CN115859622A - Method for predicting surface roughness change of ceramic matrix composite environmental barrier coating - Google Patents
Method for predicting surface roughness change of ceramic matrix composite environmental barrier coating Download PDFInfo
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Abstract
The invention provides a method for predicting surface roughness change of an environmental barrier coating of a ceramic matrix composite, aiming at the technical problems of improving the accurate prediction and control of the aerodynamic performance and the heat transfer performance of a component in a high-temperature gas environment, realizing the evolution of the EBCs surface microstructure in the high-temperature gas environment and obtaining the prediction of the EBCs/CMCs surface roughness. The method comprehensively considers the initial geometric morphology structure of the coating material, couples the action of aerodynamic force and thermochemical reaction of high-temperature gas flow, realizes the simulation of the internal stress of the coating system based on a heat/force/oxygen coupling model, and simulates the morphology of the high-temperature gas after a certain time of action. The theoretical equation related by the invention is easy to realize by programming, can accurately simulate the ablation appearance of the coating under different conditions, and lays a foundation for the life prediction of EBCs/CMCs in a high-temperature gas environment.
Description
Technical Field
The invention belongs to the field of aerospace coating surface microstructure evolution, and particularly relates to a surface roughness change prediction method of an environmental barrier coating in a high-temperature gas environment.
Background
Advanced aircraft engines, which require higher performance, higher fuel efficiency and lower nitrogen oxide emissions, can generally be achieved by the maximum inlet air temperature at the front end of the turbine component, but are limited by the material of the superalloy itself, even if aided by cooling means and thermal barrier coatings, have reached temperature resistance limits, which limit further improvements in the thrust-weight ratio of the engine. SiC Ceramic Matrix Composites (CMCs) can be used in high temperature hot end components to replace current high temperature alloys due to their low density and high strength characteristics at high temperatures. In dry air, CMCs react with oxygen to form a dense oxide film SiO 2 ，SiO 2 Can isolate oxygen and prevent CMCs from being further oxidized. However, the actual service environment contains high-temperature water vapor and SiO 2 Will react with water vapor to generate volatile Si (OH) 4 Volatile Si (OH) 4 Can be easily taken away by high-pressure heat flow, so that the silicon-based CMC can be continuously exposed in fuel gas to ensure that SiO is absorbed by the high-pressure heat flow 2 The protective effect of (a) disappears.
At present, the water and oxygen can be isolated by depositing Environmental Barrier Coatings (EBCs) on the surfaces of the CMCs, the CMCs are protected from being corroded by high-temperature gas, and the corrosion resistance of the CMCs is improved. When testing EBCs systems in a simulated combustion environment, severe corrosion of the surface occurs before the EBCs fails, resulting in a rough surface topography that greatly affects the aerodynamic and heat transfer properties of the structural member. Therefore, the method for accurately predicting the roughness evolution of the EBCs/CMCs in the gas environment has important engineering significance for predicting the service life of the component and optimizing the structure design.
Studies have shown that the failure of EBCs/CMC 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 the TGO. During the growth of the TGO, the longitudinal position is constrained by the spatial position, so that growth stress is generated in the transverse direction, while the diffusion of the fuel gas in the TGO layer is influenced by its stress distribution, which is a typical stress coupling process, and the growth of the TGO further influences the geometric appearance of the outer surface of the coating. In the existing engineering, the shape evolution of a component in the machining process is mainly predicted, the surface roughness of a material is predicted by establishing a numerical model through establishing the size, the advancing rule and the feeding parameters of a machining tool, and the prediction is usually carried out by adopting a neural network and a machine learning method and is only suitable for the morphological evolution prediction of the component in the machining process. Due to the characteristics of severe environment and complex coating evolution mechanism under the high-temperature gas environment, the data of the microstructure evolution aspect of the sample surface under the high-temperature gas environment is not published. Therefore, in order to improve the accurate prediction and control of the aerodynamic performance and the heat transfer performance of the component in the high-temperature gas environment, how to realize the evolution of the surface microstructure of the EBCs in the high-temperature gas environment and how to obtain the prediction of the surface roughness of the EBCs/CMCs are important technical problems which are difficult to solve in the technical field.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for predicting the surface roughness change of an environmental barrier coating of a ceramic matrix composite.
In order to achieve the purpose, the invention adopts the following technical scheme:
the method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating is characterized by comprising the following steps:
the method comprises the following steps: obtaining a true geometry of the environmental barrier coating based on XCT;
step two: establishing a flow field model under a high-speed gas environment based on the real geometric shape obtained in the step one, and performing flow field distribution simulation including EBCs/CMCs samples to obtain flow field parameters at a gas-solid interface;
step three: respectively taking the real geometric shape obtained in the step one and the flow field parameters obtained in the step two as a geometric model and a boundary condition of TGO layer growth, interpolating aerodynamic force and gas component concentration on a coupling wall from a fluid domain to a solid domain, and performing stress analysis on the EBCs/CMCs solid domain to obtain stress distribution inside the coating;
step four: establishing a thermal/force/oxygen coupling model for the growth of the TGO layer based on the stress distribution obtained in the step three;
step five: based on the heat/force/oxygen coupling model established in the fourth step, considering the coating phase change, ablation and spalling behaviors in the high-temperature gas environment, establishing the phase change process dynamics, the thermochemical reaction dynamics of the ablation process and the erosion dynamics of the spalling process, and obtaining the evolution law of the surface microstructure of the EBCs/CMCs;
step six: judging the EBCs/CMCs surface migration form in the service environment based on the evolution rule of the EBCs/CMCs surface microstructure obtained in the fifth step, removing the failure part of unit materials after the failure condition of the coating geometric morphology is achieved, and updating the microscopic geometric morphology of the coating surface;
step seven: and based on the updated microscopic geometric shape of the surface of the coating in the step six, correcting the flow field model in the step two, repeating the step two to the step six until the specified action time of the high-temperature gas is reached, outputting the final geometric shape of the EBCs/CMCs sample, dividing the final geometric shape into a plurality of areas according to the flow field distribution characteristics of the high-temperature gas, respectively counting the average sample height characteristics of each area, and determining the roughness change.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in the first step, the real geometric shape of the environmental barrier coating is obtained by using a mu-CT test technology, including the real shape of the outer surface of the coating and the interface of each layer of the coating.
Further, in the second step, the aerodynamic characteristics of the high-temperature gas are analyzed by a computational fluid dynamics method, a shear stress transport k-omega model is adopted to represent turbulence, a second-order windward format is adopted to carry out space dispersion on a control equation, a finite chemical reaction rate model is adopted to simulate the high-temperature gas environment, and a substance diffusion transport equation is adopted to calculate the content and distribution of the gas concentration in the high-temperature gas.
Further, in the second step, the pneumatic characteristics of the high-temperature gas are analyzed by a computational fluid mechanics method, a shear stress transport k-omega model is adopted to represent turbulence, a second-order windward format is adopted to spatially disperse a control equation, a finite chemical reaction rate model is adopted to simulate a high-temperature gas environment, and a substance diffusion transport equation is adopted to calculate the content and distribution of the gas concentration in the high-temperature gas.
Further, in the fourth step, the specific process of establishing the thermal/force/oxygen coupling model of the TGO layer growth is as follows:
the diffusion of high-temperature fuel gas and the internal thermal stress of the EBCs are mutually coupled, the growth of the TGO layer is influenced under the combined action, and the following expression is satisfied:
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 oxidizing agent through the oxide layer,
wherein H c And H ox Henry's law solubility coefficients of oxidizing agents in coatings and oxides, 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, C is the equilibrium oxidant concentration at the outer surface of the coating;
the equilibrium equation in the process of stress oxidation is:
σ ox x+σ s (H-x)＝0
where x is the thickness of the oxide film as a function of time t, σ ox And σ s Is the biaxial average stress in the oxide film and the matrix, and H is the initial thickness of the test piece relative to the axis of symmetry; the rate form is:
in the formula (I), the compound is shown in the specification,
is a biaxial average stress σ of the oxide film ox Derivative with respect to time, is>
Is the oxide film growth rate;
the total thickness of the TGO layer and the BC layer is constant in the oxidation process, and the strain is satisfied
And &>
The strain rates of the oxide layer and the substrate layer respectively;
considering the elastic model:
ε ox ＝σ ox /M ox +ε g
in the formula, epsilon ox Is the strain of the oxide layer, M ox Is an oxide layerMolar mass of (e ∈) g Is the strain caused by oxide growth;
the lateral growth strain rate of the oxide layer increases linearly with the oxide layer thickening rate:
in the formula (I), the compound is shown in the specification,
is the oxide layer growth strain rate;
strain epsilon to base layer s Has an epsilon s ＝σ s /M s ，M s Is the biaxial modulus of the substrate;
the rate form of the resulting equilibrium equation is:
it serves as a thermal/force/oxygen coupling model for TGO layer growth.
Further, in the fifth step, the evolution law of the surface microstructure is embodied in the surface recession velocity v of the coating layer total The method comprises the following steps:
in the formula, v M Indicating the rate of exfoliation due to erosion,
indicating the rate of recession by the oxidation reaction;
exfoliation rate v caused by erosion M In relation to the strength of the coating:
in the formula, k m 、ρ m 、C m The thermal conductivity, density and specific heat capacity of the coating are respectively; p is a radical of total Is the total pressure of the gas flow on the ablation surface; sigma mT Is the ultimate tensile strength of the matrix;
E Am denotes the pre-factor and activation energy, v, respectively, of the thermal decomposition process of the coating M Is the coating surface migration rate, R is the universal gas constant, T w Is the coating wall temperature;
rate of migration by oxidation
The following were used:
in the formula (I), the compound is shown in the specification,
M EBC relative molecular masses of oxygen and of the coating, respectively>
Is the partial pressure of oxygen near the ablation surface, device for selecting or keeping>
And &>
Respectively the activation energy and the prespecified factor, p, of the chemical reaction EBC Denotes the density, h, of the SiC/SiC composite c Represents the convective heat transfer coefficient of the wall surface, C P Denotes the constant-pressure specific heat capacity of the coating>
Representing the oxygen mass concentration at the ablated wall.
And further, in the sixth step, the wall surface temperature and the surface pneumatic shearing force are used as the judgment conditions for failure, partial materials are removed by controlling the movement of the grid nodes after the retreating condition is reached, and the microscopic geometric morphology of the surface of the coating is updated.
Further, in the seventh step, the roughness of the coating interface is characterized by using a surface average roughness Sa and a surface root mean square Sq, and the expressions are respectively:
in the formula, Z (x, y) represents a height coordinate of the sample surface.
The beneficial effects of the invention are: the method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating comprehensively considers the initial geometric morphology structure of the coating material, couples the action of aerodynamic force and thermochemical reaction of high-temperature gas flow, realizes the simulation of the internal stress of the coating system based on a heat/force/oxygen coupling model, and simulates the morphology of the high-temperature gas after a certain time. The theoretical equation involved in the invention is easy to realize in programming. Therefore, the method can accurately simulate the ablation appearance of the coating under different conditions, and lays a foundation for the life prediction of the EBCs/CMCs in the high-temperature gas environment.
Drawings
FIG. 1 is a general flow chart of a method for predicting surface roughness variation of an environmental barrier coating of a ceramic matrix composite;
FIG. 2 is a schematic view of a geometric model containing asperities.
FIG. 3 is a schematic view of a numerical simulation geometric model of hot gas produced by the lance.
FIG. 4 is a schematic diagram of a model for diffusion of oxidizing gases inside EBCs/CMCs.
FIG. 5 is a graph of the growth of a TGO layer under the effect of thermal-force-chemical coupling.
FIG. 6 is a schematic diagram of the rough morphology of the surface evolution of EBCs under the action of high-temperature combustion gas.
Detailed Description
The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
As shown in FIG. 1, the method for predicting the surface roughness change of the environmental barrier coating of the ceramic matrix composite material in the high-temperature gas environment provided by the invention comprises the following steps:
the method comprises the following steps: the real geometric morphology of the environmental barrier coating is obtained based on an X-ray computed tomography (XCT) technology, including the rough morphology of the outer surface of the coating and the real geometric morphology among layers, boundary conditions are provided for subsequent flow field analysis, and a geometric model is provided for subsequent stress analysis.
Specifically, the mu-CT testing technology is adopted to obtain the real internal microstructures of the EBCs/CMCs, including the real appearance of the outer surface of the coating and the interface of each layer of the coating.
Step two: and (3) establishing a flow field model under a high-speed gas environment based on the geometric shape of the surface of the coating given in the step one, realizing the distribution simulation of the flow field containing the sample, and obtaining the distribution of parameters such as the wall pressure, the temperature, the heat exchange coefficient, the gas concentration and the like of the coating.
Specifically, the aerodynamic characteristics thereof were analyzed using a Computational Fluid Dynamics (CFD) method. A Shear Stress Transport (SST) k-omega model is used to characterize turbulence. And performing space dispersion on the control equation by adopting a second-order windward format. And simulating a high-temperature gas environment by adopting a limited chemical reaction rate model. And calculating the content and distribution of the gas concentration in the high-temperature fuel gas by adopting a substance diffusion transport equation. The aerodynamic characteristics refer to high-temperature gas flow field parameters, the turbulence is used for describing flow field attributes, and the control equation refers to a basic equation used for controlling the high-temperature gas flow field parameters.
Step three: based on the real coating model (namely the real geometric morphology of the coating) obtained by the XCT technology in the first step and the flow field parameters (namely the parameter distribution such as the pressure, the temperature, the heat exchange coefficient, the gas concentration and the like of the wall surface of the coating) at the gas-solid interface obtained in the second step, the parameters are respectively used as a geometric model and boundary conditions, the aerodynamic force and the gas component concentration on the coupling wall are interpolated from the fluid domain to the solid domain, and the stress analysis of the EBCs/CMCs solid domain is carried out.
Specifically, in the evolution process of the internal microstructures of the EBCs/CMCs, the flow field on the outer surface reaches the steady-state effect, the wall surface pressure, the gas component concentration and the temperature are not changed along with the growth of the TGO layer, and the wall surface parameters are changed only when the morphology is updated again.
Step four: under the driving force action of chemical potential energy, oxidizing gas begins to diffuse into the coating, oxidation reaction begins to occur when the oxidizing gas reaches the interface of a BC (Bonding Coat) layer, a TGO layer begins to grow, the growth thickness of the TGO layer is not matched with the consumption thickness of the BC layer, so that the internal volume of the TGO layer expands to generate growth strain, the internal stress of the coating is continuously increased, meanwhile, the growth and the stress of the TGO layer are mutually coupled, and a model of TGO layer growth, oxidizing gas diffusion and stress coupling is established.
Specifically, the diffusion of the high temperature fuel gas interacts with the thermal stresses within the EBCs, which act together to affect the growth of the TGO layer. An expression of the form:
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 oxidizing agent through the oxide layer,
wherein H c And H ox Henry's law solubility coefficient of oxidizing agents in coatings and oxides, 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, C is the equilibrium oxidant concentration at the outer surface of the coating.
Equilibrium equation during stress oxidation:
σ ox x+σ s (H-x)＝0
where x is the thickness of the oxide film as a function of time t, σ ox And σ s Is the biaxial average stress in the oxide film and the matrix, and H is the initial thickness of the test piece relative to the axis of symmetry; the rate form is:
in the formula, epsilon ox Is the strain of the oxide layer, M ox Is the molar mass of the oxide layer, ε g Is the strain caused by the growth of the oxide layer. Superscript · denotes derivation.
The strain is satisfied under the condition that the total thickness of the TGO layer and the BC layer is constant in the oxidation process
And &>
The strain rates of the oxide layer and the base layer, respectively.
In the course of oxidation,. Epsilon ox Consists of two parts. One part is the stress induced strain in the film and the other part isIs the growth strain. Considering the elastic model:
ε ox ＝σ ox /M ox +ε g
in the formula, epsilon ox For strain of oxide layer, M ox Is the molar mass of the oxide layer, ε g Is the strain caused by the growth of the oxide layer.
The lateral growth strain rate of the oxide layer increases linearly with the oxide layer thickening rate:
in the formula (I), the compound is shown in the specification,
is the oxide growth strain rate.
Strain epsilon to base layer S Having a epsilon s ＝σ s /M s And Ms is the biaxial modulus of the substrate.
Thus, the rate form of the equilibrium equation can be written ultimately as:
step five: and based on the thermal/force/oxygen coupling model of TGO growth established in the fourth step, considering the coating phase change, ablation and spalling behaviors in a high-temperature gas environment, establishing the kinetics of the phase change process, the thermochemical reaction kinetics of the ablation process and the erosion kinetics of the spalling process, and obtaining the evolution law of the surface microstructures of the EBCs/CMCs.
Specifically, the evolution law of the surface microstructure is obtained on the basis of the chemical reaction kinetics, in which the rate of exfoliation due to erosion is correlated with the strength of the coating:
in the formula, k m 、ρ m 、C m The thermal physical characteristics of the coating are respectively thermal conductivity coefficient, density and specific heat capacity; p is a radical of formula total The total pressure of the gas flow on the ablation surface is considered to be related to the gas flow velocity; sigma mT Is the ultimate tensile strength of the matrix;
E Am indicating the pre-exponential factor and activation energy of the thermal decomposition process of the coating, R is the universal gas constant, T w Is the coating wall temperature.
According to the competitive relationship between oxygen diffusion and thermochemical reaction, the method can be divided into diffusion control and chemical dynamic control, and the current common mode is to adopt a component separation type minimum mechanism control model.
By controlling the retreat of the geometric boundary of the surface, the retreat rate of the geometric boundary is shown as the evolution of the microstructure, so the evolution law of the surface microstructure is shown in the retreat rate v of the boundary total The method comprises the following steps:
in the formula, v M Indicating the rate of exfoliation due to erosion,
indicating the rate of recession by the oxidation reaction;
wherein the rate of migration due to oxidation
The following were used:
in the formula (I), the compound is shown in the specification,
M EBC respectively being oxygenThe relative molecular masses of gas and coating>
Is the partial pressure of oxygen near the ablation surface, device for selecting or keeping>
And &>
Respectively, the activation energy and the pre-exponential factor, p, of the chemical reaction EBC Denotes the density, h, of the SiC/SiC composite c Represents the convective heat transfer coefficient of the wall surface, C P Denotes the constant-pressure specific heat capacity of the coating>
Representing the oxygen mass concentration at the ablated wall.
Step six: and judging the surface migration form of the EBCs/CMCs in the service environment based on the calculation result of the fifth step, removing the failure part of unit materials after the failure condition of the geometric morphology of the coating is achieved, and updating the microscopic geometric morphology of the surface of the coating.
Specifically, the wall surface temperature and the surface aerodynamic shear force are used as conditions for judging whether the coating fails or not, partial materials are removed by controlling the movement of the grid nodes after the migration condition is achieved, and the microscopic geometric morphology of the surface of the coating is updated.
Step seven: and based on the updated geometric shape obtained in the sixth step, correcting the pneumatic wall geometric model (namely the flow field model in the high-speed gas environment) in the second step, repeating the second step to the sixth step until the specified high-temperature gas action time is reached, outputting the final geometric shape of the EBCs/CMCs sample, dividing the geometric shape into a plurality of regions according to the flow field distribution characteristics of the high-temperature gas, respectively counting the average sample height characteristics of each region, and determining the roughness change.
Among them, the roughness of the coating interface is generally characterized by the surface average roughness Sa and the root mean square Sq value of the surface. Sa is a parameter that expands with Ra (linear arithmetic mean height) as a surface, and represents the average of absolute values of differences in height at points with respect to the average surface of the surface. Sq defines the root mean square of the heights of each point in the area, which is equivalent to the standard deviation of the heights. The expressions are respectively:
in the formula, Z (x, y) represents a height coordinate of the sample surface.
Next, the present example was conducted for surface roughness prediction simulation of a typical multi-layered EBCs/CMCs composite material in a hot gas environment generated by oxygen-propane combustion, wherein the TOP coating (TOP) was Yb 2 SiO 5 The intermediate layer (EBC) is Yb 2 Si 2 O 7 The bonding layer (BC) is Si. The present embodiment makes predictions and simulations of the final evolution of roughness.
1) The actual geometric model containing the roughness is obtained and is shown in fig. 2, the roughness distribution of each layer is shown in table 1, and geometric boundary conditions and numerical models are provided for subsequent solution calculation.
TABLE 1 coating interface roughness distribution and maximum fluctuation height
2) Using Yb obtained in step 1 2 Si 2 O 7 The real geometric morphology of the surface of the coating is used as a geometric boundary of the high-temperature gas effect, a flow field model under the high-speed gas environment is established based on an HVOF spray gun model used by oxygen-propane combustion, the distribution of the flow field is solved, and the wall surface pressure, the temperature, the heat exchange coefficient, the gas concentration and the like of the coating are obtainedParametric, fluid domain solution geometric models are shown in fig. 3.
3) T is calculated by using the temperature field of the initial structure i The aerodynamic heat and the ablation reaction heat at a time. Aerodynamic heat and ablative reaction heat on the coupling wall are interpolated from the fluid domain to the solid domain. Then, under the action of gas pneumatic heating, thermochemical reaction heat and latent heat load of phase change process, finishing the process from t i To t i+1 Transient structure heat transfer analysis of (1). Interpolating the wall pressure, the temperature and the gas component concentration obtained by solving the fluid domain in the step 2 into a solid domain to be used as boundary conditions of the solid domain stress and the TGO layer growth.
4) The diffusion of the high temperature combustion gas and the thermal stress inside the EBCs are coupled to each other, and the combined action affects the growth of the TGO layer, wherein the growth model is shown in fig. 4. P is the partial pressure of the oxidant in the gas environment, C is the equilibrium oxidant concentration at the outer surface of the coating, co is the oxidant concentration at the outer surface of the coating, the oxidant concentration is discontinuous at the coating/oxide interface,
is the concentration of the oxidizing agent in the coating at the coating/oxidizing interface>
Concentration of oxidizing agent in the coating at the coating/oxidation interface, C i Is the oxidation concentration at the oxide/silicon interface, delta is the coating thickness, x o Is the oxide film thickness.
At the coating/oxide interface, the oxidizing agents in the coating and oxide are assumed to be in chemical equilibrium. At partial pressure P of oxidizing agent a Next, the oxidizing agent in the coating and the oxide on the interface are also assumed to be in equilibrium with the oxidizing agent in the theoretical gas. Thus, can be written as
And &>
Wherein H c And H ox Oxygen in coatings and oxides, respectivelyHenry's law solubility coefficient of the agent. Can also be written as->
Wherein->
Under steady state conditions, the number of oxygenated molecules per unit area per unit time is equal, i.e. F 1 ＝F 2 ＝F 3 ＝F 4 。F 1 、F 2 、F 3 、F 4 The oxygen fluxes of the four stages shown in fig. 4, respectively. By formulating the expression in the formula, we can obtain:
flux expression:
oxidation flux and growth rate of TGO thickness:
wherein F denotes oxygen flux, N 1 Is the number of oxidized molecules contained in the oxide per unit volume. Rearranging to obtain:
integrating and rearranging the above equation yields an expression of the form:
wherein
In the formula, x oi Is the oxide thickness at t = 0. Considering that the diffusion coefficient of the oxidizing gas in the coating when the fuel gas was heated to 1316 ℃ is shown in Table 2, the time-dependent change in the growth curve of TGO is shown in FIG. 5, and the thickness of the coating reached 5.7 μm at 200h of oxidation.
TABLE 2 diffusion coefficient of oxygen in rare earth ytterbium silicate at different temperatures
| EBCs | D 1100 (cm 2 /s) | D 1200 (cm 2 /s) | D 1300 (cm 2 /s) | E(kJ/mol) | D 0 (cm 2 /s) |
| Yb 2 Si 2 O 7 | 1.2×10 -17 | 9.0×10 -17 | 6.5×10 -16 | 358 | 4.59×10 -4 |
The presence of stress in the oxide film affects the mobility of defects (e.g., vacancies) and, thus, the oxidation kinetics. The compressive stress reduces the oxidation rate. Indeed, during diffusion transport, oxygen or ions transition from one interstitial site to another, the compressive stress may increase the energy barrier, thereby suppressing the probability of such a transition. According to the equilibrium equation:
σ ox x+σ s (H-x)＝0
where x is the thickness of the oxide film as a function of time t, σ ox And σ s H is the initial thickness of the test piece relative to the axis of symmetry, which is the biaxial average stress in the oxide film and the matrix. The rate form is:
the strain is satisfied under the assumption that the total thickness of TGO and BC is constant during oxidation
In the course of oxidation,. Epsilon ox Consists of two parts. One of which is the stress induced strain in the film and the other of which is the growth strain. Considering the elastic model:
ε ox ＝σ ox /M ox +ε g
establishing a model by adopting a dislocation climbing process, predicting that the transverse growth strain rate of an oxide layer linearly increases along with the thickening rate of the oxide layer at a fixed oxidation temperature, and the transverse growth strain rate is consistent with an experimental observation result and can be expressed as:
for epsilon S Has an epsilon s ＝σ s /M s And Ms is the biaxial modulus of the substrate.
Therefore, the coupling equation of stress and oxide film growth rate can be obtained as follows:
5) The evolution law of the surface microstructure is obtained based on the finite chemical reaction rate, wherein the thermomechanical erosion property is related to the strength of the coating, and the thermomechanical degradation rate is the linear erosion rate:
in the formula, k m 、ρ m 、C m Is a thermophysical property of the coating;
the total pressure of the gas flow on the ablation surface is considered to be related to the gas flow velocity; sigma mT Is the ultimate tensile strength of the matrix; />
E Am Indicating the pre-exponential factor and activation energy of the thermal decomposition process of the coating.
According to the competitive relationship between oxygen diffusion and thermochemical reaction, the method can be divided into diffusion control and chemical dynamic control, and the current common mode is to adopt a component separation type minimum mechanism control model. The rate of boundary pull back caused by thermochemical reactions was:
in the formula (I), the compound is shown in the specification,
M EBC is the relative molecular mass of oxygen and coating, respectively>
Oxygen partial pressure near the ablation surface, n is the reaction order, E i And A i Is the activation energy and prespecification factor, rho, of a chemical reaction EBC Denotes the density, h, of the SiC/SiC composite c Represents the convective heat transfer coefficient of the wall surface, C P Denotes the constant-pressure specific heat capacity of the coating>
Representing the oxygen mass concentration at the ablated wall.
6) Judging whether the wall surface temperature and the surface pneumatic shearing force reach the condition of removing the coating material, removing partial material by controlling the movement of the grid nodes after the condition of moving back is reached, and carrying out t i+1 Reconstructing the solid domain grid at the moment, updating the microscopic geometric morphology of the coating surface, and solving t i+1 Fluid domain of time of day.
7) And judging whether the calculated and solved time reaches the required total time, if so, outputting the surface roughness morphology of the coating, and performing the statistical distribution of the roughness. The roughness of the coating interface is typically characterized by a surface average roughness Sa and a root mean square Sq value of the surface. Sa is a parameter that expands with Ra (linear arithmetic mean height) as a surface, and represents the average of absolute values of differences in height at points with respect to the average surface of the surface. Sq defines the root mean square of the heights of each point in the area, which is equivalent to the standard deviation of the heights. The expressions are respectively:
the resulting surface roughness profile after a given time of action is shown in fig. 6a, and fig. 6b is a geometric model above the reference plane.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.
Claims (8)
1. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating is characterized by comprising the following steps:
the method comprises the following steps: obtaining a true geometry of the environmental barrier coating based on XCT;
step two: establishing a flow field model under a high-speed gas environment based on the real geometric shape obtained in the first step, and performing flow field distribution simulation including EBCs/CMCs samples to obtain flow field parameters at a gas-solid interface;
step three: respectively taking the real geometric shape obtained in the step one and the flow field parameters obtained in the step two as a geometric model and a boundary condition of TGO layer growth, interpolating aerodynamic force and gas component concentration on a coupling wall from a fluid domain to a solid domain, and performing stress analysis on the EBCs/CMCs solid domain to obtain stress distribution inside the coating;
step four: establishing a thermal/force/oxygen coupling model for the growth of the TGO layer based on the stress distribution obtained in the step three;
step five: based on the heat/force/oxygen coupling model established in the fourth step, considering the coating phase change, ablation and spalling behaviors in the high-temperature gas environment, establishing the phase change process dynamics, the thermochemical reaction dynamics of the ablation process and the erosion dynamics of the spalling process, and obtaining the evolution law of the surface microstructure of the EBCs/CMCs;
step six: judging the EBCs/CMCs surface migration form in the service environment based on the evolution rule of the EBCs/CMCs surface microstructure obtained in the fifth step, removing the failure part of unit materials after the failure condition of the coating geometric morphology is achieved, and updating the microscopic geometric morphology of the coating surface;
step seven: and based on the microcosmic geometric appearance of the coating surface updated in the sixth step, correcting the flow field model in the second step, repeating the second step to the sixth step until the specified high-temperature gas action time is reached, outputting the final geometric appearance of the EBCs/CMCs sample, dividing the final geometric appearance into a plurality of areas according to the flow field distribution characteristics of the high-temperature gas, respectively counting the average sample height characteristics of each area, and determining the roughness change.
2. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating according to claim 1, wherein: in the first step, the real geometric morphology of the environmental barrier coating is obtained by adopting a mu-CT testing technology, and the real morphology of the coating outer surface and the real morphology of each layer interface of the coating are included.
3. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating according to claim 1, wherein: in the second step, the pneumatic characteristics of the high-temperature gas are analyzed by adopting a computational fluid mechanics method, a shear stress transport k-omega model is adopted to represent turbulence, a second-order windward format is adopted to carry out spatial dispersion on a control equation, a finite chemical reaction rate model is adopted to simulate a high-temperature gas environment, and the content and distribution of gas concentration in the high-temperature gas are calculated by adopting a substance diffusion transport equation.
4. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating according to claim 1, wherein: in the third step, in the evolution process of the internal microstructures of the EBCs/CMCs, the flow field of the outer surface reaches a steady state, and the wall surface pressure, the gas component concentration and the temperature do not change along with the growth of the TGO layer.
5. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating of claim 1, wherein: in the fourth step, the specific process of establishing the thermal/force/oxygen coupling model for the growth of the TGO layer is as follows:
the diffusion of high-temperature fuel gas and the internal thermal stress of the EBCs are mutually coupled, the growth of the TGO layer is influenced under the combined action, and the following expression is satisfied:
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 oxidizing agent through the oxide layer,
wherein H c And H ox Henry's law solubility coefficient of oxidizing agents in coatings and oxides, 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 thickness of the coating, C is the equilibrium oxidant concentration at the outer surface of the coating;
the equilibrium equation in the process of stress oxidation is:
σ ox x+σ s (H-x)＝0
where x is the thickness of the oxide film as a function of time t, σ ox And σ s Is the biaxial average stress in the oxide film and the matrix, and H is the initial thickness of the test piece relative to the axis of symmetry; the rate form is:
in the formula (I), the compound is shown in the specification,
is a biaxial average stress σ of the oxide film ox Derivative with respect to time, is>
Is the oxide film growth rate;
the total thickness of the TGO layer and the BC layer is constant in the oxidation process, and the strain is satisfied
And &>
The strain rates of the oxide layer and the substrate layer respectively;
considering the elastic model:
ε ox ＝σ ox /M ox +ε g
in the formula, epsilon ox Is the strain of the oxide layer, M ox Is the molar mass of the oxide layer, ε g Is the strain caused by oxide growth;
the lateral growth strain rate of the oxide layer increases linearly with the oxide layer thickening rate:
in the formula (I), the compound is shown in the specification,
is the oxide growth strain rate;
strain epsilon to base layer s Has an epsilon s ＝σ s /M s ，M s Is the biaxial modulus of the substrate;
the rate form of the resulting equilibrium equation is:
it serves as a thermal/force/oxygen coupling model for TGO layer growth.
6. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating of claim 1, wherein: in the fifth step, the evolution law of the surface microstructure is embodied in the surface recession rate V of the coating total The following steps:
in the formula, v M Indicating the rate of exfoliation due to erosion,
indicating the rate of recession by the oxidation reaction;
exfoliation rate v caused by erosion M In relation to the strength of the coating:
in the formula, k m 、ρ m 、C m The thermal conductivity, density and specific heat capacity of the coating are respectively; p is a radical of total Is the total pressure of the gas flow on the ablation surface; sigma mT Is the ultimate tensile strength of the matrix;
E Am denotes the pre-factor and activation energy, v, respectively, of the thermal decomposition process of the coating M Is the coating surface migration rate, R is the universal gas constant, T w Is the coating wall temperature;
rate of migration by oxidation
The following were used:
in the formula (I), the compound is shown in the specification,
M EBC relative molecular masses of oxygen and of the coating, respectively>
Is the partial pressure of oxygen near the ablation surface, device for selecting or keeping>
And &>
Respectively the activation energy and the prespecified factor, p, of the chemical reaction EBC Denotes the density, h, of the SiC/SiC composite c Represents the convective heat transfer coefficient of the wall surface, C P Denotes the constant-pressure specific heat capacity of the coating>
Representing the oxygen mass concentration at the ablated wall.
7. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating of claim 1, wherein: and in the sixth step, the wall surface temperature and the surface pneumatic shearing force are used as the judgment conditions for failure, partial materials are removed by controlling the movement of the grid nodes after the retreating condition is achieved, and the microscopic geometric morphology of the surface of the coating is updated.
8. The method for predicting the surface roughness change of the ceramic matrix composite environmental barrier coating of claim 5, wherein: in the seventh step, the roughness of the coating interface is represented by a surface average roughness Sa and a surface root mean square Sq, and the expressions are respectively as follows:
in the formula, Z (x, y) represents a height coordinate of the sample surface.
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