Method for simulating oxygen diffusion in CMCs structure based on transient heat conduction

Abstract

The invention discloses a method for simulating diffusion of oxygen in a CMCs structure based on transient heat conduction. The method comprises the following steps that 1, a finite element model of the CMCs structure is established; 2, establishing an internal oxygen diffusion control equation of the CMCs structure; 3, a finite element numerical model of oxygen diffusion in the CMCs structure is established by analogy of the transient heat conduction equation; and step 4, based on the oxygen diffusion finite element numerical model, oxygen diffusion simulation is carried out in the finite element platform, and an internal oxygen diffusion result of the CMCs structure is obtained. According to the method, the diffusion behavior of an oxygen concentration field is equivalently converted into a transient heat conduction problem by utilizing the similarity of oxygen diffusion and heat conduction in a mathematical form, rapid simulation of the oxygen diffusion process in a complex structure is realized by virtue of a mature finite element thermal analysis tool, and the method can be used for predicting the oxygen concentration field in the structure. Necessary initial boundary conditions are provided for subsequent oxidation product evolution analysis, strength degradation modeling and life prediction, and the method has good engineering practical value and popularization prospects.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of ceramic matrix composite structure performance calculation, and particularly relates to a method for simulating oxygen diffusion in a CMCs structure based on transient heat conduction. BACKGROUND

[0002] Ceramic matrix composites (CMCs) have broad application prospects in the hot end components of aerospace engines due to their outstanding advantages of high-temperature resistance and low density. However, during service, the internal oxygen diffusion behavior of CMCs structures exposed to an oxygen environment for a long time will directly affect the oxidation reaction rate of the material and the service life of the structure.

[0003] At present, scholars at home and abroad have carried out a large number of studies on the oxidation behavior of CMCs, such as oxidation kinetics models and interface oxidation morphology evolution models, and representative achievements include Chinese patents CN110246548A and CN111243681A. These studies mainly focus on the oxidation rules at the material level, assuming that the oxygen concentration is uniformly distributed, and cannot fully reflect the influence of cracks and pores on the oxygen diffusion path in complex structures. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a method for simulating oxygen diffusion in a CMCs structure based on transient heat conduction in view of the above-mentioned existing deficiencies.

[0005] To achieve the above technical purpose, the technical solution adopted by the present application is:

[0006] The method for simulating oxygen diffusion in a CMCs structure based on transient heat conduction comprises the following steps:

[0007] Step one, establishing a finite element model of the CMCs structure;

[0008] Step two, establishing an oxygen diffusion control equation in the CMCs structure;

[0009] Step three, establishing an oxygen diffusion finite element numerical model in the CMCs structure by analogy with the transient heat conduction equation;

[0010] Step four, based on the oxygen diffusion finite element numerical model, performing oxygen diffusion simulation in the finite element platform to obtain the oxygen diffusion results in the CMCs structure.

[0011] To optimize the above technical solution, the specific measures adopted include:

[0012] The specific steps of step one are:

[0013] Constructing a CMCs blade finite element model, performing mesh division on the finite element model, and applying the main direction of the element.

[0014] The specific steps for step two are as follows:

[0015] The oxygen transport process in porous media follows the law of conservation of mass and Fick's law;

[0016] The diffusion flux formula for porous media is:

[0017]

[0018] From the law of conservation of mass and Fick's first law, we can obtain:

[0019]

[0020] Because the diffusion coefficient is anisotropic, and a concentration source term is introduced, the diffusion equation can be modified as follows:

[0021]

[0022] Where J is the pore diffusion flux, C is the concentration, D is the diffusion coefficient, x, y, and z represent three directions, each with a different diffusion coefficient, R is the concentration source term, and t is time.

[0023] The specific steps for step three are as follows:

[0024] By discretizing the diffusion equation using the finite element method, the finite element numerical model of oxygen diffusion is obtained as follows:

[0025]

[0026] Where matrix [M] represents the mass matrix, Let {C} represent the derivative of the oxygen concentration matrix with respect to time, [N] represent the diffusion coefficient matrix, {C} represent the oxygen volume concentration matrix, and {W} represent the oxygen throughput matrix.

[0027] The expression for the transient heat conduction finite element equation is:

[0028]

[0029] Where [K] represents the thermal conductivity matrix and [C] represents the specific heat matrix. {Q} represents the derivative of the temperature matrix with respect to time, {T} represents the heat flux vector of the node, and {Q} represents the node temperature matrix.

[0030] In the oxygen diffusion finite element equation, matrices [M] and [N] correspond to the specific heat matrix [C] and the heat conduction matrix [K] in the transient heat conduction finite element equation expression, and {C} is the concentration matrix corresponding to the temperature matrix {T}.

[0031] When conducting oxygen diffusion analysis in a finite element platform, based on the heat conduction control equation, the physical meaning of variables and coefficients is redefined to achieve an equivalent substitution of the analysis problem, thereby simulating the diffusion behavior of oxygen in CMCs structures.

[0032] When performing oxygen diffusion analysis in a finite element platform, the temperature T in the heat conduction control equation is replaced with the concentration C, the thermal conductivity k is replaced with the diffusion coefficient D, and the heat source term Q is replaced with the concentration source term R.

[0033] The specific steps for step four are as follows:

[0034] After constructing the finite element numerical model of oxygen diffusion in the CMCs structure, the model is imported into the finite element analysis platform, and the corresponding analysis control parameters are set, including time step, solution accuracy, initial conditions and boundary conditions. Then, the platform's built-in solver is called to perform transient analysis on the oxygen diffusion problem, thereby obtaining the oxygen concentration distribution results of the CMCs structure at each time point, and realizing the numerical simulation of oxygen diffusion behavior inside the structure.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] 1. This method leverages the mathematical similarity between oxygen diffusion and heat conduction, transforming the diffusion behavior of the oxygen concentration field into an equivalent transient heat conduction problem. It utilizes mature finite element thermal analysis tools to achieve rapid simulation of the oxygen diffusion process in complex structures. By setting the oxygen concentration at the boundary as an equivalent heat flow boundary condition and introducing a temperature-concentration equivalent transformation relationship, accurate prediction of the oxygen distribution state at any given time within CMCs structures can be achieved. This method does not require pre-setting gas concentration parameters at the material contact surface and can adaptively reflect the influence of heterogeneous structures such as cracks and pores on the diffusion path.

[0037] 2. This method provides a feasible engineering approach for simulating the oxidation of ceramic matrix composite structures during service. It can be used to predict the oxygen concentration field inside the structure, providing necessary initial boundary conditions and distribution basis for subsequent oxidation product evolution analysis, strength degradation modeling and life prediction. It has good engineering practical value and application prospects. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of an oxygen diffusion simulation method.

[0039] Figure 2 It is a finite element model of a blade.

[0040] Figure 3 This is a graph showing the oxygen concentration distribution after 10 seconds of diffusion.

[0041] Figure 4This is a graph showing the oxygen concentration distribution after 100 seconds of diffusion. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this application clearer, the application is described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments provided in this application without inventive effort are within the scope of protection of this application.

[0043] Obviously, the accompanying drawings described below are merely some examples or embodiments of this application. Those skilled in the art can apply this application to other similar scenarios based on these drawings without any inventive effort. Furthermore, it is understood that although the efforts made in this development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, any changes to design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as insufficient disclosure of the content of this application.

[0044] like Figure 1 The method shown includes the following steps: Simulating oxygen diffusion in ceramic matrix composites based on transient thermal conduction.

[0045] Step 1: Establish a finite element model of the CMCs structure;

[0046] A finite element model of a ceramic matrix composite blade is constructed. The finite element model is then meshed, and principal directions of the elements are applied, such as... Figure 2 The image shows the completed finite element model of the blade.

[0047] Step 2: Establish the oxygen diffusion control equation within the CMCs structure;

[0048] From the perspective of molecular kinetic theory, the diffusion process of gas molecules is essentially a process of mass transfer. The numerous pores and cracks in woven CMCs affect gas diffusion within them; therefore, the gas-phase diffusion process of oxygen in woven CMCs can be described as the diffusion of gas in porous solids. The diffusion process of oxygen in porous media is essentially a process of oxygen mass transfer; therefore, the oxygen transport process in porous media follows the law of conservation of mass and Fick's law.

[0049] The diffusion flux formula for porous media is:

[0050]

[0051] From the law of conservation of mass and Fick's first law, we can obtain:

[0052]

[0053] Because the diffusion coefficient is anisotropic, and a concentration source term is introduced, the diffusion equation can be modified as follows:

[0054]

[0055] Where J is the pore diffusion flux, C is the concentration, D is the diffusion coefficient, x, y, and z represent three directions, each with a different diffusion coefficient, R is the concentration source term, and t is time.

[0056] Step 3: By analogy with the transient heat conduction equation, establish a finite element numerical model of oxygen diffusion inside the CMCs structure;

[0057] In the finite element method, solving Fick's second law for a three-dimensional source involves discretizing the partial differential equations and introducing source terms. The following is a detailed solution process, including the discretization of the equations, the construction of the finite element formulas, the application of boundary conditions, and the actual solution procedure.

[0058] From Fick's law and the law of conservation of mass, the finite element equation for oxygen diffusion can be derived as follows:

[0059]

[0060] The expression for the transient heat conduction finite element equation is:

[0061]

[0062] Where {C} is the concentration matrix, [K] represents the thermal conductivity matrix, and [C] represents the specific heat matrix; {Q} represents the derivative of the temperature matrix with respect to time; {T} represents the heat flux vector of the node; and {Q} represents the node temperature matrix.

[0063] In the oxygen diffusion finite element equation, matrices [M] and [N] correspond to the specific heat matrix [C] and the heat conduction matrix [K] in the transient heat conduction finite element equation expression, and {C} is the concentration matrix corresponding to the temperature matrix {T}.

[0064] The oxygen diffusion equation and the transient heat conduction equation are highly similar in mathematical form, the only difference being that the heat conduction equation has two additional physical parameters: density and specific heat capacity. Based on this similarity, the oxygen diffusion process can be transformed into a heat conduction process for solution through parameter equivalence mapping: oxygen concentration is mapped to temperature, diffusion coefficient to thermal conductivity, and density and specific heat capacity are uniformly set to 1, thus achieving consistency in the form of the governing equations without affecting numerical stability.

[0065] Table 1. Comparison of similarities between heat conduction and oxygen diffusion.

[0066]

[0067]

[0068] In the table, T(t) represents the temperature change with time t at the boundary location; C(t) represents the concentration change with time t at the boundary location; f(t) is a time function used to specify the specific form of temperature or concentration at the boundary; C0 represents the oxygen concentration at the initial moment at the boundary.

[0069] In transient heat conduction problems, the system temperature field evolves dynamically over time, while the heat flux boundary conditions and internal energy state are also updated over time. The transient thermal analysis module provided in finite element software, based on Fourier's law and the law of conservation of energy, solves for the spatiotemporal distribution of nodal temperatures using the finite element method. Its typical finite element discrete equation form is as follows:

[0070]

[0071] Correspondingly, the diffusion of oxygen in solid porous media (such as CMC) is a spontaneous migration process of gas molecules from high-concentration regions to low-concentration regions due to their own thermal motion, obeying Fick's law and the law of conservation of mass. Its finite element matrix expression is:

[0072]

[0073] Clearly, the two share a high degree of consistency in their mathematical structure. Through the following parameter mapping, an equivalent simulation of oxygen diffusion behavior can be achieved using the transient thermal analysis module of the finite element method software:

[0074] Table 3 Parameter Equivalent Correspondence

[0075]

[0076] Based on the above physical analogy, by transforming the coefficient terms in the governing equation, a finite element numerical model of oxygen diffusion suitable for ceramic matrix composite structures can be constructed, thereby simulating the diffusion behavior of oxygen in complex structures on the existing finite element platform.

[0077] Step 4: Based on the finite element numerical model, perform oxygen diffusion simulation on the finite element platform to obtain the oxygen diffusion results inside the ceramic matrix composite structure.

[0078] After constructing the finite element numerical model of oxygen diffusion in the ceramic matrix composite structure, the model was imported into the finite element analysis platform, and the corresponding analysis control parameters, including time step, solution accuracy, initial conditions, and boundary conditions, were set. Subsequently, the platform's built-in solver was used to perform transient analysis on the oxygen diffusion problem, thereby obtaining the oxygen concentration distribution results of the ceramic matrix composite structure at various time points, and realizing the numerical simulation of oxygen diffusion behavior inside the structure.

[0079] Determining boundary conditions:

[0080] Dirichlet boundary conditions (first type of boundary condition): Specifies the concentration value at the boundary, suitable for situations where the concentration at the boundary is constant. The expression is:

[0081] C(x b ,t)=f(t)

[0082] Wherein, C(x) b ,t) represents the boundary position x b The concentration at time t is given by f(t), which can be a constant (the concentration does not change with time) or a function that changes with time.

[0083] Neumann boundary conditions (second type of boundary conditions): specify the concentration gradient at the boundary, applicable to cases where there is a fixed flux at the boundary.

[0084]

[0085] Where, q b It is the known concentration gradient at the boundary.

[0086] Robin boundary condition (third type of boundary condition): There is a linear relationship between boundary flux and concentration, applicable to cases where convection and diffusion exist at the boundary.

[0087]

[0088] Where D is the oxygen diffusion coefficient, h is the mass transfer coefficient, and C(x) is the mass transfer coefficient. b ,t) represents the concentration at the boundary, C ∞ This represents the volume concentration of oxygen in the environment outside the boundary. This condition reflects the mass exchange relationship between the concentration distribution at the boundary and the external environment through the combined effects of convection and diffusion.

[0089] Determination of material parameters:

[0090] Table 3 shows the material parameters of the CMC blade structure.

[0091] Table 3 Material Parameters

[0092]

[0093]

[0094] After setting boundary conditions and assigning material parameters, finite element mesh generation and other preprocessing operations were performed on the ceramic matrix composite (CMCs) blade structure. Subsequently, a concentration load was applied to the blade blade region to simulate the diffusion process of oxygen in the structure under atmospheric conditions. In this embodiment, the applied oxygen concentration load value was 0.21, corresponding to the mole fraction of oxygen in atmospheric pressure.

[0095] See Figure 3 and Figure 4 The figures show the oxygen concentration distribution inside the CMC blade at different time points. As the diffusion time increases, oxygen gradually diffuses from the blade surface into its interior, and the concentration gradient gradually advances towards the core region. This diffusion process exhibits significant anisotropy, meaning that the diffusion rate varies along different directions, reflecting the inconsistency in oxygen transport capacity in different directions of the composite material. This anisotropic behavior is mainly determined by the fiber distribution orientation, matrix structure, and interfacial properties within the material, reflecting the complex diffusion mechanism of ceramic matrix composites at multiple scales.

[0096] This invention constructs an oxygen diffusion field in a finite element platform, which can accurately characterize the transport law of oxygen in the atmosphere inside the CMC structure, providing an effective numerical simulation basis and theoretical support for the prediction of service life, anti-oxidation design and structural safety assessment of ceramic matrix composites.

[0097] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for simulating oxygen diffusion inside CMCs structures based on transient heat conduction, characterized in that, Includes the following steps: Step 1: Establish a finite element model of the CMCs structure; Step 2: Establish the oxygen diffusion control equation within the CMCs structure; Step 3: By analogy with the transient heat conduction equation, establish a finite element numerical model of oxygen diffusion inside the CMCs structure; Step 4: Based on the finite element numerical model of oxygen diffusion, perform oxygen diffusion simulation on the finite element platform to obtain the oxygen diffusion results inside the CMCs structure.

2. The method for simulating oxygen diffusion inside CMCs structures based on transient heat conduction according to claim 1, characterized in that, The specific steps of step one are as follows: A finite element model of CMC blades is constructed, and the finite element model is meshed and the principal directions of the elements are applied.

3. The method for simulating oxygen diffusion inside CMCs structures based on transient heat conduction according to claim 1, characterized in that, The specific steps for step two are as follows: The oxygen transport process in porous media follows the law of conservation of mass and Fick's law; The diffusion flux formula for porous media is: From the law of conservation of mass and Fick's first law, we can obtain: Because the diffusion coefficient is anisotropic, and a concentration source term is introduced, the diffusion equation can be modified as follows: Where J is the pore diffusion flux, C is the concentration, D is the diffusion coefficient, x, y, and z represent three directions, each with a different diffusion coefficient, R is the concentration source term, and t is time.

4. The method for simulating oxygen diffusion inside CMCs structures based on transient heat conduction according to claim 1, characterized in that, The specific steps for step three are as follows: By discretizing the diffusion equation using the finite element method, the finite element numerical model of oxygen diffusion is obtained as follows: Wherein, matrix [M] represents the mass matrix. Let {N} represent the derivative of the oxygen concentration matrix with respect to time, [N] represent the diffusion coefficient matrix, {C} represent the oxygen volume concentration matrix, and {W] represent the oxygen throughput matrix. The expression for the transient heat conduction finite element equation is: Where [K] represents the thermal conductivity matrix and [C] represents the specific heat matrix. {Q} represents the derivative of the temperature matrix with respect to time, {T} represents the heat flux vector of the node, and {Q} represents the temperature matrix of the node. In the oxygen diffusion finite element equation, matrices [M] and [N] correspond to the specific heat matrix [C] and the heat conduction matrix [K] in the transient heat conduction finite element equation expression, and {C} is the concentration matrix corresponding to the temperature matrix {T}. When conducting oxygen diffusion analysis in a finite element platform, based on the heat conduction control equation, the physical meaning of variables and coefficients is redefined to achieve an equivalent substitution of the analysis problem, thereby simulating the diffusion behavior of oxygen in CMCs structures.

5. The method for simulating oxygen diffusion inside CMCs structures based on transient heat conduction according to claim 4, characterized in that, When performing oxygen diffusion analysis in a finite element platform, the temperature T in the heat conduction control equation is replaced with the concentration C, the thermal conductivity k is replaced with the diffusion coefficient D, and the heat source term Q is replaced with the concentration source term R.

6. The method for simulating oxygen diffusion inside CMCs structures based on transient heat conduction according to claim 1, characterized in that, The specific steps for step four are as follows: After constructing the finite element numerical model of oxygen diffusion in the CMCs structure, the model is imported into the finite element analysis platform, and the corresponding analysis control parameters are set, including time step, solution accuracy, initial conditions and boundary conditions. Then, the platform's built-in solver is called to perform transient analysis on the oxygen diffusion problem, thereby obtaining the oxygen concentration distribution results of the CMCs structure at each time point, and realizing the numerical simulation of the oxygen diffusion behavior inside the structure.

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