Method and device for evaluating effective thermal conductivity of porous materials based on multi-scale algorithm

Abstract

The application discloses a kind of based on multi-scale algorithm's porous material effective heat conduction coefficient evaluation method and equipment, belong to material thermal property simulation field.For the problem of complex micro-pore modeling and low heat transfer calculation efficiency, the present scheme constructs the discretization grid model containing controlled overlapping characteristics using random sequential adsorption algorithm;Configure anisotropic parameters and various boundary conditions;Parallel call heat resistance network or Monte Carlo random walk solver based on finite difference, calculate steady-state temperature field or particle mean square displacement;Combine physical law to invert macroscopic effective heat conduction coefficient.The application can quickly and accurately predict the influence of microstructure on macroscopic thermal performance, mainly used for formula optimization and thermal protection design of porous composite material.

Description

Technical Field

[0001] This invention relates to the field of material thermal property simulation and calculation technology, and more specifically, to a method and device for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm. Background Technology

[0002] Porous materials, due to their lightweight, high specific surface area, and excellent thermal insulation or conductivity, have broad application prospects in aerospace thermal protection, energy storage systems, and building energy conservation. The macroscopic effective thermal conductivity of porous materials depends not only on the intrinsic thermal conductivity of the matrix and the fluid within the pores, but also on the profound influence of microscopic pore morphology, porosity, pore size distribution, and spatial connectivity. Traditionally, obtaining the effective thermal conductivity mainly relies on experimental measurements using steady-state or transient methods. However, these methods are time-consuming, costly, and difficult to intuitively reveal the intrinsic influence mechanism of microscopic geometry on macroscopic thermal properties, thus hindering the reverse engineering of new material formulations. With the development of computer science, numerical simulation has become a key tool in materials design. However, existing technologies have significant drawbacks in simulating the thermal conductivity of heterogeneous porous media: First, they often rely on overly simplified ideal periodic models (such as simple series-parallel media theory), which cannot reflect the random distribution characteristics of pores in real materials; Second, they rely on traditional three-dimensional finite element analysis (FEA) software for mesh generation and solving, which is prone to failure when dealing with complex random structures with high porosity and high connectivity, and the computational cost is extremely high, making it difficult to perform large-scale data scanning and formulation optimization; Third, single macroscopic continuous medium simulation algorithms cannot simultaneously take into account the random diffusion behavior of microscopic thermal carriers, and lack an efficient evaluation mechanism that can perform cross-scale verification. Summary of the Invention

[0003] The main objective of this invention is to provide a method and device for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm, thereby addressing the problems of difficulty in modeling complex micropores, low heat transfer calculation efficiency, and lack of multi-scale cross-validation in existing technologies. To achieve the above objective, this invention provides a method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm, comprising the following steps: Step 1: Constructing a representative volume element geometric model: Using a random sequential adsorption algorithm, randomly generating pore center coordinates in a preset two-dimensional or three-dimensional space, and performing collision detection based on preset porosity and pore size parameters to generate a discretized digital mesh model of the heterogeneous porous medium; Step 2: Configuring a thermophysical simulation environment: Setting the anisotropic thermal conductivity of the matrix phase and the porous phase in different coordinate axis directions, and configuring fixed temperature boundaries, adiabatic boundaries, or periodic boundary conditions for the outer boundary of the digital mesh model; Step 3: Executing multi-solver numerical simulation: Calculating the steady-state temperature field distribution data or the mean square displacement curve of the thermal carriers within the model by parallel or selectively calling a thermal resistance network solver, a Monte Carlo random walk solver, or an effective medium approximation model; Step 4: Extracting Equivalent Thermal Conductivity Features: Based on the steady-state heat flux integral data or particle diffusion coefficient obtained in Step 3, the macroscopic effective thermal conductivity of the porous material is obtained by inversion calculation using Fourier's law of thermal conductivity or Einstein's diffusion relation. Another objective of this invention is to provide an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the program to implement the above-mentioned evaluation method steps. This invention has the following beneficial effects: It utilizes a discretized random geometry generation algorithm to replace the traditional continuous mesh generation, greatly improving the success rate and computational efficiency of modeling complex porous media. Simultaneously, it innovatively integrates a macroscopic iterative algorithm (thermal resistance network method) and a microscopic statistical algorithm (Monte Carlo random walk), allowing users to perform multi-scale numerical verification in the same physical space, significantly improving the scientific rigor and accuracy of effective thermal conductivity prediction, and providing a high-throughput digital simulation platform for the industrial formulation design and thermal performance optimization of porous materials. Attached Figure Description

[0004] Figure 1 A flowchart illustrating the steps of a method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the controlled overlapping porous microstructure matrix generated by the random sequential adsorption algorithm in an embodiment of the present invention; Figure 3 This is a schematic diagram of the heat transfer relationship between nodes in a discrete grid-based thermal resistance network in an embodiment of the present invention. Figure 4 This is a schematic diagram of the mean square displacement evolution curve with time step based on the Monte Carlo random walk algorithm in an embodiment of the present invention. Detailed Implementation

[0005] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention. This invention provides a method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm. The detailed execution steps of this method are as follows: Step 1: Construct a representative volume element geometric model. The system initializes a two-dimensional matrix of size L×W or a three-dimensional matrix of size L×W×H, with the initial value set as the matrix phase. Subsequently, the Random Sequential Adsorption (RSA) algorithm is used to generate the center coordinates (x, y, z) of the pores in the matrix space using a pseudo-random number generator. After each generation, collision detection is performed: the Euclidean distance d between the new center and the existing center is calculated. In a preferred embodiment, the system supports a controlled overlap mode. If overlap is not allowed by default, the pore is retained only when d ≥ 2r (r is the pore radius); if overlap is allowed, an overlap factor restriction is introduced. The random adsorption process is repeated, and the volume fraction of the porous phase in the matrix phase is statistically analyzed in real time until the user-preset target porosity is reached. Finally, a discretized digital mesh model consisting of 0s and 1s is output. Step 2: Configure the thermophysical simulation environment. The generated digital mesh model is mapped to a physical parameter matrix. The intrinsic thermal conductivity is assigned to the matrix phase elements and porous phase elements in the matrix, respectively. To simulate anisotropic heat transfer in real-world scenarios, thermal conductivity can be configured along different directions of the X, Y, and Z axes. Subsequently, the boundary conditions of the system are defined, for example, configuring a fixed temperature difference at the upper and lower boundaries (e.g., T_top=1.0, T_bottom=0.0), and adiabatic conditions at the left and right boundaries, thereby forcing heat flow to be stably conducted along a single macroscopic direction. Step 3: Execute multi-solver numerical simulation. This invention provides multiple cross-scale solution paths for selection: Path A (Thermal Resistance Network Solver): Employing the finite difference concept, the mesh is discretized into a resistance network. For adjacent nodes i and j, the equivalent thermal conductivity k_ij = (2 * k_i * k_j) / (k_i + k_j) is calculated using the harmonic mean. Then, the energy balance equation for the global nodes is established, and the temperature field is updated using the Gauss-Seidel iterative method until the average temperature residual between two adjacent iterations approaches a minimum threshold (e.g., 1e-5), thus obtaining the global steady-state temperature field distribution. Path B (Monte Carlo random walk solver): Thousands to tens of thousands of virtual thermal carrier particles are randomly introduced into the digital grid. Within each time step, the probability of a particle jumping to an adjacent grid depends on the thermal conductivity weight matrix of the target grid. The system tracks the trajectory of all particles in real time and records the overall mean square displacement (MSD). Step 4: Extract equivalent thermal conductivity features.For path A, the system numerically integrates the heat flux density at the cold-end boundary or global cross-section of the steady-state temperature field to obtain the total heat flux, and calculates the macroscopic effective thermal conductivity K_eff in reverse according to the one-dimensional Fourier thermal conductivity law. For path B, the slope of the mean square displacement (MSD) obtained in step three as a function of time step (t) is extracted, the diffusion coefficient D is calculated according to Einstein's diffusion relation, and multiplied by the average thermophysical constant of the matrix to calibrate the macroscopic effective thermal conductivity of the porous material. Further, this embodiment also includes a parameter scanning step: the system can set the target porosity or pore radius as a dynamic variable set, automatically repeat steps one to four above, output multiple sets of macroscopic effective thermal conductivity, and use a data fitting module to generate a physical relationship curve of thermal conductivity as a function of structural variables. Finally, a PDF experimental report is output through a report generator. In addition, this embodiment of the invention also provides an electronic device, including a central processing unit (CPU), memory, and a storage medium. The storage medium stores computer-executable instructions, and when the CPU executes these instructions, it can fully implement the above-described method for evaluating the effective thermal conductivity of porous materials. The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm, characterized in that, The method includes the following steps: Step 1: Constructing a representative volume element geometric model: Using a random sequential adsorption algorithm, the coordinates of the pore center are randomly generated in a preset two-dimensional or three-dimensional space, and collision detection is performed according to the preset porosity and radius to generate a discretized digital mesh model of the heterogeneous porous medium; Step 2: Configuring a thermophysical simulation environment: The anisotropic thermal conductivity of the matrix phase and the pore phase in different coordinate axis directions is set, and fixed temperature, adiabatic, or periodic boundary conditions are configured for the boundary of the digital mesh model; Step 3: Executing multi-solver numerical simulation: By calling the thermal resistance network solver, Monte Carlo random walk solver, or effective medium approximation model in parallel, the steady-state temperature field distribution or carrier mean square displacement curve inside the model is calculated; Step 4: Extracting equivalent thermal conductivity features: Based on the steady-state heat flux integral data or particle diffusion coefficient obtained in Step 3, the macroscopic effective thermal conductivity is obtained by inversion using Fourier's law or Einstein's diffusion relation.

2. The method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm according to claim 1, characterized in that, The random sequential adsorption algorithm in step one supports a controlled overlap mode, which can simulate the morphology of open or closed microstructures by adjusting the Euclidean distance threshold of collision detection.

3. The method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm according to claim 1, characterized in that, The thermal resistance network solver in step three uses the finite difference concept to treat the contact interface between grid nodes as equivalent thermal resistance, calculates the equivalent conductivity of adjacent nodes using harmonic mean, and solves the steady-state temperature field of each node using the Gauss-Seidel iteration method.

4. The method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm according to claim 1, characterized in that, In step three, the Monte Carlo random walk solver simulates the random jumping behavior of hot carriers at different phase interfaces by deploying virtual particles of a preset size, and records the mean square displacement of the particles as the time step evolves.

5. The method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm according to claim 1, characterized in that, Step three also includes a parameter scanning mechanism, which uses preset porosity or pore size as scanning variables, automatically traverses the variable range and performs iterative calculations to generate an evolution curve of the effective thermal conductivity as a function of structural parameters.

6. The method for evaluating the effective thermal conductivity of porous materials based on a multi-scale algorithm according to claim 1, characterized in that, Step four is followed by an automated report generation step, which summarizes and outputs the input geometric parameters, boundary conditions, convergence residual curves, and final calculation results as an electronic report document.

7. An electronic device employing the evaluation method according to any one of claims 1 to 6, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method.

Images