Collaborative Optimization Between Efficient Thermal Dissipation and Microstructure of Ceramic Matrix Composite Component Under Non-Uniform Thermal Loads

Abstract

This paper presents a collaborative optimization design methodology aimed at improving heat dissipation efficiency through the modulation of microstructural variations. The approach addresses the thermal protection requirements of high-temperature components, such as ceramic matrix composite turbine blades, which are subjected to complex and elevated thermal loads. Through the integration of numerical simulation and experimental validation, a bidirectional mapping model linking carbon nanotube (CNT) content with the macroscopic anisotropic thermal conductivity of the material was developed. Furthermore, a thermal conduction analysis and optimization framework for Ceramic Matrix Composite (CMC) high-temperature components under non-uniform thermal loads was established. This study expands the adjustable range of the material’s thermal conductivity by allowing flexible modulation of carbon nanotube content. The results demonstrate that this methodology effectively enhances the heat dissipation capacity of CMC materials in extreme thermal environments: the maximum surface temperature of the optimized flat plate is reduced by 8.96%, the peak temperature gradient is lowered by 46.64%, and the maximum thermal stress is decreased by 38.17%. This research provides new insights into the comprehensive integration of thermal dissipation requirements for CMC hot components.

1. Introduction

With the rapid rise in turbine inlet temperatures of aero-engines, Ceramic Matrix Composites (CMCs) are increasingly used in hot section components such as turbine blades, combustors, and nozzles due to their excellent high-temperature mechanical properties and thermal stability [1,2]. However, during engine operation, hot section components like turbine blades face extremely complex thermal load conditions, including non-uniform temperature fields (hot spots), high-frequency thermal shocks, and severe temperature gradient changes [3,4,5,6]. These uneven thermal loads tend to cause thermal stress buildup within CMC materials, which can lead to thermomechanical damage (such as matrix cracking and fiber debonding), significantly weakening their mechanical properties and reducing their service life. For example, Zheng Ni [7], Hu X [8], and Yang Z [9] have shown through high-temperature gradient cycling tests and cold extraction tests that high thermal shocks and intense non-uniform thermal loads can induce interfacial layer debonding and fiber damage within the material structure, resulting in the degradation of mechanical properties and a decline in the reliability of CMC materials.

To reduce the impact of non-uniform high thermal loads on the performance and lifespan of CMC materials, many thermal protection strategies have been implemented for CMC hot components. Current research mainly concentrates on two technical methods. The first involves external active cooling technologies, such as film cooling and transpiration cooling [10,11,12,13], which lower surface temperatures by using external cooling media. However, their efficiency is restricted by coolant consumption and structural complexity. The second method focuses on internal efficient heat dissipation, which improves the macroscopic anisotropic thermal conductivity of CMCs through adjustments to their microstructural weaving parameters (such as fiber spacing and weaving angle), thereby enhancing heat transfer pathways. For example, Tu Zecan et al. [14] and Wu Xinyu et al. [15] demonstrated that changing fiber weaving structures can modify the distribution of in-plane and through-thickness effective thermal conductivity, thus controlling surface temperature fields. Data show that weaving structure modifications can lead to a maximum cold efficiency regulation of 13% for single-row film-cooled flat plates and 18% for multi-row film-cooled flat plates under identical operating conditions.

However, the studies mentioned above have mainly focused on understanding the coupling mechanisms between microstructural parameters and large-scale temperature fields, and they have not yet developed a complete technical pathway from material microstructure design to improved engineering thermal protection efficiency. Specifically, although the effect of weaving structure parameters on temperature field distribution has been shown through experimental characterization and numerical simulation [16,17,18,19], there is a lack of systematic methods to turn these basic research findings into guidance for the thermal dissipation design of CMC hot components. In particular, there is a need to address key engineering challenges, such as how to achieve directional heat flow regulation through microstructural optimization and how to develop a collaborative protection mechanism with existing active cooling technologies.

To address the issues mentioned earlier, the collaborative design of multi-objective optimization algorithms and material microstructures provides new insights for the thermal protection of CMCs. Zhao Chenwei et al. [20] developed a collaborative optimization method for advanced aircraft by building a regression model with macroscopic effective thermal conductivity as a variable within a multi-scale collaborative framework, and inversely deriving the mesoscopic weaving structure that fulfills thermal protection requirements. Guo Fei et al. [21] combined particle swarm optimization to achieve inverse matching between weaving structure parameters and thermal conductivity. Ghasemi H et al. [22] used stepwise sequential optimization and reliability-based design optimization (RBDO) methods to optimize cooling capacity and fiber distribution. However, traditional approaches to adjusting the microstructural parameters of the material have limited impact on the thermal conductivity of CMC materials (no more than 5%) [23]. In this context, the gradient modification process of carbon nanotubes (CNTs) proposed by Yu Pan [24,25,26,27] demonstrates significant advantages: by employing laser processing and chemical vapor infiltration (CVI) techniques, the doping amount of CNTs can be precisely controlled in different regions of CMC components, allowing for broad-range regulation of thermal conductivity (5.73–95.56 W/(m·K)) within feasible process limits, offering a new approach for gradient thermal property design.

Based on this, the paper proposes a collaborative optimization design method for microstructure and heat dissipation based on the CNT modification process: First, a bidirectional mapping model between CNT content and effective thermal conductivity is established, then combined with a thermo-mechanical coupling simulation framework to inversely optimize the distribution of thermal conductivity to achieve enhanced heat dissipation in high-temperature areas and foster collaborative microstructure design. This study aims to overcome the process limitations of traditional woven structure optimization and provide both theoretical support and technical pathways for the reliable design and extended lifespan of CMC components in extreme thermal environments.

2. Research Model and Boundary Conditions

2.1. Research Model

The combustion process within an aero-engine is extremely complex, leading to a significantly non-uniform distribution of thermal loads on the turbine blades. Furthermore, the discrete arrangement of film cooling holes exacerbates the spatial heterogeneity of the thermal load distribution on the blade surface. Figure 1b illustrates the temperature field distribution of a first-generation turbine blade model for a certain type of engine. As shown in the figure, under the combined effects of the mainstream hot gas and film cooling, a distinct high-temperature zone forms near the upper platform region of the blade. In contrast, the pressure surface region exhibits relatively lower temperatures due to effective coverage by the film cooling. To more clearly elucidate the principles of the CMC thermophysical property optimization method and the impact of optimization on heat transport pathways, this study focuses on a CMC plate structure and establishes a numerical analysis model for a 2.5D SiC/SiC CMC plate under non-uniform thermal loads, as shown in Figure 1. The model dimensions are length L1 = 100 mm, width W1 = 60 mm, and thickness H1 = 3 mm. Based on the processing capabilities of the C-nanotube gradient modification technique, the plate is divided into 60 grid partitions, each with dimensions L2 = W2 = 10 mm. This design not only meets the practical need for localized thermophysical property control but also provides a discretized variable space for multi-objective optimization, ensuring the realizability of the optimization results.

2.2. Boundary Conditions

To simulate the complex non-uniform thermal load on the outer surface of turbine blades under aero-engine operating conditions, as well as the non-uniform characteristics of the blade surface thermal load resulting from both the low thermal conductivity of CMC materials and the discrete distribution of film cooling, this study extracts a simulation result from a film cooling structure design project for a high-pressure first-stage guide vane. As the project data are not public, the average values of the heat-flux density in the highest temperature zone, the second-highest temperature zone, and the low-temperature zone from the simulation results are taken and rounded to serve as inputs for the three types of heat-flux boundaries in the plate numerical model. The main-heat-source heat-flux density (Q_h1 = 10⁶ W/m²), secondary heat-source heat-flux density (Q_h2 = 8×10⁵ W/m²), and cold-source heat-flux density (Q_c = −8 × 10⁵ W/m²) are defined as shown in Figure 1d. Convective heat transfer boundary conditions are applied to the remaining surfaces, with fluid temperature T_f = 1200 K and convective heat transfer coefficient h = 1000 W/(m²·K). The specific parameters are listed in

Table 1. Boundary condition parameter table.

Boundary Type	Heat Flux (W/m2)	Fluid Temperature (K)	Convective Heat Transfer Coefficient (W/(m2·K))
Main heat source (Qh1)	1,000,000	-	-
Secondary heat source (Qh2)	800,000	-	-
Cold source (Qc)	−800,000	-	-
Convective boundary (Tf/h)	-	1200	1000

.

2.3. Material Property Parameter Settings

Based on the carbon nanotube (CNT) content-thermal conductivity mapping relationship established in Section 3.2, the thermophysical parameters of the material in different regions were defined. The material density and Poisson’s ratio were set as constants, while the thermal conductivity varied with the CNT content (0–15%), and the remaining parameters changed with temperature (293.15 K–1673.15 K). The results are shown in

Table 2. Table of Material Thermophysical Properties.

	Thickness Direction	In-Plane Direction
Density (kg/m3)	2520
specific heat (J/(kg·K))	841–1685	765–1345
thermal conductivity (W/(m·K))	10.8~20.12	16.2~30.18
Young’s modulus (MPa)	263.4–189.6	196.6–192.7
Poisson’s ratio	0.24	0.158

.

3. Optimization Methods

3.1. Introduction to Research Methods

Figure 2 illustrates the entire process of the microstructural multi-objective optimization design for thermal protection of CMC materials under complex high-thermal-load conditions. Firstly, based on the CNT gradient modification technology, a quantitative correlation model between microstructural parameters (fiber weaving structure, CNT content) and macroscopic thermal properties (effective thermal conductivity) is established through numerical simulation and experimental calibration. Secondly, a three-dimensional thermo-mechanical coupling simulation framework for CMC components under non-uniform thermal loads is constructed, and the NSGA-II multi-objective genetic algorithm is introduced to calculate the optimal distribution of thermal conductivity for CMC hot components under complex high-thermal-load conditions. Finally, based on the mapping relationship between macroscopic effective thermal conductivity and microstructural parameters, a microstructural design scheme for CMC hot components under complex high-thermal-load conditions is established to achieve the inverse optimization design of material thermal conductivity distribution.

3.2. Establishment of a Two-Way Mapping Model Between Microstructure and Equivalent Thermal Conductivity

Utilizing the German Diondod2 type microfocus CT scanning system (source-to-detector distance FDD = 800 mm, source-to-object distance FOD = 32 mm), a three-dimensional characterization was conducted on the standard SiC/SiC-CNTs specimen with a CNTs mass fraction of 3.75% (dimensions Φ12.6 mm × 3 mm). Through 1795 projection data (reconstruction matrix 4000 × 4000, voxel size 0.004 mm), the fiber weaving parameters (warp/weft width 1.3 mm, weaving angle 30°) and the distribution characteristics of CNT micro-columns (average diameter 0.96 mm) were precisely extracted, as shown in Figure 3. This characterization result provides high-fidelity geometric input for subsequent multi-scale modeling.

Based on the CT scan data, a predictive model for the thermal conductivity of full-thickness [14] representative volume elements (RVEs) under different CNT content conditions was established (Figure 4). In the figure, the white regions represent the SiC matrix, the light gray regions represent the SiC fibers, and the black regions represent the CNTs. The geometric dimensions of the RVE unit cell are length L_RVE = 5.0942 mm, width W_RVE = 3.8 mm, and height H_RVE = 3.06 mm. The pore characteristics present in the CMC material were equivalently homogenized and characterized as the thermal conductivity of the matrix during the modeling process.

The finite element software COMSOL Multiphysics 6.2 was employed to construct a three-dimensional steady-state heat conduction model based on Fourier’s law to calculate the effective thermal conductivity of the RVE under different CNT contents. The boundary conditions were set as follows: the temperature of the heat-source wall T_h = 1410 K, the temperature of the cold-source wall K_c = 1400 K, and the remaining walls were defined as periodic boundaries.

It is well known that CMC materials are composed of fibers and a matrix. The thermal conductivity of the SiC matrix is globally isotropic, whereas the thermal conductivity of the SiC fibers is anisotropic in the axial and radial directions. Therefore, the CMC material exhibits significant anisotropic characteristics. In terms of material parameter settings, based on the data provided by the CMC material manufacturer, the axial and radial thermal conductivities of the fibers were set at 28 W/(m·K) and 5 W/(m·K), respectively, while the matrix thermal conductivity was isotropic at 20 W/(m·K). The fiber orientation was achieved through the curvilinear coordinate module to assign the anisotropic thermal conductivity in a directional manner (Figure 5).

The CNT-doped CMC plate was produced by Northwestern Polytechnical University (Xi’an, Shaanxi Province, China), with the detailed preparation process outlined in reference [24]. The study in that publication did not consider the impact of internal pores and other defect features of CNT micropillars on their thermal conductivity. In this paper, by thoroughly examining the structural discontinuities and interface defects formed during the fabrication of CNT micropillars, the effective thermal conductivity of CNTs is calculated to be 80 W/(m·K) using finite element methods.

Finite element calculations determined the through-thickness thermal conductivity of the CMC material at different CNT contents, as shown in Figure 6. Next, a quadratic polynomial was used to establish a quantitative relationship between the CNT content (0–15%) and the thermal conductivity. The results reveal that the thermal conductivity of the material generally increases linearly with higher CNT content. Specifically, the thermal conductivity of the CMC with 15% CNT is 85.71% higher than that of the CMC without CNT doping. Compared to the traditional method of adjusting thermal conductivity through fiber weaving structure, which offers a tunability of less than 5% [23], varying the CNT content provides a significantly broader range of thermal conductivity adjustment.

To validate the accuracy of the simulation results, thermal conductivity tests were conducted on the specimen shown in Figure 3. The laser flash method was employed as the experimental technique, using an FLA 467 HT (NETZSCH Germany) apparatus in accordance with the GB/T 22588-2008 standard [28]. The experimental setup is shown in Figure 7.

Table 3. Comparison of experimental and simulation results.

Content of Carbon Nanotubes	Experimental Value (W/(m·K))	Analog Value (W/(m·K))	Error (%)
0%	9.96	10.83	8.73%
3.75%	12.75	13.62	6.823%

presents the experimental and simulation results of the through-thickness thermal conductivity of the CMC under CNT contents of 0% and 3.75%. When the CNT content was 0%, the relative error between the experimental and simulation results was 8.73%. At a CNT content of 3.75%, the relative error was 6.82%, thereby validating the reliability of the model.

3.3. Thermal Analysis Model for CMC Components

Based on the finite element method, a thermal analysis model for the CMC plate under non-uniform thermal load conditions was established. The temperature field of the plate was numerically computed by solving the heat transfer equation. The plate model and geometric boundaries were introduced in Section 2, and this subsection presents the heat transfer equation involved in the thermal analysis model.

The three-dimensional steady-state heat conduction differential equation was applied to calculate heat transfer in the plate for the thermal analysis, with the specific solution implemented using the Solid Heat Transfer module in COMSOL Multiphysics. The three-dimensional steady-state heat conduction differential equation can be expressed as:

$${\lambda }_{xx}{\displaystyle \frac{{\mathsf{\partial }}^{2}T}{\mathsf{\partial }{X}^2}}+{\lambda }_{yy}{\displaystyle \frac{{\mathsf{\partial }}^{2}T}{\mathsf{\partial }{Y}^2}}+{\lambda }_{zz}{\displaystyle \frac{{\mathsf{\partial }}^{2}T}{\mathsf{\partial }{Z}^2}}+({\lambda }_{xy}+{\lambda }_{yx}){\displaystyle \frac{{\mathsf{\partial }}^{2}T}{\mathsf{\partial }X\mathsf{\partial }Y}}+({\lambda }_{xz}+{\lambda }_{zx}){\displaystyle \frac{{\mathsf{\partial }}^{2}T}{\mathsf{\partial }X\mathsf{\partial }Z}}+({\lambda }_{yz}+{\lambda }_{zy}){\displaystyle \frac{{\mathsf{\partial }}^{2}T}{\mathsf{\partial }Z\mathsf{\partial }Y}}=q$$

(1)

where T is the temperature at any point in the computational domain, and q is the heat-flux density.

Due to the anisotropic thermal conductivity of the CMC material, the thermal conductivity matrix of the fibers in the computational coordinate system varies with the fiber orientation. The thermal conductivity matrix of the fibers in the computational coordinate system is expressed as follows:

$$\left[\begin{array}{ccc}{\lambda }_{xx}& {\lambda }_{xy}& {\lambda }_{xz}\\ {\lambda }_{yx}& {\lambda }_{yy}& {\lambda }_{yz}\\ {\lambda }_{zx}& {\lambda }_{zy}& {\lambda }_{zz}\end{array}\right]$$

(2)

Typically, the known parameters include the axial thermal conductivity of the fiber (${\lambda }_x$), the transverse thermal conductivity (${\lambda }_y,{\lambda }_z$), and the rotation angles of the fiber’s principal direction around the X, Y, and Z axes ($\alpha ,\beta ,\gamma$). The thermal conductivity matrix in the fiber’s principal coordinate system can be expressed as:

$$\left[\begin{array}{ccc}{\lambda }_x& 0& 0\\ 0& {\lambda }_y& 0\\ 0& 0& {\lambda }_z\end{array}\right]$$

(3)

The following mapping relationship exists between the thermal conductivity matrix in the fiber’s principal coordinate system and that in the computational coordinate system:

$$\left[\begin{array}{ccc}{\lambda }_{xx}& {\lambda }_{xy}& {\lambda }_{xz}\\ {\lambda }_{yx}& {\lambda }_{yy}& {\lambda }_{yz}\\ {\lambda }_{zx}& {\lambda }_{zy}& {\lambda }_{zz}\end{array}\right]=A\left[\begin{array}{ccc}{\lambda }_x& 0& 0\\ 0& {\lambda }_y& 0\\ 0& 0& {\lambda }_z\end{array}\right]A^T$$

(4)

where A is the transformation matrix, which can be represented using the rotation angles of the fiber’s principal direction:

$$A=\left[\begin{array}{ccc}\cos \gamma \cos \beta & -\cos \alpha \sin \gamma +\cos \gamma \sin \beta \sin \alpha & \sin \gamma \sin \alpha +\cos \gamma \sin \beta \cos \alpha \\ \sin \gamma \cos \alpha & \cos \gamma \cos \alpha +\sin \gamma \sin \beta \sin \alpha & -\cos \gamma \sin \alpha +\sin \gamma \sin \beta \cos \alpha \\ -\sin \beta & \cos \beta \sin \alpha & \cos \beta \cos \alpha \end{array}\right]$$

(5)

By substituting Matrix (5) into Equation (4), the thermal conductivity matrix of the fiber in the computational coordinate system can be obtained. Substituting this fiber thermal conductivity matrix into Equation (1) enables the solution of the temperature field of the CMC plate.

3.4. Optimization Design Methodology

Based on the Non-dominated Sorting Genetic Algorithm (NSGA-II), this study establishes a multi-objective optimization method for the meso-structure of CNT gradient-modified CMC under complex thermal load conditions (Figure 8). This method couples material modification process parameters with a thermal conductivity mapping model (Section 3.1). Using the thermal conductivity of a 10 × 10 mm² gridded partition of a flat plate as the design variable, and aiming to minimize both the maximum surface temperature and the peak temperature gradient as dual optimization objectives, the approach integrates a bidirectional mapping relationship model between CNT content and the macroscopic equivalent thermal conductivity of the CMC material. Ultimately, a CNT content distribution map for the entire CMC flat plate is obtained, achieving the inverse design optimization of the thermal conductivity distribution. The optimization is performed using a COMSOL Multiphysics 6.2 with MATLAB R2023a co-simulation platform. The iterative optimization process involves randomly generating an initial population (N = 70), calculating the objective functions through thermo-mechanical coupling analysis, performing non-dominated sorting and crowding distance selection, and conducting crossover (crossover probability 80%) and mutation (mutation probability 30%) operations. The computation terminates when the number of iterations reaches 1000, outputting the Pareto optimal solution set. Sensitivity analysis indicates that when the population size is ≥70 and the number of iterations is ≥1000, the improvement in the convergence of the Pareto solution set is less than 5%, validating the rationality of the parameter settings. Finally, the solution corresponding to the minimum value of the maximum temperature in the Pareto solution set is selected as the optimal solution. This prioritizes controlling extremely high-temperature risks while simultaneously addressing the need to suppress temperature gradients, meeting the high-reliability design requirements for aero-engine hot-section components.

3.5. Mesh Generation and Independence Verification

The plate model was discretized using tetrahedral elements, and the convergence of the numerical solution was verified through a grid independence study. Three sets of meshes with approximately $80\times {10}^4$, and $200\times {10}^4$ elements were generated for grid independence verification, as shown in Figure 9. When the number of elements increased from $20\times {10}^4$ to $200\times {10}^4$, the difference in temperature distribution along the characteristic line (in the length direction of the plate) was less than 0.5%, indicating that the mesh density had a negligible impact on the computational results. Consequently, the mesh with $20\times {10}^4$ elements was selected for subsequent calculations, with a maximum element size of 1 mm, a minimum element size of 0.01 mm, and a mesh growth rate set to 1.3.

4. Results and Discussion

4.1. Initial Results Analysis of the Flat Plate Before Optimization

To systematically analyze the thermomechanical response characteristics of the CMC flat plate under non-uniform thermal loads, this study first investigates the heat transfer mechanisms and temperature field distribution of the initial model without thermal property optimization. As shown in Figure 10, the numerical simulation results reveal that the temperature field on the surface of the flat plate before optimization exhibits a significant non-uniform distribution: the maximum temperature reaches 1597 K, concentrated in the center of the main-heat-source region; the temperature in the secondary heat-source region is slightly lower but still within the high-temperature range. The low-temperature region is located in the cold-source area, with a minimum temperature of 960 K. The temperature distribution in the non-heat-source regions is relatively uniform, stabilizing around 1200 K. The heat-flux density distribution map in Figure 10a further reveals the characteristics of heat transport pathways: the heat flux in the main-heat-source region shows a uniform divergent trend, with heat diffusing to the surroundings through in-plane conduction and surface convection. However, the direction of the heat-flux vectors near the secondary heat source undergoes a significant deflection, and the magnitude of the heat flux is markedly attenuated, indicating that the presence of the secondary heat source forms a local inhibitory effect on the heat dissipation direction of the main heat source. It is worth noting that, in addition to being transferred through the non-heat-source regions, part of the heat from the secondary heat source flows towards the cold-source region through a directional conduction path, forming an asymmetric heat dissipation channel. The above phenomena reveal the coupling and regulatory effects of heat-source spatial distribution on heat-flux transport pathways.

To further understand the distribution of the temperature gradient field of the CMC flat plate under non-uniform thermal loads, Figure 11 presents the temperature gradient field contour map and characteristic line temperature gradient data of the flat plate before thermal property optimization. The analysis reveals that the extreme values of the temperature gradient on the flat plate before optimization are mainly distributed in the boundary regions between the main and secondary heat sources, with a peak value of $1.05\times {10}^5\mathrm{K}/\mathrm{m}$. This phenomenon is closely related to the concentrated characteristics of the heat-flux paths: the edges of the heat sources, as the key interfaces for heat transfer from high-temperature to low-temperature regions, make these areas the regions with the highest temperature gradients. The temperature gradient values in the non-heat-source regions are generally low, further verifying the strong correlation between the temperature gradient distribution in the solid domain and the fluid temperature field.

Figure 12 presents the thermal stress field contour map and characteristic line thermal stress data of the CMC flat plate before thermal property optimization. The results show that areas with high thermal stress are located in the main heat source, secondary heat source, cold source, and the junction between the main and secondary heat sources. The highest thermal stress is found in the main-heat-source region. It can also be observed from the figure that the thermal stress field exhibits a significant spatial coupling feature with the temperature gradient field, but the spatial distribution range of the high-stress area is broader than that of the temperature gradient field. This indicates that the accumulation of thermal stress is not only driven by the temperature gradient but also closely related to the anisotropic thermal expansion behavior of the material and the boundary constraint conditions. It is worth noting that the amplitude of thermal stress in the non-heat-source regions is generally low, verifying the key impact of temperature field non-uniformity on the thermo-mechanical coupling response.

This section analyzes the thermomechanical response of the unoptimized CMC flat plate under non-uniform thermal loads. The numerical simulation results show that the surface temperature field of the initial model exhibits a significant non-uniform distribution: the highest temperature at the center of the main heat source reaches 1597 K, the lowest temperature at the boundary of the cold source is 960 K, and the temperature in the non-heat-source regions stabilizes at 1200 K. The extreme value of the temperature gradient ($1.68\times {10}^5$ K/m) is concentrated at the boundary between the main and secondary heat sources, and the thermal stress field is highly coupled with the temperature gradient distribution, with the peak thermal stress in the main-heat-source region reaching 242.77 Mpa. The results indicate that the concentrated characteristics of heat-flux transport pathways and the distribution of heat sources have a dominant influence on the temperature field, gradient field, and stress field.

4.2. Comparative Analysis of Temperature Fields Before and After Optimization

The calculation results show that the synergistic optimization design method combining material mesostructure with efficient heat dissipation can significantly improve the temperature field distribution of CMC panels under non-uniform high thermal loads. As shown in Figure 13, after optimization, the maximum temperature along the characteristic line of the primary heat source decreases from 1597.7 K to 1454.47 K (a reduction of 8.96%), while that of the secondary heat source decreases from 1559.643 K to 1437.516 K (a reduction of 7.83%). Meanwhile, the temperature in the cold-source region increases slightly by 2.74% (from 960.19 K to 986.497 K). These results indicate that the thermal conductivity regulation strategy based on gradient modification with CNTs effectively reconstructs the heat transport pathways. Specifically, the through-thickness thermal conductivity distribution shown in Figure 14 reveals the key physical mechanism: the high thermal conductivity in the primary and secondary heat-source regions significantly enhances the in-plane heat conduction capacity, promoting rapid heat diffusion from high-temperature zones to low-temperature zones, whereas the low thermal conductivity regions between the primary and secondary heat-sources and at the edges of the cold source inhibit heat-flux backflow, thereby forming directional heat dissipation channels and weakening the spatial accumulation of localized heat. From the perspective of microstructures, the incorporation of CNTs forms a continuous heat transfer network within the matrix, enhancing the local heat transport efficiency of the CMC panel. The discretely distributed CNT content modulates the local thermal resistance, enabling efficient heat diffusion along predetermined pathways. By breaking the isotropic thermal conduction limitation of traditional woven structures, this design achieves active thermal path planning, thereby reducing the thermal load in high-temperature regions at the macroscopic level.

Figure 15 illustrates the heat-flux density distribution of the flat-plate structure before and after optimization. Red arrows indicate the heat-flux density vectors before optimization, while yellow arrows show them after optimization. Post-optimization, the heat-flux density distribution reveals significant spatial reconstruction. Although the fixed heat-flux boundary conditions keep the amplitude at the heat-source and cold-source boundaries unchanged, the direction and path change notably. In the main-heat-source area, the heat-flux density vectors shift from a uniformly divergent state to a pattern biased towards the low-temperature area on the right. In this area, the direction of the optimized heat-flux vectors remains largely unchanged, but the amplitude significantly increases, indicating enhanced lateral heat conduction due to increased in-plane thermal conductivity. This adjustment directs heat along a preset high-thermal-conductivity path. A distinct heat transport channel forms between the heat source and cold source, effectively directing heat to the cold-source area. Between the heat sources, although the amplitude of the heat-flux density changes little, the flow direction deflects significantly. This suggests that the low-thermal-conductivity region between the primary and secondary heat sources effectively suppresses cross-transfer of heat flux by altering the heat-flow direction, thereby preventing the formation of secondary high-temperature points.

Analyzing the physical mechanism, this phenomenon arises from the active regulation effect of the thermal conductivity gradient distribution on the heat-flux potential field.

1. Enhanced Heat Transfer in High-Thermal-Conductivity Zones: By increasing the thermal conductivity of materials in the primary and secondary heat-source regions, the local thermal resistance is reduced, leading to an increase in in-plane heat-flux density. This facilitates more efficient heat dissipation toward lower-temperature regions.

2. Thermal-flux blocking effect in the low-thermal-conductivity region: The low-thermal-conductivity region between the primary and secondary heat sources effectively blocks thermal flux from spreading to other high-temperature areas. It increases local thermal resistance, functioning like a “thermal-flux guiding valve” and facilitating the unidirectional transport of heat along predetermined high-thermal-conductivity channels.

4.3. Analysis of Temperature Gradient Results

Figure 16 presents the spatial distribution maps of the temperature gradient and the line graphs of characteristic line data for the CMC panel before and after optimization. As shown in Figure 16a, before optimization, the extreme values of the temperature gradient are concentrated at the boundary of the primary heat source and the interface between the secondary heat source and the cold source, which is closely related to the concentrated characteristics of the heat-flux transport paths. Through the graded thermal conductivity design, after optimization, the peak value along the characteristic line of the primary heat source decreases from $1.05\times {10}^5$ K/m to $5.63\times {10}^4$ K/m (a reduction of 46.64%), and that of the secondary heat source decreases from $8.87\times {10}^4$ K/m to $4.94\times {10}^4$ K/m (a reduction of 44.29%). It is worth noting that the temperature gradient in the cold-source region increases only slightly (the blue region expands only marginally in Figure 16b), indicating that the optimization strategy suppresses heat accumulation in high-temperature zones without significantly increasing the thermal load in low-temperature zones. Combined with the thermal conductivity distribution shown in Figure 14, the high-thermal-conductivity design in the primary and secondary heat-source regions accelerates in-plane heat-flux diffusion (indicated by the dense arrow regions in Figure 15) by reducing local thermal resistance, thereby diminishing the temperature difference at the boundaries of the heat sources. Meanwhile, the low-thermal-conductivity regions block heat-flux backflow, suppressing the formation of secondary peak temperature gradients.

4.4. Analysis of Thermal Stress Results

To systematically reveal the regulatory mechanism of thermal property optimization on the thermo-mechanical coupling behavior of Ceramic Matrix Composites (CMCs), this study couples the temperature field data before and after optimization, established in the previous sections, into the thermo-mechanical analysis module to quantitatively characterize the influence of the gradient thermal conductivity design on the thermal stress distribution of the flat plate. Considering the actual assembly conditions of hot components in aero-engines, the numerical model is set with elastic constraint boundary conditions on all four sides of the flat plate (distributed spring stiffness coefficient k = 5 × 10⁸ N/m³), simulating the assembly constraint effect between CMC components and metal support structures, while the remaining surfaces are allowed to deform freely. In the constitutive equation, the stress-free reference temperature is set at 293.15 K (20 °C), and the material’s thermal expansion coefficient is taken as a constant value of 5.2 × 10⁻⁶ K⁻¹ (Table 2).

Figure 17 illustrates the spatial distribution characteristics of thermal stress in the ceramic matrix composite (CMC) panel before and after optimization. Since thermal stress is directly related to the temperature gradient, the thermal stress distribution in the panel is highly coupled with the temperature gradient distribution. After optimization, the peak thermal stress along the characteristic line of the primary heat source decreases from 240.77 MPa to 148.41 MPa (a reduction of 38.17%), while that along the characteristic line of the secondary heat source decreases from 103.26 MPa to 68.65 MPa (a reduction of 33.52%). In contrast, the thermal stress in the cold-source region shows no significant change after optimization. In summary, the optimization effect on thermal stress stems from the synergistic regulation of the temperature gradient and the thermo-mechanical coupling response through the optimized design of thermal conductivity. The high-thermal-conductivity regions reduce thermal expansion stress by lowering the temperature gradient, while the low-thermal-conductivity regions suppress secondary stress accumulation by blocking heat-flux superposition. Meanwhile, the microscopic network of CNT micropillars enhances the local heat transfer capacity of the CMC panel, improving the uniformity of temperature and temperature gradient and alleviating local thermal mismatch. Combined with the analyses in Figure 16 and Figure 17, the multi-objective optimization algorithm not only achieves a significant reduction in thermal stress peaks (up to 38.17%) but also improves the uniformity of stress distribution by reconstructing the heat-flux pathways. These results provide a multiscale theoretical basis for the reliability design and life extension of CMC components under non-uniform thermal loads, while also highlighting the potential of synergistic optimization between material modification processes and intelligent algorithms in engineering thermal protection.

5. Conclusions

This paper addresses the thermal protection requirements of CMC materials under complex high-thermal-load conditions, proposing a collaborative optimization design method based on microstructure and efficient heat dissipation. By deeply integrating multi-objective optimization algorithms with material property modification processes, this study systematically uncovers the mechanism of collaborative optimization for gradient thermal property regulation on thermo-mechanical coupling behavior. The main conclusions are as follows:

(1)

The research results show that the highest temperature on the optimized plate surface decreases from 1597.7 K to 1454.47 K (a reduction of 8.96%). Meanwhile, heat backflow is suppressed, and the formation of secondary high-temperature points is effectively prevented. In this study, a multi-scale numerical prediction model for the thermal conductivity of CMC materials with varying amounts of CNTs was developed. Additionally, a quantitative correlation equation between CNT content and the composite’s effective thermal conductivity was established. Experimental verification indicates that the maximum relative error between the model’s predictions and the measured data is 8.73%.

(2)

Thermal property optimization improves the thermal conductivity of the CMC material in areas with high temperature gradients. By lowering local thermal resistance, the temperature difference between hot zones and nearby regions is reduced, helping to prevent thermal stress concentration and extending the CMC material’s service life. The optimization of thermal conductivity redesigns the heat-flux pathways, which greatly decreases the peak temperature gradient. Compared to the state before optimization, the peak temperature gradient along the main heat source’s characteristic line drops by 46.64% after optimization. Additionally, the peak thermal stress along this characteristic line decreases by 38.17% relative to the pre-optimization level.