Method for determining the reaction kinetic parameters of a solid viscoelastic material
By combining cylindrical and Lagrange experiments, the parameters of the trinomial ignition growth reaction rate equation for high-energy solid viscoelastic materials were determined, solving the problem of poor parameter compatibility and improving the accuracy of parameter determination and the reliability of the model.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ROCKET FORCE UNIV OF ENG
- Filing Date
- 2026-06-23
- Publication Date
- 2026-07-21
AI Technical Summary
Traditional methods suffer from poor coordination among parameters when determining the reaction kinetic parameters of high-energy solid viscoelastic materials, failing to fully reflect the material's true dynamic response and thus reducing the reliability of subsequent numerical simulations of strong dynamic processes such as sympathetic detonation.
By employing a combination of analytical and numerical inversion methods, initial expansion data were obtained through cylindrical experiments, and the path line method of Lagrange experiments was used to process the data to determine the parameters of the trinomial ignition growth reaction rate equation for high-energy solid viscoelastic materials.
It improves the accuracy of parameter determination and provides a complete and highly operable calibration process for the reaction kinetics parameters of high-energy viscoelastic materials, which has important guiding significance for the performance evaluation and model construction of new viscoelastic materials.
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Figure CN122436093A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of dynamic analysis, data processing, energetic material testing and numerical simulation, and specifically to a method for determining the reaction kinetic parameters of solid viscoelastic materials. Background Technology
[0002] To accurately simulate the entire process from impact ignition to stable detonation of high-energy solid viscoelastic materials (e.g., nitrate ester plasticized polyether propellant (NEPE) viscoelastic materials), reliable parameters need to be calibrated for their "ignition growth" reaction rate model and detonation product equation of state. Traditional methods simply combine parameters obtained from different experiments or rely on experience, resulting in poor coordination between parameters and an inability to fully reflect the material's true dynamic response. This leads to reduced reliability of subsequent numerical simulations of highly dynamic processes such as sympathetic detonation. Summary of the Invention
[0003] This application provides a method for determining the reaction kinetic parameters of solid viscoelastic materials. It can obtain the parameters of the trinomial ignition growth reaction rate equation by using analytical and numerical inversion based on the parameters of the cylindrical test, combined with the path line method of the Lagrange test, thus improving the accuracy of parameter determination.
[0004] The first aspect of this application provides a method for determining the reaction kinetic parameters of a solid viscoelastic material, the method comprising: Obtain the initial expansion data of the cylinder wall surface of the high-energy solid viscoelastic material in the cylinder test; The first equation of state for the high-energy solid viscoelastic material is determined based on the initial expansion data. Obtain the state parameters of a high-energy solid viscoelastic material at each Lagrange position during the Lagrange test process; The reaction degree variation curve of the high-energy solid viscoelastic material is determined based on the first equation of state and the state parameters at each Lagrange position. Based on the reaction rate change curve, the parameters of the three-term ignition growth reaction rate equation for high-energy solid viscoelastic materials are obtained by partition fitting.
[0005] In one possible implementation, determining the first equation of state for the high-energy solid viscoelastic material based on the initial expansion data includes: The wall expansion rate is determined based on the initial expansion data; The isentropic internal energy of the high-energy solid viscoelastic material is determined based on the wall expansion rate. Construct a curve showing the relative specific volume as a function of expansion distance based on the initial expansion data; The parameters of the first reference state equation are determined based on the curves showing the variation of isentropic internal energy and relative specific volume with expansion distance. The parameters of the first reference state equation are optimized to obtain the first state equation.
[0006] In one possible implementation, the parameters of the first reference state equation are optimized to obtain the first state equation, including: Numerical simulations were performed on the initial expansion data to obtain the simulation results; The parameters of the second reference state equation are determined based on the numerical simulation results; The parameters of the first reference state equation and the parameters of the second reference state equation are fused to obtain the target state equation parameters; The state equation is constructed based on the target state equation parameters to obtain the first state equation.
[0007] In one possible implementation, determining the isentropic internal energy of the high-energy solid viscoelastic material based on the wall expansion rate includes: The isentropic internal energy of a high-energy solid viscoelastic material is determined based on the wall expansion rate using the following formula: ; in, E It is the total energy released during the detonation of high-energy solid viscoelastic materials. U The wall expansion rate, m For the quality of high-energy solid viscoelastic materials, E s It is isentropic internal energy. M This represents the total mass of gaseous products generated during the combustion of high-energy solid viscoelastic materials. Q This refers to the total energy generated by the combustion of high-energy solid viscoelastic materials.
[0008] In one possible implementation, determining the reactivity variation curve of the high-energy solid viscoelastic material based on the first equation of state and the state parameters at each Lagrange position includes: Curve fitting is performed based on the state parameters at each Lagrange position to obtain the time trajectory; By solving based on the time trajectory and the corresponding trajectory, the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of the high-energy solid viscoelastic material can be obtained. Based on the mixed-state pressure, mixed-state temperature, mixed-state specific volume, mixed-state internal energy, and the first equation of state, a curve is constructed to obtain the reaction degree change curve.
[0009] In one possible implementation, the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of the high-energy solid viscoelastic material are obtained by solving based on the time trajectory and the corresponding trajectory, including: Obtain the conservation equations in one-dimensional Lagrange coordinates when volumetric forces and thermal conduction are explicitly neglected; By taking the polynomial derivatives of the time radius and the trajectory, the partial derivatives of the isochronous lines are obtained. By solving the isochronous partial derivatives and conservation equations, the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of the high-energy solid viscoelastic material can be obtained.
[0010] In one possible implementation, the state parameters include a pressure-time curve, position parameters, pressure parameters, and time parameters. The step of curve fitting based on the state parameters at each Lagrange position to obtain a time trajectory includes: For the pressure-time curve at each Lagrange location, discretize it into N data points at equal time intervals; Based on the location, pressure, and time parameters of N data points, a quadratic polynomial fitting is performed to obtain the time trajectory of each Lagrange position.
[0011] In one possible implementation, the parameters of the trinomial ignition growth reaction rate equation for the high-energy solid viscoelastic material are obtained by partitioning and fitting the reactivity variation curve, including: By taking the time derivative of the reactivity change curve, the time distribution curve of the reaction rate is obtained. By performing partition fitting on the reaction rate time distribution curve, the parameters of the three-term ignition growth reaction rate equation are obtained.
[0012] In one possible implementation, after obtaining the parameters of the trinomial ignition growth reaction rate equation for the high-energy solid viscoelastic material by performing partitioned fitting based on the reactivity variation curve, the method further includes: Obtain the measured reaction rate value; A trinomial ignition growth reaction rate equation was constructed using parameters of the trinomial ignition growth reaction rate equation. The parameters of the three-term ignition growth reaction rate equation are optimized by using the measured reaction rate value and the calculated reaction rate value obtained from the three-term ignition growth reaction rate equation to obtain the optimized parameters of the three-term ignition growth reaction rate equation.
[0013] In one possible implementation, the cylinder used in the cylinder test is a standard 50mm cylinder.
[0014] Implementing the embodiments of this application has at least the following beneficial effects: By acquiring the initial expansion data of the cylinder wall surface of the high-energy solid viscoelastic material in a cylinder test; determining the first equation of state for the high-energy solid viscoelastic material based on the initial expansion data; acquiring the state parameters of the high-energy solid viscoelastic material at each Lagrange position during the Lagrange test; determining the reaction degree change curve of the high-energy solid viscoelastic material based on the first equation of state and the state parameters at each Lagrange position; and performing partition fitting based on the reaction degree change curve to obtain the parameters of the trinomial ignition growth reaction rate equation of the high-energy solid viscoelastic material, the accuracy of parameter determination can be improved by combining analytical and numerical inversion based on the cylinder test parameters and using the path line method to process the data in the Lagrange test. Furthermore, a complete and highly operable calibration process for the reaction kinetic parameters of high-energy viscoelastic materials is provided, which has important guiding significance for the performance evaluation and model construction of new viscoelastic materials. Attached Figure Description
[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This application provides a flowchart illustrating a method for determining the reaction kinetic parameters of a solid viscoelastic material. Figure 2 This application provides a schematic diagram of a cylindrical testing apparatus according to an embodiment; Figure 3 This application provides a schematic diagram of the relative specific volume as a function of expansion distance in an embodiment of the present application; Figure 4 This application provides a schematic diagram of relative specific volume-isoentropic internal energy test data and fitting curves for embodiments of the present application; Figure 5 This application provides another schematic diagram of relative specific volume-isoentropic internal energy test data and fitting curves for embodiments of the present application; Figure 6 This application provides a schematic diagram of a numerical simulation of the cylinder expansion process in a cylinder test, which is an embodiment of the present application. Figure 7 This application provides a schematic diagram comparing numerical simulation results with experimental results in an embodiment of the present application. Figure 8 A schematic diagram of a Lagrange test system is provided for an embodiment of this application; Figure 9This application provides a schematic diagram of the pressure time history curve of a monitoring point after conversion processing, as shown in the embodiment of the present application. Figure 10 A schematic diagram of an isochron is provided for an embodiment of this application; Figure 11 This application provides a schematic diagram of the pressure-time curves comparing numerical simulation and experiment. Detailed Implementation
[0017] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0018] The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.
[0019] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.
[0020] To better understand the method for determining the reaction kinetic parameters of solid viscoelastic materials provided in this application, a brief introduction to existing methods for determining these parameters is given below. In existing methods, different experimental data are typically combined and then solved to obtain the reaction kinetic parameters of the solid viscoelastic material, or the parameters are set based on empirical data. However, these methods suffer from poor coordination between parameters and fail to fully reflect the true dynamic response of the material, leading to reduced reliability of subsequent numerical simulations of highly dynamic processes such as sympathetic detonation.
[0021] To address the aforementioned issues, this application provides a method for determining the reaction kinetic parameters of solid viscoelastic materials. This method combines analytical and numerical inversion techniques based on cylindrical test parameters, and uses the path line method to process data from Lagrange tests, thereby improving the accuracy of parameter determination.
[0022] Please see Figure 1 , Figure 1 This application provides a flowchart illustrating a method for determining the reaction kinetic parameters of a solid viscoelastic material. Figure 1 As shown, the method includes: 101. Obtain the initial expansion data of the cylinder wall surface of the high-energy solid viscoelastic material in the cylinder test.
[0023] Specifically, when conducting cylinder tests, the following methods can be used: Figure 2 The cylindrical test apparatus shown is used for processing. The traditional method involves placing probes at different distances along the cylinder wall (where the cylinder wall refers to the outer wall of the oxygen-free copper cylindrical metal tube used in standard cylinder tests. This cylinder wall has high ductility, allowing it to expand radially without rupturing under the detonation drive of the internal high-energy solid viscoelastic material). When the high-energy solid viscoelastic material detonates, the cylinder wall expands and contacts the probes, allowing the current cylinder expansion distance to be recorded. This paper presents a cylindrical test apparatus (50mm) (…). Figure 2 The method shown (as illustrated) utilizes a Photonic Doppler Velocimeter (PDV) to measure the radial expansion velocity of a cylindrical wall, building upon traditional methods. The principle involves recording the expansion distance of the cylinder wall at different heights over a given time period using a probe-based signal transmission method. A standard cylindrical test was conducted, placing a prepared high-energy solid viscoelastic material column within a copper tube. A detonator was positioned at the top of the high-energy solid viscoelastic material column to initiate the detonation. To ensure stable detonation and reduce experimental uncertainty, a transition high-energy solid viscoelastic material column was placed below the detonator. The metal cylinder, fixed in the center of a steel plate, is made of oxygen-free copper with excellent ductility, allowing it to expand a considerable distance without breaking. Four PDV probes were placed on a metal support on the left side, 100 mm from the cylinder wall, and two sets of tests were conducted.
[0024] The booster explosive is a key component of the detonation sequence. It is located between the initiator / detonator and the main charge (in this application, a high-energy solid viscoelastic material cylinder).
[0025] Initial expansion data includes the expansion distance, velocity, and acceleration curves of the cylindrical wall. Specifically, this can be achieved by performing a Fourier transform on the data collected by a photon Doppler velocimeter to obtain the wall expansion velocity-time relationship curve. During the measurement, two measurement points were set up, with a launch time difference of 15.93 microseconds between the two points (measurement point 1 and measurement point 2) and a distance of 115 mm between them. The calculated detonation velocity was 7219.1 m / s. The expansion curves of measurement point 1 and measurement point 2 were basically consistent, indicating that the detonation had reached its full potential.
[0026] Assuming the expansion distance of the cylinder wall RR 0 and reaction time t The expression is a fourth-order polynomial function: (1) Where t is the reaction time. RR 0 represents the expansion distance of the cylindrical wall. 、 、 、 、 , where is the polynomial coefficient, which needs to be solved to obtain the actual cylinder expansion curve between the cylinder wall expansion distance and time.
[0027] Expansion distance of the cylindrical wall in the above formula RR Taking the derivative with respect to zero, we can obtain the expansion velocity of the cylinder wall as: (2) To calculate the expansion rate of the cylinder wall, the polynomial coefficients in the above formula need to be adjusted. 、 、 、 、 To solve this, we can use the least squares method to fit the average time of the experiment to the expansion distance. RR The relationship between 0 and 0 was used to finally fit the polynomial coefficients. 、 、 、 、 As shown in Table 1.
[0028] Table 1. Fitting coefficients for the expansion curve of the cylinder. The radial expansion velocity data of the cylinder obtained through experimental calculations are shown in Table 2. Table 2. Data on radial expansion velocity of the cylinder 102. Determine the first equation of state for the high-energy solid viscoelastic material based on the initial expansion data.
[0029] Specifically, a method for determining the first equation of state for a high-energy solid viscoelastic material based on the initial expansion data includes: A1. Determine the wall expansion rate based on the initial expansion data; A2. Determine the isentropic internal energy of the high-energy solid viscoelastic material based on the wall expansion rate. A3. Construct a curve showing the change in relative specific volume with expansion distance based on the initial expansion data; A4. Determine the parameters of the first reference state equation based on the curves of isentropic internal energy and relative specific volume as a function of expansion distance; A5. Optimize the parameters of the first reference state equation to obtain the first state equation.
[0030] The wall expansion velocity corresponding to the initial expansion data can be obtained according to the method for determining the expansion velocity of the cylinder wall shown in the foregoing embodiments. Wall expansion velocity: the instantaneous rate (unit: mm / μs) of radial expansion of the oxygen-free copper cylinder wall driven by the detonation of a high-energy solid viscoelastic material in the cylinder experiment. It is measured by a photon Doppler velocimeter (PDV) and used to deduce the JWL equation of state parameters.
[0031] After determining the wall expansion rate, the isentropic internal energy of the high-energy solid viscoelastic material can be determined based on the wall expansion rate using the following formula: (3) (4); in, E It is the total energy released during the detonation of high-energy solid viscoelastic materials. U The wall expansion rate, m For the quality of high-energy solid viscoelastic materials, E s It is isentropic internal energy. M This represents the total mass of gaseous products generated during the combustion of high-energy solid viscoelastic materials. Q This refers to the total energy generated by the combustion of high-energy solid viscoelastic materials.
[0032] Specifically, the first equation of state (JWL equation of state, JWL: Jones-Wilkins-Lee, an empirical equation of state describing the state of detonation products) can be transformed into the internal energy form and related to the experimental wall kinetic energy data, specifically as follows: (5); Therefore, it is necessary to solve it, and the specific solution A, B, C , R 1. R 2. ω , where A, B, R 1. R 2 are high-pressure term parameters, describing the energy contribution in the high-pressure stage at the initial stage of detonation, C , ω are low-pressure term parameters, ω is the Grüneisen coefficient.
[0033] Miller et al. summarized that the relative specific volume of the viscoelastic material and the expansion distance of the cylinder wall during the detonation reaction process can be described by the following polynomial: (6) Where R is the radius of the cylinder wall after expansion, R 0 is the initial radius of the cylinder wall, V is the relative specific volume. Specifically, the constructed curve of the relative specific volume varying with the expansion distance is as Figure 3 shown.
[0034] After determining the curve of the relative specific volume varying with the expansion distance, according to the polynomial proposed by Miller, when the system is in the low-pressure stage, the relative specific volume , the JWL equation of state can be simplified to: (7) By联立上述相关公式, the values of C = 0.198, ω = 0.0327 can be obtained by fitting. Figure 4 is shown in the relative specific volume, the isentropic internal energy experimental data and the fitting curve at
[0035] In the medium-pressure stage ( 2 < V < 5), the JWL equation of state can be simplified to: (8) Since the values of C and ω have been obtained, the value of B = 0.2413 can be obtained by fitting through the above formula, =0.419.
[0036] Figure 5 It is shown in the figure. At that time, the experimental data and fitting curves of relative specific volume and isentropic internal energy were obtained.
[0037] get C , ω、B and After obtaining the value, the following four formulas can be solved using the symbolic method to obtain the result. A =509.511、 =4.115.
[0038] (9) (10) (11) (12) In the above formula, D According to Figure 3 The calculated detonation velocity of the high-energy solid viscoelastic material, The isentropic index of the detonation products. , This represents the pressure value at the CJ (Chapman-Jouguet, the CJ surface / point in steady detonation theory) of the detonation wave. For CJ state relative to volume, The initial density of a high-energy solid viscoelastic material. e These are natural constants. Substituting the cylindrical test data, the first reference equation of state parameters of the JWL equation of state for high-energy solid viscoelastic materials can be calculated. The specific results are shown in Table 3.
[0039] Table 3. Parameters of the First Reference State Equation in the JWL State Equation After obtaining the parameters of the first reference state equation, they can be optimized. Specifically, one method for optimizing the parameters of the first reference state equation to obtain the first state equation includes: B1. Perform numerical simulation on the initial expansion data to obtain the numerical simulation results; B2. Determine the parameters of the second reference state equation based on the numerical simulation results; B3. The parameters of the first reference state equation and the parameters of the second reference state equation are fused to obtain the target state equation parameters; B4. Construct the state equation based on the target state equation parameters to obtain the first state equation.
[0040] Specifically, the expansion process of the cylindrical test is numerically simulated (i.e., the initial expansion data is numerically simulated), the parameters of the second reference equation of state of the JWL equation of state are determined, and the accuracy of the data is further verified and the error is reduced using the parameters of the second reference equation of state. When simulating high-energy solid viscoelastic materials, the simulation is performed from the detonation line of the explosive end face.
[0041] Specifically, the parameters of the second reference state equation can be obtained through simulation using the following method: First, six parameters of a set of undetermined JWLs are estimated using empirical methods. For most explosives, the parameters in their JWL equations of state are... , , ω The empirical value ranges are approximately 4~5, 1~2, and 0.2~0.4, respectively. Under low-pressure conditions, the expansion process of detonation products is similar to that of an ideal gas, therefore... Its value is usually around 0.3. , , ω Given initial values for the detonation velocity, detonation pressure, and chemical energy of a high-energy solid viscoelastic material, the detonation conditions and the Rh relationship can be used to calculate the detonation energy. A, B, C The value of , where the RH relation is used to describe the mass, momentum and energy conservation equations across the detonation wave (or shock wave), is a universal relation that all shock waves / detonation waves must satisfy: the CJ condition is a specific additional condition proposed for steady-state one-dimensional detonation waves based on the RH relation, used to determine the unique propagation velocity (CJ detonation velocity) and the post-wave state point of the detonation wave.
[0042] Numerical simulations are performed on the cylindrical test data using dynamics software (such as LS-DYNA), and the simulation results are applied to calculate the cylindrical expansion process. After obtaining the cylindrical expansion distance-time relationship curve (which yields the second reference state equation parameters), the cylindrical expansion distance-time relationship curve calculated from the simulation results is compared with the experimentally measured expansion distance-time curve. The parameters are adjusted based on the differences between the two curves, and the adjusted parameters are re-imported into the calculation program for further comparison with the experimental results. This process is repeated, adjusting the parameters and initiating the next round of calculations. Through multiple rounds of iterative calculations, the state equation parameters are continuously corrected until the error between the calculated expansion distance-time curve and the experimentally measured expansion distance-time curve is below a set threshold (usually 1%), at which point the target state equation parameters are obtained.
[0043] The models used in the numerical simulation included oxygen-free copper and viscoelastic materials. The high-energy explosive combustion material model built into LS-DYNA and the JWL equation of state were used to describe the high-energy solid viscoelastic material, with detonation initiated from the end face of the viscoelastic material. The oxygen-free copper used in the experiment was described using the Johnson-Cook constitutive model (a constitutive model describing the behavior of materials under large deformation, high strain rate, and high temperature) and the Grünesen equation of state. The parameters of the Johnson-Cook constitutive model and the relevant parameters of the Grünesen equation of state for oxygen-free copper are shown in Tables 4 and 5 below.
[0044] Table 4. Johnson-Cook constitutive model parameters for oxygen-free copper. Table 5. Relevant parameters of the Grüneisen equation of state for oxygen-free copper. Substituting the JWL equation of state parameters of the detonation products, initially estimated by analytical calculations, into the simulation calculations, and after multiple corrections and calculations, the expansion process of the cylinder wall of a 50mm cylindrical test model of a high-energy solid viscoelastic material was simulated. The numerical simulation results agree well with the experimental results, thus allowing the JWL equation of state for the detonation products of high-energy solid viscoelastic materials to be derived. Figure 6 Numerical simulation of the cylinder expansion process in a 50mm cylindrical test of a high-energy solid viscoelastic material was performed. By comparing the cylinder wall expansion process in experimental data with that in the numerical simulation, the final results show that the error between the numerical simulation and experimental results is less than 1%, meeting the calculation requirements. Specifically, as follows... Figure 7 As shown.
[0045] Through numerical simulation and analysis of the cylindrical test, the JWL equation of state parameters (i.e., the target equation of state parameters) of the detonation products of the high-energy solid viscoelastic material were obtained, as shown in Table 6.
[0046] Table 6. JWL equation of state parameters for detonation products of high-energy solid viscoelastic materials. 103. Obtain the state parameters of high-energy solid viscoelastic materials at each Lagrange position during the Lagrange test.
[0047] The state parameters include: particle velocity, specific volume, and specific internal energy. When obtaining the state parameters at each Lagrange position, methods such as... Figure 8The results were obtained after testing the Lagrange test system shown. The Lagrange test system uses a detonator to detonate a high-energy solid viscoelastic material column, generating a shock wave. The shock wave propagates and attenuates through the air before acting on the target high-energy solid viscoelastic material column. Copper-manganese pressure sensors placed at different heights record the pressure-time history curves at different locations. During the test, the incident wave pressure on the target high-energy solid viscoelastic material column was adjusted by changing the thickness of the septum. A total of six sets of tests were conducted, with pressure gauges placed at 4 mm intervals starting from the top of the high-energy solid viscoelastic material column.
[0048] The Lagrange test system, from top to bottom, consists of: an No. 8 industrial detonator, fixed in a wooden support in a drilled hole, connected to the main high-energy solid viscoelastic material column via a disconnect circuit; the main high-energy solid viscoelastic material column is made of a mixture of pentaerythritol tetranitrate (PETN) and trinitrotoluene (TNT) in a 1:1 mass ratio, possessing the advantage of stable explosive properties and producing constant detonation pressure and velocity, and is cylindrical in shape; below the main high-energy solid viscoelastic material column is a pressure attenuation device, using a hollow polyvinyl chloride (PVC) tube as a diaphragm to attenuate the pressure and adjust the intensity of the incident shock wave; and the high-energy solid viscoelastic material tablet, pre-cut into 4-piece pieces. mm thick tablets; H-type copper-manganese pressure gauges, which are fixed between high-energy solid viscoelastic material columns, can convert electrical signals into pressure signals to detect the shock wave intensity at that location; finally, the high-energy solid viscoelastic material to be tested is placed between aluminum partitions after the copper-manganese pressure gauges have been installed, and the high-energy solid viscoelastic material column to be tested is fixed.
[0049] To ensure accurate pressure data detection, interference from other signals during the experiment must be eliminated, primarily: air between the high-energy solid viscoelastic material columns and the signal disturbance of the copper-manganese pressure gauge caused by the detonation of the high-energy solid viscoelastic material itself, which is rich in aluminum powder. To reduce interference, during installation, vacuum grease is first evenly applied to the lower partition and the contact surface between the high-energy solid viscoelastic material pellet and the partition to isolate air. The terminals of the copper-manganese pressure gauge are first wrapped with a 0.1 mm thick PTFE film to prevent the influence of aluminum powder on the sensor signal during the detonation of the high-energy solid viscoelastic material, and then wrapped with insulating tape to protect the sensor. Vacuum grease is evenly applied to and covered with a PTFE film on the sensor part of the copper-manganese pressure gauge to prevent rarefaction waves from damaging the sensor; the copper-manganese gauges at different locations are placed at the center of the high-energy solid viscoelastic material column to ensure accurate stress acquisition.
[0050] At the start of the test, a 20 mm thick hollow partition was used to attenuate the shock wave. Powered by a 9A constant current source, the initial output voltage of the system was between 0.8 and 1V. The resistance of the H-type copper-manganese pressure gauge was measured before the test, and the calibration results for this model of pressure gauge are as follows: (12) in, P The pressure values before the H-type copper-manganese experiment are shown, with an effective range of 1.5~41.76 GPa and a correlation coefficient of 99%. The pressure-time history curves of the monitoring points after conversion treatment are shown below. Figure 9 As shown.
[0051] When determining the specific state parameters, in the Lagrange coordinate system, the impact initiation process of the high-energy solid viscoelastic material Lagrange test satisfies the assumption of "adiabatic non-viscosity and local thermodynamic equilibrium". Based on the three conservation equations of mass, momentum and energy, the particle velocity at each Lagrange position is solved by integration. ,specific volume Internal energy The specific derivation and calculation steps are as follows: First, let's clarify the conservation equations in one-dimensional Lagrange coordinates when volumetric force and thermal conduction are neglected: Regarding the law of conservation of mass, we have: (13) Regarding the conservation of momentum, we have: (14) Regarding the conservation of energy, we have: (15) in, The initial density of the high-energy solid viscoelastic material was measured before the experiment. For volume, Let the velocity of the particle be... For pressure, For internal energy, Using Lagrange coordinates, For time; subscript express" Fixed (along the trace), subscript t express" t "Fixed" (along the isochrones).
[0052] 104. Determine the reaction degree change curve of the high-energy solid viscoelastic material based on the first equation of state and the state parameters at each Lagrange position.
[0053] Specifically, the state parameters include pressure-time curves, position parameters, pressure parameters, and time parameters. A method for determining the reactivity variation curve of a high-energy solid viscoelastic material based on the first equation of state and the state parameters at each Lagrange position includes: C1. Perform curve fitting based on the state parameters at each Lagrange position to obtain the time trajectory; C2. Solve based on the time trajectory and the corresponding trajectory line to obtain the mixed-state pressure, mixed-state temperature, mixed-state specific volume and mixed-state internal energy of the high-energy solid viscoelastic material; C3. Based on the mixed-state pressure, mixed-state temperature, mixed-state specific volume, mixed-state internal energy, and the first equation of state, a curve is constructed to obtain the reaction degree change curve.
[0054] A method for obtaining a time trajectory by curve fitting based on state parameters at each Lagrange position includes: For the pressure-time curve at each Lagrange location, it is discretized into N data points at equal time intervals; based on the location parameters, pressure parameters, and time parameters of the N data points, a quadratic polynomial fitting is performed to obtain the time trajectory at each Lagrange location.
[0055] A method for determining the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of a high-energy solid viscoelastic material by solving based on the time trajectory and the corresponding trajectory, includes: Obtain the conservation equations in a one-dimensional Lagrange coordinate system when volumetric force and thermal conductivity are explicitly ignored; perform polynomial differentiation on the time radial lines and trajectory lines to obtain the isochronous partial derivatives; solve the isochronous partial derivatives and conservation equations to obtain the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of the high-energy solid viscoelastic material.
[0056] Mixed state: refers to a mixture of unreacted solid viscoelastic material and reacted gaseous products.
[0057] Specifically, due to direct calculation (Partial derivatives in the isochronous direction) require multiple sets of isochronous data, which can easily lead to information loss. Therefore, Grady's improved "pathline method" is used to convert the partial derivatives into derivatives in the radial direction. The radial (trajectory line) is an artificially constructed smooth curve that represents each Lagrange position. pt Connecting "physically similar characteristic points" on the curve (such as pressure peak points at various locations, corresponding points in the same decay stage) replaces the "isochronous line" as the integration path, maximizing the use of experimental data, such as... Figure 10 As shown.
[0058] The specific construction method is as follows: for each Lagrange position... - Curves, at equal time intervals μs Based on the waveform length, it is discretized into N data points to obtain... ( i Number the Lagrange positions. j (for discrete point numbering); for fixed... j (Feature points corresponding to the same discrete time), will be different corresponding and By fitting quadratic polynomials, time-course radii describing the time distribution of the same feature point at different Lagrange positions and pressure radii describing the pressure distribution of the same feature point at different Lagrange positions are obtained. Furthermore, the radii fitting must satisfy "smoothness" (continuous second derivative) and "consistency" (uniform spacing between adjacent radii) to avoid localized dense or sparse areas.
[0059] For any physical quantity (like p、u Its isochronous partial derivatives can be expressed as: (16) Among them, subscript j Indicates along the radial line, It can be obtained by differentiating the polynomial of the radial fit. It is obtained by differentiating the polynomial of the trace fitting. From time radii Differentiating, we get: Substituting (15) into equations (33), (13), and (14), we obtain: (17) (18) (19) The pressure-time variation curves at each Lagrange position have been processed and obtained. The particle velocity at each Lagrange position is then calculated by integration. ,specific volume Internal energy The integral forms of the three conservation equations are as follows: (20) (twenty one) (twenty two) in, It is a function of shock wave pressure. Let vi be the particle energy at time t-t1, and v1 be the specific volume at time t-t1. Substituting the partial derivative transformation formula into the momentum conservation equation, we obtain the integral form: (twenty three) in, Let be the particle velocity of the shock wave front at time t. shock wave front The velocity of the particle, the lower limit of integration The time it takes for the shock wave to reach that Lagrange position (from (Reading the starting point of the curve) yes The pressure value at any moment, yes The pressure value at any given moment. The integral within can be approximated by the following formula: (twenty four) yes Lagrange coordinates of time, yes Lagrange coordinates of the moment; Similarly, the general difference form of the mass, energy, and momentum conservation equations can be obtained: (25) (26) (27) in, In position Time step The velocity of the particle, In position Time step The velocity of the particle, It is a time step Inner position Physical time at that location It is a time step Inner position Physical time at that location In position Time step The pressure of the mass point, In position Time step The pressure of the mass point, In position Time step The specific volume of a particle, In position Time step The specific volume of a particle, In position Time step The energy of a point mass, In position Time step The energy of a point mass.
[0060] After filtering the converted pressure-time signal, a clearer curve can be obtained. Using the pathline method, nine feature points are extracted from each pressure-time curve, and then a refit operation is performed to finally obtain the raw data required for the Lagrange analysis method.
[0061] Based on the shock wave take-off time difference between two adjacent Lagrange positions Combining the distance between the two positions ,Depend on Calculated; It is the first Lagrange position between two adjacent Lagrange positions. It is the second Lagrange position between two adjacent Lagrange positions. It is the shock wave take-off time at position 1 and time step 2. It is the shock wave take-off time at position 1 and time step 1.
[0062] Based on the fundamental conservation equations for one-dimensional shock waves (Rankine-Hugoniot relation), solve the following simultaneously: Mass conservation law: (28) It is the particle density after the shock wave; because the wavefront is the particle velocity of the reacting substances. Based on the relationship between specific volume and density, we can summarize as follows: (29) Momentum conservation relationship: (30) wavefront pressure Organized ; Energy conservation principle: (31) Initial internal energy Negligible (relative to the internal energy of the reaction), rearranged, we get: (32) Assume the mixture satisfies the following thermodynamic equilibrium condition and compositional relationship: the pressure of the mixture equals the pressures of the unreacted substances and products, i.e. The temperature of the mixed state is equal to the temperature of the unreacted substances and the product temperature. The specific volume of the mixture is equal to the weighted sum of the specific volumes of unreacted substances and products by mass fraction, i.e. The internal energy of the mixture is equal to the weighted sum of the internal energies of the unreacted substances and the products according to their mass fractions, i.e. .
[0063] Will , and Substituting into the above equation, constructing a system based on... A system of nonlinear equations with a single unknown: Depend on Combining the JWL equation for unreacted substances, we obtain and Relationship ;Depend on Combining the product JWL equation, we obtain and Relationship ;Will and Substituting the internal energy lever rule and then simultaneously applying the specific volume lever rule, we obtain the result containing only... The equation is given. The nonlinear equation is solved using Newton's iterative method to obtain the reaction degree at any time t. The final output is the position of each Lagrange point. The curve (i.e., the reaction rate change curve).
[0064] 105. Based on the reaction rate change curve, perform partition fitting to obtain the parameters of the three-term ignition growth reaction rate equation for high-energy solid viscoelastic materials.
[0065] Specifically, the three-term ignition growth reaction rate equation can be: the reaction rate equation corresponding to the Lee-Tarver three-term ignition growth model is as follows: (33) In the formula, Represents the current level of responsiveness; , These correspond to the current density and the initial density, respectively. For pressure; and All of these are empirical parameters to be determined, and these parameters can be calibrated through experiments. The first term from left to right in the three-term equation represents the ignition term, which is often referred to as the ignition term, as the explosive ignites when internal defects are stimulated and hot spots appear. and The number of ignition hotspots is controlled; it is a function of the shock wave intensity and its duration. a The critical compressibility means that the explosive can only ignite when the shock wave intensity meets certain conditions, and The larger the value, the smaller the reaction rate; bThe value is typically a constant 0.667, indicating that the generated hotspots expand outward in a spherical shape. The second term, also known as the combustion term, involves the increase and convergence of hotspots, and the chemical decomposition and reaction of the explosive. and d The hot spot reaction and growth duration after ignition were controlled. The larger the value, the greater the reaction rate at that stage, and the easier it is for shock initiation to occur, while the intensity of the external stimulus required is also lower; and The larger the value, the lower the reaction rate; the third term, also known as the reaction term, connects hotspots, causing the reaction to proceed rapidly, leading to detonation. , f, h, z The principle for determining the reaction rate under high pressure is the same as that for the second control term, so I will not repeat it here.
[0066] Specifically, a method for obtaining the parameters of the trinomial ignition growth reaction rate equation for high-energy solid viscoelastic materials by performing partition fitting based on the reactivity change curve includes: The reaction rate time distribution curve is obtained by taking the time derivative of the reaction rate change curve; the reaction rate time distribution curve is then fitted in sections to obtain the parameters of the three-term ignition growth reaction rate equation.
[0067] Among them, the obtained The reaction rate is obtained by taking the time derivative of the curve. The time distribution curve; the derivative is calculated using the central difference method to avoid excessive single-point derivative errors, the formula is: (34) It is the first The time of the step, It is the first The time of the step; for the Lee-Tarver trinomial ignition growth reaction rate equation used in this paper, according to Range division of fitting interval: Ignition term: Slow reaction term: Fast-response items: , , , This is an empirical threshold.
[0068] After obtaining the parameters of the trinomial ignition growth reaction rate equation for high-energy solid viscoelastic materials by performing partition fitting based on the aforementioned reactivity variation curve, the following method can be used to optimize the parameters of the trinomial ignition growth reaction rate equation: Obtain the measured reaction rate value; construct the trinomial ignition growth reaction rate equation using the parameters of the trinomial ignition growth reaction rate equation; optimize the parameters of the trinomial ignition growth reaction rate equation using the measured reaction rate value and the calculated reaction rate value obtained from the trinomial ignition growth reaction rate equation to obtain the optimized trinomial ignition growth reaction rate equation parameters.
[0069] Specifically: within each interval, the following will be obtained The measured reaction rate values were compared with the calculated reaction rate values, and the parameters to be calibrated were adjusted by the least squares method to minimize the mean square error between the two. The parameters of the three-term ignition growth reaction rate equation obtained are shown in Table 7.
[0070] Table 7 Parameters of the Trinomial Ignition Growth Reaction Rate Equation like Figure 11 As shown, Figure 11 The numerical simulation and experimental pressure-time curves are shown, specifically... Figure 11 The pressure-time curves at the four Lagrange positions obtained through numerical calculations show a certain degree of error between the experimental and numerical simulation results. This may be because the copper-manganese pressure gauge, the PTFE diaphragm, and the aluminum diaphragm for the protection circuit were omitted in the numerical modeling; these components would affect pressure propagation. Additionally, in the experiment, the detonator was fixed to a wooden board, while the numerical simulation used point initiation, which affected waveform propagation.
[0071] The embodiments of this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for determining the reaction kinetic parameters of a solid viscoelastic material, characterized in that, The method includes: Obtain the initial expansion data of the cylinder wall surface of the high-energy solid viscoelastic material in the cylinder test; The first equation of state for the high-energy solid viscoelastic material is determined based on the initial expansion data. Obtain the state parameters of a high-energy solid viscoelastic material at each Lagrange position during the Lagrange test process; The reaction degree variation curve of the high-energy solid viscoelastic material is determined based on the first equation of state and the state parameters at each Lagrange position. Based on the reaction rate change curve, the parameters of the three-term ignition growth reaction rate equation for high-energy solid viscoelastic materials are obtained by partition fitting.
2. The method for determining the reaction kinetic parameters of solid viscoelastic materials according to claim 1, characterized in that, The determination of the first equation of state for the high-energy solid viscoelastic material based on the initial expansion data includes: The wall expansion rate is determined based on the initial expansion data; The isentropic internal energy of the high-energy solid viscoelastic material is determined based on the wall expansion rate. Construct a curve showing the relative specific volume as a function of expansion distance based on the initial expansion data; The parameters of the first reference state equation are determined based on the curves showing the variation of isentropic internal energy and relative specific volume with expansion distance. The parameters of the first reference state equation are optimized to obtain the first state equation.
3. The method for determining the reaction kinetic parameters of solid viscoelastic materials according to claim 2, characterized in that, The optimization process of the parameters of the first reference state equation to obtain the first state equation includes: Numerical simulations were performed on the initial expansion data to obtain the simulation results; The parameters of the second reference state equation are determined based on the numerical simulation results; The parameters of the first reference state equation and the parameters of the second reference state equation are fused to obtain the target state equation parameters; The state equation is constructed based on the target state equation parameters to obtain the first state equation.
4. The method for determining the reaction kinetic parameters of solid viscoelastic materials according to claim 3, characterized in that, The determination of the isentropic internal energy of the high-energy solid viscoelastic material based on the wall expansion rate includes: The isentropic internal energy of a high-energy solid viscoelastic material is determined based on the wall expansion rate using the following formula: ； in, E It is the total energy released during the detonation of high-energy solid viscoelastic materials. U The wall expansion rate, m For the quality of high-energy solid viscoelastic materials, E s It is isentropic internal energy. M This represents the total mass of gaseous products generated during the combustion of high-energy solid viscoelastic materials. Q This refers to the total energy generated by the combustion of high-energy solid viscoelastic materials.
5. The method for determining the reaction kinetic parameters of a solid viscoelastic material according to any one of claims 2-4, characterized in that, The step of determining the reactivity variation curve of the high-energy solid viscoelastic material based on the first equation of state and the state parameters at each Lagrange position includes: Curve fitting is performed based on the state parameters at each Lagrange position to obtain the time trajectory; By solving based on the time trajectory and the corresponding trajectory, the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of the high-energy solid viscoelastic material can be obtained. Based on the mixed-state pressure, mixed-state temperature, mixed-state specific volume, mixed-state internal energy, and the first equation of state, a curve is constructed to obtain the reaction degree change curve.
6. The method for determining the reaction kinetic parameters of a solid viscoelastic material according to claim 5, characterized in that, The process of solving based on the time trajectory and the corresponding trajectory line yields the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of the high-energy solid viscoelastic material, including: Obtain the conservation equations in one-dimensional Lagrange coordinates when volumetric forces and thermal conduction are explicitly neglected; By taking the polynomial derivatives of the time radius and the trajectory, the partial derivatives of the isochronous lines are obtained. By solving the isochronous partial derivatives and conservation equations, the mixed-state pressure, mixed-state temperature, mixed-state specific volume, and mixed-state internal energy of the high-energy solid viscoelastic material can be obtained.
7. The method for determining the reaction kinetic parameters of solid viscoelastic materials according to claim 5, characterized in that, The state parameters include pressure-time curves, location parameters, pressure parameters, and time parameters. The step of performing curve fitting based on the state parameters at each Lagrange position to obtain a time trajectory includes: For the pressure-time curve at each Lagrange location, discretize it into N data points at equal time intervals; Based on the location, pressure, and time parameters of N data points, a quadratic polynomial fitting is performed to obtain the time trajectory of each Lagrange position.
8. The method for determining the reaction kinetic parameters of a solid viscoelastic material according to claim 6 or 7, characterized in that, The step of performing partitioned fitting based on the reactivity change curve to obtain the parameters of the trinomial ignition growth reaction rate equation for high-energy solid viscoelastic materials includes: By taking the time derivative of the reactivity change curve, the time distribution curve of the reaction rate is obtained. By performing partition fitting on the reaction rate time distribution curve, the parameters of the three-term ignition growth reaction rate equation are obtained.
9. The method for determining the reaction kinetic parameters of a solid viscoelastic material according to claim 8, characterized in that, After obtaining the parameters of the trinomial ignition growth reaction rate equation for the high-energy solid viscoelastic material by performing partition fitting based on the reactivity variation curve, the method further includes: Obtain the measured reaction rate value; A trinomial ignition growth reaction rate equation was constructed using parameters of the trinomial ignition growth reaction rate equation. The parameters of the three-term ignition growth reaction rate equation are optimized by using the measured reaction rate value and the calculated reaction rate value obtained from the three-term ignition growth reaction rate equation to obtain the optimized parameters of the three-term ignition growth reaction rate equation.
10. The method for determining the reaction kinetic parameters of a solid viscoelastic material according to claim 9, characterized in that, The cylinder used in the cylinder test was a standard 50mm cylinder.