Lattice boltzmann simulation predictive method for aluminum-based solid propellant combustion agglomeration

Abstract

The present application relates to solid propellant combustion technology, aiming at providing a lattice Boltzmann simulation prediction method for aluminum-based solid propellant combustion agglomeration. It comprises: using LBM method for solid propellant combustion process simulation and aluminum particle agglomeration behavior research, through mesoscale numerical simulation of solid propellant combustion process quantitative calculation and prediction, using the statistical physics principle of LBM to couple multiple field distribution, realize the simulation of complex aluminum particle combustion. The present application can more naturally simulate the drag force, thermophoretic force and other effects of particles in fluid, and is closer to the physical reality; can realize the reduction of calculation complexity, realizes the efficient simulation of tens of thousands of aluminum particle agglomeration process, significantly improves the calculation efficiency of large-scale particle system simulation; can deeply reveal the internal mechanism of pressure, burning rate, particle size, oxidizing gas concentration and other factors affecting agglomeration; realize the coupling of multiple physical fields, and truly reflect the complex environment in the combustion chamber.

Description

Technical Field

[0001] This invention relates to the field of solid propellant combustion technology, and more specifically to a lattice Boltzmann simulation prediction method for combustion agglomeration of aluminum-based solid propellants. Background Technology

[0002] Rocket engines using solid propellants have advantages such as simple structure, high reliability, and fast response speed. Aluminum particles, as a key high-energy additive for solid propellants, can significantly improve the energy level and flame temperature of the propellant. However, aluminum particles undergo complex agglomeration during combustion, producing large-sized condensed phase combustion products. This not only affects the combustion efficiency and energy release of the propellant and reduces specific impulse, but may also cause ablation of the engine's insulation layer and nozzle, seriously affecting the operational safety of solid rocket engines.

[0003] Currently, research on the agglomeration behavior of aluminum particles mainly relies on experimental observation and numerical simulation. Existing experimental methods are limited by the extreme combustion environment of high temperature and high pressure, making it difficult to conduct detailed, dynamic observations of the entire agglomeration process. Although various numerical simulation schemes have yielded results, they all have significant shortcomings. For example, traditional CFD methods struggle to effectively handle complex interactions between particles and phase interface changes; the computational complexity of the discrete element method increases geometrically with the number of particles, making it difficult to handle large-scale particle systems; and simplified models based on empirical formulas fail to reflect the physical essence of the agglomeration process. Therefore, there is an urgent need to develop a computational method that can accurately describe the agglomeration process of aluminum particles. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a lattice Boltzmann simulation prediction method for combustion agglomeration of aluminum-based solid propellants.

[0005] To solve the technical problem, the solution of the present invention is:

[0006] A lattice Boltzmann (LBM) simulation method for predicting combustion agglomeration in aluminum-based solid propellants is provided. This method utilizes the Lattice Boltzmann (LBM) method for mesoscale numerical simulation, enabling quantitative calculation and prediction of the solid propellant combustion process. The method includes:

[0007] (1) Define the macroscopic state parameters or initial properties of aluminum particles, propellant and environment based on the physicochemical model of propellant combustion agglomeration;

[0008] (2) Based on the propellant size and combustion chamber environment, construct a two-dimensional or three-dimensional computational domain for simulating the combustion agglomeration of aluminum-based solid propellants, and set the initial solid phase region, condensed phase region, gas phase flow region and dynamic combustion surface;

[0009] (3) Establish the evolution equations of the particle distribution functions for velocity field, temperature field and component transport in the LBM model respectively; initialize each distribution function;

[0010] (4) The position of the combustion surface is updated step by step over time according to the set propellant burning rate; when the combustion surface extends to the current position of the aluminum particle, the particle combustion release mechanism is triggered.

[0011] (5) The macroscopic field is solved iteratively using the LBM method: In each time step, the distribution function of each model is calculated sequentially using collision and migration steps, and corresponding boundary conditions are applied; the velocity field, temperature field and component transport in the computational domain are updated;

[0012] (6) For the combustion process of aluminum particles, calculate particle motion and force, simulate particle combustion reaction and oxide layer growth, and detect and treat particle agglomeration; through the above coupled iterative process, realize real-time coupled calculation of flow-temperature-composition-particle dynamics;

[0013] (7) Using the computational data collected during the simulation process, output the final particle size distribution, aggregate formation process data and macroscopic field visualization results at the end of the simulation or at a specified time.

[0014] Description of the invention principle:

[0015] This invention proposes a lattice Boltzmann simulation method for predicting combustion agglomeration of aluminum-based solid propellants. This method uses the lattice Boltzmann method to perform mesoscale numerical simulations, enabling quantitative calculation and prediction of the entire process of aluminum particles being exposed to, oxidized, burned, agglomerated, and detached from the propellant combustion surface during solid propellant combustion. This allows for the acquisition of key parameters such as the particle size distribution of the agglomerates and the thickness of the oxide layer.

[0016] 1. The Lattice Boltzmann Method (LBM) is a grid-based fluid flow simulation method used in computational fluid dynamics. Compared to the typical Navier-Stokes equations, LBM can be used to compute physical propagation, with collision and migration steps occurring within each grid cell. The LBM method assumes that virtual particles move randomly within a segmented simulation region with regular grid cells. These particles propagate along constrained grid cells using a distribution function fi as statistical physics. Various methods can be used to define these constrained directions. The LBM model D2Q9 represents the velocity directions of 9 grid cells in two dimensions, and D3Q19 represents the velocity directions of 19 grid cells in three dimensions. During the time step, particles exchange physical quantities at these grid velocities through collision and migration steps. LBM has the following advantages: (1) The algorithm is simple and can simulate various complex nonlinear macroscopic phenomena; (2) It is a particle-based meshless dynamics algorithm, which avoids the complex mesh division process and can fully consider complex geometric details, thus making the calculation results more realistic; (3) It is combined with parallel processing, which improves the calculation efficiency and can accurately and effectively capture a variety of transient interfaces, and has a wide range of applications.

[0017] In traditional research, the Lattice Boltzmann (LBM) method is widely used to simulate single-phase or multiphase fluid flows, with its core advantage lying in handling complex boundaries and phase interfaces. Therefore, based on existing research, researchers in this field generally believe that LBM is primarily suitable for simple heat and mass transfer flow problems. For multiphysics coupling problems involving violent chemical reactions, particle phase transitions, complex combustion dynamics, and large-scale discrete particle dynamic interactions, its implementation process is too complex, leading to the preconceived notion that "LBM is difficult to apply to multiphysics coupling." Consequently, there are currently no publicly available records of systematically applying the Lattice Boltzmann method to the simulation of the entire agglomeration process of aluminum-containing solid propellants.

[0018] 2. This invention focuses on a novel understanding of the lattice Boltzmann simulation method, applying it to the simulation of solid propellant combustion processes and the study of aluminum particle agglomeration behavior. Through mesoscale numerical simulation, it is possible to quantitatively calculate and predict the entire process of aluminum particles in solid propellant combustion, from exposure to the propellant combustion surface, oxidation, combustion, agglomeration, and detachment from the combustion surface, and obtain key parameters such as particle size distribution and oxide layer thickness of the agglomerates. By coupling multiple field distributions using the statistical physics principles of LBM, involving velocity field, temperature field, component transport, and the momentum, energy, and component particle distribution functions and source terms of discrete particle phases, the complex combustion of aluminum particles can be simulated.

[0019] In their research on solid particle combustion, the research team of this application discovered that the Lattice Boltzmann method (LBM), as a mesoscale fluid dynamics simulation method, possesses advantages such as flexible boundary handling, high parallel efficiency, and ease of handling complex boundaries and multiphase flows, making it highly suitable for simulating particle motion and interactions in fluids. However, applying the Lattice Boltzmann method to the calculation of aluminum-based solid propellant agglomeration requires further comprehensive consideration of multiphysics coupling processes, including particle motion, chemical reactions, heat and mass transfer, and agglomeration effects, to provide an effective numerical simulation tool for a deeper understanding of the aluminum particle agglomeration mechanism and optimization of propellant formulation design. Therefore, this invention fills the gap in mesoscale multiphysics coupling simulation in this field, breaking through the limitations of those skilled in the art in applying the LBM method; it achieves efficient numerical simulation and prediction of agglomerates throughout the entire combustion process, yielding unexpected and significant results.

[0020] Compared with the prior art, the beneficial effects of the present invention are:

[0021] 1. Existing methods for calculating combustion agglomeration of aluminum-based solid propellants have significant shortcomings in terms of accuracy of physical modeling, computational efficiency, and ability to handle complex multiphase and multi-physics coupling. The innovative simulation prediction method proposed in this invention addresses these issues by overcoming the limitations of traditional computational fluid dynamics methods in accurately characterizing interparticle interactions and phase interfaces, and avoiding the bottleneck of excessive computational load in the discrete element method when simulating massive amounts of particles. At the same time, this invention surpasses the defects of overly simplified empirical models and unclear physical mechanisms in existing technologies, and realizes the simulation calculation of aluminum particles from propellant exposure, oxidation, combustion, agglomeration, and detachment at the mesoscale.

[0022] 2. The Lattice Boltzmann (LBM) method used in this invention is naturally applicable to complex boundaries and multiphase flows. It can more naturally simulate the drag force, thermophoretic force and other effects of particles in fluids, as well as the interaction between particles and fluids and between particles, making the modeling closer to physical reality.

[0023] 3. Agglomeration is essentially the collective behavior of a large number of particles. Traditional discrete element method (DEM) coupling methods involve enormous computational costs when simulating more than a thousand particles. This invention utilizes the mesoscopic and local computational properties of the LBM (Light Element Method) to directly reuse the LBM flow field lattice grid as the mesh for particle contact detection, thereby reducing computational complexity and achieving efficient simulation of the agglomeration process of tens of thousands of aluminum particles, significantly improving the computational efficiency of simulating large-scale particle systems.

[0024] 4. Starting from the particle scale, this invention explicitly simulates the entire chain of physicochemical processes of aluminum particle heating, melting, oxide layer growth, combustion reaction and collision agglomeration, and can deeply reveal the intrinsic mechanism of agglomeration affected by various factors such as pressure, combustion rate, particle size and oxidizing gas concentration.

[0025] 5. This invention realizes multi-physics coupling between the flow field, temperature field, component transport and discrete particle phase, and truly reflects the complex environment inside the combustion chamber. Attached Figure Description

[0026] Figure 1 This is a schematic diagram illustrating the physicochemical process of combustion agglomeration in aluminum-based solid propellants as an example.

[0027] Figure 2 The flowchart is shown as an example of the LBM simulation calculation for combustion agglomeration of aluminum-based solid propellants.

[0028] Figure 3 This is a schematic diagram of aluminum particle agglomeration during propellant combustion at a certain moment, calculated based on LBM.

[0029] Figure 4 This is a schematic diagram showing the changes in agglomeration size and oxide layer thickness over time during propellant combustion, based on LBM calculations.

[0030] Figure 5 The characteristic diameter D of the products during propellant combustion, calculated based on LBM. 50 D 90 D [4,3] Schematic diagram of the changes.

[0031] Figure 6 This is a schematic diagram of the agglomeration size distribution during propellant combustion, obtained based on DEM calculations. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0033] Part 1: Physicochemical Model of Propellant Combustion Agglomeration

[0034] 1. Propellant combustion

[0035] First, based on the physicochemical processes of aluminum-based solid propellant reactions, relevant incompressible Navier-Stokes macroscopic governing equations are established, including continuity equations, momentum equations, energy equations, and component transport equations.

[0036] In the continuity equations, the continuity equations for the pure gas phase region can be directly applied, where density and velocity are macroscopic quantities of the gas-phase mixture. In the two-phase flow region with solid particles, a two-fluid model is required, which includes both gas-phase and condensed-phase continuity equations.

[0037] In the energy equation, the chemical reaction source term is mainly based on the main chemical reactions in the propellant, while other source terms in the energy equation mainly involve latent heat of phase change, radiative and convective heat dissipation, and ignition heat source.

[0038] In the solid phase region, there are no convection or chemical reaction source terms, and the equations can be simplified to unsteady-state heat conduction. In the gas phase region, chemical reaction source terms are dominant. In the two-phase region, the main sources are: 1. convective heat transfer between the gas phase and the particulate phase; 2. chemical energy released by the combustion of aluminum particles; 3. thermal radiation from high-temperature alumina particles, which is one of the most important energy transfer mechanisms and needs to be included as a source term.

[0039] At the combustion surface, the energy equation needs to be transformed into boundary conditions for energy balance. On one side is the heat absorption of the solid as it heats up and the heat flow into the solid, and on the other side is the heat flow from the gas back to the surface and the net heat required for solid decomposition / phase change. The two reach equilibrium at the combustion surface.

[0040] Propellant boundary condition settings:

[0041] (1) The propellant is placed on the worktable, and the bottom can be set as an adiabatic boundary.

[0042] (2) There is no external heat flow input at the left and right boundaries of the propellant and it is in contact with the gas phase. Therefore, the left and right boundaries are set as convective radiation.

[0043] (3) The upper boundary of the propellant is ignited by an electric heating wire, resulting in heat input, convection and radiation heat exchange.

[0044] Furthermore, considering burnout, the net heat flow received by the burnout surface is used to heat the solid propellant from its initial temperature to the burnout surface temperature and to provide the energy required for its decomposition.

[0045] 2. Reaction of aluminum particles in the condensed phase zone

[0046] Considering that the energy required for the heating and phase change of aluminum particles mainly comes from radiative heat transfer, convection between the particles and the surrounding gas, and exothermic chemical reactions, the mass and energy conservation equations for aluminum particles are as follows:

[0047]

[0048] In the formula, m p v is the particle mass; t is time; v ox This represents the stoichiometric mass ratio of the oxidation gas required to consume one unit of aluminum in a chemical reaction. The mass conversion rate from liquid particles to solid oxides via surface chemical reactions; c p The specific heat capacity of aluminum particles is set as a temperature-dependent parameter; T p The temperature of the aluminum particles; , , , and These include convective and radiative heat transfer between the particles and the surrounding gas, as well as latent heat of fusion, exothermic chemical reactions of the aluminum particles, and latent heat of vaporization.

[0049] (1) The expression for the convective heat transfer between aluminum particles and the surrounding gas is:

[0050]

[0051] In the formula, D p The diameter of the aluminum particles is expressed in μ. g c represents the dynamic viscosity of the surrounding gas. pg Pr represents the specific heat capacity of the surrounding gas. g T represents the Prandtl number. g Nu represents the temperature of the surrounding gas. p Represents the Nusselt number, Re p Represents the Reynolds number, ρ g u represents the density of the surrounding gas. g u represents the velocity of the surrounding gas. p k represents the velocity of the particle. g This indicates the thermal conductivity of the surrounding gas.

[0052] (2) The expression for the radiative heat transfer between aluminum particles and the surrounding gas is:

[0053]

[0054] In the formula, ε p σ represents the emissivity of the particle, and σ is the Stefan-Boltzmann constant.

[0055] (3) The expression for the latent heat of fusion of aluminum particles is:

[0056]

[0057] In the formula, h melt For latent heat of fusion, The melting rate is denoted as .

[0058] (4) The heat of chemical reaction of aluminum particles is,

[0059]

[0060] In the formula, r p It is the radius of the particle after removing the oxide layer covering the particle surface generated during the reaction, A1 is the pre-exponential factor, and E is the particle radius. a It is the activation energy of a chemical reaction, R is the gas constant, and T is the activation energy. sls It is the temperature at the particle-solid-liquid interface, ox represents the type of oxidant, and h... ls It is the heat of a chemical reaction. The mass conversion rate from liquid particles to solid oxides via surface chemical reactions.

[0061] The chemical reaction kinetic model described above only considers the effect of temperature on the reaction rate. Higher particle temperatures can lead to excessively high reaction rates. Therefore, adding an oxidant diffusion model could be considered to provide a basis for estimating the maximum reaction rate.

[0062] (5) Considering the heat exchange effect caused by interphase mass heat transfer due to aluminum evaporation, the heat exchange effect of adding aluminum particles during evaporation should be taken into account.

[0063]

[0064] In the formula, h evap It is the latent heat of vaporization of aluminum particles. ρ is the evaporation rate; α is the ratio of the oxide surface area to the aluminum particle surface area, which is obtained by converting the calculated oxide mass into the volume covering the aluminum particle surface; Sh is the Sherwood number, ρ p D represents the density of particles. F B is the diffusion coefficient of fuel steam. M It is the Spaldin mass transfer number.

[0065] 3. Particle aggregation

[0066] The motion of each aluminum particle near the combustion surface is described by Newton's second law.

[0067]

[0068] F d It is the fluid drag force, calculated based on empirical formulas:

[0069] ,

[0070] In the formula, C D ρ f u f and u p These are the drag coefficient, fluid density, fluid velocity vector, and particle velocity vector, respectively. The drag coefficient is primarily determined by the Reynolds number Re.

[0071] F pp This refers to the interparticle interaction force, which considers both attractive and repulsive forces, and is calculated using the following formula:

[0072]

[0073] In the formula, K ik r is the stiffness factor characterizing the bond between contacting particles i and k. i and r kD is the position vector of particle i and particle k. i and D k denoted as , where is the diameter of particles i and k.

[0074] F b This represents the buoyant force exerted on the particle by the surrounding fluid, calculated using the following formula:

[0075] .

[0076] In the formula, ρ p g, β and T g These are particle density, gravitational acceleration, coefficient of volume expansion, and ambient temperature.

[0077] F thermo This is the thermophoretic force acting on the particle. Particles suspended in a gas are typically subjected to forces from gas molecules. When there is a temperature difference in the gas surrounding the particle, due to the difference in momentum transferred from gas molecules in the high and low temperature regions to the particle, the particle is typically subjected to a thermophoretic force pointing from the high temperature to the low temperature, calculated using the following formula:

[0078]

[0079] In the formula, μ is the viscosity coefficient of the surrounding fluid; K thermo It is the thermophoretic coefficient; It is the temperature gradient, which refers to the rate of change of fluid temperature in space.

[0080] The second part uses the LBM model to simulate and predict propellant combustion agglomeration.

[0081] Because the Lattice Boltzmann Model (LBM) possesses mesoscopic characteristics that fall between microscopic molecular dynamics models and macroscopic continuous models, it easily handles complex boundaries and enables dynamic tracking of all particles. This invention proposes using LBM to solve for velocity fields, temperature fields, and component transport, performing mesoscopic-scale numerical simulations to achieve quantitative calculation and prediction of solid propellant combustion processes.

[0082] As an example, this invention uses Matlab, Fortran, or Python programming software to write the main program and the function equation program. The function equation program is called in the main program to perform calculations. The function equation program is used to define various physical variables, construct a steady-state combustion agglomeration model, and compile various conservation equations. These may include, but are not limited to: aluminum particle oxide layer calculation, combustion surface temperature update, propellant-gas phase boundary adjustment, temperature field boundary conditions, component transport boundary conditions, agglomeration detection calculation, agglomeration particle merging calculation, particle size distribution statistical calculation, and particle size volume distribution calculation.

[0083] (a) Define the macroscopic state parameters or initial properties of aluminum particles, propellant, and environment.

[0084] Define the initial properties of aluminum particles, including initial temperature, particle size, quantity, density, specific heat capacity, thermal conductivity, thermal diffusivity, surface emissivity, activation energy, pre-exponential factor, heat of chemical reaction, melting temperature, latent heat of fusion, evaporation temperature, and latent heat of vaporization; define the initial properties of the propellant, including propellant size, composition, mass, density, and initial temperature, and set the propellant burn-off velocity, i.e., combustion rate, obtained experimentally; define the initial properties of the environment, including ambient temperature, fluid density, and physical properties of fluid composition.

[0085] The above parameter definitions can be found in the previous section "Physicochemical Model of Propellant Combustion Agglomeration (Part 1)".

[0086] (II) Constructing the computational domain for simulating combustion agglomeration of aluminum-based solid propellants

[0087] Referring to the description in "Physicochemical Model of Propellant Combustion Agglomeration in Part 1", a two-dimensional or three-dimensional computational domain for simulating the combustion agglomeration of aluminum-based solid propellants is constructed based on the propellant size and combustion chamber environment. An initial solid phase region, a condensed phase region, a gas phase flow region, and a dynamic combustion surface are set.

[0088] The specific details of this section will not be repeated here.

[0089] (III) Constructing and initializing the multiphysics model

[0090] Based on the Navier–Stokes macroscopic governing equations, momentum, energy, and component source terms are introduced into the LBM evolution equations. The macroscopic state parameters are then lattice-ized. In the lattice Boltzmann model, the evolution equations and equilibrium distribution functions of the velocity field particle distribution function, the temperature field particle distribution function, and the optional component transport particle distribution function are established respectively. Each particle distribution function is then initialized.

[0091] The LBM model requires the integration of a collision model (the core physics module of LBM) and boundary conditions on top of a Discrete Velocity Model (DVM). The Discrete Velocity Model is a crucial component of the LBM model; common DVM models include D2Q9, D3Q15, D3Q19, and D3Q27, each suitable for scenarios with varying accuracy and computational requirements. The following example uses D2Q9 (a two-dimensional nine-particle discrete velocity model) to simulate aluminum particle agglomeration during the combustion of aluminum-based solid propellants. However, this invention relates to physicochemical models and is also applicable to other LBM models such as D3Q19 (a three-dimensional nineteen-particle discrete velocity model). Furthermore, the evolution equations for the velocity field particle distribution function, temperature field particle distribution function, and component transport particle distribution function established in this embodiment all employ a single relaxation time (LBGK) model, where the relaxation time is correlated with the fluid's kinematic viscosity, thermal diffusivity, and mass diffusivity, respectively. A multi-relaxation model (MRT-BGK) can also be used to improve computational accuracy.

[0092] In the LBM aggregation simulation process, this invention employs the evolution equations of the velocity field particle distribution function, the temperature field particle distribution function, and the component transport particle distribution function to perform multi-physics field coupling calculations.

[0093] The velocity field particle distribution function is used to solve for the velocity and position distribution of aluminum particles. Boundary conditions are set as follows: a given combustion rate at the combustion surface with no tangential slip; an open boundary with no velocity gradient and given pressure at the gas-environment interface at the top of the computational domain; and periodic boundaries on the sides of the computational domain. The temperature field particle distribution function is used to solve for the temperature distribution and the forces acting on particles related to temperature and temperature gradients. Boundary conditions are set as follows: an isothermal boundary maintaining a constant high temperature at the combustion surface; a convection-radiation boundary at the gas-environment interface at the top of the computational domain; and periodic boundaries on the sides of the computational domain. The component transport particle distribution function is used to solve for the oxidant content in the condensed and gas phase regions. Boundary conditions are set as follows: mass fraction of oxidizing gases at the combustion surface; gas exchange between the top of the computational domain and the environment; a given oxidizing gas concentration; and periodic boundaries for component transport on the sides of the computational domain.

[0094] (iv) Achieving dynamic renewal of the combustion surface and particle release

[0095] Based on the set propellant burning rate, the position of the burning surface is updated step by step over time; when the burning surface moves back to the current position of the aluminum particle, the particle combustion release mechanism is triggered.

[0096] (v) Iteratively solving macroscopic fields using the lattice Boltzmann method

[0097] Within each time step, the particle distribution function of each model is calculated sequentially using collision and migration steps, and corresponding boundary conditions (such as combustion surface boundary, wall boundary, and open boundary) are applied; the velocity field, temperature field, and component transport within the computational domain are updated.

[0098] The core of the LBM model is the evolution of the Discrete Boltzmann equations, the most commonly used being the equations with the BGK collision model. The corresponding evolution equations using the velocity field particle distribution function are as follows:

[0099]

[0100] In the formula, x and e i , Δt, τ f f i eq and F i These are the grid point location, discrete velocity, grid time step, relaxation time, equilibrium distribution function, and discrete volume force term, respectively. i (x,t) is the particle distribution function at position x at time t along the i-th discrete velocity direction. i (x + e i Δt, t+Δt) is the particle distribution function after time Δt.

[0101] The equilibrium distribution function is defined as follows:

[0102]

[0103] In the formula, c is the weighting coefficient for direction i. s Let ρ be the lattice speed of sound, Δx be the lattice length, ρ be the density, and u be the velocity vector.

[0104] Discrete volume force F along the i-th discrete velocity direction i for,

[0105]

[0106] In the formula, F is the volume force term, which is the momentum source term involved in the macroscopic momentum equation.

[0107] Next, the evolution equation of the velocity field particle distribution function is decomposed into collision and migration steps and calculated sequentially.

[0108] Subsequently, the expressions for the macroscopic density and macroscopic velocity at each grid point are as follows:

[0109]

[0110] The particle distribution functions of velocity, temperature, and components can be modeled using a single relaxation time model or a multi-relaxation time model to improve computational accuracy. Their relaxation times are respectively related to the fluid kinematic viscosity, thermal diffusivity, and mass diffusivity.

[0111] Finally, the evolution equations for the velocity field, temperature field, and component transport particle distribution function are shown in equations (1)-(3), respectively:

[0112]

[0113] In the above formulas, f i (x + e i Δt, t+Δt), g i (x + e i Δt, t+Δt), g i (x + e i Δt, t+Δt) are the velocity field, temperature field, and particle distribution function related to component transport after time Δt, respectively; x, e i Δt and Δt represent the location of the grid point, the discrete velocity, and the grid time step, respectively; f i (x,t) 、g i (x,t), h i (x,t) are the velocity field particle distribution function, temperature field particle distribution function, and component transport particle distribution function at position x at time t, respectively, along the i-th discrete velocity direction; τ f τ g and τ h f represents the relaxation time associated with the velocity field, temperature field, and component transport, respectively; i eq (x,t), g i eq (x,t) and h i eq (x,t) represent the equilibrium distribution functions related to the velocity field, temperature field, and component transport, respectively; F i S T,i and h Y,i These represent discrete source terms for the velocity field, temperature field, and component transport, respectively.

[0114] Among them, the source term F of the velocity field i This refers to discrete volume force terms, including fluid drag force, interparticle interaction force, buoyancy, and thermophoretic force; the source term S of the temperature field. T,i Including the heat released from the combustion of aluminum particles and the ignition source of the heating wire; the source term for component transport h Y,i Consider oxidant consumption, fuel consumption, and the generation of combustion products.

[0115] (vi) Calculate the motion and forces acting on aluminum particles

[0116] It iterates through all aluminum particles entering the gas phase flow region, interpolates local flow field information (velocity, temperature, oxidizing gas concentration, etc.) based on their current position, calculates the drag force, buoyancy force, gravity, thermophoretic force and inter-particle interaction force on the particles, and updates the velocity and position of the particles in real time based on Newton's second law.

[0117] (vii) Simulated particle combustion reaction and oxide layer growth

[0118] For each aluminum particle in a combustion state, the reaction rate is calculated using the Arrhenius formula based on its local temperature and oxygen concentration. The activation energy and pre-exponential factor are set according to the kinetic research data of aluminum-oxygen combustion. The consumption of aluminum nuclei, the formation of alumina, and the dynamic growth of oxide layer thickness are simulated, and the particle diameter, mass, temperature, and combustion state are updated in real time.

[0119] Through the coupled iterative process of steps (v) to (vii) above, real-time coupled calculation of flow-temperature-composition-particle dynamics is achieved.

[0120] (viii) Detection and treatment of particulate agglomeration

[0121] The interaction force model between aluminum particles adopts a distance-based soft sphere model, defining the range of attractive and repulsive forces to simulate the physical mechanism leading to agglomeration. During the simulation of the aluminum particle agglomeration process, the contact between the aluminum particles needs to be tested continuously and periodically to determine whether the agglomeration conditions are met.

[0122] If the center-to-center distance between two aluminum particles in the simulation is less than or equal to the sum of their diameters, agglomeration is considered to have occurred. After agglomeration is detected, particle merging is performed using the following mass, momentum, and energy equations:

[0123]

[0124] In the formula, m new u new and T new These represent the particle mass, velocity, and temperature after agglomeration, respectively; m1, m2, u1, u2, T1, T2, c p1 and c p2 This represents the mass, velocity, temperature, and specific heat capacity of two particles that are about to agglomerate.

[0125] The above method is used to merge agglomerated particles into a new particle with equivalent mass, momentum, position, and size, and update its thermophysical parameters.

[0126] This invention physically couples the source terms of velocity, temperature, and component transport through LBM simulation, incorporating detailed source terms into the equations. It simultaneously simulates flow, temperature, component, and particle dynamics, considering their interactions. Therefore, it can achieve multi-field synergistic boundary condition settings by considering the mutual influence of physical quantities at the multi-physical coupling boundary in LBM, while simultaneously satisfying the velocity, temperature, and component boundary conditions. Based on this innovative approach, the simulation process of this invention considers the temperature field boundary conditions of convective-radiative heat transfer, as well as the boundary conditions of environmental component exchange, thus achieving more realistic environmental boundaries.

[0127] (ix) Data collection and result output

[0128] Throughout the simulation, data is recorded and statistically analyzed in real time. Using the collected computational data, the final particle size distribution, agglomerate formation process data, and macroscopic field visualization results are output at the end of the simulation or at a specified time. The collected simulation computational data refers to the data recorded and statistically analyzed in real time throughout the simulation, including: the number of active particles, agglomeration times, agglomerate size distribution, oxide layer thickness, combustion state information, and macroscopic field temperature and velocity data.

[0129] Finally, visualization software or modules implemented using Matlab were used for image post-processing to generate dynamic images of the aluminum particle agglomeration process and histograms of particle size distribution (including D). 50 D 90 D [4,3] Characteristic diameter), macroscopic field cloud map, and curves showing the changes of various parameters over time.

[0130] This application further performs simulation calculations using the traditional Discrete Element Method (DEM) and the LBM method respectively, and then compares and analyzes the results with those obtained in this application.

[0131] The DEM method can only obtain agglomerate size distribution data when calculating the agglomerate size distribution of propellant combustion, and cannot accurately describe the key physical states of aluminum particles at high temperatures, including the molten state of aluminum particles and the surface oxide layer (such as...). Figure 6(As shown). Agglomeration is the result of strong coupling between flow, heat transfer, combustion reaction, and particle dynamics. The DEM method itself is a mechanical framework. To couple the temperature field (which affects particle melting) and component transport (which affects combustion rate), additional and complex models are required, making integration difficult and computationally burdensome. In contrast, the LBM method in this application comprehensively considers the complex combustion and flow physicochemical processes. This application uses the fixed grid of the LBM method as the background grid for rapid and efficient agglomeration contact detection. At the same time, it can obtain effective changes in particle oxide layer thickness and output the temperature distribution and oxidizing gas distribution of the simulated region for the mechanism analysis of aluminum particle agglomeration during propellant combustion.

[0132] Although embodiments of the invention have been shown and described above, those skilled in the art will understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents. For example, the invention is not limited to aluminum particles; with appropriate modifications to the reaction kinetics and physical properties, it can also be used to simulate the agglomeration behavior of aluminum alloy fuel additives in solid propellants. The invention can also simulate propellant combustion agglomeration processes under a wider range of conditions by introducing more complex detailed gas-phase chemical reaction mechanisms, considering turbulence models (such as LES coupling), or particle fragmentation models.

[0133] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A lattice Boltzmann simulation method for predicting combustion agglomeration of aluminum-based solid propellants, characterized in that, It utilizes the LBM method for mesoscale numerical simulation to achieve quantitative calculation and prediction of solid propellant combustion processes; including: (1) Define the macroscopic state parameters or initial properties of aluminum particles, propellant and environment based on the physicochemical model of propellant combustion agglomeration; (2) Based on the propellant size and combustion chamber environment, construct a two-dimensional or three-dimensional computational domain for simulating the combustion agglomeration of aluminum-based solid propellants, and set the initial solid phase region, condensed phase region, gas phase flow region and dynamic combustion surface; (3) Establish the evolution equations of the particle distribution functions for velocity field, temperature field and component transport in the LBM model respectively; initialize each distribution function; (4) The position of the combustion surface is updated step by step over time according to the set propellant burning rate; when the combustion surface extends to the current position of the aluminum particle, the particle combustion release mechanism is triggered. (5) The macroscopic field is solved iteratively using the LBM method: In each time step, the distribution function of each model is calculated sequentially using collision and migration steps, and corresponding boundary conditions are applied; the velocity field, temperature field and component transport in the computational domain are updated; (6) For the combustion process of aluminum particles, calculate particle motion and force, simulate particle combustion reaction and oxide layer growth, and detect and treat particle agglomeration; through the above coupled iterative process, realize real-time coupled calculation of flow-temperature-composition-particle dynamics; (7) Using the computational data collected during the simulation process, output the final particle size distribution, aggregate formation process data and macroscopic field visualization results at the end of the simulation or at a specified time.

2. The method according to claim 1, characterized in that, In step (3), The initial properties of the aluminum particles include: initial temperature, particle size, quantity, density, specific heat capacity, thermal conductivity, thermal diffusivity, surface emissivity, activation energy, pre-exponential factor, heat of chemical reaction, melting temperature, latent heat of fusion, evaporation temperature, and latent heat of vaporization; the initial properties of the propellant include: propellant size, composition, mass, density, and initial temperature, and the propellant burn-out velocity obtained through testing is set; the initial environmental properties include: ambient temperature, fluid density, and physical parameters of fluid composition.

3. The method according to claim 1, characterized in that, In step (5), during the LBM aggregation simulation, the evolution equations of the velocity field particle distribution function, the temperature field particle distribution function, and the component transport particle distribution function are used to perform multi-physics field coupling calculations. Among them, the velocity field particle distribution function is used to solve the velocity and position distribution of aluminum particles. The boundary conditions are set as follows: the combustion surface is given a combustion rate and there is no tangential slip; the interface between the gas phase at the top of the computational domain and the environment is an open boundary with no velocity gradient and given pressure; and the sides of the computational domain are periodic boundaries. The temperature field particle distribution function is used to solve for the temperature distribution and the forces acting on particles related to temperature and temperature gradient. The boundary conditions are set as isothermal boundaries that maintain a constant high temperature on the combustion surface, convective-radiative boundaries at the top of the computational domain gas phase interface with the environment, and periodic boundaries on the sides of the computational domain. The component transport particle distribution function is used to solve for the oxidant content in the condensed and gas phase regions. The boundary conditions are set as the mass fraction of oxidizing gas on the combustion surface, gas exchange between the top of the computational domain and the environment, given the concentration of oxidizing gas, and the side of the computational domain is the periodic boundary of component transport.

4. The method according to claim 3, characterized in that, The evolution equations for the velocity field, temperature field, and component transport particle distribution function are shown in equations (1)-(3), respectively: ； In the above formulas, f i (x + e i Δt, t+Δt), g i (x + e i Δt, t+Δt), g i (x + e i Δt, t+Δt) are the velocity field, temperature field, and particle distribution function related to component transport after time Δt, respectively; x, e i Δt and Δt represent the location of the grid point, the discrete velocity, and the grid time step, respectively; f i (x,t) 、g i (x,t), h i (x,t) are the velocity field particle distribution function, temperature field particle distribution function, and component transport particle distribution function at position x at time t, respectively, along the i-th discrete velocity direction; τ f τ g and τ h f represents the relaxation time associated with the velocity field, temperature field, and component transport, respectively; i eq (x,t), g i eq (x,t) and h i eq (x,t) represent the equilibrium distribution functions related to the velocity field, temperature field, and component transport, respectively; F i S T,i and h Y,i These represent discrete source terms for the velocity field, temperature field, and component transport, respectively. Among them, the source term F of the velocity field i This refers to discrete volume force terms, including fluid drag force, interparticle interaction force, buoyancy, and thermophoretic force; the source term S of the temperature field. T,i Including the heat released from the combustion of aluminum particles and the ignition source of the heating wire; the source term for component transport h Y,i Consider oxidant consumption, fuel consumption, and the generation of combustion products.

5. The method according to claim 1, characterized in that, In step (6), the motion and forces of aluminum particles are calculated as follows: all aluminum particles entering the gas phase flow region are traversed, and local flow field information is obtained by interpolation based on their current position, including at least velocity, temperature and oxidizing gas concentration; the drag force, buoyancy, gravity, thermophoretic force and inter-particle interaction force of the particles are calculated, and the velocity and position of the particles are updated in real time.

6. The method according to claim 1, characterized in that, In step (6), the particle combustion reaction and oxide layer growth are simulated in the following manner: for each aluminum particle in the combustion state, the reaction rate is calculated by the Arrhenius formula based on its local temperature and oxygen concentration, and its activation energy and pre-exponential factor are set according to the kinetic research data of aluminum-oxygen combustion; the consumption of aluminum cores, the generation of aluminum oxide and the dynamic growth of oxide layer thickness are simulated, and the particle diameter, mass, temperature and combustion state are updated in real time.

7. The method according to claim 6, characterized in that, An oxidant diffusion model is introduced when simulating particulate combustion reaction to provide a basis for estimating the maximum reaction rate.

8. The method according to claim 1, characterized in that, In step (6), particle agglomeration is detected and processed in the following manner: the distance between particles is periodically detected; when the distance between two or more molten particles is less than the sum of their radii, agglomeration is determined to have occurred; the agglomerated particles are merged and calculated into a new particle with equivalent mass, momentum, position and size, and its thermophysical parameters are updated.

9. The method according to claim 8, characterized in that, After determining that agglomeration has occurred, the following mass equation, momentum equation, and energy equation are used to calculate particle aggregation: ； In the formula, m new u new and T new These represent the particle mass, velocity, and temperature after agglomeration, respectively; m1, m2, u1, u2, T1, T2, c p1 and c p2 This represents the mass, velocity, temperature, and specific heat capacity of two particles that are about to agglomerate.

10. The method according to claim 1, characterized in that, In step (6), the collected simulation process calculation data refers to the data recorded and statistically analyzed in real time throughout the simulation process, including: the number of active particles, the number of aggregations, the size distribution of aggregates, the thickness of the oxide layer, and the data on macroscopic field temperature, velocity, and oxidizing gas distribution.

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