Composite material ablation pyrolysis evaluation method based on lattice Boltzmann method

Abstract

The invention relates to a composite material ablation pyrolysis evaluation method based on a lattice Boltzmann method, belongs to the technical field of solid rocket engines, solves the problem that an ablation pyrolysis mechanism of a composite material in the prior art is difficult to simulate and evaluate, and comprises the following steps: S1, taking a calculation area from a spray pipe and constructing the calculation area into a geometric model; s2, establishing an LBGK model in a D2Q9 form of fluid flow of the gas mixture flowing through the spray pipe; s3, establishing an LBGK model in a D2Q5 form for multi-component mass transportation of the gas mixture flowing through the spray pipe; s4, establishing a D2Q5-form LBGK model of heat transfer of the geometric model; s5, establishing a heterogeneous chemical reaction model of a fluid-solid interface; s6, establishing a pyrolytic reaction model of the resin matrix; s7, establishing an updating model of the carbon fiber solid and the resin matrix; and S8, based on the established model, carrying out transient simulation on the ablation pyrolysis behavior of the composite material of the spray pipe to obtain a simulation result and an evaluation scheme.

Description

Technical Field

[0001] The present invention relates to the technical field of rocket engine thermal protection, and in particular to a composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method. Background Art

[0002] During rocket engine operation, the high-speed gas flow inside the nozzle and the enormous heat generated by the fuel combustion cause the nozzle to experience an extremely high temperature and harsh environment. Therefore, ablation resistance and thermal protection technology have always been important aspects of engine research. Phenolic impregnated carbon fiber composites are often used as engine nozzle materials due to their excellent properties such as high strength, low density, low thermal conductivity, high temperature resistance, and ablation resistance. The resin matrix also undergoes pyrolysis in high-temperature environments. The huge heat absorbed by this reaction and the pyrolysis gases produced have a significant impact on the ablation process of the carbon fiber. Based on the requirements of lightweight aircraft indicators, the evaluation and prediction of the coupling mechanism of the pyrolysis reaction and ablation process of composite materials at high temperatures at the pore scale provides an important reference for nozzle design.

[0003] Traditional methods for studying pyrolysis and ablation processes can be broadly categorized into experimental methods and numerical simulations. Experimental methods typically utilize ground-based tests in wind tunnels and arc jets under specific conditions to obtain experimental data for research. However, due to the highly variable airflow conditions in actual rocket nozzle operation, these ground-based tests do not provide sufficient information, and their contribution to understanding the mechanisms of ablation and pyrolysis is limited. Furthermore, these tests present numerous challenges, such as expensive equipment, complex implementation, and significant material loss. Existing numerical simulations are primarily categorized into macroscale and molecular-scale simulations. Macroscale simulations are primarily performed using commercial software developed using the finite element method or the finite volume method. These simulations fail to couple chemical reactions with flow and heat transfer processes and lack insight into microscopic mechanisms. Molecular-scale simulations are primarily based on molecular dynamics, studying the formation and dissociation of covalent bonds. These simulations require long computational times and ignore the coupling between surface reactions and the external flow environment, significantly deviating from actual conditions. More importantly, most current studies have not considered the impact of pyrolysis reactions on the ablation process. In fact, the heat absorbed by the resin-based pyrolysis reaction and the pyrolysis gases produced will cause significant changes in the flow field, temperature field, and concentration field of the ablation process.

[0004] The Chinese invention patent application, publication number CN112597590A, titled "Volume Ablation Mass Loss of a Resin-Based Heat-Proofing Material," provides a method for determining ablation mass loss through thermochemical ablation engineering simulation. However, this method requires experimental simulation of the heat-proof material being heated in a pneumatic heating environment, which presents problems such as expensive equipment, complex implementation, and significant material loss.

[0005] A Chinese invention patent application, publication number CN106682392A, titled "Rapid Calculation Technology for Ablation Effects of Complex Hypersonic Vehicles," provides a method for calculating ablation models based on carbon-based materials. This method is a molecular-scale simulation approach, but it is computationally intensive and fails to fully consider the coupling relationship between surface reactions and the external flow environment, making it difficult to provide accurate predictions in practical applications.

[0006] The ablation and pyrolysis of composite materials involve the coupled effects of flow, heat transfer, chemical reactions, pyrolysis reactions, and structural evolution, making their mechanisms highly complex and a key and challenging area in rocket engine design. Therefore, there is a need for an improved method for evaluating ablation and pyrolysis behavior that requires minimal computational effort and provides accurate and reliable simulation and prediction results. Summary of the Invention

[0007] In light of these issues, and to address the inability of existing experiments and macroscopic simulations to accurately analyze the coupled processes of composite material ablation and pyrolysis, the present invention provides a composite material ablation and pyrolysis assessment method based on the lattice Boltzmann method. By modeling at the pore scale, this method can simulate and analyze the microscopic mechanisms and coupled relationships of the ablation and pyrolysis processes. This method uses a carbon fiber / phenolic resin composite material to evaluate and analyze the ablation and pyrolysis behavior and microscopic mechanisms of a solid rocket motor nozzle under typical operating conditions at the pore scale.

[0008] The present invention provides a composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method, which is used to evaluate the ablation pyrolysis process of the composite material of the nozzle of a solid rocket motor, comprising the following steps: Step S1: Taking a calculation area from the nozzle and constructing it into a geometric model, and dividing the geometric model into a grid, wherein the grid includes evenly arranged nodes, and determining the boundary conditions of the geometric model, wherein the composite material of the nozzle is a carbon fiber / phenolic resin composite material; Step S2, establishing a D2Q9-type LBGK model of the fluid flow of the gas mixture flowing through the nozzle; Step S3, establishing a D2Q5 LBGK model of multi-component mass transport of the gas mixture flowing through the nozzle, where the multi-components are water vapor, carbon monoxide, and hydrogen in the gas mixture; Step S4, establishing a D2Q5 LBGK model of heat transfer in the geometric model, wherein the heat transfer includes heat transfer between fluids, between fluids and solids, and between solids in the geometric model; Step S5, establishing a heterogeneous chemical reaction model at the fluid-solid interface; Step S6, establishing a pyrolysis reaction model of the resin matrix around the carbon fiber solid; Step S7, establishing an updated model of the carbon fiber solid and the resin matrix according to the volume pixel method; Step S8, based on the established model, inputting boundary conditions, performing transient simulation on the ablation and pyrolysis behavior of the composite material of the nozzle, obtaining simulation results, and obtaining an evaluation plan based on the simulation results; The solid in the geometric model is a carbon fiber solid; the fluid is a gas mixture, including water vapor, and carbon monoxide and hydrogen generated by the chemical reaction of water vapor at the boundary of the carbon fiber solid.

[0009] Optionally, in step S1, the boundary conditions of the geometric model include inlet boundary conditions, which set the temperature, velocity and concentration of water vapor at the inlet; outlet boundary conditions, which adopt fully developed boundary conditions, including the velocity field of the gas mixture at the outlet, the concentration field of the gas mixture and the temperature field of the gas mixture; top and bottom wall boundary conditions of the geometric model, which adopt no-slip boundaries, adiabatic boundaries and zero flux boundaries for the fluid flow, temperature and mass transport of the gas mixture respectively; and fluid-solid interface boundary conditions, which adopt no-slip boundary conditions for the fluid flow of the gas mixture.

[0010] Optionally, step S2 specifically includes the following steps: Step S2.1, obtain the discrete velocity of the particles of the gas mixture in the velocity field:

[0011] in, represents the discrete directions of the particles of the gas mixture and , represents the grid velocity of the divided grid and , is the time step, is the grid spacing; Step S2.2, obtain the macroscopic density of the gas mixture and momentum :

[0012] in, is the gas mixture in discrete directions The density distribution function of Indicates time, represents the spatial position vector, Indicates the velocity of a gas mixture; Step S2.3, establish the gas mixture in discrete directions The equilibrium density distribution function of :

[0013] in, Discrete direction The weight coefficient of is the grid sound velocity of the divided grid and ; Step S2.4, obtain the dynamic viscosity coefficient of the gas mixture:

[0014] in, is the relaxation time of the flow field of the gas mixture; In step S2.5, the resistance of the resin matrix on the carbon fiber solid to the gas mixture is considered, and a source term reflecting the resistance of the resin matrix is ​​constructed:

[0015] Where, Indicates the permeability of the resin matrix; Step S2.6, establish the LBGK model of the fluid flow of the gas mixture flowing through the nozzle in the form of a D2Q9 lattice model: .

[0016] Optionally, step S3 specifically includes the following steps: Step S3.1, obtain the discrete velocity of the particles of the gas mixture in the concentration field:

[0017] in, represents the discrete directions of the particles of the gas mixture and ; Step S3.2, obtain the diffusion rate and component concentration of the gas mixture:

[0018]

[0019] in, The first The concentration of each component, The first The diffusion rate of each component, The first components in discrete directions The concentration distribution function of The first The concentration field relaxation time of each component, Number the components of the gas mixture and ; Step S3.3, construct the gas mixture components in discrete directions The equilibrium concentration distribution function of is:

[0020] in, Discrete direction The weight coefficient of Step S3.4, establish the D2Q5 form LBGK model of multi-component mass transport of gas mixtures: .

[0021] Optionally, step S4 specifically includes the following steps: Step S4.1, obtain the thermal diffusivity of the gas mixture and macroscopic temperature :

[0022]

[0023] in, represents the concentration field relaxation time, In the discrete direction Temperature distribution function of Step S4.2, build the geometric model in discrete directions The equilibrium temperature distribution function Expressed as: ; Step S4.3, obtain the source term of the heat absorbed by the oxidation reaction of the carbon fiber solid at the fluid-solid interface :

[0024] in, represents the concentration of water vapor that reacts with the carbon fiber solid, represents the oxidation reaction rate, represents the enthalpy of the oxidation reaction, represents the specific heat capacity of the gas at normal pressure, represents the inlet water vapor velocity; Step S4.4, obtaining the source term of the heat absorbed by the pyrolysis reaction of the resin matrix area around the carbon fiber solid :

[0025] in, represents the pyrolysis reaction rate of the resin matrix, represents the enthalpy of the pyrolysis reaction of the resin matrix, Indicates the resin matrix at time The density, It represents the specific heat capacity of the resin matrix at normal pressure; Step S4.5, construct the LBGK model of the D2Q5 form of heat transfer of the geometric model: .

[0026] Optionally, step S5 specifically includes the following steps: In step S5.1, the following heterogeneous reaction is assumed to occur on the surface of the carbon fiber solid:

[0027] in, represents a carbon fiber solid, Represents water vapor, represents the gaseous product of the reaction, carbon monoxide, represents the gaseous product of the reaction, hydrogen; Step S5.2, at the node of the fluid-solid interface At , we get the control equation:

[0028] in, is the discrete direction of the particles in the gas mixture =2, No. The concentration distribution function of each component, is the discrete direction of the particles in the gas mixture =4, No. The concentration distribution function of each component, Representation node Place The concentration of each component, Representation node Place The concentration of each component, express Axis direction, node For nodes adjacent fluid nodes; Step S5.3, determine the Concentration distribution function of each component in 5 discrete directions : ; Step S5.4, the gas mixture The groups are When , we get the boundary conditions:

[0029] in, Indicates components The diffusion rate, Representation node Component The concentration of Representation node Component concentration; Step S5.5, establish the components of the gas mixture , and The heterogeneous chemical reaction model with a reaction boundary is as follows:

[0030]

[0031]

[0032] in, represents the normal direction of the fluid-solid boundary, Indicates components The concentration of Indicates components The diffusion rate, Indicates components The concentration of Indicates components The diffusion rate, Indicates components concentration.

[0033] Optionally, step S6 specifically includes the following steps: Step S6.1, the pyrolysis reaction of the resin matrix is ​​expressed as:

[0034] in, represents a solid resin matrix, represents the pyrolysis gas, represents solid pyrolytic carbon; In step S6.2, the density and concentration of the gas mixture increased by the pyrolysis gas are:

[0035]

[0036] in, represents the pyrolysis gas density, represents the change in resin matrix density, represents the initial density of the resin matrix, Indicates the The proportion of each component in the pyrolysis gas, is the average molar mass of the pyrolysis gas.

[0037] Optionally, step S7 specifically includes the following steps: Step S7.1, using volume pixels, divide the carbon fiber solid and resin matrix in the geometric model into multiple pixels, each pixel is a node and has a control volume, at each time step , the updated volume of the carbon fiber solid is: ; in, is the oxidation reaction area, is the molar volume, For carbon fiber solid at the moment The dimensionless volume of When the dimensionless volume of the carbon fiber solid drops to zero, it means that the carbon fiber solid is completely consumed, and the solid node is converted to a fluid node, and the density, concentration, density distribution function and concentration distribution function of the fluid node obtained by the conversion are initialized; Step S7.2, obtaining the updated density of the resin matrix: ; The volume of the resin matrix is ​​determined based on its updated density. When the density of the resin matrix drops to zero, indicating that the resin matrix is ​​completely consumed and no pyrolysis gas is generated, the resin matrix node is converted to a fluid node, and the density, concentration, density distribution function, and concentration distribution function on this fluid node are initialized.

[0038] Compared with the existing technology, the present invention provides a composite material ablation and pyrolysis evaluation method based on the lattice Boltzmann method, which has at least the following beneficial effects: the volume pixel method is used to characterize the movement of the solid boundary during the ablation process, the microscopic ablation morphology of the material surface is reconstructed and identified by reconstruction, and the coupling mechanism between fluid flow, heat transfer, chemical reaction, ablation recession and pyrolysis reaction and the volume resistance of resin-based porous media are considered to establish a pore-scale ablation-pyrolysis model of the composite material, thereby better simulating the ablation and pyrolysis process of carbon fiber / phenolic resin composite materials, and providing more accurate evaluation results, providing a reliable basis and guidance for the thermal performance analysis and refined design of solid rocket engine nozzles. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention can be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0040] Figure 1 Schematic diagram of the fluid-solid interface in the ablation pyrolysis behavior based on the lattice Boltzmann method provided according to an embodiment of the present invention.

[0041] Figure 2 Flowchart of a composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to an embodiment of the present invention.

[0042] Figure 3 A geometric model of the ablation and pyrolysis behavior of a carbon fiber / phenolic resin composite material is provided in an embodiment of the composite material ablation and pyrolysis evaluation method based on the lattice Boltzmann method according to the present invention.

[0043] Figure 4a CO component concentration cloud diagram at t = 0.08 s for the ablation model, ablation pyrolysis model, and optimized ablation pyrolysis model in an embodiment of the composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method provided in accordance with the present invention.

[0044] Figure 4b H2 component concentration cloud diagram at t = 0.08 s for the ablation model, ablation pyrolysis model, and optimized ablation pyrolysis model in an embodiment of the composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method provided in accordance with the present invention.

[0045] Figure 5 Temperature distribution diagrams at the center line of the ablation model, the ablation pyrolysis model, and the optimized ablation pyrolysis model at t = 0.08 s in an example of the composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features therein can be combined with each other without conflict.

[0047] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0048] A composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to an embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0049] Explanation of symbols: Represents the discrete velocities of particles of a gas mixture in the velocity field; represents the discrete directions of the particles of the gas mixture, and ; represents the grid velocity of the divided grid, and ; is the time step; is the grid spacing; Expresses the macroscopic density of a gas mixture; represents the momentum of the gas mixture; is the gas mixture in discrete directions The density distribution function of Represents a gas mixture in discrete directions The equilibrium density distribution function of Discrete direction The weight coefficient of Indicates the velocity of a gas mixture; is the grid sound velocity of the divided grid, and ; Expresses the dynamic viscosity coefficient of the gas mixture; is the relaxation time of the flow field of the gas mixture; is the source term reflecting the resistance of the resin matrix to the gas mixture; Indicates the permeability of the resin matrix; Indicates time; Represents the spatial position vector; Represents the discrete velocity of particles of a gas mixture in a concentration field; represents the discrete directions of the particles of the gas mixture, and ; represents the number of the components of the gas mixture, and ; Indicates the The concentration of each component; Indicates the The diffusion rate of each component; It is components in discrete directions The concentration distribution function of Indicates the Concentration field relaxation time of each component; Indicates the components in discrete directions The equilibrium concentration distribution function of Discrete direction The weight coefficient of represents the thermal diffusivity of the gas mixture; A quantity that represents the macroscopic temperature of a gas mixture; Indicates relaxation time; In the discrete direction Temperature distribution function of In discrete directions The equilibrium temperature distribution function of The source term represents the heat absorbed by the oxidation reaction at the fluid-solid interface; Indicates the concentration of water vapor that reacts with carbon fiber for oxidation; represents the oxidation reaction rate; It represents the enthalpy of oxidation reaction; It represents the specific heat capacity of gas at normal pressure; represents the inlet water vapor velocity; The source term represents the heat absorbed by the pyrolysis reaction in the resin matrix area; Indicates the pyrolysis reaction rate of the resin matrix; Indicates the enthalpy of the pyrolysis reaction of the resin matrix; Indicates the specific enthalpy value of the pyrolysis reaction; Indicates the resin matrix at time density; It represents the specific heat capacity of the resin matrix at normal pressure; represents the enthalpy change of a heterogeneous reaction; Indicates the specific enthalpy value of enthalpy change; Representation node Place The concentration of each component; Representation node Place The concentration of each component; express Axis direction; Indicates components The diffusion rate; Representation node Component concentration; Representation node Component concentration; represents the normal direction of the fluid-solid boundary; Indicates components concentration; Indicates components The diffusion rate; Indicates components concentration; Indicates components The diffusion rate; Indicates components concentration; represents the pyrolysis gas density; Indicates the change in resin matrix density; represents the initial density of the resin matrix; Indicates the The proportion of each component in the pyrolysis gas; is the average molar mass of pyrolysis gas; is the oxidation reaction area; is the molar volume; For carbon fiber solid at the moment The dimensionless volume of .

[0050] like Figure 2 As shown, a composite material ablation and pyrolysis evaluation method based on the lattice Boltzmann method is provided according to an embodiment of the present invention, which is used to evaluate the ablation and pyrolysis process of the nozzle of a solid rocket engine. It involves a numerical simulation method of the ablation and pyrolysis behavior of the composite material at the pore scale based on the lattice Boltzmann method, and includes the following steps.

[0051] Step S1: Construct a geometric model of the composite material of the nozzle of the solid rocket motor. Figure 3 The specific method for constructing a pore-scale geometric model of the composite material of the solid rocket motor nozzle in step S1 is as follows: taking a calculation region from the nozzle and constructing a geometric model; meshing the geometric model, wherein the mesh includes uniformly arranged nodes; and determining boundary conditions for the geometric model. In this embodiment, the composite material is a carbon fiber / phenolic resin composite material.

[0052] like Figure 3 In one example shown, a geometric model of a carbon fiber / phenolic resin composite material is constructed, in which the central circular area represents a carbon fiber solid and the outer circular ring represents a resin matrix. The area of ​​the carbon fiber solid is a solid area. The resin matrix outside the carbon fiber solid and the space outside the resin matrix (i.e., the area outside the carbon fiber solid) are used as fluid areas. In the detailed description of the model establishment below, a resistance source item is set to simulate the resistance encountered by the fluid flowing in the resin matrix. Figure 3 As shown, in this example, the length and width of the geometric model are approximately 100µm*75µm, the diameter of the carbon fiber solid in the geometric model is approximately 20µm, and the outer diameter of the matrix layer outside the carbon fiber solid is 30µm, so that the distance from the matrix layer to the side edge and bottom edge of the geometric model are approximately 35µm and 22.5µm, respectively.

[0053] In this step, the boundary conditions of the geometric model include an inlet boundary condition, which sets the temperature, velocity, and concentration of the water vapor at the inlet; an outlet boundary condition, which uses a fully developed boundary condition, including the velocity field, concentration field, and temperature field of the gas mixture at the outlet; the top and bottom wall boundary conditions of the geometric model, which use a no-slip boundary, an adiabatic boundary, and a zero-flux boundary for the fluid flow, temperature, and mass transport of the gas mixture, respectively; and a fluid-solid interface boundary condition, which uses a no-slip boundary condition for the fluid flow of the gas mixture, and a chemical reaction occurs at the fluid-solid interface. In this embodiment, the solid refers to carbon fiber; the fluid refers to water vapor, and carbon monoxide and hydrogen are generated after the chemical reaction occurs at the carbon fiber solid boundary, thereby obtaining a gas mixture composed of three components: water vapor, carbon monoxide, and hydrogen.

[0054] Step S2: establishing a D2Q9 LBGK model of the fluid flow of the gas mixture flowing through the nozzle. Step S2 specifically includes the following steps.

[0055] Step S2.1, obtain the discrete velocity of the particles of the gas mixture in the velocity field: (1) in, represents the discrete directions of the particles of the gas mixture and , represents the grid velocity of the grid divided into geometric models and , is the time step, is the grid spacing.

[0056] Step S2.2, obtain the macroscopic density of the gas mixture and momentum : (2) in, is the gas mixture in discrete directions The density distribution function of Indicates time, Represents the spatial position vector, which represents the (x,y) coordinate in this model, Indicates the velocity of a gas mixture.

[0057] Step S2.3, establish the gas mixture in discrete directions The equilibrium density distribution function as follows: (3) in, Discrete direction In the established D2Q9 lattice model, the weight coefficients of each discrete direction are set as follows: = 4 / 9, = = = =1 / 9, = = = = 1 / 36. is the grid sound velocity of the divided grid and .

[0058] Step S2.4, obtain the dynamic viscosity coefficient of the gas mixture: (4) in, is the relaxation time of the flow field of the gas mixture.

[0059] In step S2.5, considering that the matrix of the carbon fiber solid periphery is phenolic resin, which is a porous material, a source term is constructed that reflects the resistance of the resin matrix as a porous medium, taking into account the Darcy effect: (5) Where, It represents the permeability of the porous medium, that is, the permeability of the resin matrix, that is, the permeability of the phenolic resin.

[0060] Step S2.6, establish the LBGK model of the fluid flow of the gas mixture flowing through the nozzle in the form of a D2Q9 lattice model: (6).

[0061] Step S3: Establishing a D2Q5 LBGK model for the multi-component mass transport of the gas mixture flowing through the nozzle. The multi-components refer to the three components in the gas mixture: water vapor, carbon monoxide, and hydrogen. Step S3 specifically includes the following steps.

[0062] Step S3.1, obtain the discrete velocity of the particles of the gas mixture in the concentration field: (7) in, represents the discrete directions of the particles of the gas mixture and .

[0063] Step S3.2, obtain the diffusion rate and component concentration of the gas mixture: (8) (9) in, The first The concentration of each component, The first The diffusion rate of each component, The first components in discrete directions The concentration distribution function of The first The concentration field relaxation time of each component, Number the components of the gas mixture and .

[0064] Step S3.3, construct the gas mixture components in discrete directions The equilibrium concentration distribution function of is: (10) Among them, for the D2Q5 lattice model, Discrete direction The weight coefficients of each discrete direction are set as follows: .

[0065] Step S3.4, establish the D2Q5 form LBGK model of multi-component mass transport of gas mixtures: (11).

[0066] Step S4: Establishing a D2Q5 LBGK model for heat transfer in the geometric model. The heat transfer includes heat transfer between fluids, between fluids and solids, and between solids in the geometric model. Step S4 specifically includes the following steps.

[0067] Step S4.1, obtain the thermal diffusivity of the gas mixture and macroscopic temperature : (12) (13) in, represents the relaxation time, is a discrete direction The temperature distribution function.

[0068] Step S4.2, build the geometric model in discrete directions The equilibrium temperature distribution function Expressed as: (14).

[0069] Step S4.3, obtain the heat source term absorbed by the oxidation reaction of the carbon fiber solid at the fluid (gas mixture)-solid (carbon fiber) interface

[0070] (15) in, represents the concentration of water vapor that reacts with the carbon fiber solid, represents the oxidation reaction rate, represents the enthalpy of the oxidation reaction, represents the specific heat capacity of a gas (i.e., a gas mixture) at constant pressure, represents the inlet water vapor velocity.

[0071] Step S4.4, obtaining the source term of the heat absorbed by the pyrolysis reaction of the resin matrix area around the carbon fiber solid As follows. Among them, for phenolic resin, pyrolysis reaction will occur as long as the pyrolysis temperature is reached: (16) in, represents the pyrolysis reaction rate of the resin matrix, represents the enthalpy of the pyrolysis reaction of the resin matrix, Indicates the resin matrix at time The density, It represents the specific heat capacity of the resin matrix at normal pressure.

[0072] Step S4.5, construct the LBGK model of the D2Q5 form of heat transfer of the geometric model: (17).

[0073] Step S5: Establishing a heterogeneous chemical reaction model at the fluid-solid interface. Here, solid refers to carbon fiber, and gas refers to reactants and products. Step S5 specifically includes the following steps.

[0074] In step S5.1, the following heterogeneous reaction is assumed to occur on the surface of the carbon fiber solid: (18) in, represents the enthalpy change of the heterogeneous reaction, The specific enthalpy value representing the enthalpy change, represents carbon fiber (solid), represents the reactant (gas), namely water vapor, and They represent the two products (gases) of the reaction, namely carbon monoxide and hydrogen.

[0075] Step S5.2, see Figure 1 A schematic diagram of the fluid-solid interface is given. After each migration (i.e., the migration of a particle at each time step), the discrete directions of the particles in the gas mixture are =2, No. The concentration distribution function of each component is a known quantity; in the discrete directions of the particles in the gas mixture =4, No. The concentration distribution function of each component is an unknown quantity; the discrete directions of the particles in the gas mixture =1,3,No. The concentration distribution function of each component and There is no effect on the flow field because the discrete direction is perpendicular to the normal direction of the fluid-solid interface. Figure 1 As shown, the discrete directions of the particles of the gas mixture are =2, 4 is along the normal direction of the fluid-solid interface, and =2 is toward the solid (i.e., carbon fiber solid) region, =4 is the direction toward the fluid (i.e., gas mixture) region; the discrete direction of the particles of the gas mixture = 1, 3 are directions perpendicular to the normal of the fluid-solid interface; the discrete directions of the particles of the gas mixture = 0, which is the location of the particle. The reaction wall is static, at the node of the fluid-solid interface At , we can get the control equation: (19) in, Representation node Place The concentration of each component, Representation node Place The concentration of each component, express Axis direction. Figure 1 As shown, the node is the node at the fluid-solid interface, node For nodes Adjacent fluid nodes. As shown in the figure, node S is adjacent to node Adjacent solid nodes.

[0076] Step S5.3, the lattice Boltzmann method is the evolution of the particle distribution function, so at each time step it is necessary to determine the Concentration distribution function of each component in 5 discrete directions =0,…,4: (20).

[0077] Step S5.4, the gas mixture For example, the concentration of The groups are , we get the boundary conditions: (twenty one) in, Indicates components The diffusion rate, Representation node Component The concentration of Representation node Component The concentration of , and unknown concentration distribution , similarly, the concentration boundaries in four directions can be obtained.

[0078] Step S5.5, heterogeneous reactions can be achieved by boundary conditions to establish the components of the gas mixture , and The heterogeneous chemical reaction model with a reaction boundary is as follows: (twenty two) (twenty three) (twenty four) in, represents the normal direction of the fluid-solid boundary, Indicates components The concentration of Indicates components The diffusion rate, Indicates components The concentration of Indicates components The diffusion rate, Indicates components concentration.

[0079] Step S6, establishes the pyrolysis reaction model of the resin matrix of the carbon fiber solid periphery. The resin matrix of the carbon fiber solid periphery forms a matrix region, and as long as the temperature reaches a given pyrolysis reaction temperature, a pyrolysis reaction will occur. The components of the pyrolysis gas obtained by the pyrolysis reaction are the same as those of the gas mixture, including three components: water vapor, carbon monoxide and hydrogen. As mentioned above, in this embodiment, the resin forming the matrix is ​​a phenolic resin. Therefore, in this embodiment, the resin matrix region is regarded as a fluid region, which avoids processing overly complex boundary conditions at the interface between the carbon fiber and the resin matrix. This step S6 specifically includes the following steps.

[0080] Step S6.1, the thermal decomposition reaction of the phenolic resin matrix is ​​expressed as: (25) in, represents the resin matrix (solid), represents the pyrolysis gas, represents pyrolytic carbon (solid), Represents the enthalpy value of the resin's thermal decomposition reaction, Indicates the specific enthalpy value of the pyrolysis reaction.

[0081] Step S6.2, constructing a pyrolysis reaction model, including establishing the density and concentration of the gas mixture added by the pyrolysis gas as: (26) (27) in, represents the pyrolysis gas density, represents the change in resin matrix density, represents the initial density of the resin matrix, Indicates the The proportion of each component in the pyrolysis gas, is the average molar mass of the pyrolysis gas.

[0082] Step S7: An updated model of the carbon fiber solid region and the resin matrix is ​​established using the volume pixel method. During the reaction process, the carbon fiber solid is consumed by oxidation, and the resin matrix is ​​consumed by pyrolysis, resulting in a decrease in volume. In this embodiment, volume pixels (VOPs) are used to update the volume of the carbon fiber solid in real time. Step S7 specifically includes the following steps.

[0083] Step S7.1, in the VOP method, the volume of the carbon fiber solid and the resin matrix in the geometric model is divided into a plurality of pixels, i.e., nodes. Among the divided nodes, the area located in the carbon fiber solid is a solid node, the area located in the resin matrix is ​​a resin matrix node, and the area located outside the resin matrix is ​​a fluid node. Each pixel has a control volume. For 2D simulation, the initial volume of the pixel unit is set. is 1×1 in grid units (i.e., the grid steps in both directions are 1). , the updated volume of the carbon fiber solid is: (28) in, is the oxidation reaction area, is the molar volume, For carbon fiber solid at the moment The dimensionless volume of the carbon fiber solid. When it drops to zero, it means that the carbon fiber solid is completely consumed, and the solid node is converted into a fluid node; and the density, concentration and corresponding distribution function of the converted fluid node are initialized.

[0084] Step S7.2, obtaining the updated density of the resin matrix: (29).

[0085] The volume of the resin matrix can be determined based on its updated density. When it drops to zero, it means that the resin matrix is ​​completely consumed and no pyrolysis gas is produced. The resin matrix node is converted to a fluid node, and the density, concentration, and corresponding distribution function on this fluid node are initialized.

[0086] Step S8: Based on the established model and inputting boundary conditions, a transient simulation of the ablation and pyrolysis behavior of the nozzle composite material is performed to obtain simulation results, and an evaluation plan is derived based on the simulation results. Specifically, the evaluation plan derived based on the simulation results may include comparing the simulation results of the ablation and pyrolysis model with the simulation results of the optimized ablation and pyrolysis model, and evaluating the impact of the pyrolysis behavior of the resin matrix on the ablation process of the carbon fiber from different perspectives, such as temperature, concentration, and changes in the micromorphology of the carbon fiber, to obtain an evaluation result. This evaluation result can be used for the design and failure analysis of the nozzle of the solid rocket motor. Simulation results of the optimized ablation pyrolysis model can be obtained by setting conditions in the models established in the aforementioned steps, for example, by setting the resin matrix (i.e., considering the pyrolysis reaction model of the resin matrix established in step S6), in which case the resistance source term of the resin matrix is ​​not considered; and by setting the resistance source term of the resin matrix (i.e., considering the resistance source term of the resin matrix in the D2Q9 form LBGK model of the fluid flow of the gas mixture established in step S2), and / or setting the source term of the heat absorbed by the pyrolysis reaction of the resin matrix (i.e., considering the source term of the heat absorbed by the pyrolysis reaction of the resin matrix in the D2Q5 form LBGK model of heat transfer established in step S4). Furthermore, by inputting different boundary conditions, corresponding simulation results and evaluation solutions can be obtained.

[0087] In order to verify the effectiveness of the algorithm proposed by the present invention, the following reference Figure 4a 、 Figure 4b and Figure 5 An exemplary embodiment of a composite material ablation and pyrolysis assessment method based on the lattice Boltzmann method according to an embodiment of the present invention is described in detail. This example further illustrates the present invention by examining the ablation and pyrolysis behavior of carbon fiber / phenolic resin in a solid rocket motor nozzle.

[0088] The first step is to construct a pore-scale geometric model of the composite material as follows.

[0089] Construct a rectangular geometric model, such as Figure 3 As shown in the figure, the gray circular area within the rectangular geometry represents the carbon fiber solid, and the outer area is the resin matrix. The top, bottom, left, and right sides of this rectangular geometry are the computational boundaries. This area is divided into 200*150 grids.

[0090] The velocity and species concentration in the initial computational domain of this geometry model are set to zero, and the temperature is 2000 K. At the inlet, the concentration of water vapor is 0.1 mol / m 3, velocity 0.0006 m / s, and temperature 3000 K. At the outlet, zero gradients are used for the velocity, temperature, and concentration fields. At the top and bottom walls of the geometric model, no-slip boundaries, adiabatic boundaries, and zero-flux boundaries are used for fluid flow, temperature, and material transport, respectively.

[0091] At the fluid-solid interface, the fluid flow adopts a no-slip boundary condition, and the chemical reaction between the carbon fiber solid and water vapor is:

[0092] The rate of chemical reaction between the carbon fiber solid and water vapor is:

[0093] Where, is the pre-factor, is the activation energy, is the molar gas constant, is the reaction surface temperature, is the reaction order and is assumed to be 1. In this example, .

[0094] The pyrolysis reaction of the resin matrix occurring in the matrix area is:

[0095] The pyrolysis reaction rate of the resin matrix is:

[0096] in, is the temperature of the resin matrix. In this embodiment, .

[0097] The second step is to establish the D2Q9 form LBGK model of the fluid flow of the gas mixture as follows.

[0098] The evolution equation of the flow field of the gas mixture is expressed as:

[0099] in, and are the density distribution function and the equilibrium density distribution function respectively.

[0100] In the third step, the D2Q5 form LBGK model of multi-component mass transport of gas mixtures is established as follows.

[0101] The evolution equation of multi-component mass transport of gas mixtures is expressed as:

[0102] Where, and They are k The concentration distribution function of each component and the equilibrium concentration distribution function are obtained. In this example, there are three components in the gas mixture: H2O, CO, and H2. Therefore, the LBGK model of the D2Q5 form of the three components is established in this step.

[0103] The fourth step is to establish the D2Q5 form of the LBGK model of heat transfer as follows.

[0104] Similar to the multi-component mass transport of gas mixtures mentioned above, the heat transfer evolution equation can be expressed as

[0105] Where, and In discrete directions The temperature distribution function and the equilibrium temperature distribution function.

[0106] The fifth step is to establish a heterogeneous chemical reaction model at the fluid-solid interface. The specific steps are as follows: The following heterogeneous reactions occur on the carbon fiber solid surface:

[0107] See also Figure 1 Schematic diagram of the fluid-solid interface. After each migration, is a known quantity; is an unknown quantity; and There is no effect on the flow field because they are perpendicular to the normal direction. The reaction wall is static and at the node R, we can get: .

[0108] The lattice Boltzmann method is the evolution of the particle distribution function, so five concentration distribution functions need to be determined at each time step.

[0109] Taking the concentration of H2O as an example, combined with the boundary conditions

[0110] Get the node Component Concentration , and unknown concentration distribution The concentration boundaries in these four directions are all realized using the above method.

[0111] Heterogeneous reactions are usually realized by boundary conditions. Therefore, the reaction boundaries of the components H2O, CO and H2 in heterogeneous reactions are as follows:

[0112]

[0113] .

[0114] The sixth step is to establish a pyrolysis reaction model for the resin matrix as follows. In the matrix region, pyrolysis occurs as long as the temperature reaches the specified pyrolysis temperature. Therefore, treating the resin matrix region as a fluid region avoids overly complex boundary conditions at the interface between the carbon fiber solid and the resin matrix.

[0115] According to the following formula, the density and concentration of the gas mixture increased by the pyrolysis gas can be obtained by setting the proportion of each component of the pyrolysis gas, H2O, CO and H2, in the pyrolysis gas:

[0116]

[0117] .

[0118] In the seventh step, an updated model of the carbon fiber solid region and the resin matrix is ​​established using the volume pixel method as follows. During the reaction process, the carbon fiber solid is consumed by oxidation and the resin matrix is ​​consumed by pyrolysis, resulting in a decrease in volume. Here, volume pixels (VOPs) are used to update the volume of the carbon fiber solid in real time.

[0119] In the VOP method, the geometric model is divided into multiple pixels. Each pixel has a control volume. For 2D simulation, the initial volume of the pixel unit is is 1×1 in grid units. In this embodiment, at each time step, the volume of the carbon fiber solid is updated as .

[0120] When the volume of carbon fiber solid When it drops to zero, the carbon fibers are completely consumed and the solid node is converted to a fluid node. At the same time, the density, concentration, and corresponding distribution function on the fluid node must be initialized.

[0121] Additionally, the volume of a resin matrix is ​​related to its density:

[0122] The volume of the resin matrix is ​​determined based on its updated density. When the density of the resin matrix drops to zero, the resin matrix is ​​completely consumed and no longer produces pyrolysis gases. At this point, the Resin Matrix node is removed and converted to a Fluid node. The density, concentration, and corresponding distribution functions on this Fluid node are initialized.

[0123] Step 8: The simulation ends and we get Figure 4a and Figure 4b The three models are ablation model, ablation pyrolysis model, and optimized ablation pyrolysis model (considering the resistance of the resin matrix as a porous medium). = 0.08 s. The black area represents the carbon fiber solid. The volume and morphology of the remaining carbon fiber solid are essentially the same in the three models. This is because, while pyrolysis produces more H2O to react with C, it also absorbs a significant amount of heat, significantly slowing the reaction rate. The black line represents the resin matrix region. The resin matrix is ​​consumed more rapidly in the ablation model (which does not consider porous media resistance) and the ablation-pyrolysis model. Figure 4a The CO concentrations obtained by the ablation model, ablation pyrolysis model, and optimized ablation pyrolysis model are shown. Figure 4b The H2 concentration is shown. The distribution trends of CO and H2 are similar across all models, but when considering the pyrolysis reaction, the CO concentration is lower than that of H2. Furthermore, the numerical results show that the CO and H2 produced by ablation are less than those produced by pyrolysis. Figure 5 The temperature distribution at the centerline at t = 0.08 s is shown. The temperature drop is more pronounced in both the ablation pyrolysis model and the optimized ablation pyrolysis model, which considers the pyrolysis reaction. In the optimized ablation pyrolysis model, which considers the pore resistance of the resin matrix, the pyrolysis gas spends more time in the resin matrix, increasing the H2O concentration. Therefore, the optimized ablation pyrolysis model minimizes temperature reduction, thereby slowing down the ablation process and pyrolysis reaction.

[0124] This example demonstrates the ability of the present invention to perform transient simulations of the ablation and pyrolysis behavior of carbon fiber / phenolic resin at the pore scale, coupling fluid flow, heat transfer, chemical reactions, ablation regression, and pyrolysis reactions, while also accounting for the influence of the porous resin matrix's resistance on fluid flow. Accurate simulation of the coupled microscopic ablation and pyrolysis processes of composite materials will facilitate the refined design of solid rocket motor nozzles and the application of new materials.

[0125] All of the above optional technical solutions can be combined in any way to form optional embodiments of the present application, and will not be described in detail here.

[0126] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0127] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method is used to evaluate the ablation pyrolysis process of composite materials of a solid rocket motor nozzle, characterized in that: The following steps are involved: Step S1: Taking a calculation area from the nozzle and constructing it into a geometric model, and dividing the geometric model into a grid, wherein the grid includes evenly arranged nodes, and determining the boundary conditions of the geometric model, wherein the composite material of the nozzle is a carbon fiber / phenolic resin composite material; Step S2, establishing a D2Q9-type LBGK model of the fluid flow of the gas mixture flowing through the nozzle; Step S3, establishing a D2Q5 LBGK model of multi-component mass transport of the gas mixture flowing through the nozzle, where the multi-components are water vapor, carbon monoxide, and hydrogen in the gas mixture; Step S4, establishing a D2Q5 LBGK model of heat transfer in the geometric model, wherein the heat transfer includes heat transfer between fluids, between fluids and solids, and between solids in the geometric model; Step S5, establishing a heterogeneous chemical reaction model at the fluid-solid interface; Step S6, establishing a pyrolysis reaction model of the resin matrix around the carbon fiber solid; Step S7, establishing an updated model of the carbon fiber solid and the resin matrix according to the volume pixel method; Step S8, based on the established model, inputting boundary conditions, performing transient simulation on the ablation and pyrolysis behavior of the composite material of the nozzle, obtaining simulation results, and obtaining an evaluation plan based on the simulation results; The solid in the geometric model is a carbon fiber solid; the fluid is a gas mixture, including water vapor, and carbon monoxide and hydrogen generated by the chemical reaction of water vapor at the boundary of the carbon fiber solid.

2. The composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to claim 1, characterized in that: In step S1: The boundary conditions of the geometric model include the inlet boundary condition, which sets the temperature, velocity and concentration of water vapor at the inlet; the outlet boundary condition, which adopts the fully developed boundary condition, including the velocity field of the gas mixture at the outlet, the concentration field of the gas mixture and the temperature field of the gas mixture; the top and bottom wall boundary conditions of the geometric model, which adopt no-slip boundary, adiabatic boundary and zero flux boundary for the fluid flow, temperature and mass transport of the gas mixture respectively; the fluid-solid interface boundary condition, which adopts no-slip boundary condition for the fluid flow of the gas mixture.

3. The composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to claim 1, characterized in that: Step S2 specifically includes the following steps: Step S2.1, obtain the discrete velocity of the particles of the gas mixture in the velocity field: in, represents the discrete directions of the particles of the gas mixture and , represents the grid velocity of the divided grid and , is the time step, is the grid spacing; Step S2.2, obtain the macroscopic density of the gas mixture and momentum : in, is the gas mixture in discrete directions The density distribution function of Indicates time, represents the spatial position vector, Indicates the velocity of a gas mixture; Step S2.3, establish the gas mixture in discrete directions The equilibrium density distribution function of : in, Discrete direction The weight coefficient of is the grid sound velocity of the divided grid and ; Step S2.4, obtain the dynamic viscosity coefficient of the gas mixture: in, is the relaxation time of the flow field of the gas mixture; In step S2.5, the resistance of the resin matrix on the carbon fiber solid to the gas mixture is considered, and a source term reflecting the resistance of the resin matrix is ​​constructed: Where, Indicates the permeability of the resin matrix; Step S2.6, establish the LBGK model of the fluid flow of the gas mixture flowing through the nozzle in the form of a D2Q9 lattice model: 。 4. The composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to claim 3, characterized in that: Step S3 specifically includes the following steps: Step S3.1, obtain the discrete velocity of the particles of the gas mixture in the concentration field: in, represents the discrete directions of the particles of the gas mixture and ; Step S3.2, obtain the diffusion rate and component concentration of the gas mixture: in, The first The concentration of each component, The first The diffusion rate of each component, The first components in discrete directions The concentration distribution function of The first The concentration field relaxation time of each component, Number the components of the gas mixture and ; Step S3.3, construct the gas mixture components in discrete directions The equilibrium concentration distribution function of is: in, Discrete direction The weight coefficient of Step S3.4, establish the D2Q5 form LBGK model of multi-component mass transport of gas mixtures: 。 5. The composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to claim 4, characterized in that: Step S4 specifically includes the following steps: Step S4.1, obtain the thermal diffusivity of the gas mixture and macroscopic temperature : in, represents the concentration field relaxation time, In the discrete direction Temperature distribution function of Step S4.2, build the geometric model in discrete directions The equilibrium temperature distribution function Expressed as: ； Step S4.3, obtain the source term of the heat absorbed by the oxidation reaction of the carbon fiber solid at the fluid-solid interface : in, represents the concentration of water vapor that reacts with the carbon fiber solid, represents the oxidation reaction rate, represents the enthalpy of the oxidation reaction, represents the specific heat capacity of the gas at normal pressure, represents the inlet water vapor velocity; Step S4.4, obtaining the source term of the heat absorbed by the pyrolysis reaction of the resin matrix area around the carbon fiber solid : in, represents the pyrolysis reaction rate of the resin matrix, represents the enthalpy of the pyrolysis reaction of the resin matrix, Indicates the resin matrix at time The density, It represents the specific heat capacity of the resin matrix at normal pressure; Step S4.5, construct the LBGK model of the D2Q5 form of heat transfer of the geometric model: 。 6. The composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to claim 5, characterized in that: Step S5 specifically includes the following steps: In step S5.1, the following heterogeneous reaction is assumed to occur on the surface of the carbon fiber solid: in, represents a carbon fiber solid, Represents water vapor, represents the gaseous product of the reaction, carbon monoxide, represents the gaseous product of the reaction, hydrogen; Step S5.2, at the node of the fluid-solid interface At , we get the control equation: in, is the discrete direction of the particles in the gas mixture =2, No. The concentration distribution function of each component, is the discrete direction of the particles in the gas mixture =4, No. The concentration distribution function of each component, Representation node Place The concentration of each component, Representation node Place The concentration of each component, express Axis direction, node For nodes adjacent fluid nodes; Step S5.3, determine the Concentration distribution function of each component in 5 discrete directions : ； Step S5.4, the gas mixture The groups are When , we get the boundary conditions: in, Indicates components The diffusion rate, Representation node Component The concentration of Representation node Component concentration; Step S5.5, establish the components of the gas mixture , and The heterogeneous chemical reaction model with a reaction boundary is as follows: in, represents the normal direction of the fluid-solid boundary, Indicates components The concentration of Indicates components The diffusion rate, Indicates components The concentration of Indicates components The diffusion rate, Indicates components concentration.

7. The composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to claim 6, characterized in that: Step S6 specifically includes the following steps: Step S6.1, the pyrolysis reaction of the resin matrix is ​​expressed as: in, represents a solid resin matrix, represents the pyrolysis gas, represents solid pyrolytic carbon; In step S6.2, the density and concentration of the gas mixture increased by the pyrolysis gas are: in, represents the pyrolysis gas density, represents the change in resin matrix density, represents the initial density of the resin matrix, Indicates the The proportion of each component in the pyrolysis gas, is the average molar mass of the pyrolysis gas.

8. The composite material ablation pyrolysis evaluation method based on the lattice Boltzmann method according to claim 7, characterized in that: Step S7 specifically includes the following steps: Step S7.1, using volume pixels, divide the carbon fiber solid and resin matrix in the geometric model into multiple pixels, each pixel is a node and has a control volume, at each time step , the updated volume of the carbon fiber solid is: ； in, is the oxidation reaction area, is the molar volume, For carbon fiber solid at the moment The dimensionless volume of When the dimensionless volume of the carbon fiber solid drops to zero, it means that the carbon fiber solid is completely consumed, and the solid node is converted to a fluid node, and the density, concentration, density distribution function and concentration distribution function of the fluid node obtained by the conversion are initialized; Step S7.2, obtaining the updated density of the resin matrix: ； The volume of the resin matrix is ​​determined based on its updated density. When the density of the resin matrix drops to zero, indicating that the resin matrix is ​​completely consumed and no pyrolysis gas is generated, the resin matrix node is converted to a fluid node, and the density, concentration, density distribution function, and concentration distribution function on this fluid node are initialized.

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