculation slice. Starting from the first slice position (i=1) at the air inlet of the system, the temperature parameters and heat flux density components of the air, phase change material, and soil in each grid slice are calculated sequentially along the axial direction. After the calculation of the last slice at the end of the air channel is completed, the program moves to the next time step and starts iterating again from the air channel inlet to calculate the parameters of the previous round. When all time steps are completed, the program calculation ends.

[0344] When calculating the interior of each thin sheet, the basic principle is to establish a linear equation system using the heat transfer control equation of the air layer, the heat transfer control equation of the phase change material phase change layer, and the heat balance equation inside the soil. After mathematical processing of the above discrete equations, the linear equation system is constructed into a tridiagonal matrix that is easy to calculate, as shown in Equation 29.

[0345] (Equation 29)

[0346] This allows us to further obtain the system of linear equations at each level:

[0347]

[0348] (Formula 30)

[0349] The linear equations in Equation 30 above constitute the numerical heat transfer model of the underground building ventilation system. During calculation, the linear equations form a tridiagonal system based on three cases: the air wall heat balance equation, the phase change material heat transfer control equation, and the soil heat transfer control equation. Therefore, when calculating the model, each grid on the radial sheet can be treated as an unknown quantity, resulting in a tridiagonal matrix with j+4 rows. The solution can then be completed using triangular decomposition.

[0350] Therefore, the core of the model calculation in this invention is solving the tridiagonal matrix. Currently, the CHASE chasing method is a fast and effective way to solve linear equation systems of tridiagonal, pentagonal, and other matrices. In implementation, the applicant further developed and wrote a calculation model of the phase change system based on the above numerical heat transfer model using a scripting language. The logical operation flowchart of the calculation model program is as follows: Figure 7 This calculation model can quickly calculate the optimal results of relevant system design parameters, such as calculating the air state parameters after cooling treatment.

[0351] In addition, to better verify the feasibility and accuracy of the present invention during implementation, the applicant conducted the following experimental verification. The specific process is as follows.

[0352] (1) Introduction to the experimental platform: The results calculated by the numerical calculation program established in step 4 are compared with the test results of the actual system operation. To ensure the reliability of the established numerical model, the applicant built a small-sized experimental platform in the laboratory, and then compared the actual test results with the numerical model calculation results of the present invention to verify the accuracy and reliability of the model. The materials used in this experimental platform include air for ventilation in the pipe, wet sand to simulate the actual soil environment, decanoic acid-palmitic acid binary composite phase change material prepared in a 97:3 ratio, and expanded graphite substrate accounting for 10% of the core material mass.

[0353] During the experiment, the phase change material (PCM) experimental section was the core research object of this experimental setup. It was wrapped with 60mm thick insulation cotton to simulate the actual conditions of buried pipelines, ensuring that the heat exchanger's far boundary remained insulated from the outside environment during the experiment. The PCM experimental section consisted of three horizontally arranged concentric circular tubes, sealed with baffles at both ends. The entire PCM experimental section was divided into three regions by these three concentric circles. Region I, the central region, was a hollow annular airflow zone, i.e., an air channel; Region II was the PCM zone, encapsulating a shaped PCM material (decanoic acid-palmitic acid binary composite shaped PCM material), which was also the core energy-saving heat exchange region of this experiment; Region III was a simulated soil region, where wet sand was used to simulate the soil environment, referred to as the wet sand zone. The entire Region III was filled with dense wet sand, its main function being to transfer heat from the PCM zone to the far boundary.

[0354] This experiment only conducted phased testing and analysis. The impact of annual cycle disturbances is not considered; penetration calculation and analysis are based solely on the daily cycle. Therefore, the disturbance period... The time was selected as 3600 × 24 = 86400 seconds, and other parameters are shown in Table 1. The specific geometric dimensions of the phase change material section of this experimental setup were determined as shown in Table 2 below.

[0355]

[0356]

[0357] (2) Comparison between model calculation results and experimental test results

[0358] The numerical model calculation process strictly follows the calculation and solution steps in step 4. First, based on the geometric dimensions of the experimental platform and the thermophysical parameters of air, phase change material, and wet sand, initialization is performed. The ventilation velocity in the input parameters is based on the test average value of 2.02 m / s, and the hourly air temperature at the inlet is based on the T data recorded by the Agilent 34972A data acquisition instrument. in The cross-sectional temperature data is used as the standard. Then, the grid and time step are verified according to the selected parameters. After verification, numerical simulation calculations are performed.

[0359] The model verification of this invention primarily studies the air temperature at the air outlet of the air passage. The temperature distribution within the air passage is a key indicator determining the accuracy of the EAHE-PCHS model. This invention will be based on the outlet temperature (T). out Cross-sectional temperature data are used to determine the accuracy of the EAHE-PCHS model.

[0360] To evaluate the consistency between model predictions and experimental measurements, two methods were used in the validation process: graphical comparison validation and numerical evaluation metrics. A review of the literature revealed commonly used error evaluation metrics including: maximum absolute error (ME), mean absolute error (MAE), and relative error of maximum absolute value (REMA). Their calculation equations are as follows:

[0361] (Equation 31)

[0362] (Equation 32)

[0363] (Equation 33)

[0364] in The sample size in this experiment is [number]. 3840; For the purpose of testing the temperature, To simulate and calculate temperature, For the selected data sample, .

[0365] This invention verifies the air channel outlet temperature, such as... Figure 9 As shown, Figure 9 This diagram illustrates the comparison between experimental and simulated temperatures. Error analysis results show that the maximum absolute error in the outlet temperature occurred at hour 1.26, at which point ME = 0.8 ℃. The mean absolute error (MAE) over the entire experimental period was 0.26 ℃, and the maximum relative absolute error (REMA) was 3.01%. Therefore, it can be considered that the calculation process of the EAHE-PCHS numerical calculation model proposed in this invention is consistent with the actual situation, and the calculation results are accurate and reliable. This model can be used to predict and analyze the thermal performance of the system in subsequent practical engineering research.

[0366] The above-mentioned test examples verified the accuracy of the model in this invention. The applicant further analyzed and evaluated the expected performance of the ventilation system and numerical heat transfer model of this invention when applied to actual subway stations, providing certain references and insights for practical engineering.

[0367] Through research and analysis, a representative standard subway station in Chongqing was selected. For the convenience of subsequent discussion, the station was uniformly named AA. The ventilation system of the present invention (abbreviated as EHAE-PCHS, i.e., the ventilation system containing the phase change material layer of the present invention) was applied to the fresh air shaft of the subway station, and the actual effect of EHAE-PCHS applied in the station was analyzed using the model developed in the present invention.

[0368] (1) Material thermophysical parameters: The materials involved in this invention mainly include the thermophysical properties of air, soil, and phase change materials. Air is stable, and its thermophysical parameters can be directly obtained from publicly available data. As for soil materials, as a mixture, its composition is complex and variable, and its thermophysical properties are not uniform. The thermophysical parameters of phase change materials are obtained by selecting manufacturers for testing after sample preparation. The thermophysical parameters of air and soil are shown in Table 3.

[0369]

[0370]

[0371] (2) Calculation domain temperature parameters: After determining the material thermal property parameters, the model in this study also needs to determine the hourly input temperature parameters of the air, as well as the original ground temperature distribution data of the underground space required during the model initialization process, in order to set the initial soil temperature.

[0372] ① Air Input Temperature: For the air temperature parameter required at the system inlet of this model, the hourly outdoor dry-bulb temperature of a typical meteorological year in this region is directly adopted. This paper uses the hour as the smallest unit of division, and statistically analyzes the outdoor dry-bulb temperature for 93 days and 2232 hours from June 15th to September 15th. The data is then recorded and saved daily and hourly in "xlsx" file format and placed in the root directory of the model calculation so that the data series can be directly called by the code during calculation.

[0373] ② Ground temperature distribution: In order to accurately obtain the ground temperature distribution at this location, the applicant conducted on-site tests in Banan District, Chongqing. In this invention, measured data is used in conjunction with existing theoretical ground temperature distribution models to predict the ground temperature distribution during the calculation process of this model.

[0374] (3) Computational domain geometry, mesh generation, and time step: After determining the material thermophysical parameters and the temperature field of the computational domain, it is also necessary to determine the overall geometry of the computational model and to mesh the time step and the overall geometry of the model.

[0375]

[0376] (4) Cooling performance analysis of EAHE-PCHS fresh air system

[0377] Based on the established EAHE-PCHS model, the applicant has created a control model without phase change material to simulate the heat exchange of conventional fresh air channels. This model is called EAHE-Normal (i.e., a ventilation system without a phase change material layer). The phase change layer of the EAHE-PCHS system is replaced with soil material, while maintaining consistency with the EAHE-PCHS model of AA station in terms of structural dimensions, other thermophysical parameters, and input parameters.

[0378] The applicant selected nine consecutive days (July 24 – August 1) from a typical summer weather month to compare the inlet and outlet air temperatures and cooling effects of the EAHE-PCHS and EAHE-Normal systems. Figures 10-12 As shown, the EAHE-PCHS system has a better cooling capacity for outdoor air compared to the EAHE-Normal system. The EAHE-PCHS system also outperforms the EAHE-Normal system in terms of total cooling capacity and energy efficiency ratio (EER). The EAHE-PCHS fresh air system achieves an EER of 10⁻¹² on a typical summer day. Figure 10 This diagram illustrates the comparison of air temperature between ventilation systems containing and without phase change material layers in Chongqing Metro stations, based on a survey and analysis. Figure 11 This diagram illustrates the comparison of cooling energy efficiency ratios of ventilation systems with and without phase change material layers in Chongqing Metro stations, based on a survey and analysis. Figure 12 This diagram illustrates the comparison of the average daily cooling capacity of ventilation systems with and without phase change material layers in Chongqing Metro stations, based on a survey and analysis.

[0379] Multifactor analysis of the impact on the performance of the EAHE-PCHS system

[0380] In the EAHE-PCHS system of a subway station, analyzing individual factor indicators alone cannot fully reflect the interrelationships between these factors. To better analyze the impact of the coupling relationships between these factors on the heat transfer performance of the EAHE-PCHS system, this invention utilizes a response surface model (RSM) to optimize the design of the EAHE-PCHS system. Before conducting the BBD response surface model experiment on the EAHE-PCHS system, it is necessary to determine the influencing factors and their levels during the experiment, as well as the response values ​​reflecting the experimental results. Three factors were selected as influencing factors for the BBD response surface model: A. Phase change energy storage body length, B. Radial thickness of the phase change material, and C. Air velocity within the ventilation duct.

[0381] Based on the response results, multiple linear regression and surface fitting were performed on the simulation results of this BBD response surface experiment using Design Expert 13.0 software to obtain the system outlet mean absolute temperature difference. The response value of the energy storage system with respect to three factors—A. length of the phase change energy storage body, B. radial thickness of the phase change material, and C. air velocity within the channel—is fitted to the following multivariate quadratic regression response surface equation:

[0382]

[0383] (Equation 34)

[0384] Therefore, this response surface model can be used to analyze the interaction between various factors and provide suggestions for the design of the EAHE-PCHS fresh air system.

[0385] The applicant further discloses the design reference analysis of the EAHE-PCHS of the present invention for subway fresh air systems.

[0386] The factors affecting the EAHE-PCHS of the subway station fresh air system discussed in this invention are A. the total length of the phase change energy storage body, B. the thickness of the phase change material, and C. the air velocity in the channel.

[0387] In practical design applications, the values ​​of fresh air volume and velocity vary in different subway stations. Based on the design air volume and geometric duct conditions of the fresh air system in different subway stations, the air velocity of factor C can be calculated. After determining the value of the air velocity in the air passage of factor C, the focus of the research is on how to combine factors A and B to more effectively improve the thermal performance of the EAHE-PCHS system.

[0388] Multifactor analysis results show that although increasing the values ​​of factors A and B can independently enhance the thermal effect of the EAHE-PCHS system, the response surface analysis coding factor equation results show that factor A has a greater impact on the "exit mean absolute temperature difference". The number of influence factors for factor B is 0.33, which is greater than that for factor B. The influence factor is 0.23, so it is reasonable to believe that the total length parameter of the phase change heat storage body should be given priority in the design process of the EAHE-PCHS system.

[0389] In conclusion, in order to make EAHE-PCHS a reasonable application to different subway station fresh air systems, this paper suggests that we should first determine factor C based on the engineering conditions of the station, then prioritize the impact of factor A on the EAHE-PCHS system, and finally adjust the level of factor B to achieve the target cooling requirements.

[0390] Based on the design recommendations of EAHE-PCHS for different subway stations, and following the design concept of the EAHE-PCHS system, this paper uses the calculated indoor air temperature of 29.0℃ in summer as the evaluation index. Using the geometric dimensions of the fresh air shaft section of station AA as a basis, it calculates the design value combinations of factors A and B under different fresh air shaft lengths (0~100 m) and air velocity within the shaft (1~4 m / s). Specific calculation results are as follows... Figure 8 As shown in the table, the portion below the stepped dividing line in the figure indicates that this combination of conditions can meet the environmental control requirements within the station.

Claims

1. A method for constructing a numerical heat transfer model of an underground building ventilation system, wherein the underground building ventilation system includes a ventilation duct, the ventilation duct being formed within a buried pipe embedded in the underground soil, the ventilation duct inlet being located at the surface, and the outlet being located within the underground building, characterized in that... The outer surface of the ventilation duct is covered with a layer of phase change material of equal thickness. The phase change material layer is filled with solid-liquid phase change material. The outer shell of the phase change material layer forms an enclosure structure and is buried and covered in the underground soil. The underground structure is a subway station, and the ventilation duct entrance is the subway station's fresh air pavilion. The phase change material layer uses a binary composite phase change material of decanoic acid and palmitic acid with a mass ratio of 97:3 as the phase change heat storage core material, and uses expanded graphite accounting for 10% of the core material mass as the substrate to prepare a porous shaped phase change material. The numerical heat transfer model of the underground building ventilation system considers the ventilation duct, the external phase change material, and the soil layer within a certain thickness as the computational domain of the system model. The physical structure of the computational domain of the model includes an air layer, a phase change layer, and a soil layer from the inside out. The model is divided into segments along the airflow direction, and the air in each segment of the ventilation duct is considered as a whole. The heat transfer of the three different material parts is theoretically analyzed using the air heat balance equation, the phase change material heat transfer control equation, and the soil heat transfer control equation. The equivalent heat capacity method is used to handle the phase change heat transfer process, and the finite difference method is used to discretize the above heat transfer control equation set. Then, the CHASE pursuit method based on the algebraic equation set is used to realize the solution process, and the numerical calculation model is obtained. The numerical heat transfer model is established by the following steps: Step 1: Perform heat transfer calculations for the phase change layer. The calculations are based on the equivalent heat capacity method to analyze the phase change heat transfer process. According to the energy conservation equation and the equivalent heat capacity method, the heat transfer differential equation for the phase change material heat transfer process is as follows: Energy conservation equation: (Equation 1) Equivalent heat capacity equation: (Equation 2) (Equation 3) In the formula: —Equivalent heat capacity of phase change materials, ; —Equivalent thermal conductivity of phase change materials ; —Latent heat of phase change in phase change materials ; —Specific heat capacity of phase change materials before melting ; —Specific heat capacity of phase change materials after melting. ; —The melting point temperature of phase change materials ; —The melting point of phase change materials ; —The thermal conductivity of the phase change material before melting. ; —The thermal conductivity of the phase change material after melting. ; T—Current temperature of the phase change material. ; Based on the definitions of equivalent heat capacity and equivalent thermal conductivity using the equivalent heat capacity method, the equivalent heat capacity and thermal conductivity of phase change materials are linearized. The resulting calculation formulas are as follows: (Equation 4) The phase transition temperature range of the decanoic acid-palmitic acid binary composite phase change material is 28.16 ℃ to 32.68 ℃, therefore =28.16℃ =32.68 ℃. The equivalent specific heat capacity has a peak value in the phase transition temperature range. For ease of calculation, the temperature corresponding to this value is introduced as... =32.06 ℃; Therefore, we obtain (Equation 5); Step 2: Establish the heat transfer control equations for the model; First, establish the basic settings, setting the underground building ventilation system to be located in a dry soil layer without direct sunlight, and make the following settings for the system's heat transfer process: ① Air is incompressible, the airflow velocity and state parameters are uniformly distributed across the same cross section, and the influence of changes in air humidity on heat transfer performance is ignored. ② The phase change material is equivalent to an isotropic homogeneous solid medium, whose density and specific heat remain unchanged within the temperature range discussed in this method. The effect of heat convection on the heat transfer of the phase change material is ignored, and only heat conduction is considered. ③ Soil is considered to be an isotropic homogeneous solid material with constant thermal properties. Due to the small axial temperature gradient, heat conduction along the axial direction is negligible. ④ The contact between the various substances within the system is good, and the contact thermal resistance between materials is not considered; ⑤ Buried pipelines usually use impermeable pipe materials and the length of the heat exchange system is limited. Therefore, the latent heat exchange process of water evaporation and condensation inside the pipe is not considered. Only the sensible heat exchange between the air and the phase change material in the system is considered. ⑥ Because the pipe wall thickness in actual engineering is relatively small when in contact with air, the thermal impact of the pipe material on the system is ignored; Then, establish the heat transfer control equations for different material layers; (1) Establish the heat transfer control equation for the air layer: According to the basic heat transfer equation, the general form of the governing equations for mass conservation, momentum conservation, and energy conservation that describe all flow and heat transfer phenomena is shown in Equation 6, which consists of four terms: from left to right, they are the unsteady-state term, convection term, diffusion term, and source term. (Equation 6) Based on Equation 6, the air layer heat transfer control equation is derived as follows: (Equation 7) In the formula: π — Pi (the mathematical constant of a circle); —Equivalent radius of the tunnel, ; —Air density, ; —Specific heat capacity of air, ; —Air temperature, °C; —Airflow speed, ; —The source term for heat and mass transfer from the phase change layer wall to the air convection. Among them, It can be expressed by the following formula: (Equation 8) In the formula: —Temperature of the phase change layer immediately adjacent to the air passage, °C; —The convective heat transfer coefficient of the air wall. ; The convective heat transfer coefficient h can be calculated by the following formula: (Equation 9) In the formula: —The thermal conductivity of air, ; D – Equivalent diameter of the air tunnel ; —Reynolds criterion number: (Equation 10) In the formula, —The dynamic viscosity of air, ; (2) Establish the heat transfer control equations for the phase change layer: Similarly, according to Equation 6, and based on the fundamental assumption that the phase change material is an isotropic homogeneous solid medium, the convection term on the left side and the diffusion term on the right side of the governing equation are ignored during axial flow; thus, the basic heat and mass transfer equations for the phase change layer are obtained as follows: (Equation 11) In the formula: —Calculate the base area of ​​the unit, in square meters; —Density of phase change materials, ; Specific heat capacity of phase change materials ; —The phase change material in this unit is subject to heat exchange sources from other adjacent contact surface materials; The source term S of the phase change layer energy control equation can be divided into three cases based on heat transfer. The first case is a single phase change layer adjacent to the air layer, where the heat exchange in the source term mainly involves convective heat exchange between the flowing air and the phase change layer, and heat conduction between adjacent phase change units. The second case is a single phase change layer inside the phase change layer, where the heat exchange mainly considers the heat conduction between the phase change materials on both sides. The third case is a single phase change layer adjacent to the soil layer, where the heat exchange mainly involves heat conduction with the phase change material on one side and heat conduction with the soil on the other side. Therefore, the source term S of the phase change layer heat transfer control equation is divided into the following three categories: (Equation 12) In the formula: —Calculate the perimeter of the cell, in meters; — Thermal conductivity of the rock mass ; —The thermal conductivity of phase change materials, ; T p1 —Temperature of the phase change material layer adjacent to the air, °C; T p2 —Temperature of the phase change material adjacent to the soil, °C; (3) Establish the soil heat transfer control equation: Regarding heat conduction in the soil layer, based on the above assumptions, the cross-section of the ventilation tunnel is approximated as a cylinder. Ignoring the convection and diffusion terms in the soil heat transfer control equation, the left side of the equation represents the unsteady-state term of the soil itself, and the right side represents the heat conduction source term between the soil and adjacent soil in the radial direction. Therefore, the soil control equation for the internal retaining structure of the buried pipeline is: (Equation 13) in: —Calculation radius of the soil layer, in meters; — Soil thermal diffusivity, m 2 / s; The formula for calculating the soil thermal diffusivity is as follows: (Equation 14) In the formula: Soil density, ; Specific heat capacity of soil ; Step 3: Discretize the heat transfer control equations established in Step 2; First, the computational domain of the system is divided into a two-dimensional mesh; In the axial direction, the computational domain of the system is defined by a thickness of... The thin sheet is discretely divided into Z / Each thin slice computational unit is represented by a subscript from 1 to z, indicating the specific axial position of each thin slice computational unit within the computational domain. In the radial direction, each radial slice of the system is divided into three large control units: ①The central region is the radius Air computing domain control unit; ②The interlayer area is of length Phase change computational domain control unit; ③ The outer region is the length The rock mass computational domain control unit; In terms of time processing, use The time discrete unit is represented by the superscript n, which indicates the current calculation time, 0 is the initial time, and N is the calculation end time. When the time calculation step is one day, the unit of n is day; when the calculation time step is hours, the unit of n is hour. The system model is divided into z layers along the axial direction of airflow and j+4 layers along the radial direction from bottom to top, including j layers of soil. Air, phase change material, and soil are distributed sequentially in the radial direction. The entire air section is divided into only one grid along the radial direction, with a grid length of [missing information]. express; The entire phase change material (PCM) was uniformly divided radially into three grid layers: PCM1, PCM2, and PCM3. The first layer, PCM1, forms the outer boundary of the PCM, adjacent to the air layer, and is used to represent the convective heat transfer between the PCM and air layers. The second layer, PCM2, forms the inner grid of the PCM, enclosed by the inner and outer PCM layers, and is used to represent the liquid phase conversion within the PCM. The third layer, PCM3, forms the inner boundary of the PCM, adjacent to the soil layer, and is used to represent the heat conduction between the PCM and the soil. The total length of the PCM grid is... The grid is divided into three equal parts, and the unit phase transition grid is used. express, ; The final soil layer mesh defines the first soil layer in the radial direction, which is the phase change material immediately adjacent to PCM3, as the SS layer. Subsequent soil layer meshes are designated as S1 to S2. j-1 To represent the second soil grid layer to the far boundary of the soil grid; the length of the entire soil layer is represented by... This indicates that the mesh is divided into j layers, and the cell mesh length is expressed as... To indicate; Then, the heat transfer control equations established in step 2 are discretized; For the discretization of the heat transfer control equations in the air layer, the unsteady-state terms are discretized using the classical first-order backward difference method, with a fully implicit scheme for time. The convective terms of the air layer heat transfer control equations, specifically the temperature-length derivative, are discretized using a second-order upwind scheme. For the phase change layer, heat transfer control equations are established for different phase change layers based on the mesh division, and the three equations are discretized. The unsteady-state terms in the heat balance equations at the soil wall are discretized using the first-order backward difference method, with the source terms approximated as one-dimensional single-layer flat-wall heat conduction. (1) Discretize the air layer heat transfer control equations: (Equation 15) For ease of subsequent calculations, Equation 15 can be combined and categorized, and written in the following form: (Equation 16) In the formula: G —Buried pipeline ventilation mass flow rate, unit kg / h; L a —Perimeter of the ventilation section of the buried pipeline, in meters; Throughout the discretization process, the following approximations are made; for the unsteady-state terms in the air layer heat transfer control equations, when n=1, This term should be the air temperature value at time 0, which is uniformly replaced by the ambient air temperature in this method; for the convection term in the air layer heat transfer control equation, when i=1, the first-order backward difference method is used at this node, and the discretized form of the air layer heat transfer control equation at this node is as follows: (Equation 17) Similarly, after merging, the form is as follows: (Equation 18) (2) Discretize the heat transfer control equations of the phase change layer: First, the following settings are made for the phase change layer material of the model: the density of the phase change material in this model is determined to be a constant value; the shape-fixed phase change material selected in this model is uniformly encapsulated and does not deform under the influence of gravity; Based on the phase change layer heat transfer control equation, equations 11 and 12 are discretized for three different heat exchange scenarios; in the unsteady-state term of equation 11, the specific heat capacity and thermal conductivity depend on the temperature range of the material, and are sequentially represented by C according to the mesh. p1 C p2 C p3 and The specific heat capacity and thermal conductivity of different phase change layers are represented by the specific parameters determined by the properties of the phase change material itself. In the formula, A represents the bottom area of ​​the current calculation unit. Since the geometry of this model is a concentric cylinder, the expression of the bottom area of ​​each grid unit is also different. The specific expression is shown in Equations 19-24. By combining Equations 11 and 12, the phase change material is divided into three different heat transfer control equations according to the current mesh generation method to accurately describe its heat exchange, and mathematical discretization is performed; the results are as follows: ① Phase transition first layer PCM1 layer Heat transfer control equation: (Equation 19) Discrete equations: (Equation 20) ② Phase transition second layer PCM2 layer Heat transfer control equation: (Equation 21) Discrete equations: (Equation 22) ③ Phase transition third layer PCM3 layer Heat transfer control equation: (Equation 23) Discrete equations: (Equation 24) In the formula: —The base area of ​​the i-th phase transition computation unit, m 2 ; —The perimeter of the i-th phase transition calculation unit, in meters; —Specific heat capacity of the i-th phase change material ; —The thermal conductivity of phase change materials, ; —Thickness of a single-layer phase change material, in meters; (3) Discretization of the heat transfer control equations of the SS layer at the wall Similarly, according to the conservation equation 6 of the heat transfer control equation, since the soil is a solid, the flow and diffusion terms in the heat transfer control equation are ignored. The heat transfer control equation of the SS layer consists of the unsteady terms of the soil itself and the boundary heat exchange source terms in contact with it. The heat exchange with the soil in the SS layer is mainly caused by the thermal conductivity of the phase change layer of P3 and the soil of S1. Therefore, the heat transfer control equation for the soil SS layer is as follows: (Equation 25) The unsteady-state terms of the heat transfer control equation 25 above are discretized using the first-order backward difference method. The source term can be approximated as a one-dimensional single-layer flat-wall heat conduction. The discretization results are as follows: (Equation 26) (4) Discretization of the heat transfer control equation of the soil layer Discretizing Equation 13 using the finite difference method yields... (Equation 27) Introduced in the formula Fo —The Fourier number is a dimensionless quantity used to describe unsteady-state heat conduction and molecular diffusion. Its expression is: (Equation 28) Step 4: Calculation and Solution Methods and Model Establishment Based on the mesh generation and discrete equation results in step 3, the internal heat transfer problem of the system is analyzed and calculated. This model adopts a time-by-time calculation model, and the calculation and solution process is mainly carried out in the following three steps. The first step is to initialize and define various calculation parameters, including the geometric dimensions of the buried pipeline, the thermal properties of air, phase change material, and soil, as well as the inlet flow rate and inlet wind speed. The second step is boundary condition assignment and mesh generation. Boundary conditions include the outdoor air input parameters at the system inlet and the temperature distribution of the soil at the far boundary. The air input parameters at the inlet are obtained based on typical meteorological data of the project site. The soil temperature distribution at the far boundary is determined based on the soil temperature disturbance depth at the project site to determine the model's far boundary range and axial temperature distribution. The outdoor air input parameters at the inlet and the soil temperature distribution at the far boundary are compiled into a "boundary input file" and added to the model calculation folder in chronological order. Then, the model is meshed and validated. The reliability of the time step is determined and verified through pre-run. The third step is to proceed with numerical calculations. Each horizontal row in the radial direction is considered a calculation slice. Starting from the first slice position (i=1) at the air inlet of the system, the temperature parameters and heat flux density components of the air, phase change material, and soil in each grid slice are calculated sequentially along the axial direction. After the calculation of the last slice at the end of the air channel is completed, the program moves to the next time step and starts iterating again from the air channel inlet to calculate the parameters of the previous round. When all time steps are completed, the program calculation ends. When calculating the interior of each thin sheet, the basic principle is to establish a linear equation system using the heat transfer control equation of the air layer, the heat transfer control equation of the phase change material phase change layer, and the heat balance equation inside the soil. After mathematical processing of the above discrete equations, the linear equation system is constructed into a tridiagonal matrix that is easy to calculate, and the basic form is shown in Equation 29. (Equation 29) This allows us to further obtain the system of linear equations at each level: (Equation 30) The linear equations in Equation 30 above constitute the numerical heat transfer model of the underground building ventilation system.

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