The three-dimensional numerical simulation of aluminized composite solid propellant combustion

A three-dimensional numerical framework is presented that examines the burning of aluminized solid propellants. The numerical solver accounts for heat conduction in the solid, combustion in the gas phase, and coupling of these by means of a level set method. The aluminium particles are treated as heat conducting solid spheres. The aluminium particle detachment process is modelled using level sets, but once the particle becomes free from the surface, its subsequent motion in the gas phase is governed by particle dynamics. Some preliminary calculations of the three-dimensional combustion field supported by a pack with embedded aluminium particles are presented.     

Burning rate of homogeneous energetic materials with thermal expansion and varying thermal properties in the condensed phase

We present a study of the one-dimensional flame structure of combusting solid propellants that focuses on the effects of thermal expansion and variable thermal properties in the condensed phase. A nonlinear heat equation is derived for a burning thermo-elastic solid with temperature-dependent specific heat, thermal expansion, and thermal conductivity coefficients. It is solved for different modelling approximations both analytically and numerically. Explicit expressions are derived for the regression rate of the propellant surface as functions of surface temperature and thermal expansion parameters. A simple one-step reaction model of the gas phase is used to study the full structure of propellent flame and illuminate the influence of temperature-dependent material properties on the regression rate, surface temperature, and flame stand-off distance. Results are displayed for HMX and compared with experimental data and numerical simulation with fair success.     

Development and characterization of high performance solid propellants containing nano-sized energetic ingredients

This paper addresses the development of a pair of layered solid propellants suitable for use in a fast-core gun-propellant charge application. A baseline propellant combination was formulated using RDX particles and thermoplastic-elastomer binder as the major ingredients and CL-20 and nitroguanadine as separate additives for high- and low-energy propellants. The propellant’s burning rate was characterized and insufficient burning-rate ratio between the fast and slow baseline propellants was found. Impetus obtained from the combustion of the combined baseline propellants was also found to be far from the demanded value of 1300 J/g. Several modifications were made by introducing nano-sized aluminum particles and ultra-fine boron particles as well as high-energy oxidizer HNF into the propellant formulation. It was found that the addition of nano-sized aluminum particles can enhance the propellant burning rate only when the propellant contains oxidizers with a positive oxygen balance. Without the presence of positive oxygen balance oxidizer, the exothermic reaction of aluminum and boron particles occurs at a large distance from the burning surface introducing an energy-sink effect. The results obtained from the combustion of the advanced propellants show that an average impetus of 1299 J/g, a flame temperature of 3380 K with a burn rate ratio around 3 between the fast- and the slow-burning layers can be achieved. These conditions are desired for fast-core layered propellant applications. The impact sensitivities of the baseline, intermediate and advanced propellants were measured. The results show that addition of HNF and nano-sized aluminum exhibited improved impact sensitivity at levels that can be considered acceptable for deployment.     

Importance of lateral momentum equation to the modeling of sandwich propellant combustion

This paper reports the results of numerical studies carried out for a periodic sandwich propellant geometry with two-dimensional unsteady gas and condensed phase. A non-planar regressing surface along with a kinetic model of two reaction steps in the gas phase was used. This paper discusses the importance of lateral momentum equation to the combustion of sandwich propellants. It demonstrates that the instabilities in sandwich combustion reported in literature are due to neglect of lateral momentum equation and incorrect boundary conditions at the regressing surface. It demonstrates that neglect of momentum equations will lead to a different result from the one obtained considering the momentum equations for sandwich propellants.     

Ammonium Nitrate as an Eco–Friendly Oxidizer for Composite Solid Propellants: Promises and Challenges

Ammonium nitrate (AN) has received attraction globally not only as a nitrogenous fertilizer but also as an oxidizer in gas generators and propellants. Nowadays, great attention is being focused on the development of composite solid propellants with green oxidizers in realizing eco–friendly combustion products. The ammonium perchlorate (AP), which is the work horse oxidizer in composite propellant, needs replacement due to its environmental and human health issues. In this context, AN is regarded as an alternative to AP because of its easy availability and environmentally friendly chlorine free combustion products. However, AN has its own inherent drawbacks such as hygroscopicity, room temperature phase transition, and low burning rate. Recently, several studies have been focused on its phase stabilization and burning rate modification so as to develop solid propellants with improved properties. The knowledge of thermal characteristics of AN is a crucial factor for its applications in propellants and gas generators. This article details the different aspects of polymorphism, phase stabilization, thermal decomposition, hygroscopicity, specific impulse, and burn rate modification of AN and also addresses ways to overcome the inherent weakness of AN as a propellant oxidizer in formulating an effective propellant composition.     

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

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.     

Quench collection of nano-aluminium agglomerates from combustion of sandwiches and propellants

An experimental investigation has been carried out to measure the size of nano-aluminium agglomerates emerging from the combustion of nano-aluminized sandwiches and composite solid propellants. Nano-aluminium of median size of 50 nm produced in-house by the electrical wire explosion method is used in these samples. Propellants with different sizes of coarse and fine ammonium perchlorate are considered. Surface features of sandwiches and a propellant whose burning was interrupted by rapid depressurization are examined in a scanning electron microscope. The combustion products of the sandwiches and propellants are quenched close to the burning surface and collected in a quench collection set-up. The surface features of rapid-depressurization quenched sandwiches exhibit relatively large nano-aluminium clusters—of the order a few micrometres—particularly in the binder lamina. Quench-collected nano-aluminium exhibits significant agglomeration, but only a small fraction of the agglomerates are in the 1–3 μm range, except for both the coarse and fine AP particles used in the formulation being large, but even there they do not exceed ∼5 μm in size. This is expected to be benign for reduced smoke propellant applications from exhaust signature point of view, and to decrease the specific impulse losses without sacrificing the energetics of the propellant.     

Experimental observations of the dependence of impedance tube behavior upon gas phase losses and propellant self-noise

Some of the unexpected behavior observed during admittance measurement of burning solid propellants in a modified impedance tube set-up is discussed. Specifically, repeated tests conducted with the same solid propellant resulted, unexpectedly, in different standing wave structures in the impedance tube when the exhaust configuration was changed. This resulted in the calculation of different admittances at the propellant surface. It is shown in this paper that the observed experimental trends can be explained when the presence of gas phase damping and a propellant self-noise are taken into consideration in the development of a simplified analytical model describing the behavior of the impedance tube.     

Holographic Observation of AluminumAgglomerates near Surface Area of SolidRocket Propellants during Burning Process

l.IntroductionMetalaluminumisusual1yaddedtosolidrocketpropellantstoincreasethrustandspecificimpu1se.Inaddition,a1uminumoxideparticlesproducedinhightemPeratureburningareacaninturnsuppresshighfrequencycombustioninstabilities.Fromthetheo-reticalcombustionmode1ofsolidproPellants['2j,oxiderandbinder,maincompositionofsolidproPellants,arefirstdecomPOsedandvaPOrizcdintheburningprocere,sothatthealuminumparticlesareexposedonthesurfaceofsolidproPCllants.SomeoftheexPOsedaluminumparticlesescaPerapedl…     

Binder melt: Quantification using SEM/EDS and its effects on composite solid propellant combustion

The present study reports the development of a novel technique to quantify binder melt on the surface of the propellant. Non-aluminized AP-HTPB propellants of 86% particulate loading are used to illustrate the technique. Elemental maps of unburnt and extinguished propellant surface are obtained using EDS (Energy Dispersive Spectroscopy). Overlap between the elements is identified and the elemental maps are processed to calculate AP and binder area exposed in unburnt and extinguished samples. The AP area exposed is found to be around 72.3% and 63.3% for unburnt and extinguished samples, respectively, indicating a reduction in AP exposed area with extinguished samples. This has been attributed to the binder melt discussed in literature but never quantified. Simulations have been carried out to analyze and understand the effects of this binder melt. A random packing algorithm is used to simulate propellant packs. Also, a methodology to account for binder melt layer is introduced and is used to capture AP exposed areas. Effect of binder melt in propellants with different solid loading and varying particle size is discussed. It is shown that fine AP particles are more prone to being covered by binder melt than the coarse AP particles. A possible explanation to the behavior of plateau burning propellants observed in literature has been provided through this analysis.     

Influence of the composition and ionizing radiation on the stability of combustion of composite propellants

The results of an experimental study of the acoustic admittance of the burning surface of composite propellants performed with the use of a two-end combustion chamber (T-chamber) are presented. The effects of the composition of the composite propellant (type of fuel-binder, content of aluminum powder, burning rate catalysts) and of ionizing γ-radiation on the acoustic admittance, which characterizes the tendency of the combustion chamber to high-frequency instability, are analyzed.     

Thermomechanical modeling of regressing heterogeneous solid propellants

A numerical framework based on the generalized finite element method (GFEM) is developed to capture the coupled effects of thermomechanical deformations and thermal gradients on the regression rate of a heterogeneous solid propellant. The thermomechanical formulation is based on a multiplicative split of the deformation gradient and regression of the heterogeneous solid propellant is simulated using the level set method. A spatial mesh convergence study is performed on a non-regressing solid heterogeneous propellant system to examine the consistency of the coupled thermomechanical GFEM solver. The overall accuracy (spatial and temporal) of the coupled thermomechanical solver for regressing solid propellants is obtained from a periodic sandwich propellant configuration, where the effects of thermomechanical deformations on its regression rate is investigated. Finally, the effects of thermomechanical deformations in a regressing two-dimensional heterogeneous propellant pack are studied and time-average regression rates are reported.     

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.     

On the structure of the combustion wave of nitroglycerine-based propellants

The parameters of the temperature distribution in the combustion wave of nitroglycerin-based propellants N and NB are analyzed and compared. The aim of the study is to explain the known experimental fact that the size of hotspots and the critical quenching diameter for propellant NB (more rapidly burning) are larger than those for propellant N. It is demonstrated that, at a given burning rate, the burning surface temperature, heat conduction zone thickness, temperature gradient near the burning surface, and the dark zone temperature for propellants N and NB are the same, but the fizz zone thickness for NB is approximately twice as wide as that for N. The dependence of the ratio of the hotspot size to the fizz zone thickness is described by a single power law for both propellants. It is also shown that the hotspot size can be defined as the distance between two consecutive transverse waves, which, in turn, is determined by the delay in the initiation of each following wave.     

Improved method of measuring pressure coupled response for composite solid propellants

Pressure coupled response is one of the main causes of combustion instability in the solid rocket motor. It is also a characteristic parameter for predicting the stability. The pressure coupled response function is usually measured by different methods to evaluate the performance of new propellant. Based on T-burner and “burning surface doubled and secondary attenuation”, an improved method for measuring the pressure coupled response of composite propellant is introduced in this article. A computational fluid dynamics (CFD) study has also been conducted to validate the method and to understand the pressure oscillation phenomenon in T-burner. Three rounds of tests were carried out on the same batch of aluminized AP/HTPB composite solid propellant. The experimental results show that the sample propellant had a high response function under the conditions of high pressure (~11.5 MPa) and low frequency (~140 Hz). The numerically predicted oscillation frequency and amplitude are consistent with the experimental results. One practical solid rocket motor using this sample propellant was found to experience pressure oscillation at the end of burning. This confirms that the sample propellant is prone to combustion instability. Finally, acoustic pressure distribution and phase difference in T-burner were analyzed. Both the experimental and numerical results are found to be associated with similar acoustic pressure distribution. And the phase difference analysis showed that the pressure oscillations at the head end of the T-burner are 180° out of phase from those in the aft end of the T-burner.     

Additive manufacturing of ammonium perchlorate composite propellant with high solids loadings

The effective solid propellant burning rate in a rocket depends on surface area and propellant composition. Currently, the surface area geometry in a rocket is limited to what can be practically cast using molds, etc. Additive manufacturing (AM) could allow the production of unique propellant grain geometries, however printing propellants with high solids loadings and viscosities is not readily possible using currently available printers. A new AM direct write system developed recently in our laboratory, is capable of printing visibly low-void propellants with high end mix viscosities into highly resolved geometries. The system was used to print ammonium perchlorate (AP) composite propellants at 85% solids loading using hydroxyl-terminated polybutadiene (HTPB) and a UV-curable polyurethane binder. The change in HTPB propellant viscosity with time after mixing was measured and the microstructure of the strands was evaluated with X-ray tomography scans. The burning rate of printed and cast strands was measured to compare the quality of the strands at high pressure, since propellants with significant voids should catastrophically fail due to flame spreading. The printed samples burned in a planar fashion up to pressures of 10.34 MPa with consistent rates that were comparable to the cast propellants. The HTPB propellant used was not optimized and showed some porosity due to gas generation, but strands printed with the UV binder exhibited extremely low porosity. A strand printed with no gaps in one half and gaps in the other failed catastrophically where intended at high pressure, demonstrating the ability to spatially grade propellants. This new system can produce adequate strands of composite propellant with high solids loadings without the addition of solvents, special binders (low viscosity, thermal softening, etc.), or restricting use to formulations with lower viscosities, and enables the fabrication of complex propellant grain geometries.     

Effect of the thermophysical properties of the material of a local energy source on conditions and characteristics of ignition of metallized composite propellants

Solid-phase ignition of metallized composite propellants by a single particle heated to a high temperature under conditions of an ideal thermal contact has been numerically studied. The effect of the thermophysical properties of the material of a local energy source on the conditions and characteristics of ignition of composite propellants has been analyzed. It has been found that sources with a high heat storage capacity exhibit shorter ignition delay times for metallized propellants (by 10–60%) and lower initial temperatures required to initiate the combustion process (by 170 K). In addition, it has been found that the presence of particles of metals (boron, aluminum, magnesium, lithium) in the propellant composition leads to an increase in the effective thermal conductivity of the propellant. The cumulative effect of the thermophysical properties of the materials of the “particle heated to a high temperature–metallized composite propellant” system leads to an increase in the ignition delay times (by 25–65%) and the heat penetration depth of the near-surface layer of the propellant (by 25–40%) at the time of combustion initiation compared with metal-free compounds.     

Using level sets for creating virtual random packs of non-spherical convex shapes

Random packs of spheres have been used to model heterogeneous and porous material morphologies during simulations of physical processes such as burning of coal char, convective burning in porous explosives, and regression of solid rocket propellant. Sphere packs have also been used to predict thermo-mechanical properties, permeability, packing density, and dissolution characteristics of various materials. In this work, we have extended the Lubachevsky–Stillinger (LS) sphere packing algorithm to create polydisperse packs of non-spherical shapes for modeling heterogeneity in complex energetic materials such as HMX and pressed gun propellants. In the method, we represent the various particle shapes using level sets. The LS framework requires estimates of inter-particle collision times, and we predict these times by numerically solving a minimization problem. We have obtained results for dense random packs of various convex shapes such as cylinders, spherocylinders, and polyhedra, and we show results with these various particles packed together in a single pack to high packing fraction.     

Optimization of global kinetics parameters for heterogeneous propellant combustion using a genetic algorithm

We examine the combustion of heterogeneous propellants for which, necessarily, the chemical kinetics is modelled using simple global schemes. Choosing the parameters for such schemes is a significant challenge, one that, in the past, has usually been met using hand-fitting of experimental data (target data) for global burning properties such as steady burning rates, burn-rate temperature sensitivity, and the like. This is an unsatisfactory strategy in many ways. It is not optimal; and if the target set is large and includes such things as stability criteria, or bounds, difficult to implement. Here we discuss the use of a general optimization strategy which can handle large data sets of a general nature. The key numerical tool is a genetic algorithm that uses MPI on a parallel platform. We use this strategy to determine parameters for HMX/HTPB propellants and AP/HTPB propellants. Only one-dimensional target data are used, corresponding to the burning of pure HMX (AP) or a homogenized blend of fine HMX (AP) and HTPB. The goal is to generate kinetics models that can be used in the numerical simulation of three-dimensional heterogeneous propellant combustion. The results of such simulations will be reported in a sequel.