Prediction Method for Surface Roughness Variation of Environmental Barrier Coatings on Ceramic Matrix Composites

Abstract

The present invention addresses the technical problems of accurately predicting and controlling the aerodynamic performance and heat transfer performance of components in a high-temperature gas environment, realizing the evolution of the surface microstructure of environmental barrier coatings (EBCs) in a high-temperature gas environment, and obtaining the prediction of the surface roughness of EBCs / ceramic matrix composites (CMCs). A method for predicting the change in surface roughness of environmental barrier coatings for ceramic matrix composites is provided. This method comprehensively considers the initial geometric morphology structure of the coating material, couples the aerodynamic force and thermochemical reaction of the high-temperature gas flow, realizes the simulation of the internal stress of the coating system based on a thermal / mechanical / oxygen coupling model, and simulates the morphology after the high-temperature gas acts for a certain period of time. The theoretical equations involved in the present invention are easy to program and implement, can accurately simulate the ablation morphology of the coating under different conditions, and lay a foundation for the life prediction of EBCs / CMCs in a high-temperature gas environment.

Description

Technical Field

[0001] The present invention belongs to the field of the evolution of the microstructure of aerospace coating surfaces, and particularly relates to a method for predicting the change in surface roughness of environmental barrier coatings in a high-temperature gas environment. Background Art

[0002] Advanced aeroengines require higher performance, higher fuel efficiency, and lower nitrogen oxide emissions, which can usually be achieved by the maximum inlet temperature at the front end of the turbine components. However, due to the limitations of the high-temperature alloy material itself, even with the assistance of cooling means and thermal barrier coatings, the temperature resistance limit has been reached, which restricts the further improvement of the engine thrust-to-weight ratio. The SiC ceramic matrix composite (CMCs) can be used for high-temperature hot-end components to replace the current high-temperature alloy due to its low density and high strength characteristics at high temperatures. In dry air, CMCs react with oxygen to form a dense oxide film SiO2, and SiO2 can isolate oxygen and prevent CMCs from being further oxidized. However, in the actual service environment containing high-temperature water vapor, SiO2 will react with water vapor to form volatile Si(OH)4, and the volatile Si(OH)4 can be easily carried away by the high-pressure heat flow, causing the silicon-based CMC to be continuously exposed to the gas, and the protective effect of SiO2 disappears.

[0003] Currently, the isolation of water and oxygen can be achieved by depositing an environmental barrier coating (EBCs) on the surface of CMCs to protect CMCs from corrosion by high-temperature gases and improve the corrosion resistance of CMCs. When testing the EBCs system in a simulated combustion environment, severe corrosion will occur on the surface before the EBCs fail, resulting in a rough surface morphology, which greatly affects the aerodynamic performance and heat transfer performance of the structural components. Therefore, accurately predicting the roughness evolution of EBCs / CMCs in a gas environment has important engineering significance for predicting the service life of components and the structural optimization design.

[0004] Research shows that the failure of EBCs / CMCs is closely related to the underlying thermally grown silica layer (TGO layer). The growth of the TGO layer plays a crucial role in the failure process. The growth rate of TGO is closely related to the gas environment and is controlled by the diffusion rate of the gas in TGO. During the growth of TGO, the longitudinal position is restricted by the spatial position, resulting in growth stress in the transverse direction. The diffusion of gas in the TGO layer is affected by its stress distribution, which is a typical stress coupling process. The growth of TGO will further affect the geometric morphology of the outer surface of the coating. At present, in engineering, the morphology evolution of components during the processing process is mainly predicted by establishing a numerical model based on the size, movement law, and feed parameters of the processing tool to predict the surface roughness of the material. This kind of prediction usually uses neural network and machine learning methods, which are only suitable for predicting the morphological evolution of components during the processing process. Due to the harsh environment and complex coating evolution mechanism in the high-temperature gas environment, there is no publicly available information on the microscopic structure evolution of the specimen surface in the high-temperature gas environment. Therefore, in order to improve the accurate prediction and control of the aerodynamic performance and heat transfer performance of components in the high-temperature gas environment, how to realize the evolution of the micro-structure on the surface of EBCs in the high-temperature gas environment and obtain the prediction of the surface roughness of EBCs / CMCs is an important and difficult technical problem in this technical field. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the present invention provides a method for predicting the change of surface roughness of environmental barrier coatings on ceramic matrix composites.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for predicting the change of surface roughness of environmental barrier coatings on ceramic matrix composites, characterized by comprising:

[0008] Step 1: Obtain the true geometric morphology of the environmental barrier coating based on XCT;

[0009] Step 2: Based on the true geometric morphology obtained in Step 1, establish a flow field model in a high-speed gas environment, perform a simulation of the flow field distribution including the EBCs / CMCs specimen, and obtain the flow field parameters at the gas-solid interface;

[0010] Step 3: Respectively take the true geometric morphology obtained in Step 1 and the flow field parameters obtained in Step 2 as the boundary conditions of the geometric model and the growth of the TGO layer, interpolate the aerodynamic force and gas component concentration on the coupling wall from the fluid domain to the solid domain, perform a stress analysis of the EBCs / CMCs solid domain, and obtain the stress distribution inside the coating;

[0011] Step 4: Based on the stress distribution obtained in Step 3, establish a thermal / mechanical / oxygen coupling model for the growth of the TGO layer;

[0012] Step 5: Based on the thermal / mechanical / oxygen coupling model established in Step 4, considering the coating phase change, ablation, and spalling behaviors in the high-temperature gas environment, establish the kinetics of the phase change process, the thermochemical reaction kinetics of the ablation process, and the erosion kinetics of the spalling process, and obtain the evolution law of the surface microstructure of EBCs / CMCs;

[0013] Step 6: Based on the evolution law of the surface microstructure of EBCs / CMCs obtained in Step 5, judge the surface recession form of EBCs / CMCs in the service environment. After reaching the failure condition of the coating geometric morphology, remove the failed part of the unit material and update the microscopic geometric morphology of the coating surface;

[0014] Step 7: Based on the updated microscopic geometric morphology of the coating surface in Step 6, correct the flow field model in Step 2, and repeat Steps 2 to 6 until the specified high-temperature gas action time is reached. Output the final geometric morphology of the EBCs / CMCs specimen. Divide the final geometric morphology into multiple regions according to the flow field distribution characteristics of the high-temperature gas, and statistically analyze the average specimen height characteristics of each region to determine the roughness change.

[0015] To optimize the above technical solutions, the specific measures taken also include:

[0016] Further, in Step 1, the μ-CT testing technology is used to obtain the true geometric morphology of the environmental barrier coating, including the true morphologies of the coating outer surface and each layer interface of the coating.

[0017] Further, in Step 2, the computational fluid dynamics method is used to analyze its aerodynamic characteristics. The shear stress transport k-ω model is used to characterize turbulence. The second-order upwind scheme is used for spatial discretization of the control equations. The finite chemical reaction rate model is used to simulate the high-temperature gas environment. The mass diffusion transport equation is used to calculate the content and distribution of gas concentrations in the high-temperature gas.

[0018] Further, in Step 2, the computational fluid dynamics method is used to analyze its aerodynamic characteristics. The shear stress transport k-ω model is used to characterize turbulence. The second-order upwind scheme is used for spatial discretization of the control equations. The finite chemical reaction rate model is used to simulate the high-temperature gas environment. The mass diffusion transport equation is used to calculate the content and distribution of gas concentrations in the high-temperature gas.

[0019] Further, in Step 4, the specific process of establishing the thermal / mechanical / oxygen coupling model for TGO layer growth is as follows:

[0020] The diffusion of the high-temperature gas and the internal thermal stress of the EBCs are coupled with each other and jointly affect the growth of the TGO layer, satisfying the following expression:

[0021]

[0022] In the formula, x o is the thickness of the oxide film, x oi is the oxide thickness at t = 0, D ox is the diffusion coefficient of the oxidant through the oxide layer, where H c and H ox are the Henry's law solubility coefficients of the oxidant in the coating and the oxide respectively, D c is the diffusion coefficient of the coating, k is the reaction rate constant, h is the flux of the gas, δ is the coating thickness, and C* is the equilibrium oxidant concentration on the outer surface of the coating;

[0023] The equilibrium equation during the stress oxidation process is:

[0024] σ ox x + σ s (H - x) = 0

[0025] In the formula, x is the function of the oxide film thickness with respect to time t, σ ox and σ s are the biaxial average stresses in the oxide film and the substrate, and H is the initial thickness of the specimen relative to the axis of symmetry; The rate form is:

[0026]

[0027] In the formula, is the derivative of the biaxial average stress σ ox of the oxide film with respect to time, is the growth rate of the oxide film;

[0028] During the oxidation process, the total thickness of the TGO layer and the BC layer remains constant, and the strains satisfy and are the strain rates of the oxide layer and the base layer respectively;

[0029] Considering the elastic model:

[0030] ε ox = σ ox / M ox + ε g

[0031] In the formula, ε ox is the strain of the oxide layer, M ox is the molar mass of the oxide layer, and ε g is the strain caused by the growth of the oxide layer;

[0032] The transverse growth strain rate of the oxide layer increases linearly with the growth rate of the oxide layer:

[0033]

[0034] In the formula, is the strain rate of oxide layer growth;

[0035] For the strain ε s of the base layer, there is ε s = σ s / M s where M s is the biaxial modulus of the substrate;

[0036] Finally, the rate form of the equilibrium equation is:

[0037]

[0038] It serves as a thermal / mechanical / oxygen coupling model for TGO layer growth.

[0039] Furthermore, in the fifth step, the evolution law of the surface microstructure is reflected in the recession rate v total of the coating surface:

[0040]

[0041] In the formula, v M represents the spallation rate caused by erosion, and

[0042] represents the recession rate caused by the oxidation reaction; M The spallation rate v

[0043]

[0044] m ρ m C m are the thermal conductivity, density and specific heat capacity of the coating respectively; p total is the total pressure of the gas flow on the ablation surface; σ mT is the ultimate tensile strength of the substrate; E Am respectively represent the pre-exponential factor and activation energy of the coating thermal decomposition process, v M is the recession rate of the coating surface, R is the universal gas constant, and T w is the wall temperature of the coating;

[0045] The recession rate caused by the oxidation reaction is as follows:

[0046]

[0047] In the formula, MEBC are the relative molecular masses of oxygen and the coating respectively, is the oxygen partial pressure near the ablation surface, and are the activation energy and the pre-exponential factor of the chemical reaction respectively, ρ EBC represents the density of the SiC / SiC composite material, h c represents the convective heat transfer coefficient of the wall surface, C P represents the specific heat capacity at constant pressure of the coating, represents the oxygen mass concentration at the ablation wall surface.

[0048] Furthermore, in the sixth step, the wall temperature and the surface aerodynamic shear force are used as the judgment conditions for failure. After reaching the retreat condition, partial material removal is carried out by controlling the movement of grid nodes to update the microscopic geometric morphology of the coating surface.

[0049] Furthermore, in the seventh step, the roughness of the coating interface is characterized by the surface average roughness Sa and the surface root mean square Sq values, and their expressions are respectively:

[0050]

[0051] In the formula, Z(x,y) represents the height coordinate of the specimen surface.

[0052] The beneficial effects of the present invention are as follows: The method for predicting the change of the surface roughness of the environmental barrier coating of the ceramic matrix composite material provided by the present invention comprehensively considers the initial geometric morphology structure of the coating material, couples the aerodynamic force and the thermal chemical reaction of the high-temperature gas flow, and realizes the simulation of the internal stress of the coating system based on the thermal / force / oxygen coupling model, and simulates the morphology after the action of the high-temperature gas for a certain time. The theoretical equations involved in the present invention are easy to be programmed and implemented. Therefore, it can accurately simulate the ablation morphology of the coating under different conditions, and lay a foundation for the life prediction of EBCs / CMCs in the high-temperature gas environment. Description of the Drawings

[0053] Figure 1 is the overall flowchart of the method for predicting the change of the surface roughness of the environmental barrier coating of the ceramic matrix composite material;

[0054] Figure 2 is a schematic diagram of the geometric model including the rough morphology.

[0055] Figure 3 is a schematic diagram of the geometric model of the numerical simulation of the high-temperature gas generated by the spray gun.

[0056] Figure 4 is a schematic diagram of the model of the diffusion of the oxidizing gas inside the EBCs / CMCs.

[0057] Figure 5 It is a curve graph of the growth law of the TGO layer under the coupled action of heat, mechanics, and chemistry.

[0058] Figure 6a and 6b It is a schematic diagram of the rough morphology of the surface evolution of EBCs under the action of high-temperature gas. Specific implementation manners

[0059] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present application.

[0060] As Figure 1 shown, a method for predicting the surface roughness change of an environmental barrier coating on a ceramic matrix composite material in a high-temperature gas environment proposed by the present invention includes the following steps:

[0061] Step 1: Based on the X-ray computed tomography (XCT) technology, obtain the true geometric morphology of the environmental barrier coating, including the rough morphology of the outer surface of the coating and the true geometric morphology between each layer, provide boundary conditions for subsequent flow field analysis, and provide a geometric model for subsequent stress analysis.

[0062] Specifically, use the μ-CT test technology to obtain the true internal microstructure of EBCs / CMCs, including the true morphology of the outer surface of the coating and the interfaces of each layer of the coating.

[0063] Step 2: Based on the geometric morphology of the coating surface given in Step 1, establish a flow field model in a high-speed gas environment, realize the simulation of the flow field distribution including the specimen, and obtain the parameter distributions such as the wall pressure, temperature, heat transfer coefficient, and gas concentration of the coating.

[0064] Specifically, use the computational fluid dynamics (CFD) method to analyze its aerodynamic characteristics. Use the shear stress transport (SST) k-ω model to characterize turbulence. Use the second-order upwind scheme to spatially discretize the control equations. Use the finite chemical reaction rate model to simulate the high-temperature gas environment. Use the mass diffusion transport equation to calculate the content and distribution of gas concentration in the high-temperature gas. Among them, the aerodynamic characteristics refer to the high-temperature gas flow field parameters, "turbulence" is used to describe the properties of the flow field, and the "control equations" refer to the basic equations used to control the high-temperature gas flow field parameters.

[0065] Step 3: Based on the true model of the coating (i.e., the true geometric morphology of the coating) obtained using XCT technology in Step 1 and the flow field parameters (i.e., the distribution of parameters such as the wall pressure, temperature, heat transfer coefficient, and gas concentration) at the gas-solid interface obtained in Step 2, use them as the geometric model and boundary conditions respectively. Interpolate the aerodynamic force and gas component concentration on the coupling wall from the fluid domain to the solid domain to perform stress analysis on the solid domain of EBCs / CMCs.

[0066] Specifically, considering that during the internal microstructure evolution process of EBCs / CMCs, the external surface flow field has reached a steady state, the wall pressure, gas component concentration, and temperature do not change with the growth of the TGO layer, and the wall parameters only change when the morphology is updated again.

[0067] Step 4: Driven by the chemical potential energy, the oxidizing gas starts to diffuse into the coating. When it reaches the interface of the BC layer (Bonding Coat), an oxidation reaction starts, and the TGO layer begins to grow. Since the growth thickness of the TGO layer does not match the consumption thickness of the BC layer, its internal volume expands to generate growth strain, and the internal stress of the coating continuously increases. At the same time, the growth of the TGO layer is coupled with the stress magnitude, and a model of the growth of the TGO layer coupled with the diffusion of the oxidizing gas and stress is established.

[0068] Specifically, the diffusion of the high-temperature gas is coupled with the internal thermal stress of the EBCs, and they jointly affect the growth of the TGO layer. The following expression is obtained:

[0069]

[0070] where x o is the thickness of the oxide film, x oi is the oxide thickness at t = 0, D ox is the diffusion coefficient of the oxidant through the oxide layer, where H c and H ox are the Henry's law solubility coefficients of the oxidant in the coating and the oxide respectively, D c is the diffusion coefficient of the coating, k is the reaction rate constant, h is the gas flux, δ is the coating thickness, and C* is the equilibrium oxidant concentration on the outer surface of the coating.

[0071] Equilibrium equation during the stress oxidation process:

[0072] σ ox x + σ s (H - x) = 0

[0073] where x is the function of the oxide film thickness with respect to time t, σ ox and σ sσ is the biaxial average stress in the oxide film and the substrate, and H is the initial thickness of the specimen relative to the symmetry axis; the rate form is:

[0074]

[0075] In the formula, ε ox is the strain of the oxide layer, M ox is the molar mass of the oxide layer, and ε g is the strain caused by the growth of the oxide layer. The superscript · represents differentiation.

[0076] Assume that the total thickness of the TGO layer and the BC layer remains constant during the oxidation process, then the strains satisfy and are the strain rates of the oxide layer and the substrate layer, respectively.

[0077] During the oxidation process, ε ox consists of two parts. One part is the strain caused by the stress in the thin film, and the other part is the growth strain. Considering the elastic model:

[0078] ε ox = σ ox / M ox + ε g

[0079] In the formula, ε ox is the strain of the oxide layer, M ox is the molar mass of the oxide layer, and ε g is the strain caused by the growth of the oxide layer.

[0080] The transverse growth strain rate of the oxide layer increases linearly with the growth rate of the oxide layer thickness:

[0081]

[0082] In the formula, is the growth strain rate of the oxide layer.

[0083] For the strain ε S of the substrate layer, there is ε s = σ s / M s , and Ms is the biaxial modulus of the substrate.

[0084] Therefore, the rate form of the equilibrium equation can finally be written as:

[0085]

[0086] Step 5: Based on the thermal / mechanical / oxygen coupling model for TGO growth established in Step 4, considering the coating phase change, ablation, and spalling behaviors in a high-temperature combustion gas environment, establish the kinetics of the phase change process, the thermochemical reaction kinetics of the ablation process, and the erosion kinetics of the spalling process, and obtain the evolution law of the surface microstructure of EBCs / CMCs.

[0087] Specifically, the evolution law of the surface microstructure is obtained based on chemical reaction kinetics, where the spalling rate caused by erosion is related to the strength of the coating:

[0088]

[0089] In the formula, k m , ρ m , C m are the thermophysical properties of the coating, which are the thermal conductivity, density, and specific heat capacity, respectively; p total is the total pressure of the gas flow on the ablation surface, which is considered to be related to the gas flow velocity; σ mT is the ultimate tensile strength of the substrate; E Am represents the pre-exponential factor and activation energy of the coating thermal decomposition process, R is the universal gas constant, and T w is the coating wall temperature.

[0090] According to the competition relationship between oxygen diffusion and thermochemical reactions, it can be divided into diffusion control and chemical kinetic control. Currently, the commonly used method is to adopt a component separation type minimum mechanism control model.

[0091] The boundary recession rate (i.e., the coating surface recession rate) controls the recession of the surface geometric boundary. The result of the geometric boundary recession is manifested as the evolution of the microstructure. Therefore, the evolution law of the surface microstructure is reflected in the boundary recession rate v total :

[0092]

[0093] In the formula, v M represents the spalling rate caused by erosion, represents the recession rate caused by the oxidation reaction;

[0094] Among them, the recession rate caused by the oxidation reaction is as follows:

[0095]

[0096] In the formula, M EBC are the relative molecular masses of oxygen and the coating, respectively, is the oxygen partial pressure near the ablation surface, and are the activation energy and pre-exponential factor of the chemical reaction, respectively, and ρ EBC represents the density of the SiC / SiC composite material, and h c represents the convective heat transfer coefficient of the wall, and C P represents the specific heat capacity at constant pressure of the coating, represents the oxygen mass concentration at the ablated wall surface.

[0097] Step 6: Based on the calculation results of Step 5, judge the surface recession form of EBCs / CMCs in the service environment. After reaching the failure condition of the coating geometry, remove the material of the failed part of the unit and update the microscopic geometry of the coating surface.

[0098] Specifically, the wall temperature and surface aerodynamic shear force are used as the judgment conditions for failure. After reaching the recession condition, partial material removal is carried out by controlling the movement of grid nodes to update the microscopic geometry of the coating surface.

[0099] Step 7: Based on the updated geometry obtained in Step 6, correct the aerodynamic wall geometry model in Step 2 (i.e., the flow field model in the high-temperature gas environment), and repeat Steps 2 to 6 until the specified high-temperature gas action time is reached. Output the final geometry of the EBCs / CMCs specimen, divide the geometry into multiple regions according to the flow field distribution characteristics of the high-temperature gas, and statistically analyze the average specimen height characteristics of each region to determine the roughness change.

[0100] Among them, the roughness of the coating interface is usually characterized by the surface average roughness Sa and the surface root mean square Sq value. Sa is a parameter extended from Ra (arithmetic mean height of the line) to the surface, representing the average value of the absolute value of the height difference of each point relative to the average surface. Sq is defined as the root mean square of the height of each point in the defined region, which is equivalent to the standard deviation of the height. Their expressions are respectively:

[0101]

[0102] In the formula, Z(x, y) represents the height coordinate of the specimen surface.

[0103] Next, in this embodiment, the surface roughness prediction simulation of typical multi-layer EBCs / CMCs composites in the high-temperature gas environment generated by oxygen-propane combustion is carried out. The top layer coating (TOP) uses Yb2SiO5, the intermediate layer (EBC) is Yb2Si2O7, and the bonding layer (BC) is Si. This embodiment makes predictions and simulations on the finally evolved roughness.

[0104] 1) Obtain the true geometric model including roughness as Figure 2 shown. The roughness distribution of each layer is shown in Table 1, which provides geometric boundary conditions and numerical models for subsequent solution calculations.

[0105] Table 1 Coating interface roughness distribution and maximum fluctuation height

[0106] Sa (μm) Sq (μm) MAX (μm) MIN (μm) TOP 2.19 2.76 +12.15 -11.50 TOP / EBC 3.14 3.91 +14.47 -15.94 EBC / TGO 1.96 2.44 +8.77 -10.37 TGO / BC 1.96 2.44 +8.77 -10.37

[0107] 2) Use the true geometric morphology of the Yb2Si2O7 coating surface obtained in step 1 as the geometric boundary for the action of high-temperature gas. Based on the HVOF spray gun model used for oxygen-propane combustion, establish a flow field model in a high-speed gas environment, solve the flow field distribution, and obtain parameters such as the wall pressure, temperature, heat transfer coefficient, and gas concentration of the coating. The geometric model for fluid domain solution is as Figure 3 shown.

[0108] 3) Calculate the aerodynamic heat and ablation reaction heat at time t using the initial structure temperature field. Couple the aerodynamic heat and ablation reaction heat on the wall and interpolate them from the fluid domain to the solid domain. Then, under the action of the latent heat load of gas aerodynamic heating, thermochemical reaction heat, and phase change process, complete the transient structural heat transfer analysis from t i to t i to t i+1 . Interpolate the wall pressure, temperature, and gas component concentration obtained from the fluid domain solution in step 2 to the solid domain as the boundary conditions for the stress in the solid domain and the growth of the TGO layer.

[0109] 4) The diffusion of high-temperature gas and the internal thermal stress of EBCs are coupled with each other, and jointly affect the growth of the TGO layer. The growth model is as Figure 4 shown. P is the partial pressure of the oxidant in the gas environment, C* is the equilibrium oxidant concentration on the outer surface of the coating, Co is the oxidant concentration on the outer surface of the coating. The oxidant concentration is discontinuous at the coating / oxide interface, is the oxidant concentration in the coating at the coating / oxidation interface, is the oxidant concentration in the coating at the coating / oxidation interface, C i is the oxidation concentration at the oxide / silicon interface, δ is the coating thickness, x o is the thickness of the oxide film.

[0110] At the coating / oxide interface, the oxidants in the coating and the oxide are assumed to be in chemical equilibrium. At the partial pressure of the oxidant P a , the oxidants in the coating and the oxide on the interface are also assumed to be in equilibrium with the oxidant in the theoretical gas. Therefore, it can be written as and where H c and H ox are the Henry's law solubility coefficients of the oxidants in the coating and the oxide respectively. It can also be written as where Under steady-state conditions, the number of oxidizing molecules passing through a unit area per unit time is equal, i.e., F1 = F2 = F3 = F4. F1, F2, F3, and F4 are the oxygen fluxes in the four stages as shown in Figure 4 respectively. By formulating the expression equations in the formula, we can obtain:

[0111]

[0112] Flux expression:

[0113]

[0114] Growth rate of oxidation flux and TGO thickness:

[0115]

[0116] where F refers to the oxygen flux, and N1 is the number of oxidizing molecules contained in the oxide per unit volume. After rearrangement, we get:

[0117]

[0118] Integrating and rearranging the above formula, we obtain an expression in the following form:

[0119]

[0120] where

[0121]

[0122] In the formula, x oi is the oxide thickness at t = 0. Considering that when the fuel gas is heated to 1316 °C, the diffusion coefficient of the oxidizing gas in the coating is shown in Table 2, and the growth curve of TGO with time is as shown in Figure 5 respectively. The thickness can reach 5.7 microns after 200 h of oxidation.

[0123] Table 2 Diffusion coefficient of oxygen in ytterbium rare earth silicate at different temperatures

[0124] EBCs <![CDATA[D 1100 (cm 2 / s)]]> <![CDATA[D 1200 (cm 2 / s)]]> <![CDATA[D 1300 (cm 2 / s)]]> E (kJ / mol) <![CDATA[D0(cm 2 / s)]]> <![CDATA[Yb2Si2O7]]> <![CDATA[1.2×10 -17 > <![CDATA[9.0×10 -17 > <![CDATA[6.5×10 -16 > 358 <![CDATA[4.59×10 -4 >

[0125] The presence of stress in the oxide film affects the mobility of defects (such as vacancies), thereby affecting the oxidation kinetics. Compressive stress reduces the oxidation rate. In fact, during the diffusion transport process, oxygen or ions jump from one interstitial position to another, and compressive stress can increase the energy barrier, thereby inhibiting the probability of this jump. According to the equilibrium equation:

[0126] σ ox x + σ s (H - x) = 0

[0127] where x is the function of the oxide film thickness with respect to time t, σ ox and σ s are the biaxial average stresses in the oxide film and the substrate, and H is the initial thickness of the specimen with respect to the symmetry axis. The rate form is:

[0128]

[0129] Assuming that the total thickness of the TGO and BC remains constant during the oxidation process, the strains satisfy

[0130] During the oxidation process, ε ox consists of two parts. One part is the strain caused by the stress in the thin film, and the other part is the growth strain. Considering the elastic model:

[0131] ε ox = σ ox / M ox + ε g

[0132] Using the dislocation climb process to establish a model, it is predicted that at a fixed oxidation temperature, the transverse growth strain rate of the oxide layer increases linearly with the oxide layer thickening rate, which is consistent with the experimental observation results and can be expressed as:

[0133]

[0134] For ε S , there is ε s = σ s / M s , and Ms is the biaxial modulus of the substrate.

[0135] Therefore, the coupled equation of stress and oxide film growth rate can be obtained as:

[0136]

[0137] 5) The evolution law of the surface microstructure is obtained based on the finite chemical reaction rate, where the thermomechanical erosion characteristics are related to the strength of the coating, and the thermomechanical ablation rate is the linear erosion rate:

[0138]

[0139] where k m , ρ m , C m are the thermophysical properties of the coating; is the total pressure of the gas flow on the ablation surface, which is considered to be related to the gas flow velocity; σ mT is the ultimate tensile strength of the substrate; E Am represents the pre-exponential factor and activation energy of the coating thermal decomposition process.

[0140] According to the competition relationship between oxygen diffusion and thermochemical reaction, it can be further divided into diffusion control and chemical kinetic control. The commonly used method at present is to adopt the component separation type minimum mechanism control model. The boundary recession rate caused by thermochemical reaction is:

[0141]

[0142] In the formula, M EBC are the relative molecular masses of oxygen and the coating respectively, is the oxygen partial pressure near the ablation surface, n is the reaction order, E i and A i are the activation energy and pre-exponential factor of the chemical reaction, ρ EBC represents the density of the SiC / SiC composite material, h c represents the convective heat transfer coefficient of the wall, C P represents the specific heat capacity at constant pressure of the coating, represents the oxygen mass concentration at the ablation wall surface.

[0143] 6) Judge whether the wall temperature and surface aerodynamic shear force reach the conditions for coating material removal. After reaching the recession conditions, control the movement of grid nodes to remove part of the material, perform the solid domain grid reconstruction at time t i+1 , update the microscopic geometric morphology of the coating surface, and solve the fluid domain at time t i+1 .

[0144] 7) Judge whether the calculation time reaches the required total time. If it reaches, output the surface rough morphology of the coating and conduct the statistical distribution of roughness. The roughness of the coating interface is usually characterized by the surface average roughness Sa and the surface root mean square Sq values. Sa is a parameter extended with Ra (arithmetic mean height of the line) as the surface, representing the average value of the absolute value of the height difference of each point relative to the average surface of the surface. Sq is defined as the root mean square of the height of each point in the defined area, equivalent to the standard deviation of the height. Their expressions are respectively:

[0145]

[0146] The finally obtained surface roughness morphology after the action of the given time is as Figure 6a shown, Figure 6b which is a geometric model higher than the reference plane.

[0147] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A method for predicting the change in surface roughness of an environmental barrier coating on a ceramic matrix composite, characterized in that, Including: Step 1: Obtain the true geometric morphology of the environmental barrier coating based on XCT; Step 2: Based on the true geometric morphology obtained in Step 1, establish a flow field model under a high-speed gas environment, conduct a simulation of the flow field distribution including the EBCs / CMCs specimen, and obtain the flow field parameters at the gas-solid interface; Step 3: Respectively take the true geometric morphology obtained in Step 1 and the flow field parameters obtained in Step 2 as the boundary conditions for the geometric model and the growth of the TGO layer. Interpolate the aerodynamic force and gas component concentration on the coupled wall from the fluid domain to the solid domain, conduct a stress analysis of the EBCs / CMCs solid domain, and obtain the stress distribution inside the coating; Step 4: Based on the stress distribution obtained in Step 3, establish a thermal / mechanical / oxygen coupling model for the growth of the TGO layer; Step 5: Based on the thermal / mechanical / oxygen coupling model established in Step 4, consider the coating phase change, ablation, and spalling behaviors under a high-temperature gas environment, establish the kinetics of the phase change process, the thermochemical reaction kinetics of the ablation process, and the erosion kinetics of the spalling process, and obtain the evolution law of the surface microstructure of EBCs / CMCs; Step 6: Based on the evolution law of the surface microstructure of EBCs / CMCs obtained in Step 5, judge the surface recession form of EBCs / CMCs in the service environment. After reaching the failure condition of the coating geometric morphology, remove the failed part of the unit material and update the surface microgeometry of the coating; Step 7: Based on the updated surface microgeometry of the coating in Step 6, correct the flow field model in Step 2, and repeat Steps 2 to 6 until the specified high-temperature gas action time is reached. Output the final geometric morphology of the EBCs / CMCs specimen. Divide the final geometric morphology into multiple regions according to the flow field distribution characteristics of the high-temperature gas, respectively count the average specimen height characteristics of each region, and determine the roughness change.

2. The method for predicting the surface roughness change of an environmental barrier coating on a ceramic matrix composite according to claim 1, wherein: In the said Step 1, the μ-CT testing technology is used to obtain the true geometric morphology of the environmental barrier coating, including the true morphologies of the outer surface of the coating and the interfaces of each layer of the coating.

3. The method for predicting the surface roughness change of the environmental barrier coating of the ceramic matrix composite material according to claim 1, wherein: In the said Step 2, the computational fluid dynamics method is used to analyze its aerodynamic characteristics. The shear stress transport k-ω model is used to characterize turbulence. The second-order upwind scheme is used for spatial discretization of the control equation. The finite chemical reaction rate model is used to simulate the high-temperature gas environment. The mass diffusion transport equation is used to calculate the content and distribution of gas concentration in the high-temperature gas.

4. The method for predicting the surface roughness change of the environmental barrier coating of the ceramic matrix composite material according to claim 1, wherein: In the said Step 3, during the internal microstructure evolution process of EBCs / CMCs, the flow field on the outer surface has reached a steady state, and the wall pressure, gas component concentration, and temperature do not change with the growth of the TGO layer.

5. The method for predicting the surface roughness change of the environmental barrier coating of the ceramic matrix composite material according to claim 1, wherein: In the said Step 4, the specific process of establishing the thermal / mechanical / oxygen coupling model for the growth of the TGO layer is as follows: The diffusion of high-temperature gas and the internal thermal stress of EBCs are coupled with each other and jointly affect the growth of the TGO layer, satisfying the following expression: where x o is the thickness of the oxide film, x oi is the oxide thickness at t = 0, D ox is the diffusion coefficient of the oxidant through the oxide layer, where H c and H ox are the Henry's law solubility coefficients of the oxidant in the coating and the oxide respectively, D c is the diffusion coefficient of the coating, k is the reaction rate constant, h is the flux of the gas, δ is the coating thickness, and C* is the equilibrium oxidant concentration at the outer surface of the coating; The equilibrium equation in the stress oxidation process is: σ ox x + σ s (H - x) = 0 where x is the function of the oxide film thickness with respect to time t, σ ox and σ s are the biaxial average stresses in the oxide film and the substrate, and H is the initial thickness of the specimen with respect to the symmetry axis; the rate form is: In the formula, is the derivative of the biaxial average stress σ of the oxide film ox with respect to time, is the oxide film growth rate; During the oxidation process, the total thickness of the TGO layer and the BC layer remains constant, and the strains satisfy and are the strain rates of the oxide layer and the base layer, respectively; Considering the elastic model: ε ox = σ ox / M ox + ε g where ε ox is the strain of the oxide layer, M ox is the molar mass of the oxide layer, and ε g is the strain caused by the growth of the oxide layer; The transverse growth strain rate of the oxide layer increases linearly with the thickening rate of the oxide layer: In the formula, is the strain rate of oxide layer growth; For the strain ε of the base layer s , there is ε s = σ s / M s , where M s is the biaxial modulus of the substrate; Finally, the rate form of the equilibrium equation is obtained: This is used as the thermal / mechanical / oxygen coupling model for the growth of the TGO layer.

6. The method for predicting the surface roughness change of the environmental barrier coating of the ceramic matrix composite material according to claim 1, wherein: In the fifth step, the evolution law of the surface microstructure is reflected in the recession rate V of the coating surface total as follows: where, v M represents the spalling rate caused by erosion, represents the recession rate caused by the oxidation reaction; The spalling rate v caused by erosion M is related to the strength of the coating: where k m , ρ m , C m are the thermal conductivity, density and specific heat capacity of the coating respectively; p total is the total pressure of the gas flow on the ablation surface; σ mT is the ultimate tensile strength of the substrate; E Am represent the pre-exponential factor and activation energy of the coating thermal decomposition process respectively, v M is the recession rate of the coating surface, R is the universal gas constant, T w is the temperature of the coating wall; Retreat rate caused by oxidation reaction is as follows: In the formula, M EBC are the relative molecular masses of oxygen and the coating respectively, is the oxygen partial pressure near the ablation surface, and are the activation energy and the pre-exponential factor of the chemical reaction respectively, ρ EBC represents the density of the SiC / SiC composite material, h c represents the convective heat transfer coefficient of the wall, C P represents the specific heat capacity at constant pressure of the coating, represents the oxygen mass concentration at the ablation wall surface.

7. The method for predicting the surface roughness change of the environmental barrier coating of the ceramic matrix composite material according to claim 1, wherein: In the sixth step, the wall temperature and the surface aerodynamic shear force are used as the judgment conditions for failure. After reaching the retreat condition, partial material removal is carried out by controlling the movement of grid nodes to update the microscopic geometric morphology of the coating surface.

8. The method for predicting the surface roughness change of the environmental barrier coating of the ceramic matrix composite material according to claim 5, wherein: In the seventh step, the roughness of the coating interface is characterized by the surface average roughness Sa and the surface root mean square Sq values, and their expressions are respectively: In the formula, Z(x, y) represents the height coordinate of the specimen surface.

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