Heterogeneous Solid Propellants Research Articles

Effects of Thermal Expansion and Pressure on Far-Field Fluctuations of Heterogeneous Propellants

In this work, we carry out three-dimensional mesoscale simulations of heterogeneous solid propellant combustion. We solve the reactive low-Mach-number equations in the gas phase with complete coupling to the solid phase. The model takes into account thermal expansion and deformation in the solid phase by using a hypoelastic law in the quasi-static limit. To account for morphology, we select two different propellant formulations with different particle size distributions and present the results as a function of pressure. The thermomechanical behavior is accessed by examining quantities such as strain and stress in the propellant as a function of pressure and propellant morphology. We also show that temperature and velocity fluctuations exist in the far field above the propellant surface and that these fluctuations can be significant. To better understand the nature of these fluctuations, we vary the pressure and make relevant plots of normal velocity and temperature probability density functions, as well as time autocorrelations. Such descriptions are necessary to account for the coupling between the mesoscale and the macroscale, where the fluctuations at the mesoscale can affect quantities at the macroscale, such as head-end pressure, trigger parietal vortex shedding, and aeroacoustics.

Three-dimensional thermo-mechanical simulations of heterogeneous solid propellants

In this work, we present a numerical framework that describes thermo-mechanical deformations in a burning heterogeneous solid propellant. These deformations are quasi-static at time scales associated with combustion, and the resulting thermo-mechanical formulation is discretized on a Cartesian grid using a hypoelastic law. We use a weak form of Chorin-type projection method to deal with large difference in shear modulus of the constituent materials. Extending our previous two-dimensional work, grid convergence studies for a three-dimensional propellant configuration are presented for the stress, velocity, and reference map components. Finally, simulations are carried out for a random propellant pack that is coupled to a gas phase, and we present results for the pack undergoing combustion, with and without deformations.

UNDERSTANDING THE BURNING OF HETEROGENEOUS SOLID PROPELLANTS THROUGH MESOSCALE MODELING

Heterogeneous solid propellants are widely used in the rocket industry. They consist of oxidizer particles embedded in a polymeric binder. The combustion and ignition of such propellants remain poorly understood, partly because they are complex and driven by physical mechanisms occurring at the micrometer scale. This paper gives an overview of some recent achievements in understanding the physics of propellant burning using mesoscale direct simulations. In this modeling, the propellant microstructure is explicitly modeled, and basic governing equations (reactive Navier-Stokes equations) are solved in three dimensions at the subparticle level. Most present findings suggest a salient role of propellant microstructure. This is the case for steady combustion where the orientation of particles (assumed as spheroids) has a strong impact on burn rate, while particle shape has a more limited effect. Ignition can also be addressed; it is found that ignition physics is strongly related to particles on the surface, like flame spreading from ignited particles. Mesoscale simulations can be part of a more general multiscale strategy applied to real motors. Two applications are discussed: the first is related to the effects of the grain manufacturing process on burning rate, and the second focuses on how local small-scale burning fluctuations above the propellant surface can trigger flow instabilities in a motor. This strengthens the interest of mesoscale modeling, both for understanding physics and predicting actual systems.

A tabulated chemistry method for heterogeneous solid propellant combustion

Detailed chemistry simulations of heterogeneous solid propellant combustion at the microstructure scale are very costly as they involve large and stiff chemical schemes in the gas phase. A usual workaround is to use global chemistry to approximate gas phase reactions. A drawback of this approach is the need for an a priori calibration which necessitates reference data and often limits the operating conditions range of validity. An alternative method based on 1-D burner-stabilized flames tabulation is proposed in this paper. The theoretical and numerical frameworks are detailed. An appropriate tabulation space is introduced to store useful thermochemical variables as well as Jacobian terms used for time-integration. Jump conditions are also rewritten to cope with tabulated chemistry formalism. Several 1-D validations are performed on classical propellant compositions. Detailed comparisons with available experimental data demonstrate the ability of the proposed methodology to tackle inner flame structure (temperature and species) as well as the evolution of the burning rate with pressure and composition. Finally, 2-D laminate propellant simulations are conducted showing the ability of the methodology to capture complex flame regimes and associated burning rate modifications.

Eulerian thermo-mechanical simulations of heterogeneous solid propellants using an approximate projection method

We present a mathematical model that describes thermo-mechanical deformations and thermal gradients on the unsteady burning of a heterogeneous solid propellant. A scaling study shows that the deformations in solid at combustion timescales can be treated as quasi-static. The resulting thermo-mechanical formulation is formulated on a Cartesian grid and makes use of a weak form of Chorin-type projection method to deal with large difference in shear modulus of constituent materials. A one-dimensional verification study is carried out by comparing numerical simulations with those of an analytical model. In addition, convergence studies for a two-dimensional propellant sandwich configuration are presented for the stress, velocity, and reference map components. Finally, simulations are carried out for a two-dimensional random propellant pack and the time-averaged burn rate and strains are reported.

Investigating Dimensional Effects on Predicting Burning Rates of Heterogeneous Solid Propellants

The combustion of a randomly packed, heterogeneous propellant consisting of ammonium perchlorate and hydroxyl-terminated polybutadiene is investigated in a two-dimensional and three-dimensional numerical model to better understand the dimensional effects on the propellant burning rate. A ammonium perchlorate particle is set in a premixed hydroxyl-terminated polybutadiene binder and investigated using a two-dimensional model with finite-rate chemistry and detailed transport properties. The results from the detailed model are compared to two-dimensional and three-dimensional burning-rate codes with reduced chemistry. The gas-phase combustion chemistry is modeled using a reduced four-step mechanism developed from a detailed microscale model of ammonium perchlorate/hydroxyl-terminated polybutadiene combustion. Simple configurations of a single ammonium perchlorate particle and sandwich propellants at varying pressures are compared to determine leading-order effects of two-dimensional and three-dimensional approaches. The reduced chemistry models are then applied to real-world propellants for which a random packing algorithm is used to construct the ammonium perchlorate/hydroxyl-terminated polybutadiene propellant in a periodic cube for a given size distribution of spherical ammonium perchlorate particles and mass ratio of the oxidizer and binder. The decomposition of the ammonium perchlorate and hydroxyl-terminated polybutadiene on the surface is determined at discrete locations and is used to determine the average burning rate over a period of time. This approach combines a more detailed description of the gas-phase combustion processes, the condensed-phase morphology, and physics in a time-dependent simulation in hopes of developing a more predictive model of solid propellant combustion.

THERMO-MECHANICAL ANALYSIS OF HETEROGENEOUS SOLID ROCKET PROPELLANT

The article presents results of thermo-mechanical analysis of heterogeneous solid rocket propellant H2, with special attention devoted to determining the glass transition temperature and softening temperature. Mechanical properties such as storage modulus (E’), loss modulus (E’’) and tan(δ) were measured using NETZSCH DMA 242C analyzer within temperature range from -120oC to +80oC at 2 K/min of heating rate and frequency of applied force f = 1 Hz. Relative thermal expansion as well as the Coefficient of Linear Thermal Expansion (CLTE) of H2 sample were determined using NETZSCH DIL 402C dilatometer within temperature range from 30oC to 80oC at 1 K/min of heating/cooling rate. The thermophysical properties including thermal conductivity, thermal diffusivity, and specific heat were determined within temperature range from -20oC to +80oC using KD2 Pro apparatus.

STUDIES OF THE INFLUENCE OF ENERGETIC ADDITIVES ON SELECTED PROPERTIES OF HETEROGENEOUS SOLID ROCKET PROPELLANT WITH LOW CONTENT OF HCL IN COMBUSTION PRODUCTS

The paper presents influence of additives like aluminium, magnesium, AMD (aluminium-magnesium dust) and boron on selected properties of heterogeneous solid rocket propellants (HSRP) based on HTPB in which ammonium chlorate was partly replaced by sodium nitrate. The presence of sodium nitrate reduces the content of hydrogen chloride (HCl) in combustion products. Theoretical values of thermochemical and thermodynamical properties like isochoric heat of combustion (Q), specific impulse (Isp) and combustion products in motor chamber and nozzle were identified by ICT-Code program. A laboratory rocket motor (LRM) was used to examine ballistic properties for prepared samples of propellants. Their temperature of decomposition, heat of combustion and hardness were tested both with sensitivity to mechanical stimuli (impact, friction) and rheological properties at curing.

NEW GREEN AND THERMALLY STABLE SOLID PROPELLANT FORMULATIONS BASED ON TNEF

The preparation of new homogeneous and heterogeneous solid propellant formulations based on the new interesting high-energy dense oxidizer 2,2,2-trinitroethyl-formate (TNEF) and different kinds of binders (nitrocellulose, hydroxyl-terminated polybutadiene, and glycidyl azide polymer) are reported. The prepared TNEF was characterized by Fourier-transform infrared spectroscopy and nuclear magnetic resonance. The thermal investigation using non-isothermal differential scanning calorimetry and thermogravimetric analysis showed high thermal stability. TNEF has a decomposition temperature of similar to 210 degrees C. The high density of TNEF (1.81 g/cm(3) at 298 K) gives the propellant high loading density in the rocket motor. The Kissinger model-free method was used to determine the kinetic parameters of the studied samples. It was concluded that the new propellant formulations are a safe manufacturing process and have green (chlorine-free) gaseous products and higher activation energy than the common traditional formulations.

STUDIES OF HIGH EXPLOSIVES IMPACT ON REDUCTION OF HCL IN HETEROGENEOUS SOLID ROCKET PROPELLANTS

The paper describes an influence of high explosives: hexogene (RDX), octogene (HMX), and dinitro-diaminoethene (FOX-7) on the properties of heterogeneous solid rocket propellant (HSRP) prepared on the base of Hydroxy Terminated Polybutadiene (HTPB) in which ammonium perchlorate (AP) was partially replaced by sodium nitrate (SN). It reduced the content of HCl in combustion products. Theoretical values of thermochemical and thermodynamic properties such as isochoric combustion heat (Q), specific impulse (Isp) and contents of combustion products in motor combustion chamber and nozzle have been identified by using the ICT-Code program. The rheological properties (virtual viscosity) of the propellant slurry during curing process, the sensitivity to mechanical stimuli (impact, friction), decomposition temperature, calorific value and hardness of propellants containing explosive materials were tested by instruments and ballistic properties were investigated by laboratory rocket motor (LRM).

The Influence of Magnetic Fields on the Combustion Processes of Heterogeneous Solid Rocket Propellants

The measured variations in burning pressure with time for a heterogeneous solid propellant with added ferromagnetic particles of size 0.2-0.5 mm are presented. The laboratory tests were conducted with and without an applied external magnetic field generated by a neodymium magnet. The magnetic induction inside the ballistic chamber in which the experiments were performed, was calculated. Variations in the recorded operating pressure reached up to 60%. At the same time it was noticed that the linear burning rate increased by 7%.

Thermo-Mechanical Analysis of Homo- and Heterogeneous Solid Rocket Propellants

The paper analyses results of experimental research of homogeneous and heterogeneous solid rocket propellants. The homogeneous sample PAC with density 1.58 g/cm3 and heterogeneous sample H2 with density 1.77 g/cm3 were both subjected to complex thermo-mechanical analysis. The thermo-physical properties of both samples were determined using KD2 Pro apparatus made by Decagon Devices, Inc. (USA). The temperature characteristics of thermal conductivity k (T), thermal diffusivity D(T), and volumetric heat capacity C(T) were measured within the temperature range from-200 C to +800 C. Mechanical properties such as storage modulus (E’), loss modulus (E’’) and tan (delta) were measured using Netzsch DMA 242C analyser within temperature range from-1200 C to +800 C at heating rate of 2K/min. The rectangular test samples were subjected to the dual cantilever mode with frequency f = 1Hz recommended by the NATO 4540 standard. Special attention was devoted to determining the glass transition temperature and softening temperature of the propellants. The temperature values obtained during DMA experiments supported by thermo-physical properties are essential for safe usage of solid rocket propellants under operating conditions and they may be applied in numerical modeling of temperature and thermal stress distributions of such materials.

Simulations of heterogeneous propellant combustion : Effect of particle orientation and shape

In this paper we have developed a direct numerical simulation approach to study the combustion of ammonium perchlorate-based heterogeneous solid propellants. Oxidizer particles are first supposed to be spheroidal and the effect of their orientation on the burning rate is examined. Particles aligned normal to the combustion surface are found to burn faster than when aligned parallel while randomly-oriented particles generally burn at an intermediate rate, at least for moderate aspect ratio. Simulations also show that the burning rate of random spheroids is relatively independent of the aspect ratio. Finally, the effect of particle shape is investigated using superellipsoidal particles but is here found to be limited for the chosen propellant and pressure.

Modeling of Heterogeneous Propellant Combustion: A Survey

H ETEROGENEOUS solid energetic materials are widely used in the aerospace and defense industries in rockets, explosives, and diverse pyrotechnic devices. Their basic microstructure consists of oxidizer particles embedded in a polymeric binder. Two important classes of energeticmaterials are solid propellants and plastic bonded explosives. A typical composite solid propellant is composed ammonium perchlorate (AP) particles embedded in a polymer such as hydroxyl-terminated polybutadiene (HTPB) or polybutadiene acrylonitrile. A common variation is the addition of metal particles (e.g., aluminum) to raise the combustion temperature. Plastic bonded explosives consist of a heterogeneous mixture of high-explosive crystals (such as cyclotetramethylenetetranitramine or cyclotrimethylenetrinitramine) and a polymeric binder. Here, the discussion is restricted to composite solid propellants. The intent of the present survey is to provide a highlighted discussion of relevant work on the multidimensional computational simulation of heterogeneous solid propellant combustion. Routine numerical simulations are now being carried out, in which many of the physical characteristics of real propellants are mimicked, including random packing of oxidizer particles in a fuel binder, unsteady three-dimensional heat conduction within the solid, unsteady regressionof thenonplanar propellant surface, andcoupling with an unsteady three-dimensional combustion field sustained by reactantfluxes from the surface. Such computations require the use of massively parallel supercomputers, and even then there are limitations onwhat physics can be included. The ultimate goal is to develop a truly predictive simulation tool that can assist in design and optimization of propellant microstructures and propellant grain designs for internal solid rocket motors. Modeling and simulation of composite propellants will remain a vital task because solid rocket motors are critical to national defense, communications, space exploration, and eventually space tourism. The value of computational combustion is eloquently presented in a recent review paper [1]. II. Modeling

Numerical Study of Erosive Burning in Multidimensional Solid Propellant Modeling

Using numerical simulations, the combustion response of heterogeneous solid propellants to an imposed crossflow velocity field are examined. It is shown that this model flow is useful to capture the influence of shear flow in the so-called erosive burning phenomenon observed in actual experiments. Previous numerical studies on a model quarter-plane problem and on homogeneous solid propellants have shown that the presence of shear in the crossflow plays a role in increasing the heat transfer to the propellant surface, thus enhancing the burn rate. In the current work, the response of twoand three-dimensional packs to an imposed velocity field are first examined for different propellant morphologies and at different pressures. The imposed velocity field has its root in a separate nonreactive multiscale analysis. It is shown that, with the model flow, the variations of the erosive burning rate with shear parameters are captured, the trends being in line with experimental results. Furthermore, a comparison with experimental results present in the literature is examined, where it is shown that the results compare qualitatively well with the experiments using the estimated shear rates from the experiment. These results suggest that the influence of the shear flow on the primary diffusion flame may be a leading factor in the erosive burning effect.

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.

The effects of turbulence-induced time-periodic shear on a flame anchored to a propellant

We examine the combustion response of a flame anchored to two 1/4-spaces of solid fuel and oxidizer, a configuration relevant to the combustion of heterogeneous solid propellants. A time-periodic shear flow is applied to model the shear that can be generated by the presence of acoustics or turbulence in a rocket chamber. To estimate the magnitude and frequency of the shear for the case of a turbulent flow, we present DNS results of a planar periodic rocket, a configuration that has its roots in a multiscale analysis. Such a configuration allows for the determination of the shear parameters as a function of motor geometry and downstream location. The response of the flame to this shear, the heat flux to the surface, and the burning rate are calculated numerically. Significant enhancement to the burn rate, commonly known as erosive burning, is found.

Nature of packs used in propellant modeling

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.

Recent progress in modeling solid propellant combustion

Tremendous progress has been achieved in the last ten years with respect to modeling the combustion of solid propellants. The vastly increased performance of computing capabilities has allowed utilization of calculation approaches that were previously only conceptual. The paper will discuss three areas of emphasis: first, numerical modeling of premixed flames using detailed kinetic mechanisms; second, development of packing models to calculate a geometrical distribution of particles simulating a heterogeneous solid propellant; and finally, calculation of diffusion same effects that are critical in the combustion of AP/hydrocarbon solid propellants.The capability of modeling premixed combustion using detailed kinetic mechanisms has been evolving and successfully applied to solid propellant ingredients based on a one-dimensional approach. Much of the early work was performed at Novosibirsk. The approach allows calculating the burning rate as a function of pressure but also the temperature sensitivity and spatial distributions of temperature and species concentrations. Generalized mechanisms have been developed and applied to many ingredients such as HMX, GAP, RDX, NG, AP, etc. The gas-phase kinetic mechanisms seem to represent the chemistry of these monopropellants and pseudo-propellants consistently well. The burning rates of these monopropellants vary by almost an order of magnitude but are essentially independent of the flame temperature. Various model calculations agree reasonably well with available experimental data.Recent work in the USA has been aimed at describing the geometrical packing of a solid propellant. These models represent significant progress toward such a description. Combining the packing model with a realistic flame model is still a significant challenge. Preliminary results are encouraging, but obviously further work is needed. Also, fundamental calculation of two-dimensional diffusion flames, incorporating realistic kinetics has progressed significantly. Recent results show encouraging promise toward simulating the minute detail involved in determining the burning rates of AP containing propellants.

Numerical solution of three-dimensional heterogeneous solid propellants

We have described, for the first time, a fully coupled low Mach number numerical algorithm which can be used to investigate the combustion of composite propellants. The code uses a body fitted grid along the moving interface by means of a mapping technique. Specifically, the surface is assumed to be single valued, thus allowing the use of a mapping function that effectively maps the propagating corrugated surface into a stationary flat surface. The transformed connection conditions are then applied along the stationary flat surface, allowing second-order one-sided derivatives to be used. This has proven to be a very robust and efficient way to treat the surface and the connection conditions. Numerical tests are performed and the scheme is shown to be second-order accurate in the spatial directions as well as in time. Selected results are presented for heterogeneous propellants.