New developments of HEMSim: a computational treatment for aluminized highly energetic materials applied to rock blasting

Revisiting the Becker-Kistiakowsky-Wilson equation of state

The development of analytical theory and experimental methods for understanding the correlation between the explosive properties and bubble dynamic characteristics in underwater explosions has important engineering application value for underwater weapons and ships. Based on the assumption of an instantaneous explosive detonation, we introduced the Jones–Wilkins–Lee equation of state to describe the high-pressure state in an explosion bubble and established the initial conditions for the bubble dynamics calculations. Considering the high-Mach-number flow and high pressure at the initial boundary of the explosion bubble, the Lezzi–Prosperetti equation with second-order Mach accuracy was used. Thus, an analytical model and a calculation method of the explosion bubble dynamics for an explosive detonation were established. This direct link between the detonation parameters and the bubble features is significant for the subtle design, selection, and optimization of explosives' properties. A micro-equivalent explosive bubble pulsation experiment was carried out in a water tank using a customized experimental system, which can offer nearly boundary-free condition to mitigate the reflective wave effects on bubbles. Three types of explosives were used in the experiment: the Research Department explosive (RDX), the Pentaerythritol tetranitrate (PETN), and the Hexanitrohexaazaisowurtzitane (CL20). Finally, the experimental results and the practicability of the experimental system were analyzed. The influence of the explosive type on the dynamic characteristics of the explosion bubbles and the differences between the theoretical and experimental results were compared. The results showed that the proposed explosion bubble dynamics model and calculation method have high accuracy and practicability. The proposed model can be used for explosives with known detonation parameters and equation of state parameters. The detonation parameters, velocity, and pressure are linked to the bubble features pulsation period and the maximum radius directly. The designed experimental system, which is capable of simulating an infinite water for the explosion of micro-equivalent explosives, was stable and easy to use. The work is significant for the subtle design, selection, and optimization of explosives' properties.

The Jones-Wilkins-Lee (JWL) equation of state (EOS) has long been used to accurately calculate the Chapman - Jouguet (C-J) state of condensed phase explosive detonation waves and the subsequent expansion of the reaction products as they do work on surrounding materials. In many applications, the states of the reaction products must also be known at higher pressures and temperatures than the C-J state. Such states occur in overdriven detonation waves supported by high velocity impacts, reflected waves, and converging waves. When the states attained in overdriven detonations were first measured experimentally, the initial JWL EOS's based only on expansion data were found to be too compressive. This problem was resolved 30 years ago by modifying the two exponential terms in the JWL EOS to yield less compressible states at higher pressures, while still matching C-J state and product expansion states at lower pressures. The experimental data on overdriven detonation waves in Pentaerythritol tetranitrate (PETN) is used to develop accurate JWL EOS's using three methods. The first method is to use the analytical formulas of Urtiew and Hayes, who used the experimental C-J detonation velocity, C-J pressure, and the heat of reaction to develop JWL EOS's that fit high and low pressure data. The second method is to use the CHEETAH chemical equilibrium code to calculate: the C-J state; the adiabatic expansion of the products; and a JWL EOS fit to its predicted expansion states. The accuracy of the CHEETAH calculated PETN C-J detonation velocities was checked against experimental detonation velocities measured at several initial densities ranging from 0.27 g/cm3 to 1.764 g/cm3. The third method is to use the CHEETAH code to calculate the overdriven Hugoniot states based on its C-J calculation. This method accounts for the changes in reaction product concentrations as the shock pressures and temperatures increase. Excellent agreement with the experimental shock pressures and densities approaching 120 GPa and 3.6 g/cm3 was obtained using all three methods.

In this paper, in order to solve the deficiency of VLW (Virial‐Wu) equation of state (EOS) and VHL (Virial‐Han‐Long) EOS in describing thermodynamic relationship in high temperature region of gaseous detonation products. Based on the Mayer expansion theory of gas virial coefficients in statistical mechanics, the fourth‐order and fifth‐order dimensionless virial coefficients for Lennard‐Jones (L−J) 6–12 pair potential in a higher temperature range are calculated by using the orthogonal integral method which proposed by Barker. By fitting the theoretical calculation values, a new high order virial EOS: VPL (Virial‐Peng‐Long) EOS for gaseous detonation products is established. Implanting the VPL EOS with the properly introduced EOS of condensed carbon and condensed metal products into the detonation thermodynamic program, the Chapman‐Jouguet (CJ) detonation parameters including detonation velocity, detonation CJ pressure, and detonation temperature of some typical CHNO high explosives and some metal‐containing primary explosives are calculated and obtained. By comparing the calculated values with the experimental values, as well as the calculation values obtained by VLW EOS, VHL EOS, and EXPLO5 (using BKWG−S EOS) software, the accuracy and applicability of VPL EOS in CJ detonation parameters calaulation are analyzed and evaluated.

Many equations of state (EOS) for detonation products have been proposed and used. Some of them are in analytical form and some in tabular form. The most popular is the Jones-Wilkins-Lee (JWL) EOS. One of the main parameters of a product's EOS is the so-called adiabatic gamma along its main isentrope (γs). For JWL EOSs γs(V) varies in a nonmonotonic way. Going down from the CJ point along the main isentrope, it first increases to create a hump, and then, as V goes to infinity, gamma decreases to perfect gas-like behavior with gamma around 1.3. But according to Davis [1], γs(V) should decrease monotonically with V. Accordingly, in this article we investigate the following: (1) Is the hump in γs(V) necessary? and (2) Is it possible to construct a product's EOS with a monotonic γs(V) that is consistent with experimental data? We find that (1) it is possible to construct a product's EOS without a hump in γs(V); and (2) without a hump in γs(V) there are not enough degrees of freedom to reproduce cylinder test data.

This work developed a method for calculating the Jones-Wilkins-Lee (JWL) equation of state (EOS) for the detonation products of aluminized explosives based on hexanitrohexaazaisowurtzitane (CL-20). On the basis of previous studies, chemical reaction equations, Hess’ law and Avogadro’s law were all incorporated in this process because of the non-ideal detonations of aluminized explosives. The EOS parameters were determined for explosive formulations comprising pure CL-20 as well as aluminized versions and compared to literature reports. Calculated pressure-specific volume curves were in good agreement with prior studies. A 50 mm cylinder test using a CL-20/Al/wax composition with a 75/20/5 mass ratio was conducted and the calculated EOS parameters were used to simulate the expansion of the cylinder wall. The experimental and simulation plots were found to agree within 5%, which confirms the validity of this method with regard to engineering analyses.

This work presents a robust box-constrained nonlinear least-squares algorithm for accurately fitting the Jones–Wilkins–Lee (JWL) equation of state parameters, which describes the isentropic expansion of detonation products from high-energy materials. In the energetic material literature, there are plenty of methods that address this problem, and in some cases, it is not fully clear which method is employed. We provide a fully detailed numerical framework that explicitly enforces Chapman–Jouguet (CJ) constraints and systematically separates the contributions of different terms in the JWL expression. The algorithm leverages a trust-region Gauss–Newton method combined with singular value decomposition to ensure numerical stability and rapid convergence, even in highly overdetermined systems. The methodology is validated through comprehensive comparisons with leading thermochemical codes such as CHEETAH 2.0, ZMWNI, and EXPLO5. The results demonstrate that the proposed approach yields lower residual fitting errors and improved consistency with CJ thermodynamic conditions compared to standard fitting routines. By providing a reproducible and theoretically based methodology, this study advances the state of the art in JWL parameter determination and improves the reliability of energetic material simulations.

Determination of performance of non-ideal aluminized explosives

In this paper, to study the output capacity of the micro detonator in MEMS flyer initiation sequence, we studied the driving Ti flyer process of micro detonator filled with “in‐situ” synthetic copper azide micro charge by combining experimental test, thermodynamic calculation, and hydrodynamic simulation. On the one hand, the flight process of the flyer is tested by an all‐fiber photonic Doppler velocimeter (AFPDV), and a complete flyer velocity curve is obtained. On this basis, the effects of different micro charge thickness, micro charge density, and accelerating chamber length on the flight process of the flyer are studied and analyzed. Thus, valuable experimental data are provided for the research of related micro detonators. On the other hand, we study the simulation of the copper azide micro charge driving flyer process. Firstly, we use the detonation thermodynamic program to calculate and fit the detonation velocity (D), detonation CJ pressure (PCJ), and JWL equation of state (EOS) parameters of detonation products of copper azide for simulation. For the gaseous detonation product, we compared the effects of three virial EOS: VLW EOS, VHL EOS, and VPL EOS on the calculation values of detonation parameters for copper azide. For the solid detonation product, a new EOS that can accurately describe the high temperature and high‐pressure state of copper was introduced to the program. Using the detonation parameters of copper azide calculated by thermodynamics, the process of driving the Ti flyer by micro charge is simulated by the 2D ALE method and compared with the experimental data under corresponding conditions.

The unreacted equation of state (EOS) for an unreacted explosive can provide fundamental information to understand any analytical model for the shock and initiation process. Based on the Hugoniot expression in Jones–Wilkins–Lee (JWL) form derived from the Mie–Grüneisen EOS and conservation equation across the shock wave, a three-point calibrating method to determine the JWL EOS parameters for unreacted explosives was developed using intelligent algorithms and shock Hugoniot relationship of the explosives considered. The calibration method proposed utilizes the back propagation neural network to predict the nonlinear system composed of different JWL parameter sets; the genetic algorithm is then used to find the optimal solution of the JWL parameter set. Unreacted JWL EOS parameters of eight typical explosives were calibrated using the calibrating method developed, and an excellent agreement can be observed between JWL EOS and experimental p–v curves for all eight explosives selected, indicating the high accuracy of the three-point calibrating method. However, the effectiveness of the three-point calibrating method was experimentally validated with the experimental data measured from the shock tests of the dihydroxylammonium 5,5′-bitetrazole-1,1′-dioxide (TKX-50)-based explosive, where the JWL p–v curve derived from the three-point calibrating method is in good agreement with the experimental curve.

Overdriven detonation waves with non-stationary, high-pressure states can be produced by high-velocity impacts or by converging detonation waves. A precise equation of states (EOS) of the detonation products is essential to evaluate detonation performance and working capacity. The Jones-Wilkins-Lee (JWL) EOS and its modified forms have an uneven ability in describing the states of detonation products; furthermore, the accuracy of the calculated sound speed is inadequate. This problem is solved by an improved EOS, which is presented by introducing a variable Grüneisen coefficient within JWL. First, the Hugoniot parameters are calculated based on JWL, Jones-Wilkins-Lee-Lee, and Jones-Wilkins-Lee-Tang, and the maximum errors in the prediction of the sound speed are all significant, ranging from 5% to 15%. An excellent agreement is obtained using our modified JWL EOS for Hugoniot pressure over a wide range from initial pressure to 90 GPa, and in the meantime the sound speed is calculated more accurately, with the maximum error being reduced to 2.14%. Then, an experiment of the head-on collisions of detonation waves is carried out to assess the viability of our optimized EOS for characterizing the dynamic evolution of the overdriven detonation process. Furthermore, the hydrodynamic code is modified to incorporate the improved EOS and the numerical simulation is implemented. A comparison between the numerical results and the experimental data confirms the applicability of the improved EOS, and it indicates that a more accurate EOS is obtained for the description of the overdriven detonation phenomenon.

In an explosion test using a shock tube, the behavior of pressure waves can be reproduced with high reliability. However, the explosion in a shock tube occurs in a confined space. It is difficult to predict the behavior of pressure waves and its effect on various concrete specimens by using the research findings related to free-field explosions. Moreover, few studies have focused on explosive-driven shock tubes. In this study, the behavior of pressure waves in a shock tube was numerically analyzed using a finite-element analysis program. The explosive used to generate the pressure waves was an ammonium nitrate fuel oil (ANFO), which exhibits non-ideal explosion characteristics. The Jones–Wilkins–Lee (JWL) and ignition-and-growth (I&G) equations of state were used for blast-pressure calculation. The analysis results were affected by factors such as the release rate of explosive energy and the development of the pressure waves in the confined explosion. The blast behaviors, such as the low release rate of explosive energy and the resulting increase in the impulse, were analyzed using the ignition-and-growth equation. The impulse produced during the development of waves reflected by the block installed at the tube inlet exceeded that produced by the tube wall. Such behaviors that occurred at the beginning of a blast affected the process of wave propagation along the shock tube and the wave reflection due to the test specimen at the outlet of the shock tube. In this study, the blast behavior in the shock tube, which could be referenced for the analysis of blast overpressure and its effect on concrete specimens, was numerically analyzed. Further research on the structural behaviors of concrete specimens due to blast overpressure is needed.

The objective of this work is to improve the robustness and accuracy of numerical simulations of both ideal and non-ideal explosives by introducing temperature dependence in mechanical equations of state for reactants and products. To this end, we modify existing mechanical equations of state to appropriately approximate the temperature in the reaction zone. Mechanical equations of state of the Mie-Grüneisen form are developed with extensions, which allow the temperature to be evaluated appropriately and the temperature equilibrium condition to be applied robustly. Furthermore, the snow plow model is used to capture the effect of porosity on the reactant equation of state. We apply the methodology to predict the velocity of compliantly confined detonation waves. Once reaction rates are calibrated for unconfined detonation velocities, simulations of confined rate sticks and slabs are performed, and the experimental detonation velocities are matched without further parameter alteration, demonstrating the predictive capability of our simulations. We apply the same methodology to both ideal (PBX9502, a high explosive with principal ingredient TATB) and non-ideal (EM120D, an ANE or ammonium nitrate based emulsion) explosives.

We discuss the implementation of genetic algorithms for modelling chemical equilibrium and detonation parameters at the Chapman–Jouguet (CJ) state. This strategy has the advantage that no initial estimate of the equilibrium product distribution needs to be made. It is also an efficient method for finding the global minimum, since for highly non-ideal condensed energetic materials, the calculation of the chemical equilibrium using deterministic algorithms can lead to a local minimum being found instead of a global minimum. This can result in an incorrect prediction of the chemical products distribution. The code was tested for several C–H–N–O energetic materials, namely cyclotrimethyline-trinitramine (RDX), nitromethane (NM), 2,4,6-trinitrotoluene (TNT), and pentaerythritol tetranitrate (PETN). The results obtained using these approaches are in good agreement with the experimental data available in the literature. A comparison with results of other modelling approaches is presented.

Characterisation and validation of the JWL equation of state parameters for PE4