Acceleration and Heating of Metal Particles in Condensed Matter Detonation
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Acceleration and Heating of Metal Particles in Condensed Matter Detonation by Robert C. Ripley A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Mechanical Engineering Waterloo, Ontario, Canada, 2010 c Robert C. Ripley 2010 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract For condensed explosives containing metal particle additives, interaction of the detonation shock and reaction zone with the solid inclusions leads to non-ideal detonation phenomena. Features of this type of heterogeneous detonation are described and the behaviour is related to momentum loss and heat transfer due to this microscopic interaction. For light metal particles in liquid explosives, 60–100% of the post-shock velocity and 20–30% of the post-shock temperature are achieved during the timescale of the leading detonation shock crossing a particle. The length scales corresponding to particle diameter and detonation reaction-zone length are related to define the interaction into three classes, bound by the small particle limit where the shock is inert, and by the large particle limit dominated by thin-detonation-front diffraction. In particular, the intermediate case, where the particle diameter is of similar order of magnitude to the reaction-zone length, is most complex due to two length scales, and is therefore evaluated in detail. Dimensional analysis and physical parameter evaluation are used to formalize the factors affecting particle acceleration and heating. Examination of experimental evidence, analysis of flow parameters, and thermochemical equilibrium calculations are applied to refine the scope of the interaction regime. Timescales for drag acceleration and convective heating are compared to the detonation reaction time to define the interaction regime as a hydrodynamic problem governed by inviscid shock mechanics. A computational framework for studying shock and detonation interaction with particles is presented, including assumptions, models, numerics, and validation. One- and two-dimensional mesoscale calculations are conducted to highlight the fundamental physics and determine the limiting cases. Three-dimensional mesoscale calculations, with up to 32 million mesh points, are conducted for spherical metal particles saturated with a liquid explosive for various particle diameters and solid loading conditions. Diagnostic measurements, including gauges for pressure, temperature, and flow velocity, as well as mass-averaged particle velocity and temperature, are recorded for analysis. Mesoscale results for particle acceleration and heating are quantified in terms of shock compression velocity and temperature transmission factors. In addition to the density ratio of explosive to metal, the solid volume fraction and the ratio of detonation reaction-zone length to the particle diameter are shown to significantly influence the particle acceleration and heating. A prototype heterogeneous explosive system, consisting of mono-disperse spherical aluminum particles saturated with liquid nitromethane explosive, is studied to develop fitting functions describing the shock compression transmission factors. iii Results of the mesoscale calculations are formulated into a macroscopic physical model describing an effective shock compression drag coefficient and Nusselt number. The novel models are explored analytically and are then applied to two challenging sets of test cases with comparison to experiment. Heterogeneous detonation is considered for aluminum particles saturated with liquid nitromethane, and inert particle dispersal is studied using a spherical explosive charge containing steel beads saturated in nitromethane. Finally, discussion of practical considerations and future work is followed by concluding remarks. iv Acknowledgements I am indebted to Dr. Fue-Sang Lien, who first formally introduced me to gas dynamics 13 years ago, and has remained supportive and engaged in my research topics including the fields of multiphase flow and condensed matter detonation. I am grateful for his teaching, supervision, and advice, which helped shape my academic and professional career. I owe my deepest gratitude to Dr. Fan Zhang, who suggested this topic and joined UW as an adjunct professor to supervise this project. I am very fortunate to have learned from such a knowledgeable mentor and outstanding teacher. He inspired and challenged me to reach a higher level of thinking and achieve a deeper understanding of the physics. I am grateful to Defence R&D Canada and Martec Limited for financial support of this project. This thesis would not have been possible without access to significant computing resources including the DRDC Suffield “Quantum” cluster, Public Safety Canada “Wildfire” cluster, Martec computer facilities, and Martec software. I would like to thank the official committee members for their efforts, constructive comments, and helpful suggestions during the comprehensive exam and thesis review processes. I would like give special mention to Dr. Gordon Stubley, who I have known since my undergraduate CFD years, as I very much appreciated his suggestion of exploring dimensional analysis in this work. It is a pleasure to thank my colleagues at Martec for their ongoing support and encouragement. In particular, I wish to thank Laura Donahue for helpful scientific discussions and technical review of my thesis, and Jeff Leadbetter for discussion of physical and numerical models. I would also like to thank David Whitehouse, who was continually supportive of my academic endeavors and provided much needed flexibility in my work schedule during my studies. Finally, I appreciate many years of assistance from everyone in the Combustion Dynamics Group who were involved in the Chinook code. I would like express my gratitude to Dr. David Frost for his interest in this project, useful discussion of my work, interpretation of related experimental results, and permission to use his figures in this thesis. I would also like to thank Dr. Yukio Kato for his helpful comments on my results and kind use of his experimental data. I have benefited from many discussions with professors, colleagues, and leading scientists, for whom I have great regard; I apologize that I could not mention everyone individually. I would like to express my sincere thanks to my parents, family, and friends for their genuine interest, optimism, and encouragement throughout this process. Of particular v significance, I extend special appreciation to my father, for his valuable editorial, proofreading, and technical review of my dissertation. Last, and most importantly, I wish to thank my wife Caroline for her boundless patience, love, and support. It would have been impossible to complete this work without her confidence, encouragement, and understanding. vi Contents List of Tables xii List of Figures xiv Nomenclature xxi 1 Introduction 1 1.1 Brieftheoryofdetonation ........................... 1 1.2 Heterogeneousexplosivematter . 3 1.3 Slurrydetonationphenomena ......................... 4 1.4 Particledispersalphenomena ......................... 9 1.5 Multiscale physics modeling . 12 1.6 Shockinteractionatthemesoscale . 14 1.7 Motivationandstateoftheart ........................ 16 1.8 Objectiveandplanofthesis .......................... 17 2 Regimes for fluid-particle interaction in detonation and explosion flow 19 2.1 Dilute particle flow regime . 20 2.1.1 Particle acceleration . 21 2.1.2 Particleheating............................. 24 2.2 Denseparticleflowregime ........................... 26 2.3 Detonationregime ............................... 28 vii 2.3.1 Homogeneousdetonation. 29 2.3.2 Dilute heterogeneous detonation . 33 2.3.3 Denseheterogeneousdetonation . 35 2.4 Detonation-to-denseflowtransition . .. 37 2.5 Regimes for detonation interaction with particles . .. 37 2.5.1 Case 1: small particle limit (d /L 1)............... 38 p R ≪ 2.5.2 Case 2: large particle limit (d /L 1) ............... 39 p R ≫ 2.5.3 Case 3: intermediate regime (d /L 1)............... 40 p R ∼ 2.6 Transmission factorsforshock anddetonation . .... 40 3 Factors affecting particle acceleration and heating 42 3.1 Dimensional analysis using the Pi Theorem . 43 3.1.1 Dragforce................................ 43 3.1.2 Heattransferrate............................ 46 3.2 Non-dimensionalization of the governing equations . ... 49 3.2.1 Conservationofmass .......................... 51 3.2.2 Conservationofmomentum . 52 3.2.3 Conservationofenergy . .. .. 54 3.3 Analysis of the dimensionless parameter groups . .. 59 3.3.1 Machnumber .............................. 59 3.3.2 Ratioofspecificheats ......................... 60 3.3.3 Reynoldsnumber ............................ 61 3.3.4 Prandtlnumber............................. 63 3.3.5 Density ratio of explosive to solid particle . 63 3.3.6 Volume fraction of particles . 65 3.3.7 Ratio of particle diameter to reaction-zone length . 66 3.4 Summary .................................... 69 viii 4 Approach for shock and detonation interaction with particles 70 4.1 Assumptionsandjustifications. 71 4.1.1 Shockcompressionofmetals. 71 4.1.2 Meltingtemperatureandphasechange . 72 4.1.3 Particledamage............................. 73 4.1.4 Hydrodynamicassumption. 74 4.1.5 Particle reactivity . 75 4.1.6 Particle shape and size distribution . 76 4.1.7 Infinitediameterassumption.