Method, equipment, medium and system for predicting heat transfer characteristics of thermal barrier coating of thermal protection structure
By introducing local mesh refinement technology on the basis of CV-FVM, the problems of accuracy and computational efficiency in thermal barrier coating thickness design are solved, and high-precision heat transfer characteristic prediction and low-redundancy design are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-07
- Publication Date
- 2026-04-03
AI Technical Summary
Existing technologies struggle to achieve precise thermal barrier coating thickness design while efficiently reducing computational load, and excessively thick coatings are prone to peeling off.
Based on the lattice-type finite volume method CV-FVM, a local mesh refinement technique is introduced. By refining the mesh at the interface between the coating and the substrate through local mesh refinement, heat flux conservation is ensured, global fine meshing is avoided, a discrete control volume is established, and midpoint integration is performed.
It achieves high accuracy and low computation time in predicting the heat transfer characteristics of thermal barrier coatings, reduces the difficulty of mesh generation, avoids coating peeling, and improves computational efficiency.
Smart Images
Figure CN121786981A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of numerical computation, and more specifically, to a method, device, medium, and system for predicting the heat transfer characteristics of thermal barrier coatings on thermal protection structures. Background Technology
[0002] When an aircraft flies through the atmosphere, shock wave compression and viscous friction cause the air temperature near the wall to rise. The high-temperature air continuously transfers heat to the low-temperature wall, resulting in intense aerodynamic heating, which places more stringent demands on heat-resistant materials. Under these conditions, the aerodynamic thermal environment is evolving towards higher enthalpy, higher peak heat flux density, and longer heating durations. Simultaneously, heat-resistant materials require improved payload ratios and reduced operating costs. Large-area heat-resistant materials must not only withstand prolonged exposure to high-temperature airflow but also maintain minimal shape change and a smooth surface after exposure to ensure good aerodynamic shape for the aircraft. This presents a severe challenge to the thermal protection technology and structural design of aircraft. Practical experience and research have shown that applying a thermal barrier coating to the surface of heated components can effectively solve these problems, while increasing heat protection costs almost without increasing production capacity.
[0003] Thermal barrier coatings are significantly affected by the fabrication process, exhibiting characteristics of non-uniformity, multi-component nature, nonlinearity, and thermal matching with the substrate. Research on these coatings primarily relies on traditional direct numerical simulation methods to predict their heat transfer capabilities. To ensure the accuracy of numerical calculations at the metal substrate-coating interface using traditional direct numerical simulation methods, both the metal substrate and the coating require extremely dense meshes during the structure-mesh topology establishment process, resulting in a massive computational burden. Even supercomputers cannot efficiently solve for meshes in the millions. Often, reducing the number of computational meshes sacrifices numerical accuracy, and increasing the coating thickness to create a safety factor facilitates rapid design. However, excessively thick coatings introduce the problem of easy detachment from the metal substrate.
[0004] Therefore, how to achieve low-redundancy design of coating thickness through fast and highly accurate numerical calculation methods has become a key aspect of current thermal barrier coating design applications. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, device, medium and system for predicting the heat transfer characteristics of thermal barrier coatings in thermal protection structures, which ensures the accuracy of heat transfer prediction without significantly increasing the calculation time.
[0006] The objective of this invention is achieved through the following solution: A method for predicting the heat transfer characteristics of a thermal barrier coating on a thermal protection structure includes the following steps: Based on the lattice-type finite volume method CV-FVM, local mesh refinement is introduced for mesh generation. Under the condition of conserving heat flux at the thermal conduction interface, the non-matching topological mesh of the substrate and thermal barrier coating is achieved to avoid global fine mesh generation. After mesh generation, a discrete control volume is established at the nodes at the interface locations; The heat dissipation and conduction equations of the control volume are established and the solution is calculated based on the midpoint integral. For different nodes, the corresponding node temperature is used as the variable to be solved in a matrix assembly and then solved to complete the prediction of the heat transfer characteristics of the thermal barrier coating of the thermal protection structure.
[0007] Furthermore, based on the lattice-type finite volume method CV-FVM, local mesh refinement is introduced to achieve mismatched topological meshing between the substrate and the thermal barrier coating while ensuring the conservation of heat flux at the thermal conduction interface, thus avoiding globally fine meshing. This specifically includes the following sub-steps: For nodes in unencrypted regions or transitional regions without meshes, the control volume is constructed using the traditional CV-FVM discretization method to form a polygonal control volume; for nodes at the interface, the center of the mesh cell and the midpoint of the edge are connected sequentially to form an irregular control volume.
[0008] Furthermore, the polygonal control body includes a quadrilateral control body.
[0009] Furthermore, the polygonal control body includes a three-dimensional quadrilateral control body.
[0010] A device for predicting the heat transfer characteristics of a thermal barrier coating on a thermal protection structure includes a processor and a memory, wherein the memory stores a computer program that, when loaded by the processor, executes the method described in any of the preceding claims.
[0011] A computer-readable storage medium storing a computer program that, when loaded by a processor, executes the method described in any of the preceding claims.
[0012] A system for predicting the heat transfer characteristics of a thermal barrier coating for a thermal protection structure includes the heat transfer characteristic prediction device for the thermal barrier coating for a thermal protection structure as described above.
[0013] The beneficial effects of this invention include: This invention addresses the heat conduction problem of thermal barrier coatings for aircraft thermal protection. Based on the existing gridded finite volume method (CV-FVM), it introduces local mesh refinement technology. By locally refining the mesh at the coating and the interface between the coating and the substrate, the computational workload is significantly reduced while ensuring the balance of heat flux at the interface. This reduces the computation time of numerical solutions while maintaining computational accuracy, thereby achieving a low-redundancy design for thermal barrier coatings.
[0014] This invention can realize non-corresponding mesh topology processes for heat conduction problems between different materials, and does not require different structural meshes to correspond one-to-one, thus reducing the difficulty of mesh generation.
[0015] This invention enables refined prediction of heat conduction response with obvious local micro-features, without requiring densification of the structural mesh around the micro-features. Therefore, it ensures the accuracy of heat transfer prediction without significantly increasing the computation time. Attached Figure Description
[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0017] Figure 1 A schematic diagram of the control volume establishment for a locally refined grid-based finite volume method; Figure 2 This is a schematic diagram of the control unit; Figure 3 The diagrams show the integration points of quadrilateral elements in different coordinate systems; (a) shows the integration points of quadrilateral elements in the global coordinate system, and (b) shows the integration points of quadrilateral elements in the local coordinate system. Detailed Implementation
[0018] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.
[0019] The specific implementation process of this invention is as follows: The present invention relates particularly to a refined prediction technique for the thermal conductivity characteristics of thermal protective coatings under aerodynamic thermal environments. In a preferred embodiment, a method for predicting the heat transfer characteristics of a thermal barrier coating on a thermal protective structure is provided, comprising the following steps: Based on the lattice-type finite volume method CV-FVM, local mesh refinement is introduced for mesh generation. Under the condition of conserving heat flux at the thermal conduction interface, the non-matching topological mesh of the substrate and thermal barrier coating is achieved to avoid global fine mesh generation. After mesh generation, a discrete control volume is established at the nodes at the interface locations; The heat dissipation and conduction equations of the control volume are established and the solution is calculated based on the midpoint integral. For different nodes, the corresponding node temperature is used as the variable to be solved in a matrix assembly and then solved to complete the prediction of the heat transfer characteristics of the thermal barrier coating of the thermal protection structure.
[0020] In other embodiments, based on the above embodiments, the following more detailed implementation steps are further provided: Step 1: After mesh generation, discrete control volumes are established for nodes at the interface locations. Specifically, taking quadrilateral mesh elements as an example, for nodes in unrefined regions (CV1) or meshless transition regions (CV4 and CV6), the control volume construction method is no different from the traditional CV-FVM discretization method, forming quadrilateral control volumes, such as... Figure 1 As shown, black represents element nodes, hollow dots represent element centers and material property storage locations, blue lines represent control volumes, and red lines represent interfaces. For nodes at interfaces, referring to the traditional CV-FVM control volume construction method, the element centers and edge midpoints are connected sequentially to form a structure like... Figure 1 The irregular control bodies shown are CV2, CV3, and CV5.
[0021] Step 2: Based on the established heat transfer equation of the control volume. Specifically, for the heat transfer equation of the control volume formed in Step 1, the transient heat transfer equation for the isotropic material without internal heat sources in the integral scheme is as follows:
[0022] in, ρ,c,T,t,k , respectively represent density, specific heat capacity, temperature, time, and thermal conductivity; n x , n y The outer normal vector n is represented along... x , y directional components, V Represents an integral body. S This represents the integral surface (for 2D problems, it is the integral line).
[0023] Taking the control body CV2 as an example ( Figure 2 As shown), the control equation (1) is discretized using CV-FVM. The control volume CV2 is composed of integral line segments within the quadrilateral units □1-2-3-4, □4-3-6-5, □9-4-7-8, and □10-11-4-9. l 1- l Composed of 8 components, based on the midpoint integral formula, the integral term on the right side of equation (1) is approximately calculated, and the integration position is as follows: Figure 2 As shown.
[0024] For the control volume CV2, the integral term on the right-hand side of equation (1) can be simplified to:
[0025] Among them, the superscript " l i "Midpoint" indicates the first i Midpoint of the integral line ( i =1~8), l i Indicates the first i The length of the integral line, k unit i Representation unit i The thermal conductivity. l i and k unit i as well as n x and n y It is a constant and is stored directly before numerical calculation.
[0026] To calculate equation (2), it is necessary to calculate the spatial derivative of the temperature in the global coordinate system at the midpoint of the integral. T / x , T / y The calculation is performed by mapping it to a standard quadrilateral element (see...). Figure 3 (a) is a schematic diagram of the integration points of the quadrilateral element in the global coordinate system, and (b) is a schematic diagram of the integration points of the quadrilateral element in the local coordinate system.
[0027] Meanwhile, in the local coordinate system, the transformation relationship between the local derivative and the global spatial derivative is established through the Jacobi matrix, which is composed of the quadrilateral element node coordinates and the local derivatives of the shape function. For the quadrilateral element, the partial derivative analytical expression of the local coordinate is expressed by the shape function, and the local coordinates of 12 Gaussian integration points are established accordingly to support subsequent numerical integration. The entire derivation process simplifies the derivative calculation using the local coordinate system and realizes the mapping with the physical coordinates through the Jacobi matrix, ultimately supporting the finite element discretization solution. On this basis, the spatial derivative derivation result in the local coordinate system of the shape function is substituted into equation (2), and the expression of the integral term on the right side of equation (1) can be obtained. This equation is a linear equation expression of the product of the nodal temperature and the constant.
[0028] The time integral term on the left side of equation (1) is approximated using forward difference:
[0029] Among them, superscript t Indicates the current moment. t -△t Indicates the previous moment, V i Indicates the control body in the first i Volume within a single cell (area for 2D problems).
[0030] Step 3: For different nodes, adjust the temperature from Step 2. T The matrix is assembled as the variable to be solved and then solved.
[0031] It should be noted that the above-mentioned scheme of the present invention introduces local mesh refinement technology on the basis of traditional CV-FVM. Under the condition of ensuring the conservation of heat flux at the thermal conduction interface, it realizes the non-matching division of the topological mesh of the substrate and the thermal barrier coating, avoiding the division of the global fine mesh. This ensures the accuracy of heat conduction prediction at key locations while reducing the computation time. This method can be easily extended to three-dimensional elements, thereby improving the prediction accuracy of heat conduction problems of thermal barrier coatings with three-dimensional effects.
[0032] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.
[0033] According to one aspect of the present invention, a computer program product or computer program is provided, the computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and executes the computer instructions, causing the computer device to perform the methods provided in the various optional implementations described above.
[0034] In another aspect, embodiments of the present invention also provide a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods described in the above embodiments.
Claims
1. A method for predicting the heat transfer characteristics of a thermal barrier coating on a thermal protection structure, characterized in that, Includes the following steps: Based on the lattice-type finite volume method CV-FVM, local mesh refinement is introduced for mesh generation. Under the condition of conserving heat flux at the thermal conduction interface, the non-matching topological mesh of the substrate and thermal barrier coating is achieved to avoid global fine mesh generation. After mesh generation, a discrete control volume is established at the nodes at the interface locations; The heat dissipation and conduction equations of the control volume are established and the solution is calculated based on the midpoint integral. For different nodes, the corresponding node temperature is used as the variable to be solved in a matrix assembly and then solved to complete the prediction of the heat transfer characteristics of the thermal barrier coating of the thermal protection structure.
2. The method for predicting the heat transfer characteristics of the thermal barrier coating of a thermal protection structure according to claim 1, characterized in that, The method introduces local mesh refinement based on the lattice-type finite volume method CV-FVM to achieve mismatched topological meshing between the substrate and the thermal barrier coating while ensuring the conservation of heat flux at the thermal conduction interface, thus avoiding globally fine meshing. This includes the following sub-steps: For nodes in unencrypted regions or transitional regions without meshes, the control volume is constructed using the traditional CV-FVM discretization method to form a polygonal control volume; for nodes at the interface, the center of the mesh cell and the midpoint of the edge are connected sequentially to form an irregular control volume.
3. The method for predicting the heat transfer characteristics of the thermal barrier coating of a thermal protection structure according to claim 2, characterized in that, The polygonal control body includes a quadrilateral control body.
4. The method for predicting the heat transfer characteristics of the thermal barrier coating of a thermal protection structure according to claim 2, characterized in that, The polygonal control body includes a three-dimensional quadrilateral control body.
5. A device for predicting the heat transfer characteristics of a thermal barrier coating on a thermal protection structure, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program that, when loaded by the processor, executes the method as described in any one of claims 1 to 4.
6. A computer-readable storage medium, characterized in that, A computer program is stored in a readable storage medium, which, when loaded by a processor, executes the method as described in any one of claims 1 to 4.
7. A system for predicting the heat transfer characteristics of a thermal barrier coating on a thermal protection structure, characterized in that, The device for predicting the heat transfer characteristics of the thermal barrier coating of the thermal protection structure as described in claim 5.