Multi-scale mechanical-thermal coupling analysis of multi-layer thermal protection structure of ceramic matrix composites

The wall of combustion chamber needs to sustain the extremely high thermal and stress load in the engine environment, so the thermal protection structure is required to ensure its safe work. At present, the multi-layer thermal protection structure with ceramic matrix composite (CMC) materials has gradually been applied as the internal resistant layer, due to its high specific strength and high temperature resistance. The mechanical-thermal coupling analysis method for CMC multi-layer thermal protection structures needs to be established, considering the complex distributed thermal and stress loads inside the combustion chambers. Firstly, for the local periodic unit of multilayer thermal protection structure, the mesoscale braided structure model and the homogenized model are constructed respectively, to explore the influence of the braided structure inside CMC layer on the temperature and stress distribution. Then, the macroscale model of the multi-layer CMC thermal protection structure is established, based on the feasibility of the local periodic element model verification method. The mechanical-thermal coupling analysis of the overall multi-layer thermal protection structure is carried out, and the temperature distribution and structural deformation are explored.


Introduction
After more than 100 years of development, the subscramjet has been widely used in supersonic missiles at home and abroad, and the world's military powers have established a subscramjet research and development system.Ramjet engine has superior performance than rocket engine and turbojet engine in the range of supersonic flight, and also has a wide range of military and commercial application background, which is one of the research focuses of various aerospace powers [1][2][3].Ramjet combustor is the core component of gas turbine engine, and its running condition directly determines the performance of aeroengine.With the increase of penetration capability for missile flight speed and range, the thrust and efficiency of the engine must be increased.Correspondingly, the inlet temperature and gas temperature of the engine combustion chamber are also increasing.The combustion chamber of aeroengine in service environment is subjected to high temperature, complex stress, water oxygen/corrosion and thermal shock, and its performance and working state directly determine the overall performance of the engine [4][5][6][7].At present, multi-layer passive thermal protection structures based on Ceramic Matrix Composites (CMC) as the inner layer of combustion chambers have been gradually applied in engineering due to their excellent properties such as high specific strength, high specific modulus and high temperature resistance [8].

Numerical models
In this paper, the passive thermal protection structure of a certain type of sub combustion ramjet combustion chamber is taken as the research object.The combustion chamber cylinder is a multi-layer thermal protection structure, and the straight section model of the engine combustion chamber shell is extracted.The overall model is composed of three layers of materials, including C/SiC layer, gradient thermal insulation layer, and metal shell layer from the inside out, as shown in Figure 1.The total length of the overall model cylinder is 785.6562mm, the diameter of the inner wall cylinder is D=418mm, and the thickness of the three layers of material is: C/SiC layer: 8mm; Gradient insulation layer: 12mm; Metal shell layer: 1.2mm.The C/SiC layer is a CMC material with woven structural characteristics, and the internal woven structural model features are shown in Figure 2. The geometric characteristic parameters such as weaving angle, weft width, warp width, and spacing in the parameterized model are shown in Table 1: Table 1.Geometric feature parameters of unit cell model.

Name
Parameter Braiding angle 45° Cross section width of weft yarn 0.25mm Cross section length of weft yarn 1.5mm Pick spacing 0.05mm Cross section width of warp yarn 0.25mm Cross section length of warp yarn 1.5mm Warp spacing 0.2mm At the same time, considering the thermal coupling analysis of the overall model of the thermal protection structure of the combustion chamber with larger geometric dimensions, the model of CMC layer, established based on the micro scale woven structure directly, will lead to a significant increase in computational complexity.Therefore, in the study, for typical periodic units of multi-layer thermal protection structures, a uniform equivalent model was established based on anisotropic equivalent thermal conductivity, and compared with the micro scale woven structure model, The thickness of each layer under the two models is consistent with that of the overall combustion chamber model.The mesoscale woven structure model and the homogenization equivalent model are shown in Figure 3

Governing equation
Firstly, a brief introduction is given to the control equation describing the force thermal coupling problem.Let Ω represent the solid region.1) Solid domain control equation Energy equation: In the equation, "  " is the stress component, "  " is an external force (such as gravity) 2) Heat transfer model The cylindrical combustion chamber with a multi-layer thermal protection structure, where the heat exchange between the combustion chamber wall and the gas is: Where, "(   )  " is the temperature gradient at the outer normal of the heat exchange surface; "k" is the material thermal conductivity; "  " is the combustion chamber wall temperature, where it is a function of time; "  " is the combustion chamber gas temperature; "h" is the combustion chamber surface heat transfer coefficient.
Differential equation for unsteady heat conduction of cylindrical walls: Where, "a" is the thermal diffusivity,  =    ; "t" is the time; "T" radial temperature distribution, which is a function of time and radius length.
For the continuous laminated structure of multi-component materials, the interlayer should meet the condition of continuous heat flow: Where, "n" is the material of the nth layer, n=1,2,3,4; "k n " is the Thermal conductivity of the nth layer material; "  " is the interface temperature of the nth layer.
Meanwhile, due to its high operating temperature, the combustion chamber exhibits strong radiative heat transfer during the heat transfer process.The amount of heat emitted by the object per unit time is: Where, "ε" is the emissivity of the gray body, "A" is the area of the radiation surface, "σ" is the Stephen Boltzmann constant, and "T" is the surface temperature.
The above formula can be used to solve and analyze the temperature field of multi-layer thermal protection structures, and obtain the model temperature field.
3)Thermal stress When the structure is heated or cooled, it will experience expansion or contraction deformation.If the deformation is constrained or different materials are combined together (resulting in uneven material deformation), thermal stress will be generated in the structure.Further consideration of the pressure loads borne by the structure will make the stress and strain distribution of multi-layer thermal protection structures more complex.
For the cylindrical model of multi-layer thermal protection structure in this article, assuming the temperature inside the elastic body is T, positive strain will be generated.The equilibrium equation and geometric equation are: The physical equation for thermal stress in the cylindrical part of the thermal protection model is: The Where, εr, εθ, εz represents radial, circumferential, and axial strains, respectively; "u" is the axial displacement; "α" is the coefficient of thermal expansion; "μ" is the poisson's ratio; "E" is the elastic modulus.

3.2.Material parameters
The thermal and mechanical properties parameters of the materials in each layer of the combustion chamber thermal protection structure are shown in Tables 2 to 4. The emissivity of superalloy GH99 is 0.18.
In Figure 3 (a), the axial thermal conductivity of the internal SiC fiber bundle in the mesoscale braided structure periodic unit model is 4.66 W/(m• K), the radial thermal conductivity is 1.48 W/(m• K), and the thermal conductivity of the matrix is 6.5 W/(m• K) [18]; the homogenization equivalent model C/SiC layer microstructure is characterized by equivalent anisotropic thermal conductivity, the thermal conductivity coefficient used in the homogenization equivalent model is: The thermal conductivity of the matrix is isotropic, and the thermal conductivity of the fiber bundle has obvious anisotropic characteristics.The direction of the weft yarn is fixed and can be directly assigned in the global coordinate system, while the anisotropic thermal conductivity of the warp yarn changes with the weaving direction.Therefore, curve coordinates are introduced.In this article, thermal conductivity in three directions is used to characterize the anisotropy of fiber bundles, that is, the axial direction of fiber bundles with higher thermal conductivity ζ (Main direction of thermal conductivity) and two directions perpendicular to the fiber bundle axis ν and η.Establish the curve coordinates of the thermal conductivity of the warp yarn, as shown in Figure 4, where the coordinate system of the main direction of the warp yarn thermal conductivity is denoted as (ζ，ν，η) [19].
According to the research results of reference [20], the anisotropic thermal conductivity of composite materials is represented as a matrix in the macroscopic coordinate system: In the principal direction coordinate system of the thermal conductivity of composite fibers, the coefficient matrix can be expressed as:

Boundary
➢ Periodic unit multi-layer structure model For the two periodic unit multi-layer structure models in Figures 3 (a) and (b), in this calculation, the third type of boundary condition is used In the local periodic model, the internal wall flow heat transfer coefficient is taken as 480.5 W/(m 2 • K), and the external fluid temperature is taken as the gas temperature of 763 K.The external Natural convection boundary condition is given for the outer wall of the model, the ambient temperature is 293.15K, the external absolute pressure is 1 atm.Considering the radiation heat transfer of the outer wall in the outer space, the Emissivity of the outermost material is given as 0.18.Set the remaining faces of the model as periodic boundaries.The wall surface of the combustion chamber is subjected to pressure (relative pressure) from high-temperature gas, and the boundary condition for the internal wall pressure is set to 66821.6 Pa in the calculation model.Fixed constraints are applied to the outer wall of the high-temperature alloy layer.All other surfaces are free surfaces.
➢ Overall model of multi-layer thermal protection structure in combustion chamber For the overall model of the multi-layer thermal protection structure of the combustion chamber in Figure 1, the third type of flow and heat transfer boundary conditions obtained based on CFD simulation were used in the study.The distribution of convective heat transfer coefficient on the inner wall surface of the multi-layer thermal protection structure of the combustion chamber is shown in Figure 6 (a).The average temperature of the gas at a position 2 mm below the combustion chamber wall was selected as the surrounding fluid temperature in the third type of boundary conditions during the force thermal coupling simulation calculation, with a value of 1680 K.The external Natural convection boundary condition is given for the wall of the combustion chamber, the ambient temperature is 293.15K, the external absolute pressure is 1atm, and the Emissivity of the outermost material is given as 0.18 considering the radiation heat transfer of the outer wall in the outer space.The residual surface of the model, namely the wall surface on both sides of the axial direction, is given with Thermal insulation.The schematic diagram of thermal boundary conditions is shown in Figure 6 (b).In the actual working environment of the combustion chamber, the inner wall surface will be subjected to pressure from hightemperature gas, and pressure boundary conditions should be set on the inner wall surface.The distribution of pressure load on the inner wall surface is shown in Figure 6 (c).The fixed constraint is applied to the end face of the combustion chamber inlet, which is located at the left end face position in Figure 6

Verification of accuracy of woven structure model
This study used the LFA laser flash method to test the material thickness and equivalent thermal conductivity in the in-plane direction of the sample in Figure 10.The testing instrument is NETZSCH LFA 467 MicroFlash, and the testing standard is ASTM E1461-13.The measurement principle is that a laser emitter emits a pulse to irradiate the lower surface of the sample, which will rapidly increase the surface temperature, and heat is transferred to the upper surface of the sample through one-dimensional thermal conduction.At the same time, an infrared temperature measuring device is used to monitor the temperature change at the center of the upper surface, and the relationship between temperature rise and time is obtained.By importing it into a computer, the equivalent thermal conductivity can be obtained [21].Because the temperature distribution in C/SiC layer is affected by the braided structure, there is a large temperature fluctuation, while the temperature distribution in gradient insulation layer and superalloy layer is similar due to their uniform structure.Therefore, the temperature distribution curves along the centerline of the thickness direction of different models are extracted for the C/SiC layer.The temperature distribution on the centerline of the braided structure model and the uniform equivalent model is shown in Figure 12. equivalent model.From the above figure, it can be seen that there is a difference in the temperature change trend on the centerline between the local periodic braided structure and the homogenization equivalent model.This is because the thermal conductivity of the warp yarns and weft yarns in the radial direction in the thickness direction of the weaving structure model is 1.48 W/(m • K), which is relatively small compared to the substrate.Moreover, the fiber bundles in the thickness direction account for a large proportion in the weaving model.Therefore, the heat transfer in the thickness direction of the weaving model is greatly affected by the thermal conductivity of the fiber bundles in the radial direction, while the equivalent thermal conductivity in the thickness direction in the homogenization equivalent model is 3.672 W/(m • K), So the temperature gradient on the centerline of the homogenization equivalent model is relatively large, and the trend of temperature change is also significant.From the above figure, it can also be seen that the temperature distribution in the thickness direction of the braided structure model fluctuates due to the internal non-uniformity of the model.However, the temperature distribution difference between the braided structure model and the homogenization equivalent model is relatively small.The maximum difference of the temperature on the centerline is about 4.98 K, and the maximum error is about 0.68%.

Comparative analysis of stress fields between two unit period models
In Figure 13, it can be seen that the local periodic braided structure model and the homogenized equivalent model are basically consistent in stress distribution.The maximum stress in the model occurs on the outermost wall surface (the wall surface imposed by fixed constraints).Due to the pressure acting on the innermost wall of the model and the overall heating, thermal stress and expansion deformation are generated, and the wall surface with fixed constraints constrains the overall model.Therefore, it is subjected to significant stress at this location.Compared with the two models, the overall stress of the braided structure is relatively small, because the temperature in the C/SiC layer of the braided structure model is lower due to the influence of the thermal conductivity of the fiber bundle and matrix, which affects the overall temperature of the model.The thermal stress is smaller than that of the homogenized model, thus affecting the overall stress of the braided structure.The maximum stress in the woven structure model is 3.417×10 9 Pa, with an average stress on the outer wall of 1.387×10 9 Pa; The maximum stress in the homogenization model is 3.394×10 9 Pa, with an average stress on the outer wall of 1.382×10 9 Pa.Comparing the stress distribution of the two models, it can be seen that the stress on the wall surface at the connection between layers is relatively large due to the uneven distribution of temperature field caused by different heat conduction and absorption abilities between layers, as well as the interlayer stress caused by different mechanical properties of each layer.
Comparing the stress field distribution of the C/SiC layer between the two models, it can be seen that the stress distribution patterns of the braided structure model and the homogeneous model are basically the same, and their values are also roughly the same.The maximum stress of the C/SiC layer in the woven structure model is 2.330×10 7 Pa, the maximum stress in the C-C/SiC layer in a homogeneous model is 2.077×10 7 Pa.

Comparative analysis of displacement fields between two unit period models
In Figure 15, it can be seen that the braided structure model and the homogenized equivalent model have consistent overall displacement distribution trends, showing a trend of outward expansion from the outer wall of the high-temperature alloy layer (fixed constraint applied wall).The maximum deformation of both models occurs on the C/SiC layer, and the maximum total displacement of the woven structure model and the homogenization model is 0.01716 mm and 0.01701 mm.At the same time, it was also found that there is a significant lateral deformation at the connection between the high-temperature alloy layer and the gradient insulation layer.This is because the outermost high-temperature alloy layer has a higher coefficient of thermal expansion, making it more prone to thermal expansion deformation compared to other layers.In the simulation calculation, the high-temperature alloy layer and gradient insulation layer are set as binding contact, so there will be significant expansion deformation at the contact position of the gradient insulation layer at the high-temperature alloy layer, and the interlayer stress at that location is also large.
Comparing the displacement distribution cloud diagrams of the C/SiC layer under two different models, it can be seen that the displacement distribution of the C/SiC layer under different models is basically consistent, and the difference in deformation between the woven structure and the uniform structure is very small.In general, although the temperature distribution in the braided structure model is slightly different from that in the homogeneous model, the temperature has little influence on the stress and deformation of the model.The deformation of the two models is basically the same, and the relative difference is within an acceptable range.Therefore, when using equivalent models and equivalent physical properties parameters for simulation calculations, the influence of woven structures on overall deformation is not significant.

Simulation calculation results of the overall model of the multi-layer thermal protection structure combustion chamber
The temperature calculation results of the overall model of the multi-layer thermal protection structure of the combustion chamber and the temperature distribution results of each layer of the combustion chamber are shown in Figure 16.The temperature distribution of the overall model is shown in Figure 16 (a) and (b).It can be seen that the overall temperature shows a gradually decreasing trend from the inner wall to the outside.Among them, the highest temperature calculated by the overall model is 1679 K, and the average temperature on the inner wall of the C/SiC layer is 1623.4K; The maximum temperature on the outer wall of the high-temperature alloy layer is 1127.8K, with an average temperature of 1110.3K.   17.From the distribution cloud diagram of the stress calculation results below, it can be seen that high-temperature alloy materials are prone to significant deformation at high temperatures due to their high coefficient of thermal expansion.However, at the same time, due to the high elastic modulus of high-temperature alloy materials, the stress when the layer undergoes deformation is relatively greater.Therefore, the overall model of the combustion chamber shows a phenomenon where the outermost stress is greater than that of other layers.It can also be seen that due to the high temperature at the outlet of the combustion chamber (at the right end face in the figure), the overall thermal stress of the combustion chamber model at the outlet is greater.The maximum stress calculated for the thermal protection structure of the combustion chamber is 2.02×10 9 Pa.

Conclusion
This article compares and analyzes the local period model of a multi-layer thermal protection structure combustion chamber with a microscale woven structure and its uniform equivalent model through simulation, to explore the influence of the microstructure characteristics of C/SiC layers on the temperature field and stress-strain field distribution characteristics of multi-layer thermal protection structures.The global model of the straight section of a multi-layer thermal protection structure combustion chamber is established, conducting an overall force thermal coupling analysis of the multilayer thermal protection structure combustion chamber.The overall thermal distribution and structural deformation of the multi-layer thermal protection structure combustion chamber are explored.The main conclusions obtained are as follows: (1) The difference in temperature, stress, and deformation distribution between the braided structure model and the homogenized equivalent model is relatively small, and different models have the same distribution trend in each layer, and the numerical values are also relatively similar.Although the calculation results of the C/SiC layer in the braided structure model are all affected by fluctuations in the braided structure of the warp yarns and weft yarns, the maximum temperature difference on the centerline of the two models is about 4.98K, and the maximum error is about

Figure 1 .
Figure 1.Calculation model of multi-layer thermal protection structure in combustion chamber.The C/SiC layer is a CMC material with woven structural characteristics, and the internal woven structural model features are shown in Figure 2. The geometric characteristic parameters such as weaving angle, weft width, warp width, and spacing in the parameterized model are shown inTable 1: Table 1.Geometric feature parameters of unit cell model.

Figure 2 .
Figure 2. Schematic diagram of warp yarns and weft yarns weaving structure.

Figure 3 .
Figure 3. Schematic diagram of two models.

Figure 4 .
Figure 4. Warp curve coordinate system.In Figure 1, the thermal conductivity of the C/SiC layer in the multi-layer thermal protection structure combustion chamber is: {3.672 W/(m• K), 4.763 W/(m• K), 4.763 W/(m• K)}, and the curve coordinates of the equivalent thermal conductivity of the multi-layer thermal protection structure combustion chamber are established, as shown in Figure 5.The thermal conductivity in the thickness direction of the C/SiC layer is 3.672 W/(m• K), and the thermal conductivity in the C/SiC layer is 4.763 W/(m• K).
(a) Distribution of convective heat transfer coefficient on the wall of the combustion chamber.(b) Schematic diagram for setting thermal boundary conditions of the overall combustion chamber model.(c) Pressure boundary load distribution.

Figure 6 .
Figure 6.Schematic diagram of boundary conditions for the overall calculation model.3.4.Computational grid partitioning➢ Periodic unit multilayer structure model In the study, grid independence experiments were first conducted on the woven structure model and the uniform equivalence model.Among them, the maximum size of the mesh in the woven structure model was reduced from 2.12 mm to 1 mm, and the number of grids is 385391, 678979, 1011816, 1600343 and 2386693, Figure7(a) shows the variation pattern of the maximum equivalent stress obtained from the simulation calculation of the braided structure model with the number of grids.It can be seen from the figure that when the number of grids increases by 1011816, the maximum equivalent stress of the model hardly changes, with a relative change of less than 2%.Therefore, the number of grids used in the calculation is 1011816, with a maximum size of 1.5 mm and a minimum size of 0.2 mm for the grid elements.The grid growth rate is 1.5, and the final woven structure grid model is shown in Figure7(b).

Figure 7 .
Figure 7. Verification of grid independence and grid partitioning for woven structure models.At the same time, grid partitioning was carried out for the uniform equivalence model.The maximum size of the grid in the uniform equivalence model was reduced from 0.9 mm to 0.35 mm, and the number of grids is 58478, 117872, 363218, 554643 and 1029659, Figure 8 (a) shows the variation pattern of the maximum equivalent stress obtained from the uniform equivalent model simulation with the number of grids.It can be seen from the figure that when the number of grids increases to 363218, the maximum equivalent stress of the model hardly changes, with a relative change of less than 1%.Therefore, the number of grids used in the calculation is 363218, with a maximum size of 0.5 mm and a minimum size of 0.0424 mm.The grid growth rate is 1.3, and the final woven structure grid model is shown in Figure 8 (b).
(a) Verification of grid Independence of uniform equivalent model.(b) Schematic diagram of uniform equivalent model grid division.

Figure 8 .➢
Figure 8. Verification of grid independence and grid division for uniform equivalent model.➢ Overall model of multi-layer thermal protection structure in combustion chamber For the overall model of multi-layer thermal protection structure of the combustion chamber, when dividing the grid, the three layers of wall at the outlet of the combustion chamber model are first divided into quadrilateral grids, and then the grid on the wall is scanned to divide the overall model.The grid in the overall model is a hexahedron grid.In the study, grid independence experiments were conducted on the model, The number of grids is 28155, 72660, 116980, 150800 and 220320.The figure shows the variation pattern of the calculated maximum equivalent stress with the number of grids.From Figure 9 (a), it can be seen that when the number of grids increases to 116980, there is almost no change, and the relative change is less than 1%.Therefore, the number of grids used in the calculation is 116980, with a maximum size of 8 mm and a minimum size of 0.8 mm.The grid growth rate is 1.45, and the final established grid model is shown in Figure 9 (b).
(a) Verification of grid independence of the overall combustion chamber model.(b) Schematic diagram of the overall grid division of the combustion chamber.

Figure 9 .
Figure 9. Verification of grid independence and grid partitioning of the overall combustion chamber model.

Figure 10 .
Figure 10.Laser flash thermal conductivity test sample.During the testing process, three tests were conducted on different positions of the sample, and the equivalent thermal conductivity test results are shown in Table 5.The final measured equivalent thermal conductivity in the thickness direction of the sample material is 3.672 W/(m• K), and the equivalent thermal conductivity in the sample material plane is 4.763 W/(m• K).This article calculates the equivalent thermal conductivity based on the braided structure model.The equivalent thermal conductivity in the thickness direction of the braided structure model is 3.834W/(m• K), and the equivalent thermal conductivity in the plane of the sample material is 4.861 W/(m• K).Compared with the experimental test values, the deviation in the thickness direction is 4.41%, and the in-plane deviation is 2.06%, further demonstrating the rationality of the parameterized model established in this paper.Table5.Comparison of thermal conductivity test data and numerical data.

4 .
Result and analysis4.1.Comparative analysis of temperature fields between two unit period modelsIn Figure11, the overall temperature results and the temperature results of the C/SiC layer under the thermal coupling simulation of the local periodic braided structure model and the homogenization equivalent model are presented.In Fig.11 (a) and (b), it can be seen that the temperature distribution of the local periodic braiding structure model is basically consistent with that of the homogenization equivalent model, the temperature gradually decreases from the inner wall to the outermost wall.The average temperature on the innermost wall of the woven structure model and the homogenization model is 747.12K and 747.33 K, and the average temperature on the outermost wall is 582.74K and 579.73 K. Comparing the temperature field distribution of the C/SiC layer between the two models, it can be seen that there are significant temperature fluctuations in the local periodic braided structure model due to the different thermal conductivity between the fiber bundle and the matrix, and the overall temperature of the model under the braided structure is affected by the thermal conductivity, this leads to an overall low temperature.The highest temperature on the upper surface of the C/SiC layer in the local periodic braided structure is 735.97K, while the highest temperature on the upper surface of the C/SiC layer in the homogenization model is 730.92K. (a) Temperature field distribution cloud diagram of the three-layer model under the woven structure model.(b) Temperature field distribution cloud diagram of three-layer model under homogenization model.(c) Cloud diagram of temperature field distribution in C/SiC layer under braided structure model.(d) Cloud diagram of temperature field distribution in C/SiC layer under homogenization model.

Figure 11 .
Figure 11.Temperature calculation results under two models.

Figure 12 .
Figure 12.Temperature distribution on the centerline of braided structure model and uniformequivalent model.From the above figure, it can be seen that there is a difference in the temperature change trend on the centerline between the local periodic braided structure and the homogenization equivalent model.This is because the thermal conductivity of the warp yarns and weft yarns in the radial direction in the thickness direction of the weaving structure model is 1.48 W/(m • K), which is relatively small compared to the substrate.Moreover, the fiber bundles in the thickness direction account for a large proportion in the weaving model.Therefore, the heat transfer in the thickness direction of the weaving model is greatly affected by the thermal conductivity of the fiber bundles in the radial direction, while the equivalent thermal conductivity in the thickness direction in the homogenization equivalent model is 3.672 W/(m • K), So the temperature gradient on the centerline of the homogenization equivalent model is relatively large, and the trend of temperature change is also significant.From the above figure, it can also be seen that the temperature distribution in the thickness direction of the braided structure model fluctuates due to the internal non-uniformity of the model.However, the temperature distribution difference between the braided structure model and the homogenization equivalent model is relatively small.The maximum difference of the temperature on the centerline is about 4.98 K, and the maximum error is about 0.68%.
(a) The stress field distribution cloud diagram of the three-layer model under the woven structure model.(b) The stress field distribution cloud diagram of the three-layer model under the homogenization model.(c) Cloud diagram of stress field distribution in C/SiC layer under braided structure model.(d) Cloud diagram of stress field distribution in C/SiC layer under homogenization model model.

Figure 13 .
Figure 13.Stress calculation results under two models.To analyze the variation trend of equivalent stress distribution inside the C/SiC layer with the braided structure, the equivalent stress distribution curve on the centerline was extracted along the thickness direction of the C/SiC layer for two models.The equivalent stress distribution curve on the characteristic line is shown in Figure14.

Figure 14 .
Figure 14.Stress distribution on the centerline of the braided structure model and the uniform equivalent model.By comparing the equivalent stress distribution along the centerline of the thickness direction of the C/SiC layer in different models.It can be seen that when using equivalent parameters for simulation calculation, the stress distribution trend calculated by the uniform equivalent model is consistent with the stress distribution trend of the braided structure model, and the numerical values are basically the same, with an error of less than 1%.
(a) Cloud diagram of the displacement field distribution of the three layer model under the braided structure model.(b) Cloud diagram of displacement field distribution in a three-layer model under homogenization model.(c) Cloud diagram of C/SiC layer displacement field distribution under the braided structure model.(d) Cloud diagram of the C/SiC layer displacement field distribution under the homogenization model model.

Figure 15 .
Figure 15.Displacement calculation results under two models.In general, although the temperature distribution in the braided structure model is slightly different from that in the homogeneous model, the temperature has little influence on the stress and deformation of the model.The deformation of the two models is basically the same, and the relative difference is within an acceptable range.Therefore, when using equivalent models and equivalent physical properties parameters for simulation calculations, the influence of woven structures on overall deformation is not significant.
(a) Overall temperature distribution nephogram of combustion chamber.(b) Temperature distribution in each layer of combustion chamber.(c) Cloud diagram of temperature distribution on the inner wall of C/SiC layer of combustion chamber.(d) Cloud diagram of temperature distribution on the outer wall of the combustion chamber superalloy layer.

Figure 16 .
Figure 16.Calculation results of combustion chamber temperature for multi-layer thermal protection structure.The equivalent stress distribution cloud diagram obtained from the simulation calculation of a multilayer thermal protection structure combustion chamber is shown in Figure17.From the distribution cloud diagram of the stress calculation results below, it can be seen that high-temperature alloy materials are prone to significant deformation at high temperatures due to their high coefficient of thermal expansion.However, at the same time, due to the high elastic modulus of high-temperature alloy materials, the stress when the layer undergoes deformation is relatively greater.Therefore, the overall model of the combustion chamber shows a phenomenon where the outermost stress is greater than that of other layers.It can also be seen that due to the high temperature at the outlet of the combustion chamber (at the right end face in the figure), the overall thermal stress of the combustion chamber model

Figure 17 .
Figure 17.Stress calculation results of combustion chamber with multi-layer thermal protection structure.The displacement distribution results of the overall model calculation of the multi-layer thermal protection structure combustion chamber are shown in Figure 18.It can be seen that the displacement distribution of the overall model shows a trend of Free expansion from the inlet end to the outlet end, where the maximum displacement of the model calculated by simulation is 4.91 mm.

Figure 18 .
Figure 18.Calculation results of combustion chamber displacement for multi-layer thermal protection structure.

Table 2 .
Physical property parameters of the three layer materials in the combustion chamber.

Table 4 .
Linear expansion coefficient of high temperature alloy GH99.

Table 5 .
Comparison of thermal conductivity test data and numerical data.