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

Modeling of Heterogeneous Propellant Combustion: A Survey

A model for erosive burning of homogeneous propellants

A 2 -D windowed combustor has been developed for the study of erosive burnin g in composite solid propellants. The modular design permits study of planar and slotted propellant configurations (as are present in segmented rocket motors) with adjustable port to -throat area ratios. The current focus is on a simple planar configurati on without optical access. Head, aft, and mid -motor pressure instrumentation is included in addition to thermocouples designed to sense local flame front approach time at head and aft ends of the grain. To date, the combustor has been fired 12 times and useful data are now being obtained. A ballistic element ballistic model has also been developed and has been used to analyze some of the tests using the classical Lenoir -Robillard erosive burning model. While more analysis is required, reasonable fits of the results are being obtained by suitable adjustment of the Lenoir -Robillard erosive burning parameters.

Experimental Program to Assess Erosive Burning in Segmented Solid Rocket Motors

Four erosive burning models, equations (11) to (14). are developed in this work by using a power law relationship to correlate (1) the erosive burning ratio and the local velocity gradient at propellant surfaces; (2) the erosive burning ratio and the velocity gradient divided by centerline velocity; (3) the erosive burning difference and the local velocity gradient at propellant surfaces; and (4) the erosive burning difference and the velocity gradient divided by centerline velocity. These models depend on the local velocity gradient at the propellant surface (or the velocity gradient divided by centerline velocity) only and, unlike other empirical models, are independent of the motor size. It was argued that, since the erosive burning is a local phenomenon occurring near the surface of the solid propellant, the erosive burning ratio should be independent of the bore diameter if it is correlated with some local flow parameters such as the velocity gradient at the propellant surface. This seems to be true considering the good results obtained by applying these models, which are developed from the small size 5 inch CP tandem motor testing, to CFD simulations of much bigger motors.

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Development of erosive burning models for cfd predictions of solid rocket motor internal environments

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.

Numerical Study of Erosive Burning in Multidimensional Solid Propellant Modeling

A 6-segment subscale motor was developed to generate a range of internal environments from which multiple propellants could be characterized for erosive burning. The motor test bed was designed to provide a high Mach number, high mass flux environment. Propellant regression rates were monitored for each segment utilizing ultrasonic measurement techniques. These data were obtained for three propellants RSRM, ETM- 03, and Castor@ IVA, which span two propellant types, PBAN (polybutadiene acrylonitrile) and HTPB (hydroxyl terminated polybutadiene). The characterization of these propellants indicates a remarkably similar erosive burning response to the induced flow environment. Propellant burnrates for each type had a conventional response with respect to pressure up to a bulk flow velocity threshold. Each propellant, however, had a unique threshold at which it would experience an increase in observed propellant burn rate. Above the observed threshold each propellant again demonstrated a similar enhanced burn rate response corresponding to the local flow environment.

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James A. Furfaro

Papers

Erosive Burning Study Utilizing Ultrasonic Measurement Techniques