C / sic nozzle ablation prediction method based on diffusion kinetics and erosion rate function

Abstract

The application provides a C / SiC nozzle ablation prediction method based on diffusion dynamics and scouring rate function, first, a three-dimensional oxidation ablation model of the C / SiC nozzle and a one-dimensional heat transfer equation set are established, and the one-dimensional heat transfer equation set is solved through time steps one by one, so that the ablation performance parameters and the temperature field of each time step are obtained, and the real-time update of the ablation performance parameters and the temperature field is realized; then, the ablation recession of each time step and the change of the surface oxide film are calculated, and the nozzle thickness is updated in real time, so that the nozzle boundary surface is reconstructed. The application analyzes the diffusion process of the oxidizing gas through the oxidation layer to the reaction wall surface by using diffusion dynamics, considers the mass loss and the morphology change of the oxidation layer and the carbon fiber caused by the gas scouring, and reconstructs the ablation morphology of the nozzle surface by updating the grid nodes, so that the ablation morphology evolution process of the C / SiC composite material nozzle can be well reflected, the ablation performance change rule of the nozzle can be accurately predicted, and the ablation prediction accuracy of the C / SiC nozzle is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of thermal protection material performance evaluation, and particularly relates to a C / SiC nozzle ablation prediction method based on diffusion dynamics and scouring rate function. BACKGROUND

[0002] Three-dimensional woven C / SiC composite material becomes a widely used material for C / SiC nozzle due to its excellent mechanical properties and thermal protection ablation resistance, and often needs to withstand high-temperature, high-speed gas flow scouring and ablation, which puts extremely strict requirements on the performance of the nozzle material. Under the ablation scouring environment of high-temperature gas, a dense SiO2 oxide film is formed on the surface of C / SiC, which hinders the diffusion of oxygen to the reaction wall, thereby delaying the ablation of the nozzle. However, under the action of high-speed gas flow, the ablation surface of C / SiC composite material shows obvious mechanical spalling behavior, and the spalling products are splashed outward under the action of gas flow. The spalling behavior of the material may present two forms of block spalling and fiber spalling. In addition, under the action of high-temperature high-speed gas flow, the distribution of the molten oxide layer will be affected, thereby further affecting the thermal chemical reaction on the surface of the material. This process is closely related to the viscosity of the molten material on the coating, substrate and fiber. Therefore, for the C / SiC composite material nozzle, the oxide film layer makes the nozzle have excellent ablation resistance, but the generation and dissipation mechanism of the oxide layer under the scouring and ablation of high-speed gas flow is difficult to quantitatively analyze, which greatly increases the difficulty of ablation performance analysis and morphology prediction of the nozzle.

[0003] The existing research usually ignores the influence of the generation and ablation influence mechanism of the molten oxide layer and the influence of carbon fiber spalling on oxidation ablation under the scouring and ablation of high-speed gas flow. In the calculation of the oxidation ablation of C / SiC composite material, there is a lack of quantitative analysis of the oxide layer generated by the activity oxidation of SiC and oxygen and separated from the material surface under the impact of high-speed gas flow. However, under the working environment of low temperature and high pressure of the nozzle, a large amount of oxide film is generated and covers the surface of the nozzle. Under the scouring and ablation of high-speed gas flow, the transient influence of the oxide film on the oxidation ablation rate of the nozzle cannot be ignored. If the influence of the oxide film on the ablation is ignored, it will be found that the chemical reaction rate of the material surface quickly reaches equilibrium, and the ablation recession amount will be much larger than the actual one, and thus the prediction accuracy of the ablation shape cannot be met.

[0004] In summary, the existing C / SiC composite material oxidation ablation model cannot accurately analyze the ablation scouring performance of C / SiC nozzle in the high-temperature high-speed gas flow environment, and cannot consider the mass loss caused by the combined action of oxide layer erosion and carbon fiber spalling, so as to accurately predict the ablation shape change of the nozzle. SUMMARY

[0005] To address the limitations of existing C / SiC composite oxidation ablation models in accurately analyzing the ablation and erosion performance of C / SiC nozzles in high-temperature, high-velocity combustion gas environments, and their failure to consider the mass loss caused by the combined effects of oxide layer erosion and carbon fiber ablation, this invention proposes a C / SiC nozzle ablation prediction method based on diffusion kinetics and erosion rate functions. The method includes the following steps:

[0006] Step 1: Establish a three-dimensional oxidation ablation model of the C / SiC nozzle, in which the C / SiC composite material includes a SiC coating and a C / SiC substrate along the thickness direction of the nozzle; take all nodes in the one-dimensional thickness direction of the three-dimensional oxidation ablation model, establish a one-dimensional heat transfer equation set, and solve the one-dimensional heat transfer equation set step by step to obtain the ablation performance parameters and temperature field at each time step, so as to realize the real-time update of the ablation performance parameters and temperature field.

[0007] Among them, the established one-dimensional heat transfer equations are:

[0008] [ 1 + 2 a SiC − 2 a SiC − a SiC 1 + 2 a SiC − a SiC ⋯ ⋯ ⋯ − a 1 + 2 a − a ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ − a C / SiC 1 + 2 a C / SiC − a C / SiC − 2 a C / SiC 1 + 2 a C / SiC ] [ T 1 n T 2 n ⋮ T j n ⋮ ⋮ T 2 N n T 2 N +1 n ] = [ T 1 n − 1 + a SiC 2 Delta x k SiC q n n − 1 T 2 n − 1 ⋮ T j n − 1 ⋮ ⋮ T 2 N n -1 T 2 N +1 n -1 ]

[0009] in This is an intermediate variable for the coating, and its value is... , As an intermediate variable for the substrate, its value is... , As the intermediate variable at the boundary point, take or ; The results of the calculations at the nth time step are respectively: Temperature of each node The results obtained from the (n-1)th time step are respectively Temperature of each node; The thermal conductivity of the SiC coating and the thermal conductivity of the C / SiC substrate are listed in order. The density of the SiC coating and the density of the C / SiC substrate are listed in order. The specific heat of the SiC coating and the specific heat of the C / SiC substrate are listed in order. For time step, The thickness corresponding to a single node; For the net heat flow entering the material at time step n-1, according to the surface energy equation:

[0010]

[0011] The calculation yielded, where For pneumatic heating heat flow, This is the wall enthalpy. To restore enthalpy, The surface emissivity, Stefan-Boltzmann constant, wall temperature, SiC coating mass change rate, carbon fiber mass change rate and SiO2 oxidation film mass change rate in the n-1th time step, respectively, SiC coating oxidation reaction heat, carbon fiber oxidation reaction heat and SiO2 oxidation film melting heat, respectively, convection heat transfer coefficient, ambient temperature; wherein in the n-1th time step, the SiC coating mass change rate , the carbon fiber mass change rate and the SiO2 oxidation film mass change rate are obtained by the following formula:

[0012]

[0013]

[0014]

[0015] wherein mass loss amount of the C / SiC composite material, mass loss amount of the carbon fiber, SiO2 oxidation film mass generated by the reaction of the SiC coating and oxygen and SiO2 oxidation film mass generated by the reaction of the SiC coating and water vapor in the n-1th time step, respectively; carbon fiber single filament density, carbon fiber mechanical denudation rate in the n-1th time step, mechanical scouring denudation rate of the SiO2 oxidation film in the n-1th time step, SiO2 oxidation film density;

[0016] Step 2: using the real-time updated ablation performance parameters and temperature field, calculating the ablation recession amount and the change of the surface oxidation film of each time step, and then real-time updating the nozzle thickness, so as to reconstruct the nozzle boundary surface.

[0017] Further, the mass loss amount of the C / SiC composite material in the n-1th time step According to the mass response control equation:

[0018]

[0019] is calculated, wherein SiC coating mass consumed by the reaction of the SiC coating and oxygen and SiC coating mass consumed by the reaction of the SiC coating and water vapor in the n-1th time step, respectively.

[0020] Furthermore, the mass of the SiO2 oxide film formed by the reaction of the SiC coating with oxygen in the (n-1)th time step... According to the formula:

[0021]

[0022] The calculation yielded, where The molar mass of SiO2 For O2 in The diffusion coefficient on the surface of the SiO2 oxide film at temperature. For O2 in Solubility on the surface of SiO2 oxide film at temperature The oxide film thickness at time step n-1; the mass of SiC coating consumed by the reaction of SiC coating with oxygen in time step n-1. for:

[0023]

[0024] in The molar mass of SiC is given.

[0025] Furthermore, the quality of the SiO2 oxide film formed by the reaction of the SiC coating with water vapor in the (n-1)th time step... According to the formula:

[0026]

[0027] The calculation yielded, where For water vapor in The diffusion coefficient on the surface of the SiO2 oxide film at temperature. For water vapor in Solubility of the SiO2 oxide film at the specified temperature; mass of SiC coating consumed by the reaction of the SiC coating with water vapor in the (n-1)th time step. for:

[0028]

[0029] in The molar mass of SiC is given.

[0030] Furthermore, the mass loss of carbon fiber in the (n-1)th time step According to the formula:

[0031]

[0032] The calculation yielded, where The molar mass of carbon fiber This is the rate factor for the oxidation reaction of carbon fiber with oxygen.

[0033] Further, the mechanical erosion rate of carbon fiber in the n-1th time step According to the formula:

[0034]

[0035] The calculation is as follows, wherein is the volume fraction of fiber phase in C / SiC composite material, is the linear ablation rate of carbon fiber, according to the formula

[0036]

[0037] The calculation is as follows.

[0038] Further, the mechanical erosion rate of SiO2 oxidation film in the n-1th time step According to the formula:

[0039]

[0040] The calculation is as follows, wherein is the bonding strength correlation coefficient of SiO2 oxidation film, is the airflow impact force, is the peeling stress of SiO2 oxidation film, is the linear ablation rate of C / SiC composite material in the n-1th time step.

[0041] Further, the linear ablation rate of C / SiC composite material in the n-1th time step is according to the formula

[0042]

[0043] The calculation is as follows.

[0044] Further, in step 2, in the n-1th time step, according to the formula:

[0045]

[0046] The nozzle thickness corresponding to the n th time step is calculated , wherein is the nozzle thickness corresponding to the n-1th time step, which is obtained by subtracting the ablation retreat amount corresponding to the n-1th time step from the nozzle thickness corresponding to the n-1th time step , and considering the oxidation reaction growth amount and the airflow erosion reduction amount , the nozzle thickness corresponding to the n th time step is obtained; the nozzle thickness corresponding to the n th time step Divide by the thickness corresponding to the set single node , obtain the node quantity corresponding to the nth time step, and reconstruct the nozzle boundary surface according to the node quantity corresponding to the nth time step, so that the ablation prediction of the nozzle is realized.

[0047] Beneficial effects:

[0048] The present application provides a C / SiC nozzle ablation prediction method based on diffusion dynamics and scouring rate function, which analyzes the diffusion process of oxidizing gas from the gas boundary layer to the reaction wall through the oxidation layer by diffusion dynamics, quantitatively analyzes the mass loss and morphology change of the oxidation layer and carbon fiber caused by gas scouring and erosion, and reconstructs the ablation morphology of the nozzle surface by updating the grid nodes. The ablation morphology evolution process of the C / SiC composite material nozzle can be well reflected, the ablation performance change rule of the nozzle can be accurately predicted, the ablation prediction accuracy of the C / SiC nozzle is improved, and a theoretical basis is laid for accurate prediction of the ablation performance of the C / SiC composite material nozzle.

[0049] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following description, or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0050] The above and / or additional aspects and advantages of the present application will become apparent and be readily understood from the description of the embodiments, given below, and the accompanying drawings, in which:

[0051] Figure 1 Comparison results of calculated values and ground thermal test values of the C / SiC composite material nozzle throat ablation inner profile. DETAILED DESCRIPTION

[0052] The embodiments of the present application are described in detail below, which are exemplary and intended to explain the present application, and cannot be understood as a limitation of the present application.

[0053] The present embodiment takes a three-dimensional braided C / SiC composite material with a SiC coating as a nozzle of an application material as a research object, and performs nozzle ablation prediction by constructing an oxidation ablation model of the C / SiC nozzle and combining diffusion dynamics and scouring rate function. Specifically, the following steps are included:

[0054] Step 1: establish a three-dimensional oxidation ablation model of the C / SiC nozzle, wherein the C / SiC composite material includes a SiC coating and a C / SiC substrate along the thickness direction of the nozzle; all nodes in the one-dimensional thickness direction of the three-dimensional oxidation ablation model are taken to establish a one-dimensional heat transfer equation group:

[0055] [ 1 + 2 a SiC − 2 a SiC − a SiC 1 + 2 a SiC − a SiC ⋯ ⋯ ⋯ − a 1 + 2 a − a ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ − a C / SiC 1 + 2 a C / SiC − a C / SiC − 2 a C / SiC 1 + 2 a C / SiC ] [ T 1 n T 2 n ⋮ T j n ⋮ ⋮ T 2 N n T 2 N +1 n ] = [ T 1 n − 1 + a SiC 2 Delta x k SiC q n n − 1 T 2 n − 1 ⋮ T j n − 1 ⋮ ⋮ T 2 N n -1 T 2 N +1 n -1 ]

[0056] wherein is an intermediate variable of the coating, and has a value of , is an intermediate variable of the substrate, and has a value of , is an intermediate variable of the interface, and has a value of or ; are, in sequence, the temperature of the nth node calculated in the nth time step, respectively, are, in sequence, the temperature of the nth node calculated in the nth time step, respectively; are, in sequence, the temperature of the nth node calculated in the nth time step, respectively; are, in sequence, the thermal conductivity of the SiC coating and the thermal conductivity of the C / SiC substrate, are, in sequence, the density of the SiC coating and the density of the C / SiC substrate, are, in sequence, the specific heat of the SiC coating and the specific heat of the C / SiC substrate; is a time step, and in this embodiment, 0.01s, is the thickness corresponding to a single node, and in this embodiment, 0.02mm; is the net heat flow entering the material interior in the nth time step, and is calculated according to the surface energy equation:

[0057]

[0058] , wherein is the aerodynamic heating heat flow, is the wall enthalpy, is the recovery enthalpy, is the surface radiation coefficient, is the Stefan-Boltzmann constant, is the wall temperature, are, in sequence, the mass change rate of the SiC coating, the mass change rate of the carbon fiber, and the mass change rate of the SiO2 oxidation film in the nth time step, are, in sequence, the oxidation reaction heat of the SiC coating, the oxidation reaction heat of the carbon fiber, and the melting heat of the SiO2 oxidation film, is the convective heat transfer coefficient, is the environmental temperature.

[0059] In this embodiment, the physical parameters and environmental parameters of the C / SiC composite material set for model simulation calculation are shown in the following table:

[0060] Table 1: Physical parameters and environmental parameters of C / SiC composite material

[0061]

[0062] and the mass change rate of the SiC in the nth time step​ carbon fiber mass change rate and the rate of change in the quality of SiO2 oxide film It is obtained through the following formula:

[0063]

[0064]

[0065]

[0066] in The values ​​are, in order, the mass loss of the C / SiC composite material, the mass loss of the carbon fiber, the mass of the SiO2 oxide film generated by the reaction of the SiC coating with oxygen, and the mass of the SiO2 oxide film generated by the reaction of the SiC coating with water vapor in the (n-1)th time step. This refers to the density of a single carbon fiber filament. The mechanical erosion rate of the carbon fiber in the (n-1)th time step. Let n be the mechanical erosion rate of the SiO2 oxide film in the (n-1)th time step. The density of the SiO2 oxide film is 2.2 g / cm³. 3 .

[0067] Mass loss of C / SiC composite material in the (n-1)th time step According to the quality response control equation:

[0068]

[0069] The calculation yielded, where The values ​​represent the mass of SiC coating consumed by the reaction of SiC coating with oxygen and the mass of SiC coating consumed by the reaction of SiC coating with water vapor in the (n-1)th time step, respectively.

[0070] Specifically, the mass of the SiO2 oxide film formed by the reaction of the SiC coating with oxygen in the (n-1)th time step According to the formula:

[0071]

[0072] The calculation yielded, where The molar mass of SiO2 is 60 g / mol. For O2 in The diffusion coefficient on the surface of the SiO2 oxide film at the specified temperature is calculated using the following formula: , It is the gas constant; For O2 in Solubility on the surface of SiO2 oxide film at temperature is the oxide film thickness at the n-1th time step; according to the chemical reaction formula, 1 mol of SiO2 is generated for every 1 mol of SiC consumed, so the mass of the SiC coating consumed by the reaction of the SiC coating with oxygen in the n-1th time step is:

[0073]

[0074] wherein is the molar mass of SiC.

[0075] The reaction of water vapor and the SiC coating is similar to the reaction of oxygen and the SiC coating, and accordingly, the mass of the SiO2 oxide film generated by the reaction of the SiC coating with water vapor in the n-1th time step According to the formula:

[0076]

[0077] is calculated, wherein is the diffusion coefficient of water vapor on the surface of the SiO2 oxide film at temperature, and the calculation formula is , is the gas constant; is the solubility of water vapor on the surface of the SiO2 oxide film at temperature; the mass of the SiC coating consumed by the reaction of the SiC coating with water vapor in the n-1th time step is:

[0078]

[0079] and the mass loss of the carbon fiber in the n-1th time step According to the formula:

[0080]

[0081] is calculated, wherein is the molar mass of the carbon fiber, which is 12 g / mol; is the reaction rate factor of the oxidation reaction of the carbon fiber and oxygen, which can be expressed in the Arrhenius form:

[0082]

[0083] wherein is the carbon-oxygen reaction rate constant, is the reaction activation energy, which is obtained by experiment according to the working environment of the nozzle in the embodiment, is the gas constant.

[0084] The mechanical denudation rate of the carbon fiber in the n-1th time step According to the formula:

[0085]

[0086] The calculation yielded, where The value represents the volume fraction of the fiber phase in the C / SiC composite material; in this embodiment, it is taken as 0.69. The ablation rate of a carbon fiber monofilament is given by the formula.

[0087]

[0088] Calculated.

[0089] The mechanical erosion rate of the SiO2 oxide film in the (n-1)th time step According to the formula:

[0090]

[0091] The calculation yielded, where The correlation coefficient for the adhesion strength of the SiO2 oxide film is 0.88 in this embodiment; The airflow impact force is taken as 1.2 MPa in this embodiment; The stress at which the SiO2 oxide film peels off is taken as 0.8 MPa in this embodiment. The linear ablation rate of the C / SiC composite material in the (n-1)th time step is given by the formula...

[0092]

[0093] Calculated.

[0094] By solving the one-dimensional heat transfer equations step by step, the ablation performance parameters and temperature field at each time step are obtained, enabling real-time updates of the ablation performance parameters and temperature field.

[0095] Step 2: Reconstruct the nozzle boundary surface using real-time updated ablation performance parameters and temperature field. Specifically, at time step n-1, according to the formula:

[0096]

[0097] The nozzle thickness at the nth time step was calculated. ,in The nozzle thickness corresponding to the (n-1)th time step, passing through the nozzle thickness corresponding to the (n-1)th time step. Subtract the ablation retreat amount corresponding to the (n-1)th time step And consider changes in the surface oxide film, including the amount of oxidation reaction growth. and airflow erosion reduction , to obtain the thickness of the nozzle corresponding to the nth time step ; using the thickness of the nozzle corresponding to the nth time step divided by the thickness corresponding to a single node set , to obtain the number of nodes corresponding to the nth time step, and the nozzle boundary surface is reconstructed according to the number of nodes corresponding to the nth time step, so as to realize the ablation prediction of the nozzle.

[0098] Through the above process, the ablation prediction of the nozzle using three-dimensional woven C / SiC composite material with SiC coating as the application material is realized. In this embodiment, based on the established C / SiC composite material nozzle ablation erosion model considering the gas erosion effect, the model is embedded into the solver through the user-defined function (UDF) for coupling calculation, and the ablation surface change rule over time is obtained. In order to analyze the ablation in the nozzle, 10 typical positions are selected near the throat in this example. The ground thermal test value of the nozzle thickness at the 10 positions is obtained through the CT scanning result. The nozzle thickness calculation value at the 10 positions is obtained by using the coupling calculation program in this project, and the nozzle surface ablation amount is taken as the ablation shape prediction parameter, Figure 1 The comparison results of the C / SiC composite material nozzle throat ablation inner surface calculation value and the test value at t=2s are shown in the table, and the results show that the calculation results of this embodiment are in good agreement with the test results.

[0099] Next, we give the theoretical analysis process of the above-mentioned method of this embodiment, which demonstrates the rationality of the present application from the theoretical point of view.

[0100] The present application constructs an oxidation ablation model of C / SiC nozzle based on diffusion dynamics; whether the aerodynamic shear force is greater than the shear modulus of SiO2 oxide film is taken as the criterion to judge whether the SiO2 oxide film is ablated; whether the aerodynamic shear force is greater than the shear modulus of carbon fiber is taken as the criterion to judge whether the carbon fiber is mechanically ablated; based on the finite difference method, the heat conduction equation is solved, the oxidation ablation, mechanical erosion and heat conduction are coupled and solved, and the characteristic parameters of each grid node are obtained; the nozzle boundary surface is reconstructed according to the number of grid nodes, and the ablation performance parameters and ablation morphology of C / SiC nozzle are obtained. The present application considers the multi-scale coupling effect of oxidation ablation and gas erosion, realizes the high-temperature ablation performance and morphology prediction of C / SiC nozzle.

[0101] (1) Based on diffusion dynamics, the solubility of oxidizing gas in SiO2 oxide film is obtained:

[0102] SiC coating will be rapidly oxidized in high temperature and high speed gas flow environment and form a dense oxide film on the surface, hinder the further oxidation of the coating, and then the oxidizing gas needs to go through many processes to reach the surface of the coating to continue to oxidize the SiC coating. O2, water vapor is first dissolved on the surface of SiO2 oxide film, and the dissolution process follows Henry's law:

[0103]

[0104] In the formula, is the solubility of O2 or water vapor on the surface of SiO2 oxide film, and the subscript represents O2 or water vapor; is the gas wall pressure of O2 or water vapor, is the Henry constant, which is affected by temperature, and the specific value needs to be determined by experiment, so the solubility of O2 or water vapor on the surface of SiO2 oxide film is also a function of surface temperature.

[0105] (2) Obtain the ablation performance parameters of the nozzle:

[0106] After O2 or water vapor is dissolved in SiO2 oxide film, it diffuses to the reaction wall through SiO2 oxide film, and the diffusion process can be represented by Fick's diffusion law:

[0107]

[0108] In the formula, is the diffusion coefficient, which is also a function of temperature; is the thickness of SiO2 oxide film.

[0109] According to the reaction formula of oxygen and SiC and Fick's law, we have:

[0110]

[0111] Substituting the initial conditions and integrating, the mass of SiO2 generated by the reaction of the material with oxygen can be obtained:

[0112]

[0113] In the formula, is the current oxide film thickness, is the time step, is the amount of increase in SiO2 oxide film thickness caused by oxygen in the time length, is the molar mass of SiO2, , are the diffusion coefficient and solubility of oxygen in SiO2 oxide film, respectively, is the density of SiO2 oxide film, is the in The quality of SiO2 oxidation film generated by the reaction between SiC coating and oxygen in time t; since the newly generated SiO2 in the ablation process will increase the thickness of the oxidation film, therefore cannot be too long, so in the examples 0.01 s is taken.

[0114] According to the chemical reaction formula, 1 mol of SiO2 is generated for every 1 mol of SiC consumed. Therefore, in time t, the mass loss of SiC coating per unit area caused by oxidation ablation is:

[0115]

[0116] In the formula, is In time t, the mass of SiC coating consumed by the reaction with oxygen, is the molar mass of SiC.

[0117] The reaction between water vapor and SiC coating is similar to the oxidation reaction between oxygen and SiC coating. By analogy with the derivation process described above, the mass changes of SiO2 and SiC caused by the SiC-H2O thermochemical reaction are:

[0118]

[0119]

[0120] In the formula, subscript H2O represents parameters related to water vapor, and the physical meaning is consistent with the parameters of oxygen described above.

[0121] The carbon fiber and oxygen undergo an oxidation reaction to generate CO, and the reaction rate factor can be expressed in the Arrhenius form:

[0122]

[0123] In the formula, is the carbon-oxygen reaction rate constant (m / s), is the reaction activation energy (J / mol), is the gas constant (J / (mol·K)), is the wall temperature (K), then The mass loss of carbon fiber per unit area in time t is:

[0124]

[0125] In the formula, is the molar mass of carbon fiber.

[0126] The mass change of C / SiC composites in the process of high-temperature and high-speed gas flow ablation and erosion is composed of three parts, i.e., the mass change of SiC coating , , the mass change of SiO2 oxidation film , and the mass change of carbon fiber . Therefore, the mass response control equation of three-dimensional braided C / SiC composites in the process of oxidation ablation is:

[0127]

[0128] In the equation, is the mass loss of three-dimensional braided C / SiC composites in the process of oxidation ablation .

[0129] Finally, the linear ablation rate of C / SiC composites , the linear ablation rate of carbon fiber is:

[0130]

[0131]

[0132] (3) According to the ablation criterion, it is judged whether the SiO2 oxidation film and the carbon fiber are mechanically ablated or not; the mass loss caused by ablation is obtained based on the erosion rate function;

[0133] The spalling stress of SiO2 oxidation film is taken as the failure criterion, i.e., when the gas flow impact force is greater than the spalling stress of the SiO2 oxidation film on the surface of C / SiC composites, the material is ablated. The strength of the oxidation film degrades with temperature and heating time during the ablation process, and is related to the oxidation ablation degree of the material, the shape of the pore structure, thermal deformation, thermal stress and other factors. Based on the thermochemical ablation rate, the gas flow pressure distribution and the characteristics of the material itself, the mechanical erosion ablation rate of C / SiC composites can be expressed as:

[0134]

[0135] In the equation, is the mechanical erosion ablation rate, is the correlation coefficient of the bonding strength of the SiO2 oxidation film, is the gas flow impact force, is the spalling stress of the SiO2 oxidation film.

[0136] The carbon fiber is broken under the shear of the gas flow, thereby causing the ablation of the carbon fiber. The relationship between the mechanical ablation rate of the carbon fiber and the ablation mass flow rate and the volume fraction of the fiber phase is:

[0137]

[0138] wherein, is the linear ablation rate of the carbon fiber monofilament along the axial direction of the carbon fiber monofilament, is the mechanical denudation rate of the carbon fiber, is the density of the carbon fiber monofilament.

[0139] The mechanical denudation rate of the carbon fiber can be expressed as:

[0140]

[0141] (4) Based on the finite difference method, the heat conduction control differential equation set is discretized into a difference equation set and solved;

[0142] The energy of the material ablation surface is composed of the energy entering the control body and the energy leaving the control body, the energy entering the surface includes the aerodynamic heating heat flow , the combustion reaction heat release of the carbon fiber , the oxidation reaction heat release of the SiC coating , the energy leaving the surface includes the radiation heat flow of the material to the outside world , the convective heat transfer , the melting endothermic of the SiO2 oxidation film , and the net heat flow into the material interior .

[0143] The mass change rate of the SiC , the mass change rate of the carbon fiber , and the mass change rate of the SiO2 oxidation film are obtained by the following formula:

[0144]

[0145]

[0146]

[0147] Accordingly, the material surface energy equation can be established:

[0148]

[0149] wherein, is the wall enthalpy, is the recovery enthalpy, is the surface radiation coefficient, is the Stefan-Boltzmann constant, is the wall temperature, is the oxidation reaction heat of the SiC coating, the oxidation reaction heat of the carbon fiber, and the melting heat of the SiO2 oxidation film, respectively, The heat transfer coefficient of convection, The ambient temperature.

[0150] The heat transfer control equation is discretely processed by using finite difference method, all nodes in one-dimensional thickness direction of the nozzle are divided into grids, and the node j is set as the C / SiC composite coating / substrate junction point, i.e. the intermediate variable before the node The coating heat transfer performance parameter is calculated, and the value is The heat transfer performance parameter of the substrate is calculated The heat transfer performance parameter of the substrate is calculated For the node j, the intermediate variable is taken as or . ρ, C, k respectively represent the material density, specific heat, thermal conductivity, and the subscripts SiC, C / SiC respectively represent the SiC coating, C / SiC substrate related physical parameters. The one-dimensional heat transfer equation group is obtained by sorting:

[0151] [ 1 + 2 a SiC − 2 a SiC − a SiC 1 + 2 a SiC − a SiC ⋯ ⋯ ⋯ − a 1 + 2 a − a ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ − a C / SiC 1 + 2 a C / SiC − a C / SiC − 2 a C / SiC 1 + 2 a C / SiC ] [ T 1 n T 2 n ⋮ T j n ⋮ ⋮ T 2 N n T 2 N +1 n ] = [ T 1 n − 1 + a SiC 2 Delta x k SiC q n n − 1 T 2 n − 1 ⋮ T j n − 1 ⋮ ⋮ T 2 N n -1 T 2 N +1 n -1 ]

[0152] The grid temperature is calculated by the heat transfer equation group, and the innermost layer grid node temperature The diffusion coefficient and solubility of O2 and water vapor on the surface of the SiO2 oxidation film are calculated, and the real-time update of the ablation performance parameters and the temperature field is realized. Finally, the nozzle boundary surface is reconstructed by using the real-time updated ablation performance parameters and the temperature field.

[0153] Although the embodiments of the present application have been shown and described above, it can be understood that the above-mentioned embodiments are exemplary and cannot be understood as limiting the present application, and the ordinary skilled in the art can make changes, modifications, replacements and modifications to the above-mentioned embodiments without departing from the principles and purposes of the present application within the scope of the present application.

Claims

1. A method for C / SiC nozzle ablation prediction based on diffusion kinetics and erosion rate function, characterized in that: Comprise the following steps: Step 1: a three-dimensional oxidation ablation model of C / SiC nozzle is established, wherein the C / SiC composite material comprises a SiC coating and a C / SiC base material along the thickness direction of the nozzle; all nodes in the thickness direction of the three-dimensional oxidation ablation model are taken to establish a one-dimensional heat transfer equation group, and the one-dimensional heat transfer equation group is solved through each time step to obtain the ablation performance parameters and the temperature field of each time step, and the real-time update of the ablation performance parameters and the temperature field is realized; Wherein, the one-dimensional heat transfer equation group established is in This is an intermediate variable for the coating, and its value is... , As an intermediate variable for the substrate, its value is... , As the intermediate variable at the boundary point, take or ; The results of the calculations at the nth time step are respectively: Temperature of each node The results obtained from the (n-1)th time step are respectively Temperature of each node; The thermal conductivity of the SiC coating and the thermal conductivity of the C / SiC substrate are listed in order. The density of the SiC coating and the density of the C / SiC substrate are listed in order. The specific heat of the SiC coating and the specific heat of the C / SiC substrate are listed in order. For time step, The thickness corresponding to a single node; For the net heat flow entering the material at time step n-1, according to the surface energy equation: is calculated, wherein is the aerodynamic heating heat flux, is the wall enthalpy, is the recovery enthalpy, is the surface radiation coefficient, is the Stefan-Boltzmann constant, is the wall temperature, are, in sequence, the SiC coating mass change rate, the carbon fiber mass change rate, and the SiO2 oxidation film mass change rate in the n-1th time step, are, in sequence, the SiC coating oxidation reaction heat, the carbon fiber oxidation reaction heat, and the SiO2 oxidation film melting heat, is the convective heat transfer coefficient, is the ambient temperature; wherein in the n-1th time step, the SiC coating mass change rate , the carbon fiber mass change rate , and the SiO2 oxidation film mass change rate are obtained by the following formula: wherein is the mass loss of the C / SiC composite material, the mass loss of the carbon fiber, the mass of the SiO2 oxidation film generated by the reaction of the SiC coating with oxygen, and the mass of the SiO2 oxidation film generated by the reaction of the SiC coating with water vapor in the n-1th time step, respectively; is the carbon fiber filament density, is the mechanical denudation rate of the carbon fiber in the n-1th time step, is the mechanical scouring denudation rate of the SiO2 oxidation film in the n-1th time step, is the SiO2 oxidation film density; Step 2: using the real-time updated ablation performance parameters and the temperature field, the ablation recession amount and the change of the surface oxide film of each time step are calculated, and then the nozzle thickness is updated in real time, so that the nozzle boundary surface is reconstructed.

2. The C / SiC nozzle ablation prediction method based on diffusion kinetics and erosion rate function of claim 1, wherein: Mass loss of C / SiC composite material in the n-1th time step According to the mass response control equation: The calculation gives The SiC coating mass consumed by the reaction of the SiC coating with oxygen and the SiC coating mass consumed by the reaction of the SiC coating with water vapor in the n-1th time step, in sequence.

3. The C / SiC nozzle ablation prediction method based on diffusion kinetics and erosion rate function of claim 2, wherein: Mass of SiO2oxide film generated by reaction of SiC coating with oxygen in the (n-1)th time step According to the formula: wherein is the molar mass of SiO2, is the molar mass of O2, is the diffusion coefficient of O2in the SiO2oxide film surface at a temperature of is the solubility of O2in the SiO2oxide film surface at a temperature of is the solubility of O2in the SiO2oxide film surface at a temperature of is the oxide film thickness at the n-1th time step; the SiC coating mass consumed by the reaction of the SiC coating with oxygen in the n-1th time step is: wherein is the molar mass of SiC.

4. The method of claim 2, wherein: Mass of SiO2oxide film generated by reaction of SiC coating with water vapor in the (n-1)th time step According to the formula: wherein Dn is the diffusion coefficient of water vapor in Dn is the solubility of water vapor in Dn is the diffusion coefficient of water vapor in Dn is the solubility of water vapor in is: wherein is the molar mass of SiC.

5. The method of claim 2, wherein: mass loss of carbon fibers in the n-1th time step According to the formula: The calculation gives, where is the molar mass of the carbon fiber, is the reaction rate factor for the oxidation reaction of the carbon fiber with oxygen.

6. The method of claim 1, wherein: Mechanical erosion rate of carbon fibers in the n-1th time step According to the formula: The calculation is as follows, wherein is the volume fraction of the fiber phase in the C / SiC composite material, is the linear ablation rate of the carbon fiber monofilament, according to the formula The linear ablation rate of the C / SiC composite material in the nth-1 time step is calculated according to the formula:

7. The method of claim 1, wherein: Mechanical erosion rate of SiO2 oxide film in the n-1th time step According to the formula: wherein is a coefficient related to the adhesive strength of the SiO2 oxide film, is the air flow impact force, is the peeling stress of the SiO2 oxide film, is the linear ablation rate of the C / SiC composite material in the n-1th time step.

8. The method of claim 7, wherein: The linear ablation rate of the C / SiC composite material in the nth-1 time step is calculated according to the formula: In step 2, in the nth-1 time step, according to the formula:

9. The method of claim 1, wherein: ​ The nozzle thickness corresponding to the nth time step is calculated wherein is the nozzle thickness corresponding to the (n-1)th time step, is calculated by subtracting the ablation recession amount corresponding to the (n-1)th time step from the nozzle thickness corresponding to the (n-1)th time step and considering the oxidation reaction growth amount and the gas flow erosion reduction amount , to obtain the nozzle thickness corresponding to the nth time step ; Divide the set thickness of the single node by the thickness of the nozzle corresponding to the nth time step to obtain the number of nodes corresponding to the nth time step , reconstruct the nozzle boundary surface according to the number of nodes corresponding to the nth time step, and realize the ablation prediction of the nozzle.

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