Simulation method of reactive melt permeation process

Abstract

The invention is applicable to the technical field of reactive melt permeation processes, and provides a reactive melt permeation process simulation method which comprises the following steps: determining an interpolation function for representing the porosity of a target porous preform through gray information of the target porous preform; obtaining basic parameters of a reaction melt permeation process to be simulated, and establishing a control equation set according to the basic parameters and the interpolation function to obtain a numerical model; and according to the numerical model, completing simulation of a reaction melt permeation process to be simulated through COMSOL Multiphysics. According to the method, the interpolation function used for representing the porosity of the target porous preform is determined according to the gray information of the target porous preform, the interpolation function is imported into COMSOL Multiphysics, and meanwhile, the influence of the pore structure on flow field distribution at different times is considered, so that the process simulation of the to-be-simulated reaction melt permeation process is more real.

Description

Technical Field

[0001] The present application belongs to the technical field of reactive melt infiltration process, and in particular to a simulation method of a reactive melt infiltration process. Background Art

[0002] Reaction melt infiltration (RMI) is an advanced material preparation technology that infiltrates liquid metal into a porous carbon preform, reacts chemically with the carbon matrix in the preform, and forms a ceramic phase, thereby obtaining a ceramic matrix composite material with excellent performance. This type of material combines the performance advantages of carbon materials and ceramic materials, such as light weight, high temperature resistance, oxidation ablation resistance, and thermal shock resistance, so it has broad application potential in aerospace, nuclear energy, and high-performance friction braking. However, in actual engineering applications, there are some technical difficulties in the preparation of ceramic matrix composites using the RMI process, mainly including insufficient comprehensive mechanical properties, difficult to control microstructure, and poor creep resistance. These problems are mainly related to the essence of the infiltration, transport, and reaction behavior of the metal melt in the porous carbon preform and its kinetic laws.

[0003] In order to solve the above problems, existing research mainly focuses on analyzing the RMI process through numerical models to accurately analyze the dynamic laws of the process. Commonly used theoretical models include Darcy's law, Washburn's equation and Richards' formula. For example, Gern introduced the self-weight of the melt on the basis of Washburn's equation and derived the relationship between the infiltration rate and the capillary radius, melt viscosity, surface tension and contact angle. Einset used Richards' formula to calculate the temperature field during the reactive infiltration process and used thermocouples to monitor the temperature inside the porous carbon preform. Yushanov coupled Richards' formula and Darcy's law to describe the infiltration reaction behavior of silicon melt in the porous carbon preform. Grugicic considered the microstructural evolution process of ceramic grains generated by infiltration reaction and applied the reactive infiltration model to the process optimization analysis of turbine ring manufacturing. Although existing numerical simulation studies have provided a certain theoretical basis for understanding the RMI process, the existing technology sets the porous carbon preform to have a single pore size distribution and uses representative volume elements (RVE) for modeling and analysis, which cannot accurately reflect the complex pore structure of the actual porous carbon preform, resulting in insufficient understanding of the response mechanism of the complex pore structure and the high-temperature melt infiltration reaction behavior. Summary of the invention

[0004] The embodiments of the present application provide a method for simulating a reactive melt infiltration process, which can solve the problem in the prior art of insufficient understanding of the response mechanism of complex pore structures and high-temperature melt infiltration reaction behavior.

[0005] The present application embodiment provides a method for simulating a reactive melt infiltration process, including:

[0006] Determine an interpolation function for characterizing the real-time porosity of the target porous preform through grayscale information of the target porous preform;

[0007] Obtaining basic parameters of the reactive melt infiltration process to be simulated, and establishing a control equation group according to the basic parameters and the interpolation function to obtain a numerical model;

[0008] According to the numerical model and the interpolation function, the reactive melt infiltration process to be simulated is simulated by COMSOL Multiphysics.

[0009] Optionally, the step of determining an interpolation function for characterizing the porosity of the target porous preform according to the grayscale information of the target porous preform comprises:

[0010] Acquire a CT scan image of the target porous preform, and extract grayscale information of the CT scan image through Python;

[0011] Determine the porosity corresponding to the grayscale information according to a preset rule;

[0012] The porosity is coupled to the reaction time according to a preset attenuation function to obtain real-time pore data at different times;

[0013] The real-time pore data at different times are used as interpolation functions at different times.

[0014] Optionally, the step of obtaining basic parameters of the reactive melt infiltration process to be simulated, and establishing a control equation group according to the basic parameters and the interpolation function to obtain a numerical model includes:

[0015] The first control equation of the flow field of the reactive melt infiltration process to be simulated is established by using the Brinkman equation and the Richard equation;

[0016] Based on Fick's law, the convection-diffusion control equations of reactants and products in the reactive melt infiltration process to be simulated are established;

[0017] The porous medium concentrated species transport equation is used to characterize the influence of porous structure characteristics on the fluid migration process in the simulated reactive melt infiltration process.

[0018] The reaction rate control equation is constructed using the derivative of the reaction specific surface area and the saturation;

[0019] The porous medium heat transfer equation of the reactive melt infiltration process to be simulated, the first control equation, the convection-diffusion control equation, the porous medium concentrated species transport equation and the reaction rate control equation are combined to obtain a numerical model.

[0020] Optionally, the numerical model further includes a basic heat transfer equation:

[0021] The mathematical expression of the basic heat transfer equation is:

[0022]

[0023] Among them C p is the specific heat capacity (J / (kg·K)), λ is the thermal conductivity (W / (cm·K)), Q is the volumetric heat source (W / m 3 Qp is the heat source term generated by pressure change (W / m 3 ), Q vd is the heat source term generated by viscous dissipation (W / m 3 ), Q chem is the heat source term generated by the chemical reaction (W / m 3 ).

[0024] Optionally, the numerical model further includes a thermal radiation equation:

[0025] The mathematical expression of the heat radiation equation is:

[0026]

[0027] Where n·q represents the projection of the heat transfer flux q along the surface normal direction n, and the projection represents the heat flux density (W / m 2 ), τ is the surface emissivity of the target porous preform (dimensionless), ranging from 0 to 1, T amb Indicates the ambient temperature.

[0028] Optionally, the numerical model also includes a physical property parameter equation:

[0029] The mathematical expression of the physical property parameter equation is:

[0030] Assume the volume fraction of consumed carbon is V C is y, the porosity of the porous body is ε, and the initial porosity is ε 0 , let V SiC / V C =m, then V SiC =my;

[0031] V SiC -V C =my-y=ε 0 -ε

[0032] y(m-1)=ε 0 -ε

[0033]

[0034] The volume fraction ratio of each phase is:

[0035]

[0036] The density, effective thermal conductivity and molar specific heat capacity of the liquid and solid phases that vary with temperature and porosity can be obtained as follows:

[0037]

[0038] ρ ll (T) = 3210 - 0.4 × T

[0039]

[0040] (λ l ) eff =λ Si ·ε

[0041]

[0042] Among them, ρ s is the density function of the solid phase, ρ l is the density function of the liquid phase, (λ s ) eff is the effective thermal conductivity equation of the solid phase, (λ l ) eff is the effective thermal conductivity equation of the liquid phase, C p，s is the specific heat capacity function of the solid phase, C p，l is the specific heat capacity function of the liquid phase.

[0043] Optionally, the step of simulating the reactive melt infiltration process to be simulated by COMSOL Multiphysics according to the numerical model and the interpolation function comprises:

[0044] Obtaining initial conditions and boundary conditions of the reactive melt infiltration process to be simulated;

[0045] and determining the constraint conditions of the numerical model according to the initial conditions and the boundary conditions;

[0046] According to the numerical model, the constraints of the numerical model and the interpolation function, the reactive melt infiltration process to be simulated is simulated by COMSOL Multiphysics.

[0047] Compared with the prior art, the embodiments of the present application have the following beneficial effects: by CT scanning the target porous carbon preform, the structural characteristics (grayscale information) of the target porous carbon preform are analyzed and imported into COMSOL Multiphysics, and the influence of the pore structure on the flow field distribution at different times is considered. In the simulation process of reactive melt infiltration, the mesoscopic and macroscopic flow field characteristics are considered respectively, the inertial effect of continuous medium flow, the viscous effect of flow in porous media, diffusion, concentrated material transfer, thermal radiation, thermal convection and other links are considered, and the control equations of flow field, thermal field and chemical field are respectively placed under the corresponding physical field nodes to realize the simulation of the reactive melt infiltration process. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0049] Figure 1 It is a flow chart of a simulation method of a reactive melt infiltration process provided in an embodiment of the present application;

[0050] Figure 2 is a flow chart of another method for simulating a reactive melt infiltration process provided in an embodiment of the present application;

[0051] Figure 3 It is a diagram of establishing a geometric model and setting property conditions under mesoscopic interpolation discretization in a simulation method for a reactive melt infiltration process provided in an embodiment of the present application;

[0052] Figure 4 It is a diagram for establishing a geometric model and setting property conditions under a macroscopic continuous medium in a simulation method for a reactive melt infiltration process provided in an embodiment of the present application. DETAILED DESCRIPTION

[0053] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0054] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, wholes, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or combinations thereof.

[0055] It should also be understood that the term “and / or” used in the specification and appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0056] As used in the specification and appended claims of this application, the term "if" can be interpreted as "when" or "uponce" or "in response to determining" or "in response to detecting" depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "uponce it is determined" or "in response to determining" or "uponce [described condition or event] is detected" or "in response to detecting [described condition or event]" depending on the context.

[0057] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0058] References to "one embodiment" or "some embodiments" etc. described in the specification of this application mean that one or more embodiments of the present application include specific features, structures or characteristics described in conjunction with the embodiment. Therefore, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0059] like Figure 1 As shown, the embodiment of the present application provides a simulation method for a reactive melt infiltration process, comprising:

[0060] S101, determining an interpolation function for characterizing the real-time porosity of a target porous preform according to grayscale information of the target porous preform;

[0061] For example, the target porous preform structure information is scanned by CT and imported into Avizo to determine the grayscale thresholds (T s , T p), use Python to parse the grayscale information of each slice, obtain the porosity of the pore area, and stack the coordinate group and porosity group vertically based on the NumPy function. s and T p Two thresholds, grayscale values ​​less than or equal to T p The porosity is set to 1. In order to ensure the rationality of the calculation of the Brinkman equation and the Richard equation, the porosity greater than or equal to T s The porosity of is set to 0.001. At the same time, the variable ε is defined, and the porosity that changes with time is calculated using a preset decay function based on the initial porosity, time, and attenuation coefficient q. The pore structure characteristic information at different times is exported and imported into COMSOL Multiphysics as an interpolation function to provide numerical values ​​for the geometric structure data required for the simulation process.

[0062] S102, obtaining basic parameters of the reactive melt infiltration process to be simulated, and establishing a control equation group according to the basic parameters and the interpolation function to obtain a numerical model;

[0063] Exemplarily, the model operation parameters, that is, the basic parameters of the reactive melt infiltration process to be simulated, are determined by literature research and analysis of the behavioral characteristics of the reactive melt infiltration process, as well as experimental measurements or empirical values.

[0064] Exemplarily, the porosity is set as a conditional function, that is, the corresponding pore structure characteristic interpolation function is activated at different times; considering the distribution forms of both mesoscopic and macroscopic flow fields, the first control equation of the flow field is established using the Brinkman equation and the Richard equation; based on Fick's law, the convection-diffusion control equations of reactants and products are established, and considering the influence of the porous structure characteristics on the fluid during the migration process, the porous medium concentrated substance transfer equation is adopted; the porous medium heat transfer equation is added and the radiation response of the preform to the environment is considered, and the reaction rate control equation is constructed using the derivative of the reaction specific surface area and the saturation, the established equations are combined, and the basic parameters of the reaction melt infiltration process to be simulated are brought in to obtain a numerical model.

[0065] S103 , simulating the reactive melt infiltration process to be simulated by using COMSOL Multiphysics according to the numerical model and the interpolation function.

[0066] For example, a multi-physics coupling interface is constructed: the "Brinkman" equation is added to simulate the viscous flow of melt in porous media at the mesoscopic level, and the "Richard equation" interface is added to simulate the unsaturated flow of melt in porous media at the macroscopic level. The "concentrated species transfer in porous media" physical field is added to simulate the diffusion, convection and other distribution of reactive molten silicon in the pore structure of the carbon preform. The "porous medium heat transfer" is added to simulate the temperature distribution in the porous preform during the reaction infiltration process, and the exothermic effect caused by the chemical reaction is included. The function expressions of the physical and chemical properties of the silicon melt and the carbon porous preform are defined in the components, and the parameter properties are set and constrained by initial conditions, boundary conditions, etc. Among them, a swept mesh is constructed for the geometric model, and each unit corresponds to the porosity under a coordinate.

[0067] Exemplarily, a transient study is added, and the calculation time of the transient study is consistent with the calculation time of the interpolation function. The absolute tolerance, time step, termination method and criterion in the solver are adjusted as needed, and the calculation results are post-processed. By adding drawings, the liquid volume fraction, Brinkman velocity field, Richard concentration field, and Richard velocity field in the pore structure at different times are displayed.

[0068] In a possible implementation manner, the step of determining an interpolation function for characterizing the porosity of the target porous preform according to the grayscale information of the target porous preform includes:

[0069] Acquire a CT scan image of the target porous preform, and extract grayscale information of the CT scan image through Python;

[0070] Determine the porosity corresponding to the grayscale information according to a preset rule;

[0071] The porosity is coupled to the reaction time according to a preset attenuation function to obtain real-time pore data at different times;

[0072] The real-time pore data at different times are used as interpolation functions at different times.

[0073] For example, for grayscale values ​​less than or equal to T P Porosity settings:

[0074] φ(x)=1,if I(x)≤T P T P =6503

[0075] For grayscale values ​​greater than or equal to T s Porosity settings:

[0076] φ(x)=0.001,if I(x)≥T S TS =8004

[0077] For grayscale values ​​between T P and T s Porosity settings between:

[0078]

[0079] where φ(x) represents the porosity (dimensionless), I(x) represents the gray value (dimensionless), and T s and T p are the grayscale thresholds of the solid area and the pore area, respectively. In order to characterize the changes in the pore structure during the reactive infiltration process, an attenuation function of the porosity changing with time (preset attenuation function) is constructed:

[0080] φ(t)=φ 0 ·e -qt 0.001≤φ(t)≤1

[0081] where φ(t) is the porosity at time t (dimensionless), φ 0 is the initial porosity (dimensionless), q is the attenuation coefficient (s -1 ). Calculate the current porosity based on the initial porosity, time and attenuation coefficient, and limit it to between 0.001 and 1. Finally, select the data columns to be saved for output. Import each array as an interpolation function at different times into COMSOL Multiphysics and set the porous body porosity ε variable:

[0082]

[0083] Among them, int i(x,y,z) is the interpolation function of the pore structure characteristics at different times, and the conditional function χ |a,b| (t) takes the value 1 when a≤t≤b, and 0 otherwise:

[0084]

[0085] The variable ε is the value of the int function in each interval of time t. The porosity is calculated by selecting the corresponding int interpolation function based on the interval where t is located using the conditional function.

[0086] In one possible implementation, the step of obtaining basic parameters of the reactive melt infiltration process to be simulated, and establishing a control equation group according to the basic parameters and the interpolation function to obtain a numerical model includes:

[0087] The first control equation of the flow field of the reactive melt infiltration process to be simulated is established by using the Brinkman equation and the Richard equation;

[0088] Based on Fick's law, the convection-diffusion control equations of reactants and products in the reactive melt infiltration process to be simulated are established;

[0089] The porous medium concentrated species transport equation is used to characterize the influence of porous structure characteristics on the fluid migration process in the simulated reactive melt infiltration process.

[0090] The reaction rate control equation is constructed using the derivative of the reaction specific surface area and the saturation;

[0091] The porous medium heat transfer equation of the reactive melt infiltration process to be simulated, the first control equation, the convection-diffusion control equation, the porous medium concentrated species transport equation and the reaction rate control equation are combined to obtain a numerical model.

[0092] For the melt flow characteristics in porous preforms at the mesoscopic level, the inertial effect and viscosity effect of continuous medium flow need to be considered. Based on the Brinkman equation, the flow model adopts Darcy flow, as follows:

[0093] Momentum conservation equation:

[0094] The mass conservation equation:

[0095]

[0096] Among them, ρ f is the density of silicon melt (kg / m 3 ), p is the fluid pressure (Pa), I is the unit matrix (dimensionless), K is the stress tensor (Pa), μ is the dynamic viscosity (Pa·s), κ -1 is the inverse of the porous medium permeability (m-2), defined as: -1 =1 / (k 0 ×ε), represents the anisotropy of pore structure characteristics, k 0 is the initial permeability (m 2 ); β is the Forchheimer coefficient (m -1 ), Q m represents the mass source or absorption term in porous media (kg / (m 3 ·s)), F is the body force (N / m), u is the Darcy velocity or unit flow vector (m·s -1 ), defined as Where g is the gravitational acceleration constant (taken as 9.8m·s -2 ); g is the gravitational acceleration vector (m·s -2 ), defined as Where H is the elevation (m) and ΔH is the unit vector in the direction of gravity (m).

[0097] The flow field simulation of unsaturated fluid under macroscopic conditions needs to be based on the Richard equation, combined with the continuity of the motion of unsaturated silicon melt and Darcy's law. The local liquid phase mass needs to be multiplied by the effective saturation S e , as follows:

[0098] The mass balance equation of the liquid phase in the unsaturated region is:

[0099]

[0100] Where S e is the effective saturation (dimensionless), and considering the compressibility of liquid and solid phases, the general equation for unsaturated seepage in deformable porous media is:

[0101]

[0102] Among them C w is the actual water content (m -1 ), S p is the water storage coefficient (Pa -1 ).

[0103] Furthermore, the diffusion control equations of reactants and products based on Fick's law are as follows:

[0104]

[0105]

[0106] where w i is the mass fraction of the substance (dimensionless), t represents time (s), J F is the mass diffusion flux based on Fick's law (kg / (m 2 ·s)), R represents the chemical reaction rate (kg / (m 3 ·s)), D i is the diffusion coefficient of each component (m 2 / s). In order to maintain the conservation of fluid mass during the simulation of reactive melt infiltration, it is necessary to add the continuity equation to the diffusion equation. At the same time, there are concentration gradients, temperature gradients and convection exchange in the reactive melt infiltration process in the porous medium. Therefore, it is also necessary to consider the diffusion caused by the effective molar mass gradient, temperature gradient and convection in the porous body. The corresponding diffusion fluxes are Among them J M is the effective molar mass gradient diffusion flux (kg / (m 2 ·s)), M n is the average molecular weight (kg / mol), J T is the temperature gradient diffusion flux (kg / (m2 ·s)), T represents temperature (K), J conv is the convection diffusion flux (kg / (m 2 ·s)), x k is the molar fraction of component k (dimensionless). The reactive melt reacts chemically with the contact surface of the porous body, so it can be considered that the reaction occurs in the pore structure. Based on the above description, the governing equation for the transport simulation of reactants and products in porous media is:

[0107]

[0108]

[0109]

[0110] Among them, M i is the molecular weight of component i (kg / mol). In order to unify the diffusion coefficients D of different diffusion terms iM , D ik , D iT (m 2 / s), the effective diffusion coefficient is determined by the Millington Quiek model as follows:

[0111]

[0112] In a possible implementation manner, the numerical model further includes a basic heat transfer equation:

[0113] The mathematical expression of the basic heat transfer equation is:

[0114]

[0115]

[0116] Among them C p is the specific heat capacity (J / (kg·K)), λ is the thermal conductivity (W / (cm·K)), Q is the volumetric heat source (W / m 3 Qp is the heat source term generated by pressure change (W / m 3 ), Q vd is the heat source term generated by viscous dissipation (W / m 3 ), Q chem is the heat source term generated by the chemical reaction (W / m 3 ).

[0117] In a possible implementation manner, the numerical model further includes a thermal radiation equation:

[0118] The mathematical expression of the heat radiation equation is:

[0119]

[0120] Where n·q represents the projection of the heat transfer flux q along the surface normal direction n, and the projection represents the heat flux density (W / m 2 ), τ is the surface emissivity of the target porous preform (dimensionless), ranging from 0 to 1, T amb Indicates the ambient temperature.

[0121] In a possible implementation manner, the numerical model further includes a physical property parameter equation:

[0122] The mathematical expression of the physical property parameter equation is:

[0123] Assume the volume fraction of consumed carbon is V C Let V SiC / V C =m, then V SiC =my;

[0124] V SiC -V C =my-y=ε 0 -ε

[0125] y(m-1)=ε 0 -ε

[0126]

[0127] The volume fraction ratio of each phase is:

[0128]

[0129] The density, effective thermal conductivity and molar specific heat capacity of the liquid and solid phases that vary with temperature and porosity can be obtained as follows:

[0130]

[0131] ρ ll (T) = 3210 - 0.4 × T

[0132]

[0133] (λ l ) eff =λ Si ·ε

[0134]

[0135]

[0136] Among them, ρ sis the density function of the solid phase, ρ l is the density function of the liquid phase, (λ s ) eff is the effective thermal conductivity equation of the solid phase, (λ l ) eff is the effective thermal conductivity equation of the liquid phase, C p，s is the specific heat capacity function of the solid phase, C p，l is the specific heat capacity function of the liquid phase.

[0137] For example, heat transfer during melt transport involves the flow of the melt in the pores and heat conduction through the solid matrix, as well as chemical reactions and heat release in the porous domain. The basic heat transfer equation is obtained based on the law of conservation of energy, as follows:

[0138]

[0139] Among them C p is the specific heat capacity (J / (kg·K)), λ is the thermal conductivity (W / (cm·K)), Q is the volumetric heat source (W / m 3 ). The heat source can be considered to be provided by chemical reactions, that is, Q = R × V SiC . Where V SiC is the molar volume of silicon carbide (m 3 / mol); in the simulation of melt transport in porous media, the heat conduction equation needs to consider the effective thermal conductivity λ eff and effective specific heat capacity (C p ) eff As well as heat source items generated by viscous dissipation, pressure changes, etc., heat transfer flux The unit is W / m 2 , as follows:

[0140]

[0141] Where Q p is the heat source term generated by the pressure change (W / m 3 ), Q vd is the heat source term generated by viscous dissipation (W / m 3 ), Q geo is the heat source term generated by geology (W / m 3 ). In the porous media heat transfer field, the thermal radiation equation of the porous body surface to the environment is also constructed. The details are as follows:

[0142]

[0143] Where n·q represents the projection of the heat flux q along the surface normal direction n, that is, the heat flux density (W / m 2). τ is the surface emissivity (dimensionless), ranging from 0 to 1, indicating the efficiency of the surface relative to a black body radiation, T amb Indicates the ambient temperature.

[0144] As a further solution of the present invention: the physical and chemical properties of the silicon melt and the carbon porous preform will change with the change of their content and temperature, so it is necessary to construct the physical property parameter equations of the liquid phase and the solid phase, and use the mixing law to estimate the change of material properties during the formation of silicon melt and silicon carbide, as follows:

[0145] Assume the volume fraction of consumed carbon is V C is y, the porosity of the porous body is ε, and the initial porosity is ε 0 , let V SiC / V C =m, then V SiC =my;

[0146] V SiC -V C =my-y=ε 0 -ε

[0147] y(m-1)=ε 0 -ε

[0148]

[0149] The volume fraction ratio of each phase is:

[0150]

[0151] The density, effective thermal conductivity and molar specific heat capacity of the liquid and solid phases that vary with temperature and porosity can be obtained as follows:

[0152]

[0153] ρ l (T) = 3210 - 0.4 × T

[0154]

[0155] (λ l ) eff =λ Si ·ε

[0156]

[0157]

[0158] Among them, ρ s is the density function of the solid phase (kg / m 3 ), ρ lis the density function of the liquid phase (kg / m 3 );(λ s ) eff is the effective thermal conductivity equation of the solid phase (W / (cm·K)), (λ l ) eff is the effective thermal conductivity equation of the liquid phase (W / (cm·K)); C p,s is the specific heat capacity function of the solid phase (J / (kg·K)), C p,l is the specific heat capacity function of the liquid phase (J / (kg·K)).

[0159] For example, the effective saturation S e , specific water content C w , Storage coefficient S p The pressure dependence of is given by the Van Genuchten relationship as follows:

[0160]

[0161]

[0162] S p =θ f χ f +(1-θ f ) s

[0163] where α, n and η are the Van Genuchten parameters (dimensionless) for molten silicon infiltration, θ s and θ r are the saturated and residual liquid volume fractions (dimensionless), θ f is the volume fraction of silicon melt (dimensionless), χ f and χ s are the compressibility of the infiltrated melt and the porous body (Pa -1 ).

[0164] In one possible implementation, the step of simulating the reactive melt infiltration process to be simulated by COMSOL Multiphysics according to the numerical model and the interpolation function includes:

[0165] Obtaining initial conditions and boundary conditions of the reactive melt infiltration process to be simulated;

[0166] and determining the constraint conditions of the numerical model according to the initial conditions and the boundary conditions;

[0167] According to the numerical model, the constraints of the numerical model and the interpolation function, the reactive melt infiltration process to be simulated is simulated by COMSOL Multiphysics.

[0168] Exemplarily, a simulation method for a reactive melt infiltration process includes: S1: obtaining real porous body structure information; S2: obtaining basic data; S3: establishing a numerical model; and S4: COMSOL simulation.

[0169] Embodiment 1:

[0170] The simulation of the reactive melt infiltration process includes:

[0171] Scenario description: The flow characteristics of the reaction melt in the porous structure from a mesoscopic perspective are simulated. The process considers the influence of the change of the pore structure on the flow field, the inertial effect of the continuous medium flow, the viscosity effect of the flow in the porous medium, the diffusion, the concentrated material transfer, the thermal radiation, the thermal convection and other effects. The geometric model is established based on the real porous structure. The research area is a three-dimensional rectangular block of 350×350×350μm, the initial ambient temperature is 1783K, the initial permeability is 2.04e-12m2, and the inlet pressure is 1000Pa.

[0172] Parameter and boundary condition settings:

[0173] The initial conditions and boundary conditions set in the case simulation are as follows: Figure 3 shown.

[0174] In the physical field, add the "Brinkman equation", "Concentrated species transport in porous media" and "Heat transfer in porous media" interfaces to simulate the transport behavior of the reaction melt in the porous structure. Import the pore interpolation function into COMSOL Multiphysics to obtain the functional relationship of porosity:

[0175]

[0176] The system coordinates, fluid properties, porous matrix properties, mass source, reaction source and other parameter conditions are set step by step. The specific values ​​and calculation formulas are shown in Table 1.

[0177] Table 1 Parameter property setting table

[0178]

[0179]

[0180] Consider the gravity effect in the flow field simulation, add the domain condition "gravity" and set the condition to the specified elevation H. The formula is expressed as Add domain conditions "inlet" and "outlet", select pressure as the boundary condition in the flow field and set it to p 0, check the "Suppress backflow" checkbox, select the "normal flow" as the flow direction, and consider the mass transfer in the reverse reaction process. Add a mass source to the flow field. The formula is Q m =R×M SiC ;

[0181] In the "Concentrated Species Transport in Porous Media" field, select Fick's law as the diffusion model, select silicon melt as the mass constraint, and assume that the porous carbon content is sufficient. Set two dependent variables, namely the mass fraction of silicon melt and silicon carbide. Select the velocity field transmitted by the "Brinkman equation" in the fluid properties, and select the Millington Quiek model to determine the effective diffusion coefficient. The formula expression is: The porosity of the porous matrix adopts the porosity function consistent with the flow field. The initial value sets the mass fraction of SiC to 1, and adds the flow conditions "inlet" and "outlet" and the domain condition reaction source. The formula expression is R = k f A v c;

[0182] In the "Porous Media Heat Transfer" field, the porous media type adopts the local thermal equilibrium model, the velocity field adopts the velocity field transmitted by the "Brinkman equation", and the density, effective thermal conductivity and constant pressure heat capacity of the defined liquid and solid phases are added. The formula expression is:

[0183]

[0184] ρ l (T) = 3210 - 0.4 × T

[0185]

[0186] (λ l ) eff =λ Si ·ε

[0187]

[0188]

[0189] Results and analysis: By observing the pore structure distribution characteristics in the Brinkman flow field distribution and comparing the cross-section of the real porous body scanned by CT, it can be found that the imported pore structure information is completely coupled with the flow field distribution, and the finer the grid division, the higher the coupling accuracy. At the same time, it is found that the areas with higher flow velocity are basically located in the areas with better connectivity, and the maximum flow velocity can reach 2.0×10 -3 m / s, while the velocity in the center of the porous body is relatively low, basically distributed in the range of 1.4×10 -3m / s. The melt transport simulation reaction melt infiltrates into the porous body, and there is a chemical reaction on the contact surface. The product will gradually deposit in the porous body, causing the volume fraction of the melt entering the porous body to gradually decrease. Based on the Brinkman equation, the heat transfer of porous media and the concentrated material transfer of porous media are coupled to analyze the volume fraction of the melt infiltrating into different pore structures at different times. The cloud diagram of the melt volume distribution under the slices at 0s and 10s respectively shows that: at the beginning, the volume fraction of the melt in the pore structure does not reach 1, indicating that in the real porous structure, the melt will not completely fill all the pore structures. At the same time, the melt will react when it enters and deposit on the wall of the porous body, resulting in less and less pore space, thereby reducing the volume fraction of the melt entering. According to the change in the volume fraction of the melt, it can be judged that there is a suffocation effect in the reaction infiltration process, and the initial pore structure characteristics will not be changed during the entire melt transport process.

[0190] In one possible implementation, the unsaturated flow characteristics of the reaction melt in the porous structure are simulated from a macroscopic perspective, and the effects of convection, advection, diffusion, and material transfer are considered in the process. The research area is a rectangular area of ​​12.6×46 mm, the initial ambient temperature is 1783K, and the density of the porous carbon preform is 1.48×10 3 kg / m 3 , the intrinsic permeability is 2.29×10 -14 m 2 At the same time, the temperature monitoring points were selected for calculation with a distribution distance of 3 mm (TC1), 5 mm (TC2), 8 mm (TC3) and 11 mm (TC4) at the bottom of the preform.

[0191] Parameter and boundary condition settings:

[0192] The initial conditions and boundary conditions set in the case simulation are as follows: Figure 4 shown.

[0193] In the physical field settings, the "Richard Equation" interface is added to simulate the unsaturated flow behavior of the reaction melt in the porous structure. The established flow field simulation control equation is modified to the default equation in a weak form, that is, the saturated flow field simulation control equation:

[0194]

[0195] The system coordinates, fluid properties, porous matrix properties, mass source, reaction source and other parameter conditions are set step by step. The specific values ​​and calculation formulas are shown in Table 1. The water storage model selects linear water storage, adds the domain condition "initial value", and sets the initial value of the pressure head in the simulation area to p0; adds flow conditions, selects the y=0mm boundary as the inlet, the y=46mm boundary as the outlet, and selects the remaining boundaries as the default no flow condition. The formula is expressed as -n·ρu=0, and the effective saturation S e , specific water content C w , Storage coefficient S p The pressure dependence of is given by the Van Genuchten relationship.

[0196] In the "Concentrated Species Transport in Porous Media" field, select Fick's Law as the diffusion model, select silicon melt as the mass constraint, and assume that the porous carbon content is sufficient. Set two dependent variables, namely the mass fraction of silicon melt and silicon carbide. Select the velocity field transmitted by the "Richard equation" in the fluid properties, and select the Millington Quiek model to determine the effective diffusion coefficient. The formula expression is:

[0197]

[0198] The porosity of the porous matrix properties adopts the porosity function consistent with the flow field. The initial value sets the mass fraction of sic to 1, and adds the flow conditions "inlet" and "outlet" and the domain condition reaction source. The formula expression is:

[0199] R = k f A v c;

[0200] In the "Porous Media Heat Transfer" field, the porous media type adopts the local thermal equilibrium model, the velocity field adopts the velocity field transmitted by the "Richard equation", and the density, effective thermal conductivity and constant pressure heat capacity of the defined liquid and solid phases are added.

[0201] Results and analysis:

[0202] The comparison between the experimental monitoring temperature and the model predicted temperature shows that the model predicted value matches the thermocouple test result well overall. In the initial stage of infiltration (0-7s), the reaction temperature rise is obvious, and the temperature rise begins to weaken in the later stage of the reaction. This is because a large amount of melt infiltrates into the porous body in the initial stage, and a violent reaction occurs instantly, causing the temperature to rise. As the reaction proceeds, the ceramic phase generated is continuously filled in the pores, resulting in a continuous decrease in the channels available for melt infiltration in the preform. Therefore, the volume fraction of the melt entering the porous body gradually decreases, and the reaction temperature rise slows down. The overall trend is that the temperature rise amplitude is obvious in the early stage of infiltration and the temperature rise amplitude is small in the later stage. In addition, the calculated values ​​of monitoring points TC1 and TC2 have a large error with the experimental value. This is mainly because the formation of the ceramic matrix in the early stage of the reaction is dominated by the dissolution precipitation mechanism, while the chemical reaction and mass transfer equations in the model mainly consider the diffusion effect, resulting in a large error. The later stage of the infiltration reaction is mainly affected by the diffusion reaction. Therefore, the model calculated values ​​of monitoring points TC3 and TC4 are basically consistent with the experimental values. The calculated peak temperature errors at the four positions are less than 3%. This result shows that the multi-physics field model constructed for the reactive infiltration process can reliably predict the mass transfer reaction process of the high-temperature melt in the porous preform.

[0203] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0204] In the embodiments provided in the present application, it should be understood that the disclosed devices / network equipment and methods can be implemented in other ways. For example, the device / network equipment embodiments described above are merely schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0205] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0206] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for simulating a reactive melt infiltration process, characterized in that: include: Determine an interpolation function for characterizing the real-time porosity of the target porous preform through grayscale information of the target porous preform; Obtaining basic parameters of the reactive melt infiltration process to be simulated, and establishing a control equation group according to the basic parameters and the interpolation function to obtain a numerical model; According to the numerical model and the interpolation function, the reactive melt infiltration process to be simulated is simulated by COMSOL Multiphysics.

2. The method for simulating a reactive melt infiltration process according to claim 1, characterized in that: The step of determining an interpolation function for characterizing the porosity of the target porous preform according to the grayscale information of the target porous preform comprises: Acquire a CT scan image of the target porous preform, and extract grayscale information of the CT scan image through Python; Determine the porosity corresponding to the grayscale information according to a preset rule; The porosity is coupled to the reaction time according to a preset attenuation function to obtain real-time pore data at different times; The real-time pore data at different times are used as interpolation functions at different times.

3. The method for simulating a reactive melt infiltration process according to claim 1, characterized in that: The step of obtaining basic parameters of the reactive melt infiltration process to be simulated, and establishing a control equation group according to the basic parameters and the interpolation function to obtain a numerical model includes: The first control equation of the flow field of the reactive melt infiltration process to be simulated is established by using the Brinkman equation and the Richard equation; Based on Fick's law, the convection-diffusion control equations of reactants and products in the reactive melt infiltration process to be simulated are established; The porous medium concentrated species transport equation is used to characterize the influence of porous structure characteristics on the fluid migration process in the simulated reactive melt infiltration process. The reaction rate control equation is constructed using the derivative of the reaction specific surface area and the saturation; The porous medium heat transfer equation of the reactive melt infiltration process to be simulated, the first control equation, the convection-diffusion control equation, the porous medium concentrated species transport equation and the reaction rate control equation are combined to obtain a numerical model.

4. The method for simulating a reactive melt infiltration process according to claim 1, wherein: The numerical model also includes the basic heat transfer equation: The mathematical expression of the basic heat transfer equation is: Among them C p is the specific heat capacity (J / (kg·K)), λ is the thermal conductivity (W / (cm·K)), Q is the volumetric heat source (W / m 3 ). Q p is the heat source term generated by the pressure change (W / m 3 ), Q vd is the heat source term generated by viscous dissipation (W / m 3 ), Q chem is the heat source term generated by the chemical reaction (W / m 3 ).

5. The method for simulating a reactive melt infiltration process according to claim 1, wherein: The numerical model also includes the thermal radiation equation: The mathematical expression of the heat radiation equation is: Where n·q represents the projection of the heat transfer flux q along the surface normal direction n, and the projection represents the heat flux density (W / m 2 ), τ is the surface emissivity of the target porous preform (dimensionless), ranging from 0 to 1, T amb Indicates the ambient temperature.

6. The method for simulating a reactive melt infiltration process according to claim 1, wherein: The numerical model also includes physical property parameter equations: The mathematical expression of the physical property parameter equation is: Assume the volume fraction of consumed carbon is V C is y, the porosity of the porous body is ε, the initial porosity is ε0, let V SiC / V C =m, then V SiC =my; V SiC -V C =my-y=ε0-ε y(m-1)=ε0-ε The volume fraction ratio of each phase is: The density, effective thermal conductivity and molar specific heat capacity of the liquid and solid phases that vary with temperature and porosity can be obtained as follows: Among them, ρ s is the density function of the solid phase, ρ l is the density function of the liquid phase, (λ s ) eff is the effective thermal conductivity equation of the solid phase, (λ l ) eff is the effective thermal conductivity equation of the liquid phase, C p，s is the specific heat capacity function of the solid phase, C p，l is a function of the specific heat capacity of the liquid phase.

7. The method for simulating a reactive melt infiltration process according to claim 1, characterized in that: The step of simulating the reactive melt infiltration process to be simulated by COMSOL Multiphysics according to the numerical model and the interpolation function comprises: Obtaining initial conditions and boundary conditions of the reactive melt infiltration process to be simulated; and determining the constraint conditions of the numerical model according to the initial conditions and the boundary conditions; According to the numerical model, the constraints of the numerical model and the interpolation function, the reactive melt infiltration process to be simulated is simulated by COMSOL Multiphysics.

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