Validation of the Gurney Model for Heterogeneous Systems Jason Loiseau Supervisor: Prof. Andrew J. Higgins Department of Mechanical Engineering McGill University A dissertation submitted to McGill University in partial fullfilment of the requirements for the degree of Doctor of Philosophy Copyright©2017 Jason Loiseau February 2018 Acknowledgements I first and foremost thank my supervisor, Prof. Andrew J. Higgins, for his support above and beyond the call of duty. In my Master’s thesis I had written about using up all of my second chance(s); in finishing my PhD I have most certainly burned through many more. This disser- tation, and my current career track would not be what they are today without Prof. Higgins. I would also like to thank Prof. David Frost for his unofficial supervisory role. Prof. Frost was instrumental in completing much the work presented here, as well as motivating the studies involving metallized explosives and the explosive dispersal of granular material. This thesis would be a shell of its present form without his contributions and interpersonal support. I am also grateful for the support of my fellow graduate students: Justin Huneault and Myles Hildebrand were instrumental in the development of the implosion gun that consumed the early years of my PhD (which sadly didn’t make it into this thesis for the sake of coherence). They also provided the all-important social backdrop of bike rides and inebriation that seems to help so many of us make it through graduate school. William Georges was essential in getting the experiments that comprise the first two chapters done, as well as keeping me sane in the lab. Finally, I acknowledge XiaoCheng Mi for consistently drinking the lot of us under the table! Many of my experiments would not have been possible without the help of some dedicated technical staff. I thank Gary Savard, John Boisvert, Mathieu Beauchesne, and Andreas Hofmann for helping to machine the considerable amount of disposable hardware I needed when it seemed like the Faculty was determined to make sure no one got anything done. I also thank Rick Guilbeault and Lorne McCauley for their help in conducting the many tests done at the Canadian Explosives Research Laboratory. You can’t do anything without money: I appreciate the funding support from NSERC, FQRNT, Fan Zhang at DRDC Suffield, and MITACs along with General Fusion Inc. Finally, I thank my parents, who have been very understanding while I have not been the most dutiful son over the past few years. iv Abstract Accelerating material to very high speed (up to multiple km/s) is one of the primary uses of high explosives. Thus, the magnitude and mechanisms of energy transfer from a detonating high explosive (HE) to material placed in contact with the charge are critical in engineering applications. When heterogeneous, non-conventional explosives are used to drive material, or when heterogeneous material is driven by explosives, mesoscale multiphase interactions and dissipative mechanisms complicate the analysis and modelling of the explosive-material inter- action using both analytic techniques and finite element codes. Explosives that have been heavily diluted with inert material are of interest in metal driving applications where elimination of a transmitted shock into the metal is desirable: spallation and material ejection can be suppressed in flyer launching, and shock-driven heating and shearing can be reduced in dynamic compaction/compression experiments. Alternatively, the addition of reactive metals can increase the output of an explosive when driving metal, provided the particles react sufficiently quickly. Explosives heavily diluted with dense particles are also of interest for reduced collateral, high-near-field impulse charges. The ancillary casing accelera- tion capability of these explosives is thus also important to quantify. When explosives are used to drive granular materials, shock compaction of the material bed dissipates explosive energy, resulting in a dispersed material velocity lower than what would be predicted for homogeneous casings. Quantifying the velocity of dispersants is critical for buried blast momentum transfer, impulse/blast mitigation by granular materials, and the performance of certain blast-enhanced charges. Heterogeneous effects are thus of interest in a number of specialized explosive engineering applications. In the present thesis, the effects of heterogeneities on the explosive acceleration of material was considered in detail through experimentation. Results were analysed in the context of the Gurney model; one of the most ubiquitous analytic tools for estimating the veloc- ity at which materials are driven by explosives and for comparing the thermochemical output of explosives. Various modifications of the Gurney model were proposed and/or evaluated to account for the heterogeneous effects. First, a planar flyer plate charge leveraging Photonic Doppler Velocimetry (PDV) was de- signed to measure the explosive output of heterogeneous HEs. Homogeneous, amine-sensitized liquid nitromethane was used as a benchmark explosive, and the flyer-mass to charge-mass ra- tio (M/C) was varied from 0.03 to 4.65. These experiments validated that the Gurney model is accurate to within 5%, except for very small values of M/C where the error grows to 10%. Impor- tantly, these experiments also validated flyer launch angle predictions and PDV tilt correction techniques up to very large launch angles. Second, the validated flyer plate charge was used to measure the metal driving output of explosives loaded with inert additives. Photonic Doppler Velocimetry was again used to mea- sure flyer acceleration. A wide range of formulations and particle additives were tested: packed particle beds saturated with nitromethane, gelled nitromethane with suspended particles, and C-4 admixed with particles. A slapper initiated charge was also used in order to determine the effect of detonation wave incidence angle on flyer acceleration. The Gurney curves for sev- eral formulations were also measured. Results were analysed in the context of a modified form of the Gurney equation which included the entrainment of the inert particles in the detonation products with no slip. Agreement was found to be acceptable for an engineering model for all but the very heavily loaded explosives. Third, a modified, symmetric version of the experimental geometry was used to evaluate the effect of aluminium addition on the propulsive capability of gelled nitromethane. Unlike typical studies of aluminized explosives using the cylinder test, in the present experiments flyer plates of widely varying thickness were used to ascertain if casing expansion timescale influences energy deposition by the aluminium. Time-resolved flyer surface velocity measurements were performed with PDV. Regardless of flyer thickness and aluminium particle size, aluminized explosives drove the flyer plates faster than an equivalent neat explosive within 4–6 µs. This implied prompt reaction and energy delivery by the aluminium to the detonation products. Finally, the explosive dispersal of a wide variety of granular materials in spherical geometry was performed and various phenomenology related to consolidated shell fracture and particle jet formation were discussed – particularly the segregation and jetting of binary mixtures. The ter- vi minal velocity of the jet tips for all experiments were compared to the spherical Gurney model. Experimental terminal velocities were 40–70% lower than what was predicted by the Gurney model, demonstrating that compaction significantly dissipates explosive energy. A modified Gurney model accounting for dissipation as a function of M/C and porosity was compared and shown to accurately predict the dispersant velocity over the full range of M/C and materials considered with a maximum error of 17%. Conclusively, the amenability and engineering accuracy of the Gurney model was demon- strated for a variety of heterogeneous systems. Because the Gurney model is effectively an energy transfer scaling law, it can be readily modified by changing the conservation equations to account for additions to the system or by adding scaling terms to the M/C ratio and effective explosive energy, 퐸. vii Abrégé L’accélération du matériel à très grande vitesse (jusqu’à plusieurs km/s) est l’une des princi- pales utilisations des explosifs à haute teneur. Ainsi, l’ampleur et les mécanismes du transfert d’énergie de la détonation des explosifs élevés (HE) à des matériaux mis en contact avec la charge sont essentiels dans les applications d’ingénierie. Lorsqu’un explosif hétérogène et non conventionnel est utilisé pour conduire du matériel, ou lorsqu’un matériel hétérogène est en- traîné par des explosifs, les interactions multiphasiques à mésoéchelle et les mécanismes dissi- patifs sont difficilement modélisés par des codes d’éléments finis et des outils analytiques. Les explosifs qui ont été fortement dilués avec du matériel inerte intéressent les applica- tions de conduite en métal où l’élimination d’un choc transmis dans le métal est souhaitable: la spallation et l’éjection du matériau peuvent être supprimées et le chauffage et le cisaillement peuvent être réduits. Alternativement, l’ajout de métaux réactifs peut augmenter la performance d’un explosif lors de la conduite de métal, à condition que les particules réagissent suffisam- ment rapidement. Les explosifs fortement dilués avec des particules denses sont également intéressants pour des charges d’impulsions limitées à longue distance et de haute intensité