Upgraded Analytical Model of the Cylinder Test

A Gurney‐type equation was previously corrected for wall thinning and angle of tilt, and now we have added shock wave attenuation in the copper wall and air gap energy loss. Extensive calculations were undertaken to calibrate the two new energy loss mechanisms across all explosives. The corrected Gurney equation is recommended for cylinder use over the original 1943 form. The effect of these corrections is to add more energy to the adiabat values from a relative volume of 2 to 7, with low energy explosives having the largest correction. The data was pushed up to a relative volume of about 15 and the JWL parameter ω was obtained directly. The total detonation energy density was locked to the v=7 adiabat energy density, so that the Cylinder test gives all necessary values needed to make a JWL.     

A Constant-Density Gurney Approach to the Cylinder Test

The previous analysis of the Cylinder test required the treatment of different wall thicknesses and wall materials separately. To fix this, the Gurney analysis is used, but this results in low values for full-wall standard, ideal explosives relative to CHEETAH analyses. A new constant metal-density model is suggested, which takes account of the thinning metal wall as the cylinder expands. With this model, the inner radius of the metal cylinder moves faster than the measured outer radius. Additional small corrections occur in all cylinders because of energy trapped in the copper walls. Also, the half-wall cylinders have a small correction because the relative volumes of the gas products are smaller at a given outside wall displacement. The Fabry-Perot and streak camera measurements are compared. The Fabry method is shown to equate to the constant density model.     

Cylinder Test Correction for Copper Work Hardening and Spall

As a basis for the corrections to be discussed, an analytical equation is first presented for calculating detonation energy densities from copper wall velocities in the Cylinder test. Steinberg‐Guinan work hardening is sufficient for the Cylinder problem, between 1 and 60 GPa, with a change of Y_o to 0.10 kJ cm⁻³ for annealed copper. An air gap correction was the first to be applied, which is a function of the initial air gap width and the tilt angle of the cylinder. Irreversible heat loss was also found to be a small error. Spall is calibrated using new copper gun shot data and this energy is also small. The model up through work hardening agrees with the code, which does not contain heat loss or spall, both of which equal the error of repetitive calculation. The effect of the many additions to the original Gurney energy is shown.     

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.     

Influence of out‐of‐plane fiber orientation on reaction‐to‐fire properties of carbon fiber reinforced polymer matrix composites

This work investigates the influence of the out‐of‐plane orientation of carbon fibers on the reaction‐to‐fire characteristics of polymer matrix composites. A deep insight into combustion processes is gained, which is necessary to fully understand and assess advantages of composites with out‐of‐plane fiber angles. Epoxy‐based Hexply 8552/IM7 specimens with primarily low fiber angles between 0° and 15° are characterized by cone calorimetry. Heat release during fire is greatly affected by the out‐of‐plane fiber angle because of the thermal boundaries created by the fibers. The advancement of the pyrolysis front during fire was determined from peak heat release rates and validated by temperature measurements along the back surface of the panels, representing a novel method of determining position‐dependent pyrolysis migration velocity. These measurements show a transverse shift in pyrolysis front velocity for increasing out‐of‐plane fiber angles. Pyrolysis pathways between the fiber boundaries facilitate faster combustion through the composite thickness, especially for increasing angles from 0° to 15°. It was determined that under the chosen conditions, the pyrolysis front advances approximately 4 times faster when propagating parallel to the fibers than perpendicular.     

Detonation Performance of TATP/AN‐Based Explosives

The detonation velocity and performance were determined for four mixtures of triacetone triperoxide (3,3,6,6,9,9‐hexamethyl‐1,2,4,5,7,8‐hexoxonane, TATP), ammonium nitrate (AN) and water (W) by cylinder expansion tests. The composition of these mixtures varied in the following ranges: 21–31% TATP, 37–54% AN and 19–32% W. The obtained results were compared with those of powdery 2,4,6‐trinitrotoluene (TNT), AN‐fuel oil explosive (ANFO) and emulsion explosive. It was found that the tested TATP/AN/W mixtures represent typical non‐ideal explosives with relatively low critical diameter and with high sensitivity to initiation despite the high content of water due to the presence of the primary explosive (TATP). The detonation velocity is comparable to that of powdery TNT (at similar density). However, the acceleration ability is significantly lower than that of powdery TNT.     

Quantum Chemical Studies on the Structure and Performance Properties of 1,3,4,5‐Tetranitropyrazole: A Stable New High Energy Density Molecule

Molecular orbital calculations were performed for the geometric and electronic structures, band gap, thermodynamic properties, density, detonation velocity, detonation pressure, stability and sensitivity of 1,3,4,5‐tetranitropyrazole ( R23 ). The calculated density (approx. 2060 kg m⁻³), detonation velocity (approx. 9.242 km s⁻¹) and detonation pressure (approx. 41.30 GPa) of the model compound are appearing to be promising compared to hexahydro‐1,3,5‐trinito‐1,3,5‐triazine (RDX) and octahydro‐1,3,5,7‐tetranitro‐l,3,5,7‐tetrazocine (HMX). Bader’s atoms‐in‐molecules (AIM) analysis was also performed to understand the nature of the intramolecular N ⋅⋅⋅ O interactions and the strength of trigger X NO₂ bonds (where XC, N) of the optimized structure computed from the B3LYP/aug‐cc‐pVDZ level.     

NATURAL CONVECTION INSIDE A HORIZONTAL CYLINDER

Natural convection of a fluid contained in an infinitely long horizontal cylinder at large Prandtl number and unit-order Grashof number is analyzed. The motion is generated by an imposed cosine wall temperature distribution which includes an arbitrary phase angle. The phase angle is a measure of the location of the wall temperature extrema.

From an asymptotic ordering of the energy and vorticity transport equations for large Prandtl number it is shown that the core region, which contains fluid surrounded completely by a boundary-layer flow along the cylinder wall, may assume either of two configurations.

For heating angles near the heating-from-the-side case (wall temperature extrema at the ends of the horizontal diameter) linearized forms of the boundary-layer equations are developed which yield solutions that match the core configuration not considered previously. The form of the results agrees generally with experimental evidence for heating-from-the-side.     

NATURAL CONVECTION INSIDE A HORIZONTAL CYLINDER

Natural convection of a fluid contained in an infinitely long horizontal cylinder at large Prandtl number and unit-order Grashof number is analyzed. The motion is generated by an imposed cosine wall temperature distribution which includes an arbitrary phase angle. The phase angle is a measure of the location of the wall temperature extrema.

From an asymptotic ordering of the energy and vorticity transport equations for large Prandtl number it is shown that the core region, which contains fluid surrounded completely by a boundary-layer flow along the cylinder wall, may assume either of two configurations.

For heating angles near the heating-from-the-side case (wall temperature extrema at the ends of the horizontal diameter) linearized forms of the boundary-layer equations are developed which yield solutions that match the core configuration not considered previously. The form of the results agrees generally with experimental evidence for heating-from-the-side.     

A New Method for Evaluating the Energy Characteristics of C?H?N?O Energetic Compounds

From the law of conversation of energy, the release energy from the initiation to the Chapman–Jouguet point during the detonation of an energetic compound has been deduced as a function of initial density, detonation velocity, and detonation pressure. For C H N O energetic compounds the relative release energy per unit volume (I_v) approaches the relative specific wall kinetic energy (E_cyl/E_HMX) at 19 mm wall displacement from the cylinder test with HMX as reference. A good linear relationship between I_v and E_cyl/E_HMX has been regressed, implying that E_cyl/E_HMX is also a function of initial density, detonation velocity, and detonation pressure. It has been concluded that I_v can reflect the driving force of detonation products of energetic compounds and is appropriate to be used for the evaluation of energy characteristics. The assessment of the energy for a series of synthesized and theoretically designed high‐energy compounds reveals that the future of C H N O energetic compounds is promising after CL‐20 and ONC.     

Boron‐Based High Explosives

The detonation velocity, detonation pressure, and cylinder expansion energy of a series of boron compounds including nitroalkylborates, and mixed amino‐nitrosusbtituted borazines, borazenes, iminoboranes, and azaboridines were calculated with Cheetah 2.0. The detonation velocity of the boron compounds is always superior to the all‐carbon analogues at the corresponding densities. Nitro‐substituted boron compounds bearing amino groups instead of hydrogen display even higher performance.     

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.     

A Few Remarks About the Gurney Energy of Condensed Explosives

After reconsidering the definition and characteristics of the Gurney energy, we explain some points related to the evaluation and practical use of this quantity. We correct a recently published relationship between the detonation velocity of an explosive and its Gurney energy at infinite expansion. Then, in the framework of cylinder tests, we indicate that the Gurney energy gives only a rough evaluation of experimental results; it can, however, be reasonably used to compare the ability of explosives to accelerate metals. Besides, the value γ=3 classically evoked for the polytropic gamma of the detonation products generally leads to significant errors in the evaluation of the Gurney energy at infinite expansion.     

The Role of Aluminum in the Detonation and Post‐Detonation Expansion of Selected Cast HMX‐Based Explosives

In order to improve understanding of how aluminum contributes in non‐ideal explosive mixtures, cast‐cured formulations have been analyzed in a series of cylinder tests and plate‐pushing experiments. This study describes the contribution of 15 % aluminum (median size of 3.2 μm) vs. lithium fluoride (an inert substitute for aluminum; <5 μm) in cast‐cured HMX formulations in different temporal regimes. Small cylinder tests were performed to analyze the detonation and wall velocities (1–20 μs) for these formulations. Near‐field blast effects of 58 mm diameter spherical charges were measured at 152 mm and 254 mm using steel plate acceleration. Pressure measurements at 1.52 m gave information about free‐field pressure at several milliseconds. While the observed detonation velocities for all formulations were within uncertainty, significantly higher cylinder wall velocities, plate velocities, and pressures were observed for the aluminum formulations at ≥2 μs. Additionally, hydrocode calculations were performed to determine how non‐ideal behavior affected the plate test results. Collectively, this work gives a clearer picture of how aluminum contributes to detonation on timescales from 1 μs to about 2 ms, and how the post‐detonation energy release contributes to wall velocities and blast effects. The experiments indicate that significant aluminum reactions occur after the CJ plane, and continue to contribute to expansion at late times.     

Detonation Energies from the Cylinder Test and CHEETAH V3.0

The cylinder test for deriving detonation energies is fully described and analyzed, including the relation between streak camera and Fabry‐Perot interferometer data. The 6, 12.5 and 19 mm scaled displacements are modified to represent average relative volumes of 2.2, 4.4 and 7.2. CHEETAH V3.0 is introduced with its new all‐Hugoniot calibration, which produces the most accurate detonation energies to date. Using CHEETAH V3.0 energies at the three cylinder volumes, we find that 107 cylinder shots show full burn. Of these, 52 are taken as standards with an error of ±2.6 %. Another 26 show higher energies, which cannot be explained. Finally, 111 shots show lower energies and these are taken to represent slow kinetics. The composite explosive PBXN‐111 is taken as a special problem, because unconfined and confined Size Effect data plus two different‐size cylinder tests have been done. The form of JWL++ with one fully‐reacted JWL, as copied from Ignition & Growth, failed to fit the data. The two rate constants interact too strongly, so that the form works for 90 % cylinder energies but not for the 25 % found in PBXN‐111. We, therefore, constructed a 2‐JWL form with the first, fast rate describing the detonation velocity and the second, slow rate the cylinder energies. This form of JWL++ isolates the rate constants and works for slow‐reacting explosives. The simple form of JWL++ allows the fast and slow rates to be estimated directly from the data. The Gurney velocity divided by the detonation velocity for the standard explosives is found to be 0.30, 0.33, 0.34 and 0.35 for the relative volumes v=2.2, 4.4, 7.2 and the maximum measured.     

Computational Fluid Dynamics Modeling of Gas‐Liquid Two‐Phase Flow around a Spherical Particle

Microscale studies, which can provide basic information for meso‐ and macroscale studies, are essential for the realization of flow characteristics of a packed bed. In the present study, the effects of gas velocity, liquid velocity, liquid‐solid contact angle, and liquid viscosity on the flow behavior were parametrically investigated for gas‐liquid two‐phase flow around a spherical particle, using computational fluid dynamics (CFD) methodology in combination with the volume‐of‐fluid (VOF) model. The VOF model was first validated and proved to be in good agreement with the experimental data. The simulation results show that the film thickness decreases with increasing gas velocity. This trend is more obvious with increasing operating pressure. With increasing liquid velocity, the film thickness tends to be uniform on the particle surface. The flow regime can change from film flow to transition flow to bubble flow with increasing contact angle. In addition, only at relatively high values does the liquid viscosity affect the residence time of the liquid on the particle surface.     

Detonation Measurements on Damaged LX‐04

We have applied thermal insults on LX‐04 at 185 °C and found that the material expanded significantly, resulting in a bulk density reduction of 12%. Subsequent detonation experiments (three cylinder tests) were conducted on the thermally damaged LX‐04 samples and pristine low‐density LX‐04 samples and the results showed that the fractions reacted were close to 1.0. The thermally damaged LX‐04 and pristine low‐density LX‐04 showed detonation velocities of 7.7–7.8 mm μs⁻¹, significantly lower than that (8.5 mm μs⁻¹) of pristine high‐density LX‐04. Detonation energy densities for the damaged LX‐04, low‐density pristine LX‐04, and hot cylinder shot of LX‐04 were 6.48, 6.62, and 6.58 kJ cm⁻³, respectively, lower than the detonation energy density of 8.11 kJ cm⁻³ for the high density pristine LX‐04. The break‐out curves for the detonation fronts showed that the damaged LX‐04 had longer edge lags than the high density pristine LX‐04, indicating that the damaged explosive is less ideal.     

Boundary effects on thermophoresis of aerosol cylinders

An analytical study is presented for the thermophoretic motion of a circular cylindrical particle in a gaseous medium with a transversely imposed temperature gradient near a large plane wall parallel to its axis in the quasisteady limit of negligible Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The presence of the confining wall causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall enhance the viscous retardation of the moving particle. Through the use of cylindrical bipolar coordinates, the transport equations governing this problem are solved and the wall effects on the thermophoresis of the aerosol cylinder are computed for various cases. The presence of the plane wall can reduce or enhance the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle, the relative particle-wall separation distance, and the direction of the applied temperature gradient. The direction of the thermophoretic motion of a cylindrical particle near a plane wall is different from that of the prescribed thermal gradient, except when it is oriented parallel or perpendicular to the wall. The effects of the plane wall on the thermophoresis of a cylinder are found to be much more significant than those for a sphere at the same separation.     

Initiation Pressure Thresholds from Three Sources

Pressure thresholds are minimum pressures needed to start explosive initiation that ends in detonation. We obtain pressure thresholds from three sources. Run‐to‐detonation times are the poorest source but the fitting of a function gives rough results. Flyer‐induced initiation gives the best results because the initial conditions are the best known. However, very thick flyers are needed to give the lowest, asymptotic pressure thresholds used in modern models and this kind of data is rarely available. Gap test data are in much larger supply but the various test sizes and materials are confusing. We find that explosive pressures are almost the same if the distance in the gap test spacers are in units of donor explosive radius. Calculated half‐width time pulses in the spacers may be used to create a pressure‐time curve similar to that of the flyers. The very‐large Eglin gap tests give asymptotic thresholds comparable to extrapolated flyer results. The three sources are assembled into a much‐expanded set of near‐asymptotic pressure thresholds. These thresholds vary greatly with density: for TATB/LX‐17/PBX 9502, we find values of 4.9 and 8.7 GPa at 1.80 and 1.90 g/cm³, respectively.     

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.