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Determining the hazard classification of energetic materials is important for transportation safety and storage concerns. To avoid costly grain redesign and additional testing, a model that adequately predicts the shock sensitivity of energetic materials is required, particularly the outcome of the Naval Ordnance Laboratory Large Scale Gap Test. The goals of this effort are to develop and validate computational tools that predict the shock sensitivity of energetic materials. Specifically, to use our packing code, Rocpack, to generate morphologies of interest for shock sensitivity assessments, and to use our CFD code, RocSDT, to propagate shocks of various strengths through the pack to predict the onset of detonation. Dealing accurately with the material interfaces in this problem is a long-standing challenge, as familiar strategies lead to spurious temperature spikes, and therefore spurious reaction rate spikes. We describe a new strategy, which does not generate spurious spikes, and demonstrate via a number of test problems that numerical convergence can be achieved. We also examine two problems that are stepping stones to a complete simulation; both are planar. In the first, we consider the passage of a shock wave through pure HMX in which a line of hot spots of the kind generated by void collapse are located a short distance behind the shock. When the hot spot spacing is large, the shock remains a shock; when small, transition to detonation occurs. In the second problem we also insert hot spots, but into a matrix of HMX particles and binder.

Flame-balls are stationary spherical premixed flames observed in certain near-limit mixtures. It is believed that radiative heat losses are an important stabilizing influence. Numerical solutions of flame balls are constructed for hydrogen-air mixtures using an accurate description of the chemical kinetics, diffusive transport, and radiation losses. A lean limit equivalence ratio of 0.0866 is predicted and a rich limit of 2,828. For any equivalence ratio between the two limits there are two solutions. One is characterized by a small flame, incomplete reactant consumption, and negligible radiation losses. The other by a large flame, complete consumption of one of the reactants, and significant radiation losses. The maximum temperature varies between 1200 and 900 K as the two solution branches are traversed. Much of our discussion is a reprise and modification of previously published analytical results, for these provide physical insight into the nature of the solutions, and suggest that a portion of the large flame branch near the lean limit is stable and so corresponds to observable flames.

This review paper on the structure and stability of laminar flames considers such phenomena as heterogeneous mixtures, acoustic instabilities, flame balls and related phenomena, radiation effects, the iodate oxidation of arsenous acid and 'liquid flame fronts', approximate kinetic mechanisms and asymptotic approximations, and tribrachial or triple flames. The topics examined here indicate three themes that may play an important role in laminar flame theory in the coming years: microgravity experiments, kinetic modeling, and turbulence modeling. In the discussion of microgravity experiments it is pointed out that access to drop towers, the Space Shuttle and, in due course, the Space Station Freedom will encourage the development of experiments well designed to isolate the fundamental physics of combustion.

A computational framework has been developed to investigate nozzle erosion in solidpropellant rocket motors. Highly resolved simulations are performed to understand the effects caused by non-uniform and unsteady inlet conditions. The thermal boundary layer is captured along the nozzle walls to compute the heat flux and erosion rates. To optimize the computational resources, the SRM nozzle configuration is studied by itself and appropriate inflow conditions are imposed. Two complementary formulations to apply these conditions are described: the first one based on extracting flow field from the full motor configuration; while the second invokes a multiscale asymptotic analysis of turbulent flows inside rocket motor.

A numerical framework of simulating erosion in rocket nozzle is developed and verified. The focus is to examine three-dimensional effects due to either non-trivial inlet condition or geometry. Such a tool will provide new insights into thermal management, a topic of critical importance for the Air Force and rocket companies. In order to examine 3D effects, both flows in a nozzle with turbulent inlet condition and a thrust vector control nozzle were simulated, and 3D effects were clearly demonstrated for the thrust vector control nozzle. To obtain turbulent inlet conditions in these simulations, two types of approach are proposed either based on a full-configuration simulation including chamber or from a periodic rocket simulation through multiscale analysis. The first approach is developed for laminar flow for the moment whereas the second approach is developed for turbulent flows.

The ignition of lean H2/air mixtures under microgravity (μg) conditions can lead to the formation of spherical premixed flames (flame balls) with small Péclet number (Pe). A central question concerning these structures is the existence of appropriate stationary stable solutions of the combustion equations. In this paper we examine an individual flame ball that is suspended in a fluid whose velocity far from the flame is steady and varies linearly in space. Detailed results are obtained for simple shear flows and simple straining flows, both axisymmetric and plane.Convection enhances the flux of heat from the flame and the flux of mixture to the flame, but because the Lewis number (Le) is less than unity the relative impact on the former is greater than on the latter. Consequently, there is a net loss of energy from the flame to the far field, and if large enough this will quench the flame. For values of shear or strain less than the quenching value there are two possible stationary solutions, but one of these is unstable to spherically symmetric disturbances of the flame ball. The radius of the other solution is unbounded as Pe goes to zero. Examination of a class of three-dimensional disturbances reveals no additional instability when the energy losses are due only to convection, but sufficiently large flame balls are unstable when volumetric heat losses from radiation are accounted for. This last result is in agreement with previous results that have been obtained for zero Pe, albeit with inadequate accounting for the flow field generated by the perturbations.

A theory of spherical premixed flames in which the only transport processes are diffusion and radiation (“flame balls”) is extended to include the effects of heat loss from the far-field (unburned gas). Using matched asymptotic expansions for large activation energy, stationary solutions are constructed and an evolution equation for the radial motion of the flame is derived. Linear stability analyses are performed for both one-dimensional and three-dimensional perturbations. It is shown that when far-fieldlosses are included, the stability properties are qualitatively changed. A smaller range of conditions produces flames that are stable to one-dimensional disturbances and, in some cases, the linear growth rates are found to have imaginary components. Numerical intergation of the evolution equation reveals oscillations (but not limit cycles), in agreement with a bifurcation analysis. The minimum flame-ball radius for which three-dimensional instabilities will occur is shown to depend only on the near-field losses, and becomes arbitrarily large as these losses are reduced.

In recent years we have constructed closely packed spheres using the Lubachevsky-Stillinger algorithm to generate morphological models of heterogeneous solid propellants. Improvements to the algorithm now allow us to create large polydisperse packs on a laptop computer, and to create monodisperse packs with packing fractions greater than 70% which display significant crystal order. The use of these models in the physical context motivates efforts to examine in some detail the nature of the packs, including certain statistical properties. We compare packing fractions for binary packs with long-known experimental data. Also, we discuss the near-neighbor number and the radial distribution function (RDF) for monodisperse packs and make comparisons with experimental data. We also briefly discuss the RDF for bidisperse packs. We also consider bounded monodisperse packs, and pay particular attention to the near-wall structure where we identify significant order.

The role of thermal non-equilibrium and endothermic pyrolysis is discussed in the context of a simple model of reverse smoulder combustion. It is shown that nonequilibrium has little qualitative effect on the nature of the solutions, but endothermic pyrolysis can lead to quenching at sufficiently large blowing rates.

Recent experiments in microgravity suggest the possibility of stationary spherical premixed flames (flame balls) in which the only fluxes are diffusional. We construct stationary solutions of this nature, starting with simple model equations and using activation energy asymptotics. Sufficiently large volumetric heat losses quench the flame, and for heat losses less than the quenching value there are two possible solutions, a small flame, and a large flame. For vanishing heat loss the small solution is identical to one constructed by Zeldovich, and is known to be unstable, whereas the large solution is characterized by a flame of infinite radius. We examine the linear stability of these stationary solutions, and show that all small flames are unstable to one-dimensional (radial) perturbations. Large flames are unstable to three-dimensional perturbations, but only if they have a radius greater than some critical value. Thus there is a band of large flames, lying between the quenching point and unstable flames, that are stable.

Lean hydrogenair mixtures confined to a flammability tube can support “flame-bubbles”—very small, highly curved flames that rise because of buoyancy. An approximate description of the flow field associated with a single unbounded flame is provided by numerical solution of the Navier-Stokes equations for distributed heat sources rising at constant speed in a gravitational field. Zeldovich has proposed a theoretical model valid at 0 g (zero Reynolds number) but it has only unstable solutions. We describe a “flame-cap” model, valid for finite g , and suggest that the flow field is an essential stabilizing mechanism.

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We report 3-dimensional simulations of aluminized propellant combustion, accounting for heat conduction in the solid, combustion in the gas-phase, and coupling of these via the irregularly moving propellant surface, one that can not be defined by a single-valued height function. The simulations are used to examine the dynamics of aluminum particles in the near-neighborhood of the surface after detachment, and to provide an estimate of the time to ignition of the particles, and their speed and height above the surface at ignition. In addition we examine the temperature history of the particles during their rise to the surface, determine whether they melt or not, and in this way test Cohen’s well-known melting criterion. And we discuss a simple model which provides insights into how aluminum particles floating on a binder melt layer would migrate because of surface tension effects, and calculate an average migration distance that is consistent with previous agglomeration studies.

We report the first 3-dimensional simulations of aluminized propellant combustion, accounting for heat conduction in the solid, combustion in the gas-phase, and coupling of these via the irregularly moving propellant surface, one that can not be defined by a single-valued height function. The simulations are used to examine the dynamics of aluminum particles in the near-neighborhood of the surface after detachment, and to provide an estimate of the time to ignition of the particles, and their speed and height above the surface at ignition. In addition we examine the temperature history of the particles during their rise to the surface, determine whether they melt or not, and in this way test Cohen’s well-known melting criterion. And we discuss a simple model which provides insights into how aluminum particles floating on a binder melt layer would migrate because of surface tension effects, and calculate an average migration distance that is consistent with previous agglomeration studies.

This research is concerned with theoretical studies of combustion and related flow problems that are relevant to the Air Force mission. Recent topics that have been examined include heterogeneous propellant flame modeling, the construction of 1-dimensional flame models from subgrid 3-dimensional descriptions, aluminum agglomeration, the combustion of heterogeneous propellants containing aluminum, the use of a genetic algorithm to optimally define false kinetics parameters in propellant combustion modeling, and instabilities of smolder waves.

A numerical description of heterogeneous propellant combustion enables us to examine the spatial and temporal fluctuations in the flow field arising from the heterogeneity. Particular focus is placed on the fluctuations in a zone intermediate between the combustion field (where reaction is important) and the chamber flow domain, for these define boundary conditions for simulations of the turbulent chamber flow. The statistics of the temperature field and the normal velocity field are described, and characteristic length scales and time scales are identified. The length scales are small compared to any relevant length scale of the chamber flow, and so the boundary conditions for this flow at any mesh point are statistically independent of those at any other mesh point. But the temporal correlations at a fixed point are significant, and affect the nature of the chamber flow in a variety of ways. We describe the fluctuations in the head-end pressure that arise because of them, and contrast these results with those calculated using a white-noise assumption. 1

We examine the geometry of diffusion flames generated by the burning of a heterogeneous solid propellant, using a simple model designed to provide qualitative insights. In the fast chemistry limit a strategy is used which has its roots in Burke and Schumann's 1928 study of diffusion flames, albeit with different boundary conditions. This shows that the stoichiometric level surface (SLS) intersects the propellant surface at a point displaced from the fuel/oxidizer interface, and the variations of this displacement with Peclet number are discussed We show that for model sandwich propellants, or their axisymmetric counterpart, the geometry of the SLS when the core is oxidizer is quite different for the geometry of the SLS when the core is fi approx. el. Also, it is much easier to quench the flame on an oxidizer core, by reducing the Peclet number, than it is to quench the flame on a fuel core. When finite chemistry effects are accounted for, the flame only occupies a portion of the SLS, and there is a leading edge structure in which premixing plays a role. Enhancement of the burning rate due to premixing is identified, but a well-defined tribrachial structure is not observed We show how a sharp reduction in pressure can lead to a detachment of the flame from the SLS, with subsequent quenching as it is swept down stream.