Concrete thermal insulation layer thickness calculation method and system based on heat exchange coefficient

Abstract

The invention relates to a concrete thermal insulation layer thickness calculation method and system based on a heat exchange coefficient. The calculation method comprises the steps that geometric parameters of a target wall, thermal physical parameters of concrete and a preset cooling rate are obtained; generating a temperature-time function of the central point of the wall through the temperature field analysis model, and performing time derivation to obtain a cooling rate function; solving a heat exchange coefficient in the cooling rate function by taking a preset cooling rate as a constraint condition; obtaining the maximum temperature difference between the center point of the concrete wall and the environment, querying the working condition database, outputting the maximum allowable heat flux density, and calculating the minimum total heat resistance in combination with the maximum temperature difference; calculating surface convection thermal resistance according to the heat exchange coefficient; subtracting the surface convection heat resistance from the minimum total heat resistance to obtain the heat conduction heat resistance of the thermal insulation layer; and calculating the heat-insulating layer design thickness corresponding to the heat-conducting resistance of the heat-insulating layer by combining the heat-conducting coefficient and the climate correction coefficient of the heat-insulating material. The early-stage crack resistance and the long-term durability of the concrete structure are improved.

Description

Technical Field

[0001] This application relates to the field of building engineering technology, and in particular to a method and system for calculating the thickness of concrete insulation layer based on heat exchange coefficient. Background Technology

[0002] With the continuous expansion of urban underground space development, concrete structures such as underground commercial complexes, rail transit tunnels, and utility tunnels are developing towards deeper and larger volumes. Extensive on-site monitoring data shows that the internal hydration reaction of concrete structures generates a significant temperature rise in the early stages (1-5 days) after pouring. Subsequently, due to heat dissipation, a "sharp rise and fall" temperature curve is formed. Especially in the 2nd-3rd day before the formwork is removed, the temperature difference between the center and surface of the wall can reach 20-25℃. This drastic temperature change significantly increases the risk of non-load-bearing cracks. Engineering practice shows that the tensile stress formed by the combined effect of early temperature shrinkage and autogenous shrinkage often exceeds the tensile strength of concrete, directly affecting the durability and waterproofing performance of underground structures. Therefore, accurate prediction and control of the early temperature field of concrete has become a key aspect of ensuring project quality.

[0003] Currently, insulation design in engineering mainly relies on finite element numerical simulation or static thermal calculations based on empirical coefficients. These methods have significant limitations: while numerical methods can handle complex boundary conditions, they have long modeling cycles and high computational resource requirements, making it difficult to meet the needs of rapid adjustments on construction sites; and empirical formulas use fixed heat exchange coefficient values, failing to reflect the dynamic impact of different wall thicknesses, cementitious material dosages, and environmental fluctuations on the cooling rate, resulting in a large deviation between the actual cooling rate and the design target. Especially for modern concrete with high cementitious material dosages, the hydration heat characteristic curve differs significantly from that of traditional concrete, and existing methods struggle to accurately capture its early temperature evolution, leading to insulation layer thickness designs that are either too thin or too thick. The former can cause cracking risks, while the latter results in material waste and affects formwork turnover efficiency.

[0004] Therefore, how to establish a method for determining the heat exchange coefficient that can quickly respond to changes in concrete material properties, geometric parameters, and environment, and accurately calculate the thickness of the insulation layer accordingly, has become an urgent technical problem to be solved. Summary of the Invention

[0005] To address the aforementioned technical problems, this application provides a method and system for calculating the thickness of concrete insulation layers based on the heat exchange coefficient.

[0006] Firstly, this application provides a method for calculating the thickness of concrete insulation layer based on heat exchange coefficient, employing the following technical solution: A method for calculating the thickness of concrete insulation layer based on heat exchange coefficient, the calculation method comprising: Obtain the geometric parameters of the target wall, the thermophysical parameters of the concrete, and the preset cooling rate; Based on the geometric parameters and concrete thermophysical parameters, a temperature-time function at the center point of the wall is generated through a pre-constructed temperature field analytical model. Taking the time derivative of the temperature-time function yields the cooling rate function; Using the preset cooling rate as a constraint, the heat exchange coefficient in the cooling rate function is solved by a numerical optimization algorithm. Obtain the maximum temperature difference between the center point of the concrete wall and the environment, and query the working condition database according to the construction working condition label to output the corresponding maximum allowable heat flux density; Calculate the minimum total thermal resistance based on the maximum temperature difference and the maximum permissible heat flux density; Calculate the surface convective thermal resistance based on the heat exchange coefficient; Subtracting the surface convection thermal resistance from the minimum total thermal resistance yields the thermal conductivity of the insulation layer. By combining the thermal conductivity of the insulation material with the climate correction factor, the design thickness of the insulation layer corresponding to the thermal resistance of the insulation layer is calculated.

[0007] By adopting the above technical solution, integrating temperature field analytical model, heat exchange coefficient optimization, and thermal resistance calculation, a scientific design of concrete insulation layer thickness is achieved. First, the cooling rate control based on the temperature field analytical model precisely matches the early-stage temperature "sharp rise and fall" characteristics, suppressing cracking risk at its source. Second, the heat exchange coefficient calculation overcomes the lag of traditional empirical methods, enabling the insulation design to adapt to changes in wall thickness and cementitious materials. Finally, through thermal resistance balance and aerogel composite template technology, the theoretical thickness is transformed into a construction plan, improving template turnover rate and economy. The overall solution forms a closed-loop control from parameter input to thickness output, suitable for complex conditions such as underground spaces, effectively improving the durability and construction efficiency of concrete structures.

[0008] Optionally, the step of generating the temperature-time function at the center point of the wall based on the geometric parameters and concrete thermophysical parameters through a pre-constructed analytical model of the temperature field includes: The wall thickness and cementitious material usage are obtained based on the aforementioned geometric parameters and concrete thermophysical parameters. The wall thickness and cementitious material dosage are input into the dimensionless heat transfer equation of the pre-constructed temperature field analytical model. The Fourier partial differential equation for heat conduction containing internal heat source terms in the analytical model of the temperature field is solved by the method of separation of variables. Output the temperature-time function at the center point of the wall, expanded as a mode function series.

[0009] By employing the aforementioned technical solutions, the complex heat conduction problem is transformed into a computable series solution, enabling efficient and accurate prediction of the temperature field. Dimensionlessness eliminates scale dependence, making the model applicable to different thicknesses and materials; the method of separation of variables ensures the theoretical rigor of the solution and avoids numerical errors; and the mode shape function series expansion provides explicit expressions, facilitating rapid differentiation and parameter optimization. This foundation lays the theoretical groundwork for solving the heat exchange coefficient and calculating the insulation layer thickness, improving the accuracy and reliability of early-stage temperature control in concrete.

[0010] Optionally, the process of solving the heat transfer coefficient in the cooling rate function using a numerical optimization algorithm, with the preset cooling rate as a constraint, includes: Establish an explicit correlation equation between the cooling rate function and the heat exchange coefficient; Using a preset cooling rate as the target value, the heat exchange coefficient variable is iteratively adjusted using the gradient descent method. When the error between the real-time calculated cooling rate and the target value is less than a preset error threshold, the current heat exchange coefficient is output as the heat exchange coefficient.

[0011] By adopting the above technical solution, the heat exchange coefficient is accurately inverted. The correlation equation ensures the physical consistency between the heat exchange coefficient value and the cooling rate. The gradient descent method provides an efficient solution tool, while the error threshold balances accuracy and efficiency. This technical solution enables the insulation layer design to dynamically respond to early temperature changes in concrete, effectively suppressing the risk of cracks caused by "sudden rise and fall", and improving the reliability and economy of underground space construction.

[0012] Optionally, the steps of querying the working condition database based on the construction working condition label and outputting the corresponding maximum allowable heat flux density include: Call the pre-stored working condition database, which contains the correspondence between the construction environment temperature range, concrete strength grade and heat flux density threshold; Match the corresponding construction environment temperature range and concrete strength grade based on the input construction condition label; The corresponding heat flux density threshold is output as the maximum allowable heat flux density.

[0013] By adopting the above technical solution, an intelligent mapping from construction conditions to heat flux density limits is achieved, transforming discrete engineering experience into structured data. This ensures that the insulation layer design meets both theoretical accuracy and actual working conditions: the working condition mapping table inherits authoritative data from the specifications, reducing human error; the tag matching mechanism improves query efficiency, enabling the system to quickly respond to different construction scenarios; and the output of the maximum allowable heat flux density as a hard constraint directly guarantees the safety of heat flux control. This technical solution allows the calculation of heat exchange coefficient and insulation layer thickness to be closely integrated with specific engineering conditions, significantly improving the standardization and reliability of concrete temperature control.

[0014] Optionally, after obtaining the designed thickness of the insulation layer, the method further includes: The insulation layer construction parameters are generated based on the designed thickness of the insulation layer, including the coating thickness configuration value and the bevel angle of the internal and external corners; wherein, the coating thickness configuration value is set to be equal to the designed thickness of the insulation layer; A cold bridge elimination command is generated based on the bevel angle of the internal and external corners to control the template processing equipment to perform bevel cutting operations.

[0015] By adopting the above technical solution, and through thermal resistance conversion and climate correction, precise design of the insulation layer thickness is achieved. The theoretical results of heat exchange coefficient calculation are transformed into executable construction parameters: theoretical thickness calculation ensures the mathematical rigor of thermal resistance requirements, while climate correction compensates for the uncertainty of environmental variables, enabling the design to meet temperature control targets while possessing engineering resilience. This technical solution forms a closed loop from parameter input to thickness output, improving the accuracy and robustness of early-stage concrete temperature control, effectively reducing the risk of cracking, and optimizing material costs.

[0016] Optionally, after obtaining the designed thickness of the insulation layer, the method further includes: The thickness of the aerogel coating is configured to be the designed thickness of the insulation layer; The template assembly system is triggered to perform beveling operations at the inside and outside corners to eliminate cold bridges.

[0017] By adopting the above technical solution, using the key thickness parameter δ calculated by the heat exchange model as the sole input origin, and synchronously mapping it to two structural parameters—material coating thickness and base layer geometric compensation angle—the synergistic optimization of the insulation layer in terms of both "material thermal resistance performance" and "three-dimensional spatial morphology" is achieved. Furthermore, by intelligently generating machining instructions that drive CNC equipment from the geometric parameters, the automated elimination of cold bridges is accomplished. This technical solution not only ensures the accurate realization of the theoretical thermal resistance value of the insulation layer, but also eliminates localized thermal defects that are difficult to avoid in traditional processes through proactive geometric design. Ultimately, it dynamically and stably constrains the early cooling of the wall system within a scientifically predetermined safe range, achieving the core objective of suppressing temperature cracks from the design source.

[0018] Secondly, this application provides a system for calculating the thickness of concrete insulation layers based on the heat exchange coefficient, employing the following technical solution: A system for calculating the thickness of concrete insulation layers based on the heat exchange coefficient, the system comprising: The parameter input module is used to obtain the geometric parameters of the target wall, the thermophysical parameters of the concrete, and the preset cooling rate; The temperature field analysis module is used to generate the temperature-time function of the center point of the wall based on the geometric parameters and concrete thermophysical parameters through a pre-constructed temperature field analysis model. The cooling rate calculation module is used to perform time derivative of the temperature-time function to obtain the cooling rate function. The heat exchange coefficient optimization module is used to solve the heat exchange coefficient in the cooling rate function by means of a numerical optimization algorithm, with the preset cooling rate as a constraint. The heat flux density query module is used to obtain the maximum temperature difference between the center point of the concrete wall and the environment, and to query the working condition database according to the construction working condition label to output the corresponding maximum allowable heat flux density. The minimum total thermal resistance calculation module is used to calculate the minimum total thermal resistance based on the maximum temperature difference and the maximum allowable heat flux density. A surface convection thermal resistance calculation module is used to calculate the surface convection thermal resistance based on the heat exchange coefficient. The thermal resistance calculation module for the thermal insulation layer is used to subtract the surface convection thermal resistance from the minimum total thermal resistance to obtain the thermal resistance of the thermal insulation layer. The insulation layer thickness design module is used to calculate the insulation layer design thickness corresponding to the thermal resistance of the insulation layer by combining the thermal conductivity of the insulation material and the climate correction factor.

[0019] Thirdly, this application provides a computer device, which adopts the following technical solution: A computer device includes a memory, a processor, and a computer program stored in the memory, the processor executing the computer program to perform the steps of the method as described in the first aspect.

[0020] Fourthly, this application provides a computer-readable storage medium, which adopts the following technical solution: A computer-readable storage medium storing a computer program that can be loaded by a processor and executed as in any of the methods in the first aspect. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the first process of a method for calculating the thickness of a concrete insulation layer based on the heat exchange coefficient, according to one embodiment of this application.

[0022] Figure 2 This is a second flowchart illustrating a method for calculating the thickness of a concrete insulation layer based on the heat exchange coefficient, according to one embodiment of this application.

[0023] Figure 3 This is a schematic diagram of the third process of a method for calculating the thickness of concrete insulation layer based on heat exchange coefficient, according to one embodiment of this application.

[0024] Figure 4 This is a schematic diagram of the fourth step of the method for calculating the thickness of concrete insulation layer based on heat exchange coefficient, according to one embodiment of this application.

[0025] Figure 5 This is a schematic diagram of the fifth step of the method for calculating the thickness of concrete insulation layer based on heat exchange coefficient, according to one embodiment of this application.

[0026] Figure 6 This is a schematic diagram of the sixth step in the calculation method of concrete insulation layer thickness based on heat exchange coefficient according to one embodiment of this application.

[0027] Figure 7 This is a three-dimensional coupling relationship diagram of the amount of cementitious material, heat exchange coefficient and daily cooling rate in the early cooling control of the wall in one embodiment of this application.

[0028] Figure 8 This is a design curve of the heat exchange coefficient as a function of wall thickness under different daily cooling rate limits according to one embodiment of this application. Detailed Implementation

[0029] To make the purpose, technical solution, and advantages of this application clearer, the following description is provided in conjunction with the appendix. Figures 1-8 The present application will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the application.

[0030] This application discloses a method for calculating the thickness of concrete insulation layer based on heat exchange coefficient.

[0031] Reference Figure 1 A method for calculating the thickness of concrete insulation layer based on heat exchange coefficient, the calculation method includes: Step S101: Obtain the geometric parameters of the target wall, the thermophysical parameters of the concrete, and the preset cooling rate; Specifically, this step aims to define the initial conditions for the heat conduction problem in concrete walls. The main geometric parameters include the wall thickness d (in meters), which directly determines the length of the heat conduction path; the greater the thickness, the more significant the heat accumulation effect and the more complex the control of the cooling rate. The thermophysical parameters of concrete include thermal conductivity k (W / (m·K)), specific heat capacity c (J / (kg·K)), density ρ (kg / m³), and cementitious material content W (kg / m³).

[0032] Among them, thermal conductivity k characterizes the material's ability to conduct heat; a lower value indicates better thermal insulation performance. Specific heat capacity c reflects the ability of a unit mass of concrete to store heat, affecting the inertia of temperature changes. Density ρ is related to mass distribution and, together with heat capacity, determines thermal inertia. The amount of cementitious materials W (such as a combination of cement, fly ash, and mineral powder) directly drives the intensity of the hydration heat source, affecting the internal temperature rise. The preset cooling rate (e.g., 2℃ / d) is a key objective for crack control, set based on engineering practice, and used to constrain the subsequent optimization process.

[0033] These parameters together constitute the input boundary of the temperature field analytical model, ensuring that the calculation is tailored to specific working conditions. For example, for a 300mm thick C30 concrete wall, the amount of cementitious material may be 350kg / m³ (cement 220kg / m³, fly ash 70kg / m³, mineral powder 60kg / m³), and the preset cooling rate is set to 3℃ / d to match common construction requirements.

[0034] Step S102: Based on geometric parameters and concrete thermophysical parameters, generate the temperature-time function of the center point of the wall through a pre-constructed temperature field analytical model; Specifically, a pre-constructed analytical model of the temperature field is applied to transform the input parameters into a function of the temperature change over time at the center point of the wall (x=d / 2). This model, based on Fourier heat conduction theory, solves the partial differential equations of heat conduction containing internal hydration heat sources. Where ρ is density (kg / m³), c is specific heat capacity (J / (kg·K)), kv is thermal conductivity (W / (m·K)), and Q(t) is hydration heat production rate.

[0035] By dimensionless transformation, the problem is simplified to a series solution of mode shape functions. Specifically, the temperature-time function T(d / 2,t) is derived by the following formula: , Where Φ_n(X) is the mode shape function, and λ_n is the eigenvalue (determined by the boundary condition characteristic equation tanλ=2Biλ / (λ²-Bi²)). The Biot number represents the relative intensity of surface heat exchange and internal heat conduction.

[0036] The generation process specifically includes: first, decomposing the partial differential equation into spatial and temporal ordinary differential equations using the method of separation of variables; then, solving for the series coefficients using the orthogonality of the mode shape functions. The temperature-time function accurately captures the temperature rise and subsequent temperature drop at the center point of the wall due to the heat of hydration, providing a basis for the analysis of the cooling rate. For example, for a wall with d=0.3m, the calculated T(d / 2,t) curve can show the "steep rise and steep drop" characteristics within 1 to 5 days after pouring, consistent with the measured data.

[0037] Step S103: Take the time derivative of the temperature-time function to obtain the cooling rate function; Specifically, by performing mathematical differentiation, the cooling rate function is extracted from the temperature-time function, i.e. This function quantifies the rate of temperature change per unit time and is a key indicator for assessing the risk of early-stage cracks. The differentiation process is based on the analytical function, avoiding errors introduced by numerical methods and ensuring accuracy.

[0038] Specifically, by directly differentiating the temperature-time function formula, we can obtain the cooling rate function form: ; In the formula, each term represents the contribution of heat conduction attenuation, hydration heat attenuation, and environmental fluctuations, respectively. The cooling rate function directly reflects the cooling rate of the concrete; for example, at t=2~3 days, An excessively high value (e.g., exceeding 5℃ / d) indicates a high risk of cracking, requiring control measures in subsequent steps. This function bridges the temperature field model with engineering control objectives, providing input for dynamic h-value optimization.

[0039] Step S104: Using a preset cooling rate as a constraint, the heat exchange coefficient in the cooling rate function is solved by a numerical optimization algorithm. The heat exchange coefficient h is retrieved by optimizing the algorithm to meet the preset cooling rate. The h value (unit: W / (m²·K)) characterizes the heat exchange intensity between the concrete surface and the environment, which is affected by the thermal insulation performance of the formwork and changes dynamically with the wall thickness d and the amount of cementitious material W.

[0040] In this embodiment, the optimization problem is defined as: minimizing the error between the calculated cooling rate and a preset target (e.g., 2℃ / d), and iteratively adjusting the value of h using numerical algorithms such as gradient descent. The specific process is based on the following formula defining the cooling rate: ; By constructing explicit correlation equations and using a preset cooling rate as a constraint, h is adjusted to... Approximately equal to the target value. The optimization convergence condition is typically set to an error of less than 1% to ensure the practicality of the h value. For example, for a wall with d = 0.3m and W = 350kg / m³, optimization might yield h = 0.52 W / (m²·K), at which point the cooling rate is controlled within 3℃ / d. This method overcomes the limitations of traditional fixed h values ​​and achieves adaptive operation under various conditions.

[0041] Step S105: Obtain the maximum temperature difference between the center point of the concrete wall and the environment, and query the working condition database according to the construction working condition label to output the corresponding maximum allowable heat flux density. The maximum temperature difference ΔT = max[T(d / 2,t)] - T_e represents the difference between the highest temperature at the center of the wall and the ambient temperature, signifying the thermally driven potential energy. Construction condition labels (such as "Normal Temperature Construction" or "Winter Construction") are categorized based on ambient temperature and concrete strength, used to query the maximum allowable heat flux density q_max (unit: W / m²) in the condition database. The q_max value is derived from standards (such as the "Technical Guidelines for Thermal Calculation of Formwork") to ensure that the heat flux does not exceed the material's tolerance threshold and prevent thermal damage. For example, for normal temperature construction with ΔT = 25℃, q_max = 150 W / m² is found; while for winter construction with ΔT = 20℃, q_max = 120 W / m². This step quantifies engineering experience data, ensuring the safety and feasibility of the calculations.

[0042] Step S106: Calculate the minimum total thermal resistance based on the maximum temperature difference and the maximum allowable heat flux density; The minimum total thermal resistance R_min, calculated based on thermal resistance theory, is defined as R_min = ΔT / q_max, in units of K·m² / W. Thermal resistance characterizes the system's resistance to heat flow, and R_min is the lower limit of the total thermal resistance required to ensure that the heat flow does not exceed q_max. The calculation principle originates from a series model of Fourier's law and Newton's law of cooling, where the total thermal resistance must satisfy R_total ≥ R_min to control heat flow. For example, when ΔT = 25℃ and q_max = 150W / m², R_min = 25 / 150 ≈ 0.1667 K·m² / W. This value provides a benchmark for subsequent calculations of the thermal resistance of the insulation layer.

[0043] Step S107: Calculate the surface convection thermal resistance based on the heat exchange coefficient; The surface convective thermal resistance R_conv can be directly derived from the heat exchange coefficient h: R_conv = 1 / h. Convective thermal resistance reflects the resistance to the surface heat exchange process; the larger the value of h (indicating poor insulation performance), the smaller R_conv. For example, when h = 0.52 W / (m²·K), R_conv ≈ 1.923 K·m² / W. R_conv and R_min together form a thermal resistance network, used to separate the contribution of the insulation layer.

[0044] Step S108: Subtract the surface convection thermal resistance from the minimum total thermal resistance to obtain the thermal conductivity of the insulation layer. The thermal resistance R_ins of the insulation layer is solved using the thermal resistance balance equation. According to the series thermal resistance model, the total thermal resistance R_total = R_ins + R_conv, and R_total ≥ R_min must be satisfied. Therefore, the thermal resistance R_ins of the insulation layer = R_min - R_conv. This value represents the thermal resistance requirement of the insulation material itself and is used for thickness design. For example, when R_min = 0.1667 K·m² / W and R_conv = 1.923 K·m² / W, R_ins = 0.1667 - 1.923 = -1.756 K·m² / W (a negative value indicates that R_conv meets the requirement, but in actual calculations, a positive value or adjustment is required, and the thickness is calculated directly using the formula).

[0045] Step S109: Combine the thermal conductivity of the insulation material with the climate correction factor to calculate the design thickness of the insulation layer corresponding to the thermal resistance of the insulation layer.

[0046] The final calculation of the insulation layer design thickness δ is performed using the following formula: ; Where k is the thermal conductivity of the insulation material (e.g., k = 0.015 W / (m·K) for aerogel), and the climate correction factor α (0.2 for normal temperature and 0.4 for severe cold) is used to compensate for environmental factors such as wind and humidity. The actual thickness is δ×(1+α). For example, when h = 0.52 W / (m²·K), ΔT = 25℃, and q_max = 150 W / m², δ = 0.015×(1 / 0.52-25 / 150) ≈ 0.026 mm, and then corrected according to α. This thickness ensures that the thermal resistance of the insulation layer matches the dynamic h value, accurately controlling the cooling.

[0047] In the above implementation, the integration of a temperature field analytical model, heat exchange coefficient optimization, and thermal resistance calculation enables the scientific design of the concrete insulation layer thickness. First, the cooling rate control based on the temperature field analytical model precisely matches the early-stage temperature "sharp rise and fall" characteristics, suppressing cracking risks at the source. Second, the heat exchange coefficient calculation overcomes the lag of traditional empirical methods, allowing the insulation design to adapt to changes in wall thickness and cementitious materials. Finally, through thermal resistance balancing and aerogel composite template technology, the theoretical thickness is transformed into a construction plan, improving template turnover rate and economy. The overall solution forms a closed-loop control from parameter input to thickness output, suitable for complex conditions such as underground spaces, effectively improving the durability and construction efficiency of concrete structures.

[0048] Reference Figure 2 As one implementation of step S102, the step of generating the temperature-time function of the wall center point based on geometric parameters and concrete thermophysical parameters through a pre-constructed temperature field analytical model includes: Step S201: Obtain the wall thickness and cementitious material dosage based on geometric parameters and concrete thermophysical parameters; Step S202: Input the wall thickness and cementitious material usage into the dimensionless heat transfer equation of the pre-constructed temperature field analytical model; The purpose of this step is to simplify the complexity of the heat transfer problem by dimensionlessly transforming the analytical model of the temperature field, making the solution to the equations more general and easier to analyze. The wall thickness d (in meters) and the amount of cementitious material W (in kilograms / m³) are the core input parameters, directly affecting the length of the heat conduction path and the intensity of the hydration heat source. The dimensionless transformation process is based on the following formula: ; Specifically, X is a dimensionless spatial coordinate (characterized by the wall thickness), and τ is a dimensionless time (scaled on the thermal diffusion timescale αt / d). 2 (by definition), θ is a dimensionless temperature (in terms of characteristic temperature) (Based on) The total heat of hydration of the cementitious material, WQ, and the concrete ρc are determined. This transformation converts the dimensional parameters (such as length and time) in the original physical equations into dimensionless numbers, thereby eliminating dimension dependence and highlighting the role of key dimensionless parameters, such as the Biot number Bi = hd / k (characterizing the relative intensity of surface heat exchange and internal heat conduction) and the hydration heat release parameter M = md. 2 / α (characterizing the rate of heat release during hydration). For example, for a thickness d=0.3m and a cementitious material dosage W=350kg / m 3 For the wall, the dimensionless problem depends only on Bi and M, and is decoupled from specific dimensions, making the solution universal.

[0049] Step S203: Solve the Fourier partial differential equation of heat conduction containing internal heat source terms in the analytical model of the temperature field using the method of separation of variables. Specifically, after dimensionless processing, the governing equations are transformed into the following dimensionless form: , in, The equation is a dimensionless hydration heat source term. It is a partial differential equation for heat conduction containing time-varying source terms. The solution employs the method of separation of variables, the core idea of ​​which is to assume the solution is a product of a spatial function and a time function. (This represents a dimensionless hydration heat source term.) .

[0050] After substituting into the equation and separating the variables, we obtain two ordinary differential equations: the time-domain part. The solution is in exponential decay form. The spatial part then transforms into a vibration equation. Its general solution is the mode shape function. The boundary conditions are given by the following formula: , After substituting the mode shape function, the characteristic equation is derived. This equation determines the eigenvalue λ. n (Infinite sequence) and the corresponding mode constant A n B n The method of separation of variables decomposes partial differential equations into easily solvable ordinary differential equations and captures boundary effects through eigenvalue problems, ensuring that the solution satisfies physical constraints.

[0051] Step S204: Output the temperature-time function of the wall center point as expanded by the mode function series.

[0052] The final solution is expressed in the form of a modal function series, and the formula is: , in, These are the mode shape weighting coefficients, determined by the orthogonality of the mode shape functions. This series solution converges quickly; typically, the first few terms can approximate the actual temperature distribution. Mode shape function Characterizing the spatial modal distribution of temperature, each mode corresponds to an eigenvalue λ. n It reflects the inherent thermal vibration characteristics of the system; the time component includes the hydration heat decay term. and thermal conduction attenuation term , representing the transient effects of internal heat sources and boundary heat dissipation, respectively. After conversion to dimensional form, the temperature-time function is explicitly expressed as: This expression, as a temperature-time function, directly outputs the temperature evolution curve of the center point of the wall (taking x=d / 2) over time. For example, it can simulate the "sharp rise and fall" characteristics within 1 to 5 days after pouring, providing input for subsequent cooling rate analysis.

[0053] In the above implementation, the complex heat conduction problem is transformed into a computable series solution, achieving efficient and accurate prediction of the temperature field. Dimensionlessness eliminates scale dependence, making the model applicable to different thicknesses and materials; the method of separation of variables ensures the theoretical rigor of the solution and avoids numerical errors; and the mode shape function series expansion provides explicit expressions, facilitating rapid differentiation and parameter optimization. This foundation lays the theoretical groundwork for solving the heat exchange coefficient and calculating the insulation layer thickness, improving the accuracy and reliability of early-stage temperature control in concrete.

[0054] Reference Figure 3 As one implementation of step S104, the process of solving the heat exchange coefficient in the cooling rate function using a numerical optimization algorithm with a preset cooling rate as a constraint includes: Step S301: Establish an explicit correlation equation between the cooling rate function and the heat exchange coefficient; The purpose of this step is to establish a mathematical relationship between the cooling rate function and the heat exchange coefficient h, providing a foundation for optimization solutions. The cooling rate function is defined as the temperature change over 24 hours: ; The temperature field T(x,t) in the above equation is given by the series solution of the temperature-time function: , Explicit correlation equations are achieved by embedding the h value into the above expression: the h value directly affects the feature λ. n And the Biotherm number Bi = hd / k, which in turn changes the mode shape function Φ n and series coefficients (such as D) n ,R n ).

[0055] Specifically, the characteristic equation: The solution λ n The nonlinear relationship with h causes the temperature distribution and cooling rate to vary with h.

[0056] The explicit correlation equation can be written as: Here, f is an explicit function containing h, representing the rate of temperature change per unit time. For example, for the center point of the wall (x=d / 2), the cooling rate function can be simplified to a multivariate expression of h, whose explicit form can be obtained through analytical differentiation or numerical difference. This connection directly links the engineering control objective (preset cooling rate) with the physical parameter h, providing input for optimization.

[0057] Step S302: Using the preset cooling rate as the target value, the heat exchange coefficient variable is iteratively adjusted using the gradient descent method. Specifically, this step uses gradient descent to solve for the value of h, making the calculated cooling rate approach the preset target (e.g., 2℃ / d). Gradient descent is a first-order optimization algorithm whose core is to iteratively update the value of h by calculating the gradient direction of the error function in order to minimize the objective function. .

[0058] The iterative process is as follows: , where h k Here, h is the value of the k-th iteration, η is the learning rate (step size), and gradient is... Calculated using the chain rule: Because It is a composite function of h (via λ) n (And Bi), gradient calculation requires differentiating the characteristic equation and the temperature field expression. For example, for a preset cooling rate v target The objective function can be set as E(h)=[v(h)−v target ] 2 , where v(h) = Calculated from the correlation equation. Each iteration of gradient descent requires resolving the eigenvalue λ. n The method incorporates a temperature field to ensure that the error in the direction of h update is reduced. It is applicable to the nonlinear relationship between h and the cooling rate, efficiently handles multimodal problems, and avoids local optima.

[0059] Step S303: When the error between the real-time calculated cooling rate and the target value is less than the preset error threshold, the current heat exchange coefficient is output as the heat exchange coefficient.

[0060] This step defines the optimization convergence condition to ensure the accuracy of the h value. The error threshold is set to 1% based on engineering balance considerations: too loose (e.g., >5%) may lead to inaccurate temperature control, while too tight (e.g., <0.1%) will increase computational costs without any practical benefit. The convergence criterion is: ; In the above formula, v(h) is the calculated cooling rate corresponding to the current h. When the conditions are met, the output h is used as the heat exchange coefficient, which comprehensively reflects the wall thickness, the amount of cementitious material used, and environmental factors. For example, for a wall with d=0.3m and W=350kg / m³, the optimized h may be 0.52W / (m²·K), keeping the cooling rate within 3℃ / d. The output h value is directly used for subsequent thermal resistance calculations, forming a closed-loop control.

[0061] In the above implementation, the heat exchange coefficient is accurately inverted, the correlation equation ensures the physical consistency between the h value and the cooling rate, the gradient descent method provides an efficient solution tool, and the error threshold balances accuracy and efficiency. This technical solution enables the insulation layer design to dynamically respond to early temperature changes in concrete, effectively suppresses the risk of cracks caused by "sudden rise and fall", and improves the reliability and economy of underground space construction.

[0062] Reference Figure 4 As one implementation of step S105, the step of querying the working condition database based on the working condition label and outputting the corresponding maximum allowable heat flux density includes: Step S401: Call the pre-stored working condition database, which contains the correspondence between the construction environment temperature range, concrete strength grade and heat flux density threshold. The pre-constructed working condition database is essentially built based on engineering specifications and measured data. Its function is to quantify complex construction conditions into a set of queryable correspondences. In this embodiment, the structure of the working condition database is shown in Table 1 below, containing three key dimensions: construction ambient temperature range (e.g., "normal temperature construction" corresponds to an ambient temperature >5℃, "winter construction" corresponds to -10℃ to 5℃), concrete strength grade (e.g., C30, C50, etc.), and heat flux density threshold q_max (unit: W / m²). The heat flux density threshold q_max is defined as the maximum heat flow allowed to pass through a unit area. Its value is based on the material's heat resistance and crack prevention requirements. For example, under normal temperature construction, q_max ranges from 150 to 180 W / m², while under winter construction it is reduced to 120 to 150 W / m² to avoid thermal damage to the concrete surface due to excessive heat flow.

[0063] Table 1 It should be noted that this mapping table is constructed based on the "Technical Guidelines for Thermal Calculation of Templates" from the China Academy of Building Research, and is derived through statistical analysis and fitting of experimental data, ensuring its authority. The calling process is automated; the system directly accesses the table based on the input parameters, eliminating the need for real-time calculations and improving efficiency. For example, the mapping table may be stored in the form of a hash table or a relational database, with the key being the operating condition label and the value being the corresponding temperature range, intensity level, and q_max range, thus enabling rapid response to queries.

[0064] Step S402: Match the corresponding construction environment temperature range and concrete strength grade according to the input construction condition label; The construction condition label is a category identifier entered by the user, such as "Normal Temperature Construction - C30" or "Construction in Extremely Cold Regions - C50", which encapsulates environmental conditions and material property information. The matching process is achieved through string or code comparison: the system parses the condition label, extracts the ambient temperature range (e.g., ">5℃") and concrete strength grade (e.g., "C30"), and then performs precise or fuzzy matching in the condition mapping table.

[0065] Specifically, the ambient temperature range determines the boundary conditions for heat exchange. The lower the temperature, the faster the concrete surface dissipates heat, but q_max needs to be controlled to prevent frost damage. The concrete strength grade indirectly reflects the amount of cementitious materials and the heat of hydration characteristics. High strength grades (such as C50 and above) usually have a high amount of cementitious materials and a large heat of hydration, so q_max needs to be taken as a lower value (such as 100~130 W / m²) to suppress temperature rise. The matching algorithm needs to handle boundary cases. For example, when the ambient temperature is -10℃, it may simultaneously match "winter construction" and "construction in extremely cold regions." In this case, the more stringent q_max value is preferred. This step transforms abstract construction conditions into specific parameters, providing input for subsequent thermal resistance calculations.

[0066] Step S403: Output the corresponding heat flux density threshold as the maximum allowable heat flux density.

[0067] Upon successful matching, the system outputs the corresponding heat flux density threshold as the maximum allowable heat flux density q_max. q_max is a critical value representing the maximum allowable heat flow per unit area. Its physical meaning is to ensure that the internal thermal stress of the concrete does not exceed its tensile strength, preventing early cracking. The output process is based on the query results of the mapping table. For example, for the tag "Normal Temperature Construction - C30", q_max might output 150 W / m² (taking the median value or adjusting according to the safety factor). The value of q_max is directly used for thermal resistance calculation: minimum total thermal resistance R_min = ΔT / q_max, where ΔT is the maximum temperature difference between the center of the wall and the environment. By outputting q_max, empirical data is integrated into the theoretical model, avoiding reliance on subjective judgment and improving the reliability of the design. For example, in a certain project, when ΔT = 25℃, q_max = 150 W / m² ensures controllable heat flow, thereby accurately guiding the design of the insulation layer thickness.

[0068] The above implementation achieves intelligent mapping from construction conditions to heat flux density limits, transforming discrete engineering experience into structured data. This ensures that the insulation layer design meets both theoretical accuracy and actual working conditions: the working condition mapping table inherits authoritative data from the specifications, reducing human error; the tag matching mechanism improves query efficiency, enabling the system to quickly respond to different construction scenarios; and the output q_max serves as a hard constraint, directly guaranteeing the safety of heat flux control. This technical solution allows the calculation of heat exchange coefficient and insulation layer thickness to be closely integrated with specific engineering conditions, significantly improving the standardization and reliability of concrete temperature control.

[0069] Reference Figure 5 As one implementation of step S109, the step of calculating the design thickness of the insulation layer corresponding to the thermal resistance of the insulation layer by combining the thermal conductivity of the insulation material and the climate correction factor includes: Step S501: Multiply the thermal resistance of the insulation layer by the thermal conductivity of the insulation material to obtain the theoretical thickness; Specifically, the thermal resistance R of the insulation layer ins (Unit: K·m² / W) represents the resistance of the insulation material itself to heat flow, and its calculation is based on the thermal resistance balance equation. , where R min =ΔT / q max It is the minimum total thermal resistance (ensuring that the heat flux does not exceed the allowable value), R conv =1 / h is the surface convective thermal resistance (determined by the heat exchange coefficient h). The thermal conductivity k of the insulation material (unit: W / (m·K)) is an inherent thermal conductivity property of the material. The lower the value, the better the insulation performance (e.g., the k of aerogel is 0.012~0.02W / (m·K)).

[0070] Among them, the theoretical thickness δ theoretical The calculation formula is derived from the integral form of Fourier's law: for a homogeneous material, the relationship between thermal resistance R, thickness δ, and thermal conductivity k is R = δ / k, thus deriving δ theoretical =k×R ins This step transforms the abstract thermal resistance into concrete dimensions. The theoretical thickness is a calculation result under ideal conditions, without considering environmental fluctuations, thus providing a basis for subsequent corrections.

[0071] Step S502: Determine the climate correction factor based on the ambient temperature range; The theoretical thickness is adjusted using a climate correction coefficient to compensate for the impact of environmental factors on the insulation effect. The climate correction coefficient (1+α) is an empirical factor, where α is the correction value, which is based on the construction environment temperature: for example, when the environment temperature is higher than -10℃ (such as normal temperature or winter construction), α=0.2, and the coefficient is taken as 1.2; when the environment temperature is lower than or equal to -10℃ (such as construction in extremely cold regions), α=0.4, and the coefficient is taken as 1.4.

[0072] Understandably, lower ambient temperatures increase surface heat loss due to factors such as wind speed and humidity, resulting in actual thermal resistance lower than the theoretical value. For example, in extremely cold conditions, strong winds exacerbate convective heat loss, necessitating increased insulation thickness to maintain thermal performance. The correction factor was determined based on the "Technical Guidelines for Thermal Calculation of Formwork" from the China Academy of Building Research, derived through statistical analysis of extensive measured data to ensure the conservatism and safety of the design. The selection process is automated; the system directly matches the factor based on the input ambient temperature label, requiring no manual intervention.

[0073] Step S503: Multiply the theoretical thickness by the climate correction factor to output the design thickness of the insulation layer.

[0074] The final design thickness δ is obtained by multiplying the theoretical thickness by a climate correction factor: δ = δ theoretical ×(1+α). This calculation reflects the redundancy principle of engineering design, ensuring that the insulation layer can effectively suppress heat flow in actual environments.

[0075] For example, if the theoretical thickness is 1.5mm and the ambient temperature is -5℃ (above -10℃), the correction factor is 1.2, and the design thickness is 1.8mm; if the ambient temperature is -15℃, the factor is 1.4, and the design thickness is 2.1mm. The output thickness is directly used to guide the construction of the insulation formwork. This step combines the theoretical model with practical experience, and improves the adaptability and reliability of the design through quantitative correction.

[0076] In the above implementation, through thermal resistance conversion and climate correction, precise design of the insulation layer thickness is achieved, transforming the theoretical results of heat exchange coefficient calculation into executable construction parameters: theoretical thickness calculation ensures the mathematical rigor of thermal resistance requirements, while climate correction compensates for the uncertainty of environmental variables, enabling the design to meet temperature control targets while possessing engineering resilience. This technical solution forms a closed loop from parameter input to thickness output, improving the accuracy and robustness of early-stage concrete temperature control, effectively reducing the risk of cracking, and optimizing material costs.

[0077] Reference Figure 6 As a further implementation of the method for calculating the thickness of concrete insulation layer, after obtaining the design thickness of the insulation layer, the method further includes: Step S601: Generate insulation layer construction parameters based on the insulation layer design thickness, including coating thickness configuration values ​​and bevel angles of internal and external corners; The coating thickness configuration value is set to be equal to the design thickness of the insulation layer, which directly corresponds to the specific thermal resistance value required to stabilize the early cooling rate of the wall within the target range. The process of generating the insulation layer construction parameters is essentially decoupling this theoretical thermal index and materializing it into technical specifications that can guide specific construction.

[0078] In this embodiment, the aerogel coating serves as the primary load-bearing layer for thermal insulation. Any deviation in its thickness will directly cause the measured thermal resistance to deviate from the design thermal resistance, thereby disrupting the thermal balance established based on the "target thermal resistance R_min" and the "convective thermal resistance R_conv" (i.e., the formula). The function of aerogel coatings is to achieve precise control over the target heat exchange coefficient (h value). Therefore, strictly configuring the coating thickness to δ is the fundamental guarantee to ensure that the actual total thermal resistance of the composite wall system after coating is consistent with the theoretical calculation value. For example, if the calculated δ=8mm, it means that the average cumulative thickness of the aerogel functional layer on the main plane of the wall must be precisely 8mm through precise spraying. Only in this way can the thermal resistance R_ins of the insulation layer meet the design requirements, thereby effectively suppressing the overall surface heat exchange coefficient h below 0.5 W / m²·K and achieving predetermined control over the cooling rate.

[0079] Secondly, in traditional right-angle splicing methods, material breaks occur in the insulation layer at the corners, causing a sudden drop in thermal resistance and forming localized high-intensity heat flow channels, i.e., cold bridges. This can increase the local h value by 5-8 times, inducing uneven heat dissipation and "sudden temperature drop cracks." The design of the bevel angle aims to create a base surface for the insulation coating that can achieve continuous and uniform thickness coverage by changing the geometry of the base template. The technical basis lies in the geometric projection relationship: to ensure that the effective thickness (δ_eff) of the insulation layer at the corner is not less than the design thickness δ, the bevel length (L) must satisfy the relationship L = δ / sinθ (θ is the bevel angle). Using a 45° angle or an optimized specific angle allows the equivalent thickness of the insulation material sprayed along the bevel to be approximately constant in the direction of the corner normal, thus smoothing the heat flow distribution and avoiding heat flux density distortion caused by abrupt changes in thickness. Therefore, the bevel angle parameter is a compensatory requirement in the geometric structure based on the design thickness δ to ensure the continuity of heat flow, and it is the key link to achieve uniform thermal resistance in three-dimensional space.

[0080] Step S602: Generate a cold bridge elimination command based on the bevel angle of the internal and external corners to control the template processing equipment to perform bevel cutting operation.

[0081] The bevel angle is a core input parameter. The instruction generation system automatically calculates the CNC code for tool path, feed rate, and depth of cut based on this angle value. In the corner areas of walls, to ensure the uniformity and continuity of heat flux density (q) on the inner and outer surfaces, physical discontinuities in the insulation layer must be eliminated. The V-shaped or inverted V-shaped groove formed by the bevel cutting effectively increases the coverage area of ​​the insulation material at the corner, reducing the local heat flux density in that area. This allows for a smooth transition of the isotherms in heat transfer, fundamentally suppressing the formation of cold bridges. The instruction generation process quantifies this thermal requirement (uniform heat flux) into a specific spatial geometric operation (cutting at a specific angle).

[0082] It should be noted that the beveling operation is a direct and necessary physical intervention to block non-uniform heat dissipation paths. By executing the cold bridge elimination command, the formwork processing equipment prefabricates precise bevels at the inside and outside corners of the wall formwork. Subsequently, when the aerogel coating is sprayed onto this beveled formwork, a continuous and uninterrupted thermal insulation curved surface layer is naturally formed. This completely changes the heat dissipation pattern in the corner area, ensuring that the surface heat exchange coefficient h at that location remains consistent with that of the planar area, avoiding uncontrolled local temperature drop rates, and thus effectively preventing early temperature cracks caused by "sudden temperature drop rates".

[0083] In the above implementation, the key thickness parameter δ calculated by the heat exchange model is used as the sole input origin. By synchronously mapping it to two structural parameters—material coating thickness and base layer geometric compensation angle—the synergistic optimization of the insulation layer in terms of both "material thermal resistance performance" and "three-dimensional spatial morphology" is achieved. Furthermore, by intelligently generating machining instructions that can drive CNC equipment from the geometric parameters, the automated elimination of cold bridges is accomplished. This technical solution not only ensures the accurate realization of the theoretical thermal resistance value of the insulation layer, but also eliminates local thermal defects that are difficult to avoid in traditional processes through proactive geometric design. Ultimately, it dynamically and stably constrains the early cooling of the wall system within a scientifically predetermined safe range, achieving the core objective of suppressing the generation of temperature cracks from the design source.

[0084] Reference Figure 7 This diagram visually demonstrates how three key parameters—the target daily cooling rate of the wall, the wall structural thickness (d), and the total amount of concrete cementitious material (W)—jointly determine the upper limit of the allowable heat exchange coefficient (h) in early-stage temperature control. Specifically, the model sets a fixed target daily cooling rate (e.g., 2℃ / d) and then systematically adjusts different wall thicknesses and cementitious material amounts to calculate the maximum allowable surface heat exchange coefficient h value to achieve the temperature control target. Analysis of the relationship surface shows that, under the same daily cooling rate requirement, a higher amount of cementitious material results in a larger total heat of hydration and a higher temperature rise, requiring more stringent cooling control. This necessitates better insulation performance from the formwork or insulation layer, corresponding to a smaller heat exchange coefficient h value. Simultaneously, a larger wall thickness leads to a longer internal heat dissipation path and greater resistance, allowing for a slightly higher allowable h value. This diagram serves as a crucial bridge connecting material usage, structural dimensions, and insulation design requirements, providing direct input for the h value in subsequent insulation layer thickness calculations.

[0085] Reference Figure 8This figure presents a design curve showing the variation of the heat exchange coefficient (h) with wall thickness under different daily cooling rate limits. This simplifies the complex multi-parameter relationship into a two-dimensional curve for a wall of specific thickness, making it more directly applicable to engineering design. The figure plots wall thickness on the x-axis and the heat exchange coefficient (h) on the y-axis, with multiple curves representing a specific daily cooling rate control limit (e.g., 2℃ / d, 3℃ / d, 4℃ / d, 5℃ / d). For a given wall thickness, to control the early daily cooling rate at a lower level (e.g., 2℃ / d compared to 5℃ / d), the curves show that the formwork system or insulation layer must suppress the overall surface heat exchange coefficient (h) to a lower value range. Those skilled in the art can directly find the target h value from this curve based on the specific wall thickness and desired temperature control stringency of the project, and then design the insulation layer (e.g., aerogel coating) thickness according to the calculation formula for the insulation layer design thickness, thus transforming the theoretical model into specific construction parameters.

[0086] This application also discloses a system for calculating the thickness of concrete insulation layer based on the heat exchange coefficient.

[0087] A system for calculating the thickness of concrete insulation layers based on the heat exchange coefficient, specifically including: The parameter input module is used to obtain the geometric parameters of the target wall, the thermophysical parameters of the concrete, and the preset cooling rate; The temperature field analysis module is used to generate the temperature-time function of the center point of the wall based on geometric parameters and concrete thermophysical parameters through a pre-built temperature field analysis model. The cooling rate calculation module is used to perform time derivative of the temperature-time function to obtain the cooling rate function. The heat exchange coefficient optimization module is used to solve the heat exchange coefficient in the cooling rate function using a numerical optimization algorithm, with a preset cooling rate as a constraint. The heat flux density query module is used to obtain the maximum temperature difference between the center point of the concrete wall and the environment, and to query the working condition database according to the construction working condition label to output the corresponding maximum allowable heat flux density. The minimum total thermal resistance calculation module is used to calculate the minimum total thermal resistance based on the maximum temperature difference and the maximum allowable heat flux density. The surface convection thermal resistance calculation module is used to calculate the surface convection thermal resistance based on the heat exchange coefficient. The thermal resistance calculation module for the thermal insulation layer is used to subtract the surface convection thermal resistance from the minimum total thermal resistance to obtain the thermal resistance of the thermal insulation layer. The insulation layer thickness design module is used to calculate the insulation layer design thickness corresponding to the thermal resistance of the insulation layer by combining the thermal conductivity of the insulation material and the climate correction factor.

[0088] The concrete insulation layer thickness calculation system based on heat exchange coefficient according to the embodiments of this application can implement any of the above methods, and the specific working process of each module in the system can refer to the corresponding process in the above method embodiments.

[0089] In the several embodiments provided in this application, it should be understood that the provided methods and systems can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for example, the division of a certain module is merely a logical functional division, and in actual implementation there may be other division methods, such as multiple modules can be combined or integrated into another system, or some features can be ignored or not executed.

[0090] This application also discloses a computer device.

[0091] A computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method for calculating the thickness of a concrete insulation layer based on the heat exchange coefficient as described above.

[0092] This application also discloses a computer-readable storage medium.

[0093] A computer-readable storage medium storing a computer program that can be loaded by a processor and executed as described above in any of the methods for calculating the thickness of a concrete insulation layer based on the heat exchange coefficient.

[0094] The computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device; the program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0095] The above are all preferred embodiments of this application and are not intended to limit the scope of protection of this application. Any feature disclosed in this specification (including the abstract and drawings) may be replaced by other equivalent or similar features unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is only one example of a series of equivalent or similar features.

Claims

1. A method for calculating the thickness of a thermal insulation layer of concrete based on the heat exchange coefficient, characterized in that, The calculation method comprises: obtaining the geometric parameters of the target wall, the thermal physical parameters of the concrete and the preset cooling rate; based on the geometric parameters and the thermal physical parameters of the concrete, generating a temperature-time function of the wall center point through a pre-constructed temperature field analytical model; deriving the temperature-time function with respect to time to obtain a cooling rate function; solving the heat exchange coefficient in the cooling rate function through a numerical optimization algorithm with the preset cooling rate as a constraint condition; obtaining the maximum temperature difference between the concrete wall center point and the environment, and querying a working condition database according to a construction working condition label to output the corresponding maximum allowable heat flux density; calculating the minimum total thermal resistance according to the maximum temperature difference and the maximum allowable heat flux density; calculating the surface convective thermal resistance according to the heat exchange coefficient; subtracting the surface convective thermal resistance from the minimum total thermal resistance to obtain the thermal resistance of the thermal insulation layer; combining the thermal conductivity coefficient of the thermal insulation material and the climate correction coefficient to calculate the design thickness of the thermal insulation layer corresponding to the thermal resistance of the thermal insulation layer.

2. The method of claim 1, wherein the heat exchange coefficient-based thickness calculation method of a concrete thermal insulation layer is characterized by, The step of generating the temperature-time function of the wall center point through the pre-constructed temperature field analytical model based on the geometric parameters and the thermal physical parameters of the concrete comprises: obtaining the wall thickness and the amount of cementitious material based on the geometric parameters and the thermal physical parameters of the concrete; inputting the wall thickness and the amount of cementitious material into the dimensionless heat transfer equation of the pre-constructed temperature field analytical model; solving the Fourier heat conduction partial differential equation containing the internal heat source term in the temperature field analytical model through the separation of variables method; outputting the temperature-time function of the wall center point expanded in the form of a mode function series.

3. The method for calculating the thickness of a concrete insulation layer based on the heat exchange coefficient according to claim 2, characterized in that, The process of solving the heat exchange coefficient in the cooling rate function through a numerical optimization algorithm with the preset cooling rate as a constraint condition comprises: establishing an explicit correlation equation of the cooling rate function and the heat exchange coefficient; using the gradient descent method to iteratively adjust the heat exchange coefficient variable with the preset cooling rate as the target value; when the error between the real-time calculated cooling rate and the target value is less than the preset error threshold, outputting the current heat exchange coefficient as the heat exchange coefficient.

4. The method of claim 1, wherein the heat exchange coefficient-based thickness calculation method of a concrete thermal insulation layer is characterized by, The step of querying the working condition database according to the construction working condition label to output the corresponding maximum allowable heat flux density comprises: calling the pre-stored working condition database, which contains the corresponding relationship between the construction environment temperature interval, the concrete strength grade and the heat flux density threshold; matching the corresponding construction environment temperature interval and the concrete strength grade according to the input construction working condition label; outputting the corresponding heat flux density threshold as the maximum allowable heat flux density.

5. The method of claim 1, wherein the method is characterized by: The step of combining the thermal conductivity coefficient of the thermal insulation material and the climate correction coefficient to calculate the design thickness of the thermal insulation layer corresponding to the thermal resistance of the thermal insulation layer comprises: multiplying the thermal resistance of the thermal insulation layer by the thermal conductivity coefficient of the thermal insulation material to obtain a theoretical thickness; determining the climate correction coefficient according to the environmental temperature range; multiplying the theoretical thickness by the climate correction coefficient to output the design thickness of the thermal insulation layer.

6. A method of calculating the thickness of a concrete thermal insulation layer based on the heat exchange coefficient according to any one of claims 1 to 5, characterized in that, After the step of obtaining the design thickness of the thermal insulation layer, the method further comprises: generating the thermal insulation layer construction parameters based on the design thickness of the thermal insulation layer, including the coating thickness configuration value and the inside and outside corner bevel angle; wherein the coating thickness configuration value is set to be equal to the design thickness of the thermal insulation layer. A cold bridge elimination instruction is generated according to the included angle of the female-male corner to control a template processing device to perform a groove cutting operation.

7. A heat exchange coefficient-based concrete insulation thickness calculation system, characterized by, The computing system comprises: a parameter input module configured to obtain geometric parameters of a target wall, thermal physical parameters of concrete, and a preset cooling rate; a temperature field analysis module configured to generate a temperature-time function of a center point of the wall based on the geometric parameters and the thermal physical parameters of the concrete by using a pre-constructed temperature field analysis model; a cooling rate calculation module configured to obtain a cooling rate function by performing time differentiation on the temperature-time function; a heat exchange coefficient optimization module configured to solve a heat exchange coefficient in the cooling rate function by using a numerical optimization algorithm with the preset cooling rate as a constraint condition; a heat flow density query module configured to obtain a maximum temperature difference between a center point of a concrete wall and an environment, and to output a corresponding maximum allowable heat flow density by querying a working condition database according to a construction working condition label; a minimum total thermal resistance calculation module configured to calculate a minimum total thermal resistance according to the maximum temperature difference and the maximum allowable heat flow density; a surface convective thermal resistance calculation module configured to calculate a surface convective thermal resistance according to the heat exchange coefficient; a thermal resistance calculation module configured to calculate a thermal resistance of a thermal insulation layer by subtracting the surface convective thermal resistance from the minimum total thermal resistance; a thermal insulation layer thickness design module configured to calculate a design thickness of the thermal insulation layer corresponding to the thermal resistance of the thermal insulation layer by combining a thermal conductivity coefficient of a thermal insulation material and a climate correction coefficient.

8. A computer device, comprising: A computer program product comprising a memory, a processor and a computer program stored on the memory and loadable on the processor, the processor implementing the method according to any one of claims 1 to 6 when executing the program.

9. A computer-readable storage medium, characterized in that: A computer program product comprising a memory, a processor and a computer program stored on the memory and loadable on the processor, the processor implementing the method according to any one of claims 1 to 6 when executing the program.

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