Detonation velocity deficit and curvature radius of flexible detonation fuses

The detonation velocity deficit in bending flexible detonating fuses is studied, based on the detonation wave’s corner effects and delay time phenomenon. A physical model and a theoretical mathematical equation of the detonation velocity deficit are established by using the dimensional analysis. Based on experimental data, a semi-empirical formula of the detonation velocity deficit for bending fuses in the same charge size is derived. It is shown that the detonation velocity deficit and the reciprocal of the curvature radius are in an exponential relationship.     

A Discussion of the Kamlet‐Jacobs Formula for the Detonation Pressure

The main features of the Kamlet‐Jacobs formula for the detonation pressure of C H N O explosives are analytically derived from a BKW (Becker‐Kistiakowsky‐Wilson) equation of state of the detonation products. In the derivation, well‐known typical values at the Chapman‐Jouguet state, in particular the nearly constant value of the relative volume of the detonation products, are used.     

Predicting the Detonation Velocity of CHNO Explosives by a Simple Method

A simplified method is shown, based on a semi‐empirical procedure, to estimate the detonation velocities of CHNO explosives at various loading densities. It is assumed that the product composition consists almost of CO, CO₂, H₂O and N₂ for oxygen‐rich explosives. In addition solid carbon and H₂ are also counted for an oxygen‐lean explosive. The approximate detonation temperature, as a second needed parameter, can be calculated from the total heat capacity of the detonation products and the heat of formation of the explosive by PM3 procedure. The detonation velocities of some well‐known CHNO explosives, calculated by the simple procedure, fit well with measured detonation velocities and the results from the well‐established BKW‐EOS computer code.     

Predicting Detonation Performance of CHNOFCl and Aluminized Explosives

A new “hand‐calculated” method is introduced for prediction of detonation pressure of explosive and mixture of explosives with general formula CHNOFClAl. Suitable decomposition paths are used to estimate heat of detonation and detonation pressure. These decomposition paths are based on the distribution of oxygen atoms between carbon and hydrogen atoms as well as the degree of oxidation of aluminum. For CHNOFCl explosives, it is shown that the predicted detonation pressures with the new method are more reliable with respect to one of the best available empirical methods for loading densities greater than or equal 0.8 g cm⁻³. Since aluminized explosives have non‐ideal behavior, the new method does not require using full or partial oxidation of aluminum, which is usually required by a computer code. The predicted results of the new model also provide more reliable results than outputs of complex computer code with the BKWS equation of state.     

Predicting Maximum Attainable Detonation Velocity of CHNOF and Aluminized Explosives

This paper describes a simple method to predict the detonation velocity of pure and mixed CHNOF explosives as well as aluminized explosives at their maximum nominal density as one of the most important detonation properties. The new correlation uses the contribution of some structural parameters to apply for a wide range of ideal and non‐ideal explosives. Aluminized explosives have non‐ideal behavior and the Chapman Jouguet detonation velocities significantly differ from those expected from existing thermodynamic computer codes for equilibrium and steady state calculations. With the presented method, there is no need to use any assumed detonation products, heat of formation and experimental data. Detonation velocities at maximum nominal density of explosives predicted by this procedure show good agreement with respect to experimental values. They are more reliable compared to the calculated results of well‐known empirical methods and computed outputs using BKWS equation of state for CHNOF and aluminized explosives.     

Effect of Al/O Ratio on the Detonation Performance and Underwater Explosion of HMX‐based Aluminized Explosives

The performance of detonation and underwater explosion (UNDEX) of a six‐formula HMX‐based aluminized explosive was examined by detonation and UNDEX experiments. The detonation pressures, detonation velocities, and detonation heat of HMX‐based aluminized explosive were measured. The reliability between the experimental results and those calculated by an empirical formula and the KHT code was verfied. UNDEX experiments were carried out on the propagation of a shock wave and a bubble pulse of a 1 kg cylindrical HMX‐based aluminized explosive underwater at a depth of 4.7 m. Based on the experimental results of the shock wave, the coefficients of similarity law equation for the peak pressure and attenuation time constant of shock wave were in acceptable agreement. The bubble motion during UNDEX was simulated using MSC.DYTRAN software, and the radius time curves of bubbles were determined. The effect of the aluminum/oxygen ratio on the performance of the detonation and UNDEX for an HMX‐based aluminized explosive was discussed.     

A Detonation Model of High/Low Velocity Detonation

A new detonation model that can simulate both high and low velocity detonations is established using the least action principle. The least action principle is valid for mechanics and thermodynamics associated with a detonation process. Therefore, the least action principle is valid in detonation science. In this model, thermodynamic equilibrium state is taken as the known final point of the detonation process. Thermodynamic potentials are analogous to mechanical ones, and the Lagrangian function in the detonation process is L=T−V. Under certain assumptions, the variation calculus of the Lagrangian function gives two solutions: the first one is a constant temperature solution, and the second one is the solution of an ordinary differential equation. A special solution of the ordinary differential equation is given.     

Titania Nanocrystalline Prepared by Detonation Method and Calculation of Detonation Parameters

As a promising method for synthesizing nanosized materials, detonation method was used to prepare TiO₂ nanoparticles. A new method for predicting the Chapman‐Jouguet (C‐J) detonation parameters of C_aH_bO_cN_dTi_e explosives, such as detonation heat, detonation temperature, and detonation pressure, was introduced according to the approximate reaction equations of detonation. The coefficient of oxygen balance of explosive was also calculated according to the specific detonation synthesis experiment. The calculation method was more useful in predicting the formation processes of detonation products and optimizing the experimental procedure. It could also support theory foundation for further experiments to some extent.     

Studies of Detonation Characteristics of Aluminum Enriched RDX Compositions

Research on the effect of aluminum contents and of its particle size on detonation characteristics of RDX‐based compositions containing 15–60% aluminum was carried out. Measurements of detonation velocity for different charge diameters and confinements were performed. To measure the shock curvature of the detonation wave, X‐ray photography was applied. Unconfined charges and charges confined with a water envelope were tested. The radius of the detonation front curvature was determined. The cylinder test results were the basis for determination of the acceleration ability and energetic characteristics of the detonation products of the mixtures. The Gurney energy describing the acceleration ability was found. The detonation energy of the mixtures tested was also estimated from the cylinder test data.     

Detonation Velocities and Pressures,and their Relationships with Electric Spark Sensitivities for Nitramines

The DFT‐B3LYP method, with basis set 6–31G*, is employed to optimize molecular geometries and electronic structures of eighteen nitramines. The averaged molar volume (V) and theoretical density (ρ) are estimated using the Monte‐Carlo method based on 0.001 electrons/bohr³ density space. Subsequently, the detonation velocity (D) and pressure (P) of the explosives are estimated by using the Kamlet‐Jacobs equation on the basis of the theoretical density and heat of formation (Δ_fH), which is calculated using the PM3 method. The reliability of this theoretical method and results are tested by comparing the theoretical values of ρ and D with the experimental or referenced values. The theoretical values of D and P are compared with the experimental values of electric spark sensitivity (E_ES). It is found that for the compounds with metylenenitramine units ( CH₂N(NO₂) ) in their molecules (such as ORDX, AcAn and HMX) or with the better symmetrical cyclic nitramines but excluding metylenenitramine units (such as DNDC and TNAD), there is a excellent linear relationship between the square of detonation velocity (D²) or the logarithm of detonation pressure (lg P) and electric spark sensitivity (E_ES). This suggests that in the molecular design of energetic materials, such a theoretical approach can be used to predict their E_ES values, which have been proven to be difficult to predict quantitatively or to synthesize.     

The Effects of Containment on Detonation Velocity

Reactive flow cylinder code runs on six explosives were made with rate constants varying from 0.03 to 70 μs⁻¹. Six unconfined/steel sets of original ANFO and dynamite data are presented. A means of comparing confinement effects both at constant radius and at constant detonation velocity is presented. Calculations show two qualitatively different modes of behavior. For U_s/C_o≥1.2, where U_s is the detonation velocity and C_o the zero‐pressure sound speed in steel, we find a sharp shock wave in the metal. The shock passes through the steel and the outer wall has a velocity jump‐off. For U_s/C_o≤1.04, we find a pressure gradient that moves at the detonation velocity. A precursor pulse drives in the explosive ahead of the detonation front. The outer wall begins to move outward at the same time the shock arrives in the explosive, and the outer wall slowly and continuously increases in velocity. The U_s/C_o≥1.2 cylinders saturate in detonation velocity for thick walls but the U_s/C_o<<1.04 case does not. The unconfined cylinder shows an edge lag in the front that approximately equals the reaction zone length, but the highly confined detonation front is straight and contains no reaction zone information. The wall thickness divided by the reaction zone length yields a dimensionless wall thickness, which allows comparison of explosives with different detonation rates. Even so, a rate effect is found in the detonation velocities, which amounts to the inverse 0.15–0.5 power.     

Calculation of Detonation Velocity,Pressure, and Electric Sensitivity of Nitro Arenes Based on Quantum Chemistry

The DFT‐B3LYP method, with basis set 6‐31G*, is employed to optimize molecular geometries and electronic structures of thirty‐nine nitro arenes. The averaged molar volume (V) and theoretical density (ϱ) are estimated using the Monte‐Carlo method, based on 0.001 electrons/bohr³ density space and a self‐compiled program. The detonation velocity (D) and pressure (P) of the explosives are estimated by using the Kamlet–Jacbos equation on the basis of the theoretical density and heat of formation (Δ_fH), which is calculated using the PM3 method. The reliability of this theoretical method and results are tested by comparing the theoretical values of ϱ and D with the experimental or referenced values. The theoretical values of D and P are correlated with the experimental values of electric sensitivity (E_ES). It is found that, for the nitro arenes, there is a linear relationship between the square of detonation velocity (D²) or detonation pressure (P) and electric sensitivity (E_ES), which suggests that such a theoretical approach can be used to predict or judge the magnitude of E_ES, which is difficult to measure in the molecular design of energetic materials. In addition, we have discussed the influence of the substituted groups and the parameters of the electronic structure on density, detonation velocity, pressure, and electric sensitivity, and have shown that the substituted groups have the effect of activity or insensitivity, and that the influence of Q_‐NO2 and E_LUMO is important.     

Energetic Material Detonation Characterization: A Laboratory‐Scale Approach

A novel energetic‐material detonation and air‐blast characterization technique is proposed through the use of a laboratory‐scale‐based modified “aquarium test.” A streak camera is used to record the radial shock wave expansion rate at the energetic material air interface of spherical laboratory‐scale (i.e., gram‐range) charges detonated in air. A linear regression fit is applied to the measured streak record data. Using this in conjunction with the conservation laws, material Hugoniots, and two empirically established relationships, a procedure is developed to determine fundamental detonation properties (pressure, velocity, particle velocity, and density) and air shock wave properties (pressure, velocity, particle velocity, and density) at the energetic material air interface. The experimentally determined properties are in good agreement with published values. The theory’s applicability is extended using historical experimental test data due to the limited number of experiments able to be performed. Predicted detonation wave and air shock wave properties are in good agreement for a multitude of energetics across various atmospheric conditions.     

Study of the Effect of Covolumes in BKW Equation of State on Detonation Properties of CHNO Explosives

Due to its simplicity, the Becker‐Kistiakowsky‐Wilson (BKW) equation of state has been used in many thermochemical codes in the calculation of detonation properties. Much work has been done in the calibration of the BKW EOS parameters to achieve agreement with experimental detonation velocities and pressures thus resulting in many different sets of BKW constants (α, β, κ and θ) and covolumes of detonation products, with varying levels of accuracy over broad density limits, i.e. broad pressure limits. The covolumes of the product gases in BKW EOS may be regarded as measures of intermolecular interactions, and their values should affect the predicted detonation properties, particularly at higher explosives densities. This work aims to study the effect of covolumes on calculated values of detonation parameters. Several sets of covolumes available from literature and derived by different methods (matching experimental Hugoniots of individual products, by stochastic optimization, and calculated from van der Waals radii), were studied. In addition, the covolumes of the product gases were also calculated by ab initio methods. The effect of covolumes is studied comparing detonation properties calculated using different sets of covolumes, and experimental data for a series of standard CHNO explosives. It was found that it is possible to reproduce experimental detonation velocities and pressures within reasonable accuracy (root mean square error of less than 5 % for all tested sets) using different set of covolumes, and simultaneously optimizing constants in BKW EOS. However, different values of covolumes strongly affect the composition of detonation products at the Chapman‐Jouguet state. It particularly applies to oxygen‐deficient explosives and at higher densities, where formic acid appears to be an important detonation product.     

Influence of Ammonium Nitrate Prills' Properties on Detonation Velocity of ANFO

Prilled/granulated ammonium nitrate is commonly used as a fertilizer and a basic ingredient of industrial explosives, especially of ANFO. One of the most important factors that affect the explosive properties of ANFO is the porosity of the prills/granules. This paper describes an attempt to manufacture ammonium nitrate prills of determined porosity in order to investigate its influence on the ANFO detonation velocity. A method of manufacturing porous ammonium nitrate prills with a high‐level of oil absorption (up to 20% by volume) was developed. The relations between porosity and granulometric distribution of ammonium nitrate prills versus the detonation velocity of ANFO were examined. It has been proved that the detonation velocity of ANFO increases significantly with higher porosity and smaller size of ammonium nitrate prills/granules. The influence of ANFO oxygen balance (researched by changing the content of fuel oil in the mixture) on detonation velocity has been determined for two kinds of ammonium nitrate prills–one with a low and another one with a high level of porosity.     

Detonation Wave Propagation in Double‐layer Cylindrical High Explosive Charges

The flow fields associated with regular and irregular reflections of detonation waves in double‐layer cylindrical (DLC) high explosives (HE) are analyzed, and an analytical model for predicting the detonation wave configurations is proposed. Regular reflection and three‐shock Mach reflection during detonation wave propagation are discussed. Calculated results of pressure, flow velocity, and specific volume are presented and the Mach stem height is also determined based on mass conservation. The corresponding numerical simulation based on the Lee–Tarver model is developed to generate data comparable with an ordinary cylindrical charge. It is shown that steady convergent detonation wave propagation occurs in the DLC charge. The maximum pressure up to 4.0 times of Chapman–Jouguet (CJ) pressure is reached at the collision point related to the Mach reflection, and the predictions based on the proposed model correlate well with corresponding numerical results.     

Acceleration Profile of a Flat Flyer Driven by Detonation Isentrope

In the design of explosive devices, understanding of the behavior of explosively propelled matter is one of the important steps to optimize the performance of the device. In a typical flat, metallic flyer and explosives charge system, the flyer reaches its maximum velocity after a certain degree of expansion of the detonation gas. During this expansion, the flyer is deformed in an arced‐shape by the incoming rarefaction from nearby surfaces. In this work, an acceleration/deformation profile of an explosively propelled flat, metallic plate was studied based on the isentropic expansion of detonation gas and subsequent rarefaction intrusion to the center of the flyer. In order to properly describe the arced deformation of the flyer, a rather simplified new term of the pressure release ratio behind the flyer η is introduced based on the expansion of the detonation isentrope behind the flyer. A theoretical model was built to predict the behavior of an explosively driven flyer and the rarefaction intrusion into the center of the explosives charge. The results are compared to a hydrocode simulation and exhibit favorable agreement in a limited application.     

Divergent Detonation Wave Processes in PBX Based on RDX

In order to characterize the initial phase of the divergent detonation wave in PBX, a hemispheric explosive sample was initiated by a long cylindrical charge of the same explosive. The tested PBX is composed of 85 wt% of RDX and 15 wt% of binder based on HTPB. This PBX‐RDX presents an effective density of 1.57 g/cm³, and a detonation velocity of 7.90 mm/μs.     

Substituent Effects on Thermodynamic and Detonation Properties of Polynitrobenzenes

Density functional theory (DFT) calculations were performed for a series of polynitrobenzene derivatives. Some nitrobenzenes with amino groups attached were also investigated as a benchmark or as a precursor. Heats of formation (HOF) were evaluated. The isodesmic reactions used for the prediction of HOFs are of permutation type in terms of the substituents. The HOFs increase non‐additively with increasing number of nitro groups. The attachment of the amino groups to polynitrobenzenes dramatically decreases the HOF. The HOF of hexanitrobenzene (HNB) is 344.05 kJ mol⁻¹ at the B3LYP/6‐311+G** level. This value is much larger than that of the widely used 1,3,5‐triamino‐2,4,6‐trinitrobenzene (TATB), which engenders HNB a large chemical energy of detonation. The strengths of the group interactions were analyzed according to the disproportionation energy. The nearest‐neighbor interactions in polynitrobenzenes are in the range of 27.20–55.90 kJ mol⁻¹. The energy barrier for the internal rotation of nitro group in nitrobenzene is 24.6 kJ mol⁻¹. However, the energy barrier for the internal rotation of 2‐position nitro group of 1,2,3‐trinitrobenzene is as large as 216.3 kJ mol⁻¹. The chemical energies of detonation for polynitrobenzenes with three or more nitro groups are over 6000 J g⁻¹. Pentanitroaniline and HNB have good performances in terms of detonation velocity and pressure.     

Effect of Mixing Methods on the Thermal Stability and Detonation Characteristics of Ammonium Nitrate and Sodium Chloride Mixtures

A study has examined the effect of mixing methods on the thermal stability and detonation characteristics of ammonium nitrate (AN) and sodium chloride (NaCl) mixtures. NaCl was mixed with AN by two methods. The thermal stability, detonation velocity and structural properties were investigated by differential scanning calorimetry (DSC), measurement of detonation velocity and X‐ray diffraction (XRD). For the mechanical mixing method, in all tested scope of proportions of NaCl in the mixtures, activation energies increase when the proportion of NaCl increases; for solution mixing method, the activation energies decrease first and then start to increase as the proportion of NaCl increases. The detonation velocity of AN‐NaCl mixtures prepared by two mixing methods also showed different results. The results indicate that the mixing methods significantly affect the thermal stability and detonation characteristics of AN.