The process of agglomeration of aluminum particles on the burning surface of an ammonium perchlorate-based composite propellant is modeled using a computer algorithm. A random pack of particulate ingredients of given size and mass specifications is cast on the computer to simulate the propellant microstructure as reported previously. The aluminum particles are tracked as they emerge at a regressing burning surface, accumulate into filigrees, and get ignited by the near-surface leading-edge oxidizer-binder diffusion flamelets attached to the exposed areas of certain ammonium Perchlorate particles. An approximate heat transfer model is incorporated to estimate the ignition delays radially inward and outward from the leading-edge flamelets into the filigrees accumulated over ammonium Perchlorate particles and surrounding binder-fine ammonium Perchlorate matrix layers. The delay influences the number of parent aluminum particles constituting a filigree, and consequently the size of the agglomerate that the filigree rolls up into. The implementation of the algorithm is validated against experimental results available in the literature, which were specifically obtained to investigate the relationship between the decrease in the agglomerate size and attachment of leading-edge flamelets over the fine ammonium Perchlorate particles in the propellant with increase in pressure.

Satyanarayanan R. Chakravarthy

Department of Aerospace Engineering

Vishal Srinivas

AGGLOMERATE SIZE

Ammonium perchlorate

BURNING SURFACE

LEADING-EDGE FLAMELETS

Agglomeration

Algorithms

microstructure

Solid propellants

Aluminum

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IIT Madras

Computer model of aluminum agglomeration on burning surface of composite solid propellant

Journal of Propulsion and Power

The Heterogeneous Quasi One-dimensional (HeQu1-D) model for AP/HTPB composite propellant combustion is extended to aluminized propellants. Following the serial burning approach of HeQu1-D, a statistical particle path through an aluminized propellant is taken to consist of aluminized binder-matrix coated AP particles of various sizes. Extending the idea of homogenization of fine-AP particles, aluminum particles are assumed to be homogenized with the binder-matrix. Large Al particles (nominal size ≥ 15 µm) in the binder-matrix are assumed to get ejected into the gas phase and hence do not contribute to heat feedback to the burning surface. With these modifications, the model is shown to accurately predict the burn rate variation with pressure and initial temperature of propellants using Al of nominal sizes in the range of 15–50 µm (termed conventional aluminum, CAl). The experimentally observed reduction in propellant burn rate with substitution of AP by CAl is shown to be due to the increase in fuel richness and energy sink effect of melting of Al. Catalytic effects due to addition of burn rate modifiers (Fe2O3 in space shuttle booster propellant, for instance) are also accounted for by modifications to gas phase rate parameters. Increase in burn rate up to 25% with Al particles of a few µm (3–6 µm) in comparison with non-aluminized propellant is explained by recognizing that there will be non-negligible fraction of sub-micron Al due to the associated particle size distribution. This leads to heat release by sub-micron Al combustion close to the surface and an enhancement in the heat feedback, by a combination of convective and radiative mechanisms. Dramatic increase in burn rate with sub-micron Al (a factor of 4–5 as compared to CAl) is captured by invoking radiation from fine-Al/Al2O3 particles to propellant surface. Agglomeration of sub-micron Al particles is invoked to explain the saturation of burn rate enhancement with reduction in Al particle size and the effectiveness of sub-micron Al substitution in smaller fractions (bi-modal Al). Predictions for over fifteen different propellants with varying fractions of fine and coarse aluminum from earlier literature have been presented. Comparisons of the predictions from the model with experimental results from different sources is shown to be excellent-to-good for most cases. The hitherto unknown radiation dominated ablation (r˙&gt;50mm/s) of coarse AP particles and the effect of Al particle size on propellant temperature sensitivity are brought out. The MATLAB® code based on the model offers opportunity for design of AP-HTPB composite propellants with combination of fine and coarse aluminum with confidence. © 2018 The Combustion Institute

Combustion and Flame

Aluminized composite propellant combustion modeling with Heterogeneous Quasi-One dimensional (HeQu1-D) approach

Previously reported computer modelling of agglomeration of micrometre-sized aluminium particles during the combustion of composite solid propellants fails when applied to nano-aluminium particles because of the enormous number of the latter particles. A modified algorithm for three-dimensional casting and burning of composite propellants containing nano-aluminium particles on the computer is developed in the present work. In this, a regular grid is constructed overlaying the computer cast of coarse and fine ammonium perchlorate (AP) particles in the propellant, and the nano-aluminium particles are placed at randomly selected grid points outside of previously placed AP particles. Moreover, this is done one grid layer at a time in the burning direction to save computer memory. Further, since the burning surface is regressed at known burning rates over a larger step size than the above grid spacing, all the nano-aluminium particles located at grid points within one step of surface regression are lumped together and represented by an equivalent micrometre-sized particle. The agglomeration algorithm previously reported is then applied to this representative computer propellant cast. Results are compared with previously reported experimental data for two propellants with different coarse AP particles, one of them at three pressures. The predicted agglomerate size distribution agrees well with the experimental data. © 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Proceedings of the Combustion Institute

Computer modelling of nano-aluminium agglomeration during the combustion of composite solid propellants

Sixteen propellant formulations based on ammonium perchlorate (AP), hydroxyl-terminated polybutadiene, and aluminium particles have been tested for size distribution of aluminium agglomerates emerging from their burning surface. The formulations are based on a bimodal size distribution of AP particles. Ten of the formulations exhibit one or two plateaus/mesa in their burning rate variation with pressure (zero/negative pressure exponent of burning rate). The relevant formulation variables, namely, coarse and fine AP sizes and coarse-to-fine ratio, aluminium size and content, and two different curing agents, have been varied. Tests are performed in the 1-10 MPa pressure range. A direct correlation between burning rate and agglomerate size exists for propellants with normal burning rate trends but a neutral or inverse correlation is observed for those exhibiting plateau burning behaviour. Larger the parent aluminium size, lesser the agglomeration, as expected; but the effect of aluminium content is non-monotonic. The coarse AP size influences the aluminium agglomerate size as expected from the pocket model regardless of plateau burning effects. The agglomerate size decreases with increase in fine AP size, however. A computer model developed earlier at this laboratory for prediction of aluminium agglomerates based on three-dimensional packing of particles and deduction of AP particles with attached leading edge diffusion flames is applied to the present formulations. The model under-predicts the agglomerate size, only marginally for propellants that do not exhibit plateau burning rate trends, but substantially, otherwise. This is because it does not take into account effects of binder melt flow and is independent of the curing agent of the binder. © 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Experimental data and model predictions of aluminium agglomeration in ammonium perchlorate-based composite propellants including plateau-burning formulations

This paper reports the production of nanoaluminum particles using the wire explosion process at our laboratory. Electrical energy is applied to the aluminum wire in an argon atmosphere to yield spherical particles around 50 nm in size. The material is also characterized by a number of methods. The nano-Al is included in bimodal ammonium Perchlorate composite solid propellants, and their burning rates are compared with those containing normal micron- sized aluminum and nonaluminized propellants in a total of 21 formulations in the 1-12 MPa pressure range. Nanoaluminized propellants show ∼100% increase in burning rate relative to nonaluminized or microaluminized ones, but only when large-sized coarse ammonium Perchlorate particles are used. Burning-rate plateaus observed in non- and microaluminized propellants are washed out with the addition of nano-Al, but the burning rates of nanoaluminized propellants register low pressure exponents in the elevated pressure range. The results suggest that the heat feedback from the diffusion-limited combustion of nano-Al particles near the propellant burning surface controls the propellant burning rate when sufficiently large parts of the burning surface are made up of the nanoaluminized fine ammonium-perchlorate/binder matrix.

Production, characterization, and combustion of nanoaluminum in composite solid propellants

Nano-aluminium particles of ∼50 nm size, produced at this laboratory, are added to composite solid propellants based on ammonium perchlorate and hydroxyl-terminated poly-butadiene binder that exhibit plateau burning rate trends and those including burning rate catalysts. The nano-aluminized propellant burning rates are compared with corresponding micro-aluminized and non-aluminized ones in the 1-12 MPa pressure range. The mid-pressure extinction of the matrixes containing the fine-sized ammonium perchlorate particles in the propellant along with the binder is investigated in all the cases to understand the mechanism of plateau-burning. Further, the variations in aluminium content, the aluminium size (within nano- and micro-ranges), bimodal combination of nano- and micro-aluminium are considered. Ferric oxide and titanium dioxide are the burning rate catalysts considered. Large scale accumulation of aluminium is observed not only in micro-aluminized matrixes, but also in nano-aluminized ones as clusters of 1-5 μm size. Since aluminium is added at the expense of the coarse ammonium perchlorate particles to preserve the total-solids loading in the present formulations, addition of micro-aluminium decreases the burning rate; whereas, nano-aluminized propellants exhibit ∼80-100% increase in the burning rate under most conditions. The near-complete combustion of nano-aluminium close to the burning surface of the propellant provides heat feedback that controls the burning rate. Mid-pressure extinctions of matrixes and plateau burning rates of propellants are washed out when nano-aluminium is progressively added beyond 50% in bimodal aluminium blends, but low pressure-exponents are observed in the nano-aluminized propellant burning rates at elevated pressures. Adjusting the plasticizer content in the binder alters the pressure range of plateau burning rates in non-aluminized propellants. Catalysts increase the burning rate by ∼50-100% in non-aluminized and micro-aluminized propellants, but in nano-aluminized propellants, the μm-sized catalyst does not affect the burning rate significantly; whereas, the nanometre size catalysts increases the burning rate merely by ∼5-15%. © 2009 The Combustion Institute.

Effect of nano-aluminium in plateau-burning and catalyzed composite solid propellant combustion

The onset of the midpressure extinction of certain formulations (termed matrixes) of ammonium perchlorate (AP) of monomodal particle size distribution and hydroxyl-terminated polybutadiene binder, in the pressure range around 2-5 MPa, is examined. These matrixes, besides being tested in isolation, have been included in between AP laminas to form sandwiches and mixed with coarse AP particles to form high solids-loading (87.5%) non-aluminized propellants. The burning rates of the sandwiches show abnormal trends with pressure such as low or negative exponents in ranges corresponding to the onset of the midpressure extinction of their respective matrixes. The propellants exhibit this behavior to a lesser degree. Quenched surfaces (self-extinguished or intentionally interrupted during burning) of all the three types of samples were analyzed using a scanning electron microscope, and the burning history of the samples was captured with a high-speed digital camera. The results indicate the prevalence of intermittent burning of the matrixes as the pressure is varied across the boundary between continuous burning and self-extinction (burn/ no-burn boundary) of the matrixes. The burning surfaces are marked by extreme three dimensionality coupled with a redistribution of the fine AP particles and the binder. The observations are explained based on the combined effects of the need for the AP particles and the binder to accumulate relative to each other on the burning surface depending on the difference in their pyrolysis rates and the existence of the binder in a molten state on the burning surface.

Intermittent Burning of Ammonium Perchlorate-Hydrocarbon Binder Monomodal Matrixes, Sandwiches, and Propellants

The paper attempts to obtain an approximate distribution of oxidizer/fuel (O/F) flamelets on the burning surface of a composite solid propellant, mainly of the ammonium perchlorate (AP)-hydrocarbon (HC) binder variety commonly used in rocket propulsion applications today. A computer model is developed to simulate the random packing of oxidizer particles of different size distributions in the propellant. The focus of the present work is on the distinction between pockets of fine AP particles amidst the binder that may burn in a premixed O/F flame and the sufficiently large AP particles that burn with the surrounding vapor flow in an attached diffusion flame. A transition occurs between premixed burning and attached diffusion flamelet-burning over each oxidizer particle as the ambient pressure is varied. A simple criterion evolved earlier to delineate the two regimes of burning in the particle size-pressure domain has been employed to determine the flamelet type that prevails over each exposed particle of the model propellant at a given pressure. Delaunay triangulation is adopted to deal with regions of fine AP-binder corresponding to premixed burning. The results are compared with previously reported experimental observations of burning rate for specific propellant formulations that exhibited distinct jumps in their burning rate with variation in pressure. It was argued that the burning rate jumps corresponded to a concerted shift in the burning regime of a majority of fine particles. The present simulation supports this argument.

Combustion Science and Technology

A computer model of flamelet distribution on the burning surface of a composite solid propellant

The transition from particle flamelet burning to premixed flame burning of ammonium perchlorate (AP)/hydrocarbon (HC) binder propellants is identified with detachment of the oxidizer/fuel (O/F) flamelet from the stoichiometric tip of the diffusion field over the AP particle. The conditions (pressure, particle area, local stoichiometry) for detachment are revealed by singular regions of the burning rate versus pressure curves for selected bimodal propellants.

Journal	Journal of Propulsion and Power
ISSN	07484658
Open Access	No