Integrated simulation method and system for non-impact ignition and combustion reaction of solid propellant

Abstract

This invention discloses an integrated simulation method and system for non-impact ignition and combustion-explosion reactions of solid propellants, belonging to the field of aerospace propulsion and solid rocket motor safety assessment technology. To address the problem of the inability to achieve integrated simulation of the entire process from local ignition triggered by fragment impact to overall combustion-explosion, this invention constructs an ignition model to calculate flow stress, plastic strain, pressure, heat transfer, and thermal decomposition reactions during fragment intrusion. An adaptive finite element-smooth particle fluid dynamics coupling algorithm is employed to convert failed elements into further mechanical and thermal calculations. The process from fragment intrusion, structural failure, hot spot formation to ignition is simulated. Based on the ignition threshold judgment, the recorded ignition parameters are used as initial conditions, and the combustion-explosion model is used to simulate subsequent combustion wave propagation, shell rupture, and other evolutionary processes. This invention can simulate the entire chain of physical processes with high confidence and is mainly used for the safety design and assessment of solid rocket motors.

Description

Technical Field

[0001] This invention relates to the field of aerospace propulsion and solid rocket motor safety assessment technology. More specifically, this invention relates to an integrated simulation method and system for non-impact ignition and combustion-detonation reactions of solid propellants. Background Technology

[0002] The ignition and combustion-detonation response of solid propellant charges under impact loads is a key issue in their safety assessment, directly affecting the survivability of solid rocket motors under unexpected stimuli. Fragment impact is a typical non-impact ignition scenario, involving multi-physics coupled processes such as fragment intrusion, structural failure, frictional heat generation, heat conduction, and chemical reaction evolution. Numerical simulation is an important tool for studying this complex process, but existing methods struggle to accurately predict the entire process from local ignition to overall combustion-detonation.

[0003] Currently, numerical models used to evaluate the ignition and combustion-detonation response of energetic materials mainly include the following categories: (1) Phenomenological macroscopic ignition criteria, such as the HERMES criterion (Reaugh JE, White BW, Curtis JP, et al. A computer model to study the response of energetic materials to a range of dynamic loads[J]. Propellants, Explosives, Pyrotechnics, 2018, 43(7):703-720.) and the Browning criterion (Browning R V. Microstructural model of mechanical initiation of energetic materials[C]. AIPConference Proceedings. AIP, 1996,370(1): 405-408.). These methods integrate or weight a function of macroscopic mechanical parameters such as pressure and shear strain rate, and determine that ignition has occurred when the integral or weighted value exceeds an empirical threshold. However, such criteria can only determine whether ignition has occurred, and cannot describe the growth of chemical reactions and the evolution of combustion and explosion after ignition. Moreover, their parameters are heavily dependent on the calibration of specific experimental configurations, resulting in poor universality.

[0004] (2) Impact-initiated detonation models, such as the Lee-Tarver ignition growth model. This type of model is based on the physical mechanism of shock wave compression initiating hot spots and then developing into detonation, and is suitable for describing the detonation process under high-speed impact. However, in many actual scenarios of fragment impact charges, ignition is mainly dominated by mechanical stimulation and heat generation mechanisms such as friction and shearing generated by fragments and debris intrusion (Wang Xin, Wu Yanqing, Yang Kun, et al. Experimental study on the deflagration mechanism of high-energy propellant charge impacted by fragments [J]. Acta Ordnance et al., 2025, 46(03): 147-160.), which belongs to non-impact reaction initiation. Impact-initiated detonation models cannot describe this kind of force-thermal coupling process, so when simulating non-impact ignition and subsequent combustion and detonation response, their prediction results deviate from the physical facts.

[0005] (3) For numerical simulation methods of structural failure, Lagrange finite element meshes are usually used to simulate structural deformation, and the element deletion method is used to handle material failure. This method has inherent defects: after the element is deleted, the subsequent mechanical contact and heat exchange between the material (especially the fragments formed after the shell breaks) and the surrounding propellant are forcibly interrupted, resulting in the complete loss of the real physical process of the fragments continuing to invade, squeeze, and rub against the propellant and make a continuous heating contribution to ignition; at the same time, the element deletion directly removes the element mass and energy, causing the system mass and energy to be non-conserved, and is prone to numerical oscillation.

[0006] In addition, researchers have conducted numerical simulation studies on the impact initiation problem of solid rocket motors impacted by fragments. Wang et al. (Wang ZJ, Qiang HF, Geng B, et al. Numerical simulation offragment impacting solid rocket motors[J]. AIP Advances, 2022, 12: 055204.) used the critical energy criterion and equivalent analysis method, combined with the Johnson-Cook material model, Grünesen equation of state and Lee-Tarver ignition growth model, to simulate the impact response of the engine under different conditions. However, this method still belongs to the category of impact initiation and does not involve non-impact ignition mechanisms. The HERMES model developed by Reaugh et al. (Reaugh JE, White BW, Curtis JP, et al. A computer model to study the response of energetic materials to a range of dynamic loads[J]. Propellants, Explosives, Pyrotechnics, 2018, 43(7):703-720.) includes modules such as partial constitutive model, yield criterion, equation of state, ignition criterion and reaction rate equation, which can simulate the structural-level charge response. However, its two pressure balance iterations and discontinuous changes in yield strength lead to high computational cost and difficulty in convergence. Wu Song (Wu Song. Numerical simulation study on thermal response behavior of explosive-containing structures under fire environment[D]. China Academy of Engineering Physics, 2014.) proposed a sequential calculation method for the combustion process. First, Fluent is used to calculate the temperature field and ignition position of the explosive under fire environment. Then, the region is equivalent to the ignition charge, and the deflagration model in LS-DYNA is used to simulate the rapid response after ignition. This method is applicable to the burning scenario under thermal stimulation, but it does not consider the contribution of mechanical deformation, frictional heat generation and structural failure under fragment impact to ignition, and the physical mechanisms between the ignition model and the subsequent reaction model are mismatched.

[0007] In summary, existing numerical simulation methods suffer from several disconnected physical processes when dealing with the non-impact ignition and subsequent combustion-explosion response of solid propellant charges impacted by fragments: phenomenological ignition criteria cannot describe the post-ignition combustion-explosion evolution; impact initiation models are not applicable to non-impact ignition mechanisms; the element deletion method ignores the continuous contribution of failed fragments to ignition; and there is a lack of effective linkage between ignition and combustion-explosion models, making it difficult to achieve integrated simulation of the entire chain of physical processes from fragment intrusion, structural failure, hotspot formation to local ignition, combustion propagation, pressure increase, and ultimately shell rupture. Therefore, the prediction accuracy for the ignition hazard and combustion-explosion intensity of solid propellant charges under non-impact stimuli is insufficient, failing to provide a high-confidence simulation analysis tool for the safety design of solid rocket motors. Summary of the Invention

[0008] One object of the present invention is to solve at least the above-mentioned problems and to provide at least the advantages that will be described later.

[0009] To achieve these objectives and other advantages according to the present invention, an integrated simulation method for non-impact ignition and combustion-detonation reaction of solid propellants is provided, comprising: S1. Obtain mechanical property parameters, failure parameters, friction parameters, thermophysical parameters, equation of state parameters, and kinetic parameters of thermal decomposition reaction of energetic components; S2. Based on mechanical performance parameters, friction parameters, thermophysical parameters, and thermal decomposition reaction kinetic parameters, a force-thermal-chemical coupled ignition model is constructed. The flow stress and plastic strain of the propellant during fragment intrusion are calculated according to the strain rate-dependent and temperature-dependent yield criteria. The propellant pressure is calculated based on the Mie-Grüneisen equation of state. The heat generated by plastic work and heat generation within the propellant and the heat generated by friction at the fragment-propellant interface are calculated using the plastic work heat generation formula and the friction heat generation formula, respectively. The heat transfer within the propellant and between the fragment and the propellant is calculated using Fourier's law of thermal conductivity. The reaction rate and exothermic rate of the thermal decomposition of the energetic components are calculated based on the Arrhenius equation. S3. Based on the failure parameters, an adaptive finite element-smooth particle fluid dynamics coupling algorithm is used to simulate the structural failure process of the shell and propellant. When the finite element element reaches the preset failure criterion, it is converted into a smooth particle fluid dynamics particle. The converted particle retains the mass, momentum, internal energy and temperature of the original element and continues to perform contact force and heat conduction calculations with the surrounding finite element elements or particles. S4. Using explicit dynamic numerical methods, based on the ignition model and particle state and contact information, the entire process from fragment intrusion, structural failure, hot spot formation to ignition is simulated using a force-thermal-chemical coupling method to obtain the temperature field distribution and reactivity distribution of the propellant. S5. Determine whether the propellant ignites in a local area based on the preset ignition threshold. If no ignition occurs, terminate the simulation. If ignition occurs, record the ignition time, ignition location, ignition area size, ignition area pressure, and ignition area reactivity, and use the recorded data as the initial conditions for the combustion and explosion stage simulation. S6. Based on the parameters of the equation of state and the combustion and explosion reaction rate parameters, a propellant combustion and explosion model is constructed, which includes the equation of state of unreacted substances, the equation of state of reaction products, the reaction rate equation, and the mixing rule; the ignition region in the initial conditions is equivalent to an ignition source with initial pressure and initial reactivity, and the combustion and explosion model is used to simulate the evolution process of combustion wave propagation, pressure increase, shell deformation, and shell rupture after ignition, until the reaction is complete or the shell is completely destroyed. S7 outputs the pressure time history curve, shell deformation and rupture morphology, and reactivity evolution data obtained from the combustion and explosion stage simulation.

[0010] Preferably, the strain rate-dependent and temperature-dependent yield criterion adopts a flow stress expression, which includes a strain hardening term, a strain rate hardening term, and a thermal softening term; the parameters in the flow stress expression include the initial yield strength at the reference strain rate, the hardening modulus, the hardening exponent, the strain rate sensitivity coefficient, the reference temperature, and the melting temperature.

[0011] Preferably, the friction coefficient in the friction heat generation formula varies with the relative sliding speed of the contact surfaces and is determined by the static friction coefficient, dynamic friction coefficient, and attenuation coefficient. The total heat generated by friction is distributed based on the thermal conductivity, density, and specific heat of the materials on both sides of the contact interface. The thermal inertia is determined by the product of the square roots of the thermal conductivity, density, and specific heat. The heat distribution coefficients flow into the fragments and the propellant, respectively.

[0012] Preferably, a multi-step series reaction kinetic model is adopted for the thermal decomposition process of the energetic components in the propellant, wherein the energetic components include RDX and / or ammonium perchlorate; wherein the thermal decomposition of RDX adopts a three-step series reaction model, the reaction rate of each step is expressed by the Arrhenius equation, the reaction heat of each step is a constant, and the parameters in the Arrhenius equation include the pre-exponential factor, activation energy and gas constant.

[0013] Preferably, the adaptive finite element-smooth particle hydrodynamic coupling algorithm automatically transforms failed finite element elements into smooth particle hydrodynamic particles through a preset element transformation criterion; the element transformation criterion adopts the Johnson-Cook failure model; the transformed particles retain the mass, momentum, internal energy and temperature of the original element, and participate in subsequent contact force calculation and heat conduction calculation.

[0014] Preferably, the equations of state for both unreacted materials and reaction products in the propellant combustion-detonation model adopt the Jones-Wilkins-Li equation of state. The parameters in the Jones-Wilkins-Li equation of state include initial density, sound velocity, Grignard coefficient, and several fitting constants. The reaction rate equation adopts a pressure-dependent exponential form, expressed as: In the formula, ∂F / ∂t represents the reaction rate, t represents time, F=0 indicates no reaction, F=1 indicates complete reaction, F0 is the initial combustion fraction, P0 is the initial pressure, and Z1, y, x, Z2, ω, u, r, s, and F are also present. limit1 and F limit2 All are constants, calibrated through propellant thermal decomposition experiments, sealed burner experiments, and standard combustion and explosion experiments. Z1 and Z2 are reaction rate coefficients, y and x are reactivity indices of the first reaction stage, ω is the pressure index of the first stage, u and r are the reactivity indices of the second reaction stage, and s is the pressure index of the second stage; F limit1 and F limit2 This marks the boundary between different stages of the reaction. The mixing principle assumes pressure equilibrium, with the relative volumes of unreacted substances and reaction products weighted by reactivity.

[0015] Preferably, the preset ignition threshold is the critical detonation temperature at which the local temperature of the propellant reaches the thermal decomposition of its RDX components, or the local reactivity reaches the preset reactivity threshold.

[0016] An integrated simulation system for non-impact ignition and combustion-detonation reaction of solid propellants is provided for the above-mentioned method, comprising: One or more processors; Memory, used to store one or more computer programs; When the one or more computer programs are executed by the one or more processors, the one or more processors implement the above-described integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants.

[0017] The present invention has at least the following beneficial effects: First, this invention, by constructing a fully coupled force-thermal-chemical ignition model and employing an adaptive finite element-smooth particle fluid dynamics coupling algorithm to handle structural failure, achieves for the first time an integrated simulation of the entire chain of physical processes, from fragment intrusion, structural failure, hot spot formation to local ignition, combustion propagation, pressure increase, and ultimately shell rupture. This method overcomes the technical bottlenecks of traditional phenomenological ignition criteria, which can only determine ignition but cannot describe subsequent reaction evolution; the inapplicability of impact-induced detonation models to non-impact ignition mechanisms; and the interruption of force-heat exchange caused by element deletion methods. It provides a high-confidence simulation analysis tool for predicting the non-impact ignition hazards and combustion-explosion intensity of solid propellant charges under fragment impact, offering a reliable numerical simulation method for the safety design of solid rocket engines.

[0018] Secondly, this invention addresses the technical shortcomings of existing coupled ignition models, such as incomplete constitutive mathematical forms and unclear parameter systems, by clearly defining the specific composition and parameter system of the strain rate-dependent and temperature-dependent yield criterion. This yield criterion fully encompasses strain hardening, strain rate hardening, and thermal softening terms, and clarifies key parameters such as initial yield strength, hardening modulus, hardening exponent, strain rate sensitivity coefficient, reference temperature, and melting temperature. This enables the ignition model to accurately describe the simultaneous strain hardening, strain rate hardening, and thermal softening behavior caused by adiabatic temperature rise during propellant fragment intrusion under different impact velocities, ambient temperatures, and propellant formulations. This significantly improves the calculation accuracy of flow stress, plastic strain accumulation, and plastic heat generation rate, thereby ensuring the accuracy of predicting the hotspot formation time and ignition location.

[0019] Third, this invention addresses the problem of insufficient confidence in simulating hotspot formation caused by the simplistic value of the friction coefficient and empirical approach to heat distribution in existing friction-generating models by defining the variation law of the friction coefficient and the heat distribution mechanism in the friction-generating formula. This technical solution expresses the friction coefficient as a function of the relative sliding velocity of the contact surfaces, introducing static friction coefficient, dynamic friction coefficient, and attenuation coefficient for a complete description, realistically reflecting the dynamic changes in interfacial shear force and frictional power during fragment intrusion. Simultaneously, it establishes a quantitative correlation between the distribution ratio of total frictional heat and the thermal conductivity, density, and specific heat of the materials on both sides of the interface, enabling accurate calculation of the heat share entering the propellant side based on actual material properties. This solution allows the ignition model to realistically reproduce the contribution of frictional heating to the non-impact ignition of the propellant during fragment intrusion, significantly improving the prediction accuracy of the local temperature rise rate and the timing of hotspot formation.

[0020] Fourth, this invention addresses the problem of overly simplified reaction pathways in existing ignition models, which fail to characterize multi-step reaction kinetics, by employing a multi-step series reaction kinetic model for the thermal decomposition process of energetic components. Specifically, this technical solution decomposes the actual thermal decomposition path of RDX into a three-step series reaction involving carbon-nitrogen bond breaking, ring structure fragmentation, intermediate product transformation, and the formation of stable gaseous products. The reaction rate of each step is expressed by the Arrhenius equation, and the heat of reaction is an independent constant. This model can realistically reproduce the complete chemical evolution sequence of RDX crystals from initial endothermic decomposition and intermediate product formation to final violent exothermic reaction, accurately reflecting the inhibitory effect of the endothermic step on ignition delay. It significantly improves the simulation accuracy of ignition delay time, exothermic reaction rate, critical ignition temperature, and pre-ignition reaction accumulation process of propellants under fragment impact heating conditions.

[0021] Fifth, this invention solves the technical problems of interrupted force and heat exchange, non-conservation of mass and energy, and loss of ignition contribution caused by traditional element deletion methods by employing an adaptive finite element-smooth particle fluid dynamics coupling algorithm and defining the element conversion criteria and the retention and interaction mechanism of the converted particles' properties. When an element reaches the failure criterion, the algorithm automatically converts it into a smooth particle fluid dynamics particle. The converted particle fully retains the original element's mass, momentum, internal energy, and temperature, and continues to perform contact force calculations and heat conduction calculations with surrounding elements or particles. This technical solution ensures that the ignition contribution of the failed shell fragments during propellant intrusion, including friction, compression, and heat conduction, is fully preserved, fundamentally guaranteeing the conservation of system mass and energy. This allows the ignition model to realistically reproduce the continuous frictional heating contribution of the failed fragments to non-impact ignition, significantly improving the simulation confidence of the hot spot formation mechanism and ignition timing throughout the fragment impact process.

[0022] Sixth, this invention solves the technical problems of existing combustion-explosion models' inapplicability in non-impact ignition scenarios, lack of model parameter system, and disconnect between ignition and combustion-explosion models by fully defining the forms of the equations of state, reaction rate equations, and mixing rules for unreacted substances and reaction products in the propellant combustion-explosion model. This technical solution uses the Jones-Wilkins-Li equation of state to describe unreacted substances and reaction products, and its parameters are directly correlated with data from propellant impact compression experiments and isentropic expansion experiments. The reaction rate equation adopts a pressure-related exponential form, directly corresponding to the pressure-time history curves and burning rate-pressure exponents measured in propellant combustion-explosion experiments, and can be independently calibrated through standard experiments. Combined with ignition parameters recorded during the ignition stage as initial conditions, it achieves a physical mechanism match and a closed-loop connection in data transfer between the ignition model and the combustion-explosion model, enabling the sequential calculation method to realistically reproduce the entire chain of physical processes from local ignition to overall combustion-explosion evolution.

[0023] Seventh, this invention addresses the technical shortcomings of existing ignition determination methods by directly limiting the preset ignition threshold to the critical decomposition temperature of the propellant's local temperature at the point of thermal decomposition of its RDX components, or the local reactivity reaching a preset reactivity threshold. This resolves the ambiguity of the physical meaning of phenomenological indirect criteria, the strong dependence on experimental calibration, and the mismatch between the ignition threshold and the calculated state of the ignition model. This technical solution transforms the ignition criterion from an indirect empirical criterion based on mechanical parameters to an intrinsic criterion based on thermodynamic and chemical reaction states. The physical meaning of the ignition threshold is clear: the critical decomposition temperature is an inherent thermal decomposition characteristic parameter of RDX materials, and the reactivity threshold can be directly calibrated based on the exothermic acceleration inflection point determined by thermal decomposition experiments. The ignition threshold and the temperature and reactivity fields output by the ignition model are completely consistent in physical dimension, achieving seamless connection from process quantity calculation to result determination. Furthermore, through the reactivity threshold determination path, the ignition determination result can output a quantitative reactivity value as the initial input for subsequent combustion and explosion models, resolving the state transmission breakpoint problem caused by the mismatch of criterion types between the ignition model and the combustion and explosion model.

[0024] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the sequential calculation method for the ignition-ignition-explosion response of a solid propellant charge impacted by a fragmentation, provided in an embodiment of the present invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to examples, so that those skilled in the art can implement it based on the description.

[0027] It should be noted that, unless otherwise specified, the experimental methods described in the following embodiments are conventional methods, and the reagents and materials mentioned are commercially available. The embodiments of this invention use GRT propellant as an example. GRT propellant is a composite solid propellant, whose typical components include RDX, ammonium perchlorate (AP), and binders. This propellant has good energy characteristics and mechanical properties, and is a widely used type of propellant in solid rocket engines. The method described in this invention is also applicable to other solid propellant propellants with similar force-thermal-chemical coupling response characteristics.

[0028] This invention provides a sequential calculation method for the ignition-ignition-detonation response of GRT propellant charges impacted by fragments, such as... Figure 1 As shown, it mainly includes three stages: parameter determination and model establishment, ignition stage calculation, and combustion and explosion stage calculation.

[0029] Step 1: Parameter Acquisition The parameters required for the model are obtained through five types of experiments, including: mechanical property parameters (such as initial yield strength, hardening modulus, hardening index, strain rate sensitivity coefficient, reference temperature, melting temperature at reference strain rate), failure parameters (such as Johnson-Cook failure model parameters), friction parameters (static friction coefficient, dynamic friction coefficient, attenuation coefficient), thermophysical parameters (thermal conductivity, density, specific heat), equation of state parameters (initial density, sound velocity, Grignard coefficient, impact Hugoniot parameter, JWL equation of state fitting constant), and kinetic parameters of thermal decomposition reaction of energetic components (pre-exponential factor, activation energy, heat of reaction, gas constant).

[0030] Step 2: Construct a fully coupled force-thermal-chemical ignition model This model is the core of simulating non-impact ignition during fragment intrusion. It comprehensively considers mechanical deformation, heat generation and conduction, and chemical reactions, and consists of the following sub-models: (1) Stress calculation submodule The viscoplastic deformation and strain softening behavior of the propellant are described using strain rate-dependent and temperature-dependent yield criteria. The expression for the flow stress is as follows: In the formula, For reference strain rate =10 s -1 The initial yield strength corresponding to the time; The equivalent plastic strain is given by: h and n, representing the hardening modulus and hardening exponent, respectively; C is the strain rate coefficient; and T is the current temperature, determined by the temperature rise calculation formula. For reference temperature, and This is the melting temperature.

[0031] (2) Pressure Calculation Submodule The pressure-volume deformation relationship of GRT propellant is described by the Mie-Grüneisen equation of state, as follows: In the formula, The initial density; Here, represents the Grüneisen coefficient; c0 and s are the impact Hugoniot parameters; e0 is the specific internal energy. Let v be the compression ratio, and v0 be the instantaneous specific volume and the initial specific volume, respectively.

[0032] (3) Temperature rise calculation submodule In temperature rise calculations, the sources of heat generated by non-chemical reactions include heat generated by mechanical deformation, heat generated by friction, and heat conduction.

[0033] A. Mechanical deformation generates heat Under the stimulation of fragments, some of the fragment's kinetic energy is converted into localized propellant heat energy in the form of plastic work. The formula for calculating the heat generated by plastic work is: In the formula, Plastic heat (plastic heat generation rate); It represents the percentage of work converted to heat, with a value ranging from 0.85 to 0.95. Equivalent stress; It represents the equivalent plastic strain rate.

[0034] B. Heat generated by friction When fragments (tungsten alloy balls / hot debris) come into contact with the propellant, they move at a relative velocity v rel Relative movement occurs. The total heat generated by friction is: In the formula, Q f For the total heat generated by friction; μ c F is the coefficient of friction; N For the normal pressure of the interacting surfaces; L rel This represents relative displacement.

[0035] friction coefficient μ c Depending on the relative sliding speed, the calculation formula is: In the formula, μ s and μ d These are the coefficients of dynamic friction and static friction, respectively; d c This is the attenuation coefficient.

[0036] The total heat Q generated by friction f It splits into two parts, which flow into two objects that are in contact with each other: The distribution coefficient is determined by the thermophysical properties of the materials on both sides of the contact interface, and the formula for the distribution of frictional heat between the two sliding interfaces is: In the formula, η f λ1 and λ2 are the thermal conductivity of the two materials, respectively; ρ1 and ρ2 are the densities of the two materials, respectively; C v1 C v2 The specific heats are for the two materials respectively.

[0037] C Thermal conduction When fragments come into contact with propellant, the thermal conductivity between the contact surfaces is determined by the contact gap: When fragments (tungsten alloy balls / hot fragments) come into contact with propellant, the heat generated by the impact friction of the former is transferred to the propellant, and the thermal conductivity between the contact surfaces is determined by the contact gap l. gap Decide: In the formula, l min l max These represent the minimum and maximum contact intervals between the two materials, respectively; λ0 and λ... cond Let be the thermal conductivity of the two materials, and let be the thermal conductivity of the material itself.

[0038] (4) Ignition reaction calculation submodule GRT propellant, as a composite solid propellant, has an overall energy density equivalent to or higher than that of high-energy explosives. However, its energy release rate is limited by certain factors. The propellant / binder / plasticizer needs to evaporate and vaporize first, and then combine with oxidant gaseous products to release potential chemical energy. Therefore, the reaction sequence of the energetic components in GRT propellant is: RDX → AP → other components.

[0039] A three-step series reaction kinetic model is adopted for the thermal decomposition process of RDX crystals: Step 1: CN bonds break and other rings break, forming H2C=N-NO2. This process absorbs heat and is the slowest. Step 2: H2C=N-NO2 is converted into CH2O, N2O or HCN, HNO2, generating NO2 free radicals. This process is slightly exothermic. Step 3: CH2O + N2O (or HCN + HNO2) is converted into the stable gaseous product H2O. This process is exothermic.

[0040] Therefore, the exothermic chemical reaction of RDX crystals can be represented by the Arrhenius equation. In the formula, N1-N3 represent the mole fractions of the first to third steps of the reaction; Q R1 -Q R3 Z is the heat of reaction for the first to third steps of the reaction; R1 -Z R3 E is the pre-exponential factor (also called the frequency factor); R1 -E R3 R is the activation energy; R is the gas constant (8.314 J / mol·K). -1 ); T is the temperature.

[0041] (5) Overall temperature rise calculation Taking into account the contributions of the various heat sources mentioned above, the overall temperature rise T of the GRT propellant is...bulk Governed by the following energy conservation equation: In the formula, C vp For specific heat, the first term on the right is the heat conduction term, K. cond For thermal conductivity, ∇ 2 For Laplace notation; , and These represent the heating power caused by viscoplasticity, friction effect, and fragment thermal conduction effect, respectively, with ϑ representing the percentage of heat generation converted; ξ R This represents the percentage of heat generated by ignition.

[0042] Step 3: Structural Failure Simulation To address the issues of interrupted force and heat exchange and non-conservation of mass caused by "element deletion" in the traditional Lagrange method, this invention employs an adaptive finite element-smooth particle hydrodynamics (SPH) coupling algorithm to simulate the structural failure process of the shell and propellant. When a finite element reaches a preset failure criterion, the corresponding finite element is automatically converted into a SPH particle. The element conversion criterion adopts the Johnson-Cook failure model. The converted particle retains the original element's mass, momentum, internal energy, and temperature, and continues to perform contact force calculations and heat conduction calculations with surrounding finite element elements or other particles. This algorithm is implemented using the "DEFINE ADAPTIVE SOLID TO SPH" keyword in the LS-DYNA software.

[0043] When a shell or propellant unit meets the failure criteria (such as the Johnson-Cook failure model), it is not deleted, but automatically converted into a smooth particle hydrodynamic (SPH) particle.

[0044] The converted SPH particles continue to engage in mechanical contact and thermal coupling with surrounding FEM elements or other SPH particles. This ensures that the ignition contributions of the failed shell fragments, such as friction, compression, and thermal conduction, are fully preserved during propellant intrusion, thus more realistically simulating non-impact ignition mechanisms.

[0045] Step 4: Ignition process simulation Using an explicit dynamic numerical method, based on the ignition model constructed in step 2 and the particle state and contact information output in step 3, a force-thermal-chemical coupling simulation was performed on the entire process of the fragment from propellant intrusion, structural failure, hot spot formation to ignition, to obtain the temperature field distribution and reactivity distribution of the propellant.

[0046] Step 5: Ignition Determination and Data Transmission The simulation determines whether ignition occurs in a localized area of ​​the propellant based on a preset ignition threshold. The ignition threshold is defined as the local propellant temperature reaching the critical ignition temperature for the thermal decomposition of its RDX components, or the local reactivity reaching a preset reactivity threshold. If ignition does not occur, the simulation terminates; if ignition occurs, the ignition time, ignition location, ignition area size, ignition area pressure, and ignition area reactivity are recorded, and the recorded data are used as the initial conditions for the combustion-detonation stage simulation. The recorded ignition area pressure is not an independent variable, but rather a macroscopic result naturally calculated at the end of the ignition stage from the local high temperature (from plastic work, frictional heat, and exothermic chemical reactions) and reactivity using the Mie-Grüneisen equation of state in a fully coupled force-heat-chemical model. This pressure comprehensively reflects the contribution of the hotspot's high temperature, reactivity, and surrounding mechanical constraints to the pressure.

[0047] Step 6: Construction of combustion and explosion model and simulation of combustion and explosion evolution The combustion-explosion reaction evolution stage is calculated using a combustion-explosion model.

[0048] Unlike the shock wave-dominated SDT process, combustion involving fragment intrusion is a reaction evolution following non-shock ignition. Therefore, the I&G model using critical compressibility as the ignition term is unsuitable for describing this physical process. This invention employs the EOS PROPELLANT DEFLAGRATION (or simply deflagration model) propellant deflagration model provided in LS-DYNA to describe the combustion reaction evolution of GRT propellant charges. Based on the equation of state parameters and the combustion-deflagration reaction rate parameters, a propellant combustion-deflagration model is constructed. The model includes equations of state for unreacted materials, equations of state for reaction products, reaction rate equations, and mixing rules. It is described using a deflagration model suitable for pressure-driven combustion.

[0049] The equation of state for unreacted GRT propellants adopts the JWL equation of state: In the formula, P u It is the pressure of unreacted propellant; V u and T u R1, R2, R3, R5, and R6 are constants, and FRER is the remaining volume of unreacted propellant.

[0050] The equation of state for the GRT propellant reaction products also adopts the JWL equation of state: In the formula, P p It is the pressure of the reaction products; V p and T pis the relative volume and temperature of the propellant reaction products. A, B, XP1, XP2, and G are constants, and CCRIT is the residual volume of the propellant reaction products.

[0051] As the reaction proceeds, assuming that the unreacted substances and reaction products are in thermal and pressure equilibrium (T u = T p = T, P u = P p = P), the relative volume is weighted average by the degree of reaction: In the formula, F is the combustion fraction (also known as the degree of reaction), F = 0 indicates no reaction, and F = 1 indicates complete reaction.

[0052] The reaction rate equation of the deflagration model adopts the pressure-dependent exponential form: In the formula, ∂F / ∂t is the reaction rate (t is time); F = 0 indicates no reaction, and F = 1 indicates complete reaction. F0 is the initial combustion fraction, and P0 is the initial pressure. Z1, y, x, Z2, ω, u, r, s, F limit1 and F limit2 are all constants, which can be calibrated through propellant thermal decomposition experiments, closed bomb experiments, and standard deflagration experiments. Z1 and Z2 are reaction rate coefficients, characterizing the reaction rate at different reaction stages; y and x are the reaction degree exponents in the first reaction stage (0 < F < F limit1 ), respectively controlling the influence of the remaining amount of unreacted substances (1 - F) and the amount of reacted substances (F) on the reaction rate; ω is the pressure exponent in this stage, reflecting the driving intensity of pressure on the reaction rate; u and r are the reaction degree exponents in the second reaction stage (F limit2 < F < 1); s is the pressure exponent in this stage; F limit1 and F limit2 are the reaction stage demarcation points, used to distinguish different reaction kinetic characteristics in the early and late stages of deflagration. The above constants are all adjustable parameters of the model, and need to be calibrated through propellant thermal decomposition experiments, closed bomb experiments, and standard deflagration experiments to ensure that the model has accurate prediction ability for the deflagration behavior of different propellant formulations and different loading conditions.

[0053] The ignition region in the initial conditions recorded in step 5 is equivalent to an ignition source with initial pressure and initial reactivity. The aforementioned combustion-explosion model is used to simulate the evolution process after ignition, including combustion wave propagation, pressure increase, shell deformation, and eventual shell fracture, until the reaction is complete or the shell is completely destroyed. The physical basis for this equivalent treatment is that once ignition occurs, the exothermic rate of the chemical reaction in the local area exceeds the heat dissipation rate, forming a self-sustaining reaction. At this point, the reaction evolution is mainly driven by the pressure wave, the sensitivity of the reaction rate to temperature decreases, and the dependence on pressure becomes dominant (as shown in the reaction rate equation). Therefore, using the "pressure" and "reactivity" that integrate the temperature effect at the end of the ignition stage as the initial input of the combustion-explosion model can accurately connect the two stages, achieving a natural transition from heat-dominated ignition to pressure-dominated combustion-explosion. This sequential calculation method ensures both the continuity of the physical mechanism and computational efficiency.

[0054] Step 7: Output Results The pressure time history curves, shell rupture morphology, and reactivity evolution data obtained from the combustion-detonation stage simulation are used for solid rocket motor safety assessment.

[0055] The thermal decomposition process of the energetic component, ammonium perchlorate, is also described using a multi-step series reaction kinetic model. The specific reaction steps and kinetic parameters are determined based on the thermal decomposition mechanism of ammonium perchlorate. The reaction rate equation parameters in the combustion-detonation model are calibrated based on experimental data from ammonium perchlorate-based propellants.

[0056] Figure 1 This is a flowchart illustrating the sequential calculation method for the ignition-ignition-explosion response of GRT propellant charges impacted by fragments. It visually presents the entire sequential calculation logic for the GRT composite solid propellant charge impacted by fragments, from parameter preparation and model construction to ignition stage simulation, ignition determination, and then to the combustion-explosion stage simulation and result output. The overall process forms a closed loop of "input-calculation-determination-continue / termination-output," serving as the basis for achieving integrated simulation of the entire process from non-impact ignition to overall combustion-explosion. The flowchart divides the simulation process into three core stages, each interconnected, and incorporates the core technologies of this invention (such as force-thermal-chemical coupling, adaptive FEM-SPH coupling algorithm, and intrinsic ignition threshold determination).

[0057] Preliminary Stage: Parameter Determination and Core Model Construction. This is the foundational preparatory stage for the entire simulation, providing parameter inputs and model support for subsequent numerical calculations in the ignition and combustion / detonation stages. It is a prerequisite for ensuring simulation accuracy and includes two key operations: Full parameter acquisition: Through five types of experiments—mechanical properties, failure characteristics, frictional characteristics, thermophysics, equation of state, and thermal decomposition kinetics of energetic components—all parameters required for simulation are determined, such as the initial yield strength at the reference strain rate, Johnson-Cook failure model parameters, static / dynamic friction coefficients, thermal conductivity, JWL equation of state fitting constants, and pre-exponential factor / activation energy of the three-step thermal decomposition reaction of RDX.

[0058] Dual-core model construction: A fully force-thermal-chemical coupled ignition model is constructed, including five sub-modules: stress calculation, pressure calculation, temperature rise calculation, ignition reaction calculation, and overall temperature rise calculation. This model comprehensively characterizes the coupling effects of mechanical deformation of the propellant, heat generation / conduction, and thermal decomposition of energetic components during fragment intrusion. An adaptive FEM-SPH (finite element-smooth particle fluid dynamics) coupled structural failure model is constructed, using the Johnson-Cook failure model as the element transformation criterion to solve the problems of interrupted force and heat exchange and non-conservation of mass and energy caused by the traditional element deletion method.

[0059] Ignition Stage: Full-process force-thermal-chemical coupling simulation. This stage is the key link in simulating the core physical process of non-impact ignition. The core adopts explicit dynamic numerical method. Based on the parameters of the previous stage and the dual-core model, the complete process of fragment impacting the propellant is coupled and simulated. The specific simulation process is as follows: fragment intrusion into propellant → shell / propellant structural failure → hot spot formation → pre-ignition reaction evolution.

[0060] The key to simulating structural failure is that when a finite element reaches the Johnson-Cook failure criterion, it is automatically converted into an SPH particle, retaining the original element's mass, momentum, internal energy, and temperature. The converted particles continue to perform contact force and heat conduction calculations with the surrounding FEM elements / SPH particles, realistically restoring the contribution of the failed shell fragments to the propellant through continuous friction, compression, and heating. Simulation output results: The temperature field distribution and reactivity distribution of the propellant are obtained, which are the core data basis for subsequent ignition determination.

[0061] Key Node: Ignition Detection and Branch Processing. This is the core node for achieving sequential integration between the ignition model and the combustion-detonation model. Based on the intrinsic ignition threshold, it determines whether a local region of the propellant will ignite. The determination result is divided into two branches, allowing for flexible selection during the simulation process. Ignition threshold: When the local temperature of the propellant reaches the critical ignition temperature of the thermal decomposition of the RDX components, or when the local reactivity reaches the preset reactivity threshold (calibrated by the exothermic acceleration inflection point of the thermal decomposition experiment), it is different from the traditional phenomenological mechanical parameter criteria, has a clear physical meaning and is seamlessly connected with the calculation results of the ignition model. Branch 1: No ignition occurred: The simulation is terminated directly, corresponding to a scenario of low-energy fragment impact where ignition conditions were not met, and there is no subsequent combustion or explosion process; Branch 2: Ignition occurs: Record key ignition parameters (ignition time, ignition location, ignition zone size, ignition zone pressure, ignition zone reactivity), and use these parameters as initial conditions for the combustion and explosion stage simulation to achieve a closed-loop connection between the ignition and combustion and explosion models in terms of physical mechanisms and data transmission.

[0062] Combustion and Explosion Stage: Post-Ignition Evolution Simulation. This stage involves numerical simulation of the overall combustion and explosion evolution of the propellant after ignition. The core is to construct a propellant combustion and explosion model adapted to non-impact ignition scenarios, replacing the traditional, unsuitable impact initiation (I&G) model. Specific operations include: Combustion and explosion model construction: Based on the parameters of the equation of state and the parameters of the combustion and explosion reaction rate, a complete combustion and explosion model is constructed, including the JWL equation of state for unreacted substances, the JWL equation of state for reaction products, the pressure-dependent exponential reaction rate equation, and the mixing law of the pressure balance assumption. Ignition source equivalence: The ignition area recorded in the ignition determination stage is equivalent to an ignition source with initial pressure and initial reactivity. Evolution process simulation: Based on the combustion and explosion model and the initial conditions of the ignition source, the simulation simulates the entire process of propellant combustion wave propagation, internal pressure increase, shell deformation and rupture after ignition. The simulation terminates when the propellant reaction is complete or the shell is completely destroyed.

[0063] Final stage: Simulation result output. After the combustion and explosion phase simulation is completed, the core data / morphological results required for the safety design and evaluation of solid rocket motors are output, specifically including: Pressure-time history curve: The variation of propellant / shell internal pressure over time, reflecting the pressure evolution characteristics of the combustion-detonation process; Shell deformation and fracture morphology: Visually presents the deformation trend, fracture location, and fracture extent of the shell under combustion and explosion pressure; Reactivity evolution data: The variation of propellant global reactivity over time and space reflects the propagation speed of combustion waves and the intensity of combustion and explosion.

[0064] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. Other modifications can be easily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. An integrated simulation method for non-impact ignition and combustion-detonation reaction of solid propellants, characterized in that, include: S1. Obtain mechanical property parameters, failure parameters, friction parameters, thermophysical parameters, equation of state parameters, and kinetic parameters of thermal decomposition reaction of energetic components; S2. Based on mechanical performance parameters, friction parameters, thermophysical parameters, and thermal decomposition reaction kinetic parameters, a force-thermal-chemical coupled ignition model is constructed. The flow stress and plastic strain of the propellant during fragment intrusion are calculated according to the strain rate-dependent and temperature-dependent yield criteria. The propellant pressure is calculated based on the Mie-Grüneisen equation of state. The heat generated by plastic work and heat generated by friction within the propellant and at the interface between the fragment and the propellant are calculated using the plastic work heat generation formula and the friction heat generation formula, respectively. The heat transfer within the propellant and between the fragment and the propellant is calculated using Fourier's law of thermal conductivity. Calculation of reaction rate and exothermic rate of thermal decomposition of energetic components based on the Arrhenius equation; S3. Based on the failure parameters, an adaptive finite element-smooth particle fluid dynamics coupling algorithm is used to simulate the structural failure process of the shell and propellant. When the finite element element reaches the preset failure criterion, it is converted into a smooth particle fluid dynamics particle. The converted particle retains the mass, momentum, internal energy and temperature of the original element and continues to perform contact force and heat conduction calculations with the surrounding finite element elements or particles. S4. Using explicit dynamic numerical methods, based on the ignition model and particle state and contact information, the entire process from fragment intrusion, structural failure, hot spot formation to ignition is simulated using a force-thermal-chemical coupling method to obtain the temperature field distribution and reactivity distribution of the propellant. S5. Determine whether the propellant ignites in a local area based on the preset ignition threshold. If no ignition occurs, terminate the simulation. If ignition occurs, record the ignition time, ignition location, ignition area size, ignition area pressure, and ignition area reactivity, and use the recorded data as the initial conditions for the combustion and explosion stage simulation. S6. Based on the parameters of the equation of state and the combustion and explosion reaction rate parameters, a propellant combustion and explosion model is constructed, which includes the equation of state of unreacted substances, the equation of state of reaction products, the reaction rate equation, and the mixing rule; the ignition region in the initial conditions is equivalent to an ignition source with initial pressure and initial reactivity, and the combustion and explosion model is used to simulate the evolution process of combustion wave propagation, pressure increase, shell deformation, and shell rupture after ignition, until the reaction is complete or the shell is completely destroyed. S7 outputs the pressure time history curve, shell deformation and rupture morphology, and reactivity evolution data obtained from the combustion and explosion stage simulation.

2. The integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants according to claim 1, characterized in that, The strain rate-dependent temperature-dependent yield criterion adopts the flow stress expression, which includes strain hardening term, strain rate hardening term and thermal softening term; The parameters in the flow stress expression include the initial yield strength at the reference strain rate, hardening modulus, hardening exponent, strain rate sensitivity coefficient, reference temperature, and melting temperature.

3. The integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants according to claim 1, characterized in that, The friction coefficient in the friction heat generation formula varies with the relative sliding speed of the contact surfaces and is determined by the static friction coefficient, dynamic friction coefficient, and attenuation coefficient. The total heat generated by friction is distributed based on the thermal conductivity, density, and specific heat of the materials on both sides of the contact interface. The thermal inertia is determined by the product of the square roots of the thermal conductivity, density, and specific heat. The heat distribution coefficients flow into the fragments and the propellant, respectively.

4. The integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants according to claim 1, characterized in that, For the thermal decomposition process of energetic components in propellants, a multi-step series reaction kinetic model is adopted, wherein the energetic components include RDX and / or ammonium perchlorate; wherein the thermal decomposition of RDX adopts a three-step series reaction model, the reaction rate of each step is expressed by the Arrhenius equation, the heat of reaction of each step is a constant, and the parameters in the Arrhenius equation include the pre-exponential factor, activation energy and gas constant.

5. The integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants according to claim 1, characterized in that, The adaptive finite element-smooth particle hydrodynamic coupling algorithm automatically transforms failed finite element elements into smooth particle hydrodynamic particles through a preset element transformation criterion; the element transformation criterion adopts the Johnson-Cook failure model; the transformed particles retain the mass, momentum, internal energy and temperature of the original element and participate in subsequent contact force calculation and heat conduction calculation.

6. The integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants according to claim 1, characterized in that, In the propellant combustion-detonation model, both the equations of state for unreacted materials and the equations of state for reaction products adopt the Jones-Wilkins-Li equations of state. The parameters in the Jones-Wilkins-Li equations of state include initial density, sound velocity, Grignard coefficient, and several fitting constants. The reaction rate equation adopts the pressure-dependent exponential form, expressed as: In the formula, ∂F / ∂t represents the reaction rate, t represents time, F=0 indicates no reaction, F=1 indicates complete reaction, F0 is the initial combustion fraction, P0 is the initial pressure, and Z1, y, x, Z2, ω, u, r, s, and F are also present. limit1 and F limit2 All are constants, calibrated through propellant thermal decomposition experiments, sealed burner experiments, and standard combustion and explosion experiments. Z1 and Z2 are reaction rate coefficients, y and x are reactivity indices of the first reaction stage, ω is the pressure index of the first stage, u and r are the reactivity indices of the second reaction stage, and s is the pressure index of the second stage; F limit1 and F limit2 This marks the boundary between different stages of the reaction. The mixing principle assumes pressure equilibrium, with the relative volumes of unreacted substances and reaction products weighted by reactivity.

7. The integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants according to claim 1, characterized in that, The preset ignition threshold is when the local temperature of the propellant reaches the critical ignition temperature for the thermal decomposition of its RDX components, or when the local reactivity reaches the preset reactivity threshold.

8. An integrated simulation system for non-impact ignition and combustion-detonation reaction of solid propellants, used to perform the method according to any one of claims 1 to 7, characterized in that, include: One or more processors; Memory, used to store one or more computer programs; When the one or more computer programs are executed by the one or more processors, the one or more processors implement the integrated simulation method for non-impact ignition and combustion-explosion reaction of solid propellants as described in any one of claims 1 to 7.

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