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Buckmaster J.,Buckmaster Research | Jackson T.L.,University of Illinois at Urbana - Champaign | Jackson T.L.,University of Florida
Combustion Theory and Modelling | Year: 2014

We pose the following question: 'Within the context of the classical shrinking-core model for sub-micron aluminium combustion, allowing only for the diffusion of atomic oxygen (no aluminium diffusion), but with two non-classical ingredients (large Knudsen number heat losses to the ambient atmosphere and a fractal reacting surface), are the solutions consistent with four experimental facts and data sets: (i) burn times; (ii) particle temperatures; (iii) maximum temperatures independent of particle size for small Damköhler numbers; and (iv) also for small Damköhler numbers a burn law of the form d1 - ν-t (where d is the particle diameter and ν ~ 0.7 or so)?' In the analysis we first consider a non-fractal model and scale the lengths with (where is the diffusion coefficient and k is the reaction-rate constant) and time with (where ρ- is the aluminium density and co is a characteristic value of the O density within the alumina). Burn times are calculated which follow a linear d-t law for small values of kL/D(L = D/2), the Damköhler number, and a quadratic d2-t law for large values of. Enhanced temperatures (greater than the ambient) arise for small values of with maximum values that are size independent. Since the small Damköhler d-t law does not agree with experimental data, we introduce a fractal concept into the model, as this can generate a burn law of the observed form. However, we then find that the maximum temperature is not independent of particle size. © 2014 Taylor & Francis. Source


Buckmaster J.,Buckmaster Research | Jackson T.L.,University of Illinois at Urbana - Champaign | Jackson T.L.,IllinoisRocstar, LLC
Combustion Theory and Modelling | Year: 2013

We revisit the shrinking-core model of sub-micron aluminum combustion with particular attention to the mass flux balance at the reaction front which necessarily leads to a displacement velocity of the alumina shell surrounding the liquid aluminum. For the planar problem this displacement simply leads to an equal displacement of the entire alumina layer, and therefore a straightforward mathematical framework can be constructed. In this way we are able to construct a single curve which defines the burn time for arbitrary values of the diffusion coefficient of O atoms, the reaction rate, the characteristic length of the combustion field, and the O atom mass concentration within the alumina provided that it is much smaller than the aluminum density. This demonstrates a transition between a 'd2-t' law for fast chemistry and a 'd-t' law for slow chemistry. For the spherical geometry, the one of physical interest, the outward displacement velocity creates not a simple displacement, but a stress field which, when examined within the framework of linear elasticity, strongly suggests the creation of internal cracking. We note that if the molten aluminum is pushed into these cracks by the high internal pressure characteristic of the stress field, its surface, where reaction occurs, could be fractal in nature and affect the fundamental nature of the burning law. Indeed, if this ingredient is added to the planar model, a single curve for the burn time can again be derived, and this describes a transition from a 'd2-t' law to a 'dν-t' law, where 0<ν<1. © 2013 Copyright Taylor and Francis Group, LLC. Source


Jackson T.L.,University of Illinois at Urbana - Champaign | Hooks D.E.,Los Alamos National Laboratory | Buckmaster J.,Buckmaster Research
Propellants, Explosives, Pyrotechnics | Year: 2011

In this article, we present a strategy for packing realistic crystals, critical for mesoscale simulations, and predictions. The current packing code uses a dynamic algorithm, with crystal shapes represented by level sets, to create appropriate packs of the microstructure for an energetic material. Crystal shapes include the nitramines HMX, RDX, PETN, and CL20. Two series of packs are considered: a bidisperse pack with size ratio 1:0.3 and a polydisperse pack. We also construct equivalent packs of spheres for comparison purposes. Higher-order statistics are computed and compared. We show that the second-order statistics are essentially independent of particle shape when the packing fraction is held constant. The second-order statistics do, however, depend on the polydispersity. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source


Grant
Agency: Department of Defense | Branch: Air Force | Program: STTR | Phase: Phase I | Award Amount: 100.00K | Year: 2009

Determining the hazard classification of new propellant formulations is important for transportation safety and storage concerns. To avoid costly grain redesign and additional testing, a model that adequately predicts the shock sensitivity, including the outcome of the Naval Ordnance Laboratory Large Scale Gap Test, of modern solid propellants is required. The goals of this proposal are to develop and validate computational tools that predict the shock sensitivity of solid propellant formulations. In particular, we plan to (i) use our packing code, Rocpack, to generate morphologies of interest for shock sensitivity assessments, (ii) modify our CFD code to include appropriate chemistry models, (iii) modify our CFD code to propagate shocks of various strengths through the pack to predict the onset of detonation. We also plan to carry out an experimental program to validate the numerical solvers.


Grant
Agency: Department of Defense | Branch: Air Force | Program: STTR | Phase: Phase II | Award Amount: 750.00K | Year: 2010

Determining the hazard classification of new propellant formulations is important for transportation safety and storage concerns. To avoid costly grain redesign and additional testing, a model that adequately predicts the shock sensitivity, including the outcome of the Naval Ordnance Laboratory Large Scale Gap Test, of modern solid propellants is required. The goals of this proposal are to develop and validate computational tools that predict the shock sensitivity of solid propellant formulations. In particular, we plan to (i) use our packing code, Rocpack, to generate morphologies of interest for shock sensitivity assessments, (ii) modify our CFD code to include appropriate chemistry models, (iii) modify our CFD code to propagate shocks of various strengths through the pack to predict the onset of detonation. In Phase I, we made key steps toward these objectives. We also plan to carry out an experimental program to validate the numerical solvers. BENEFIT: Determining the hazard classification of new propellant and explosive formulations is important for transportation, safety, and storage concerns. To avoid costly grain redesign and additional testing, a model that adequately predicts the shock sensitivity, including the outcome of the Naval Ordnance Laboratory Large Scale Gap Test, of modern solid propellants is required. This information will be of great value to solid rocket manufacturers, to large gun manufacturers, and their customers in the U.S. Department of Defense

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