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Volume II is a user's manual for computer programs written to perform theoretical analyses described in Volume I. This volume describes the main routines and subroutines used in the analysis of the combustion of composite solid propellants both steady state and nonsteady state. Also, a detailed description of the input parameters required as well as the output generated is presented. Sample cases are provided to facilitate understanding of the programs so described. (Author).
In this report, the theoretical, steady state combustion model, the Petite Ensemble Model (PEM), is described in detail. The PEM is based upon a combination of a unique statistical treatment of the burning propellant surface and a comprehensive multiple flame type, physio-chemical combustion model. Due to this statistical treatment, the PEM can account for both oxidizer particle size and oxidizer particle size distribution effects on burning rate behavior; an unique feature of this model. The effects on propellant burning rate behavior due to the inclusion of aluminum particles have been taken into account within this version of the PEM, as have any possible effects caused by the presence of a crossflow velocity above the propellant surface (erosive burning). The PEM is capable of modeling the burning behavior of AP-based/hydrocarbon binder, composite solid propellants. Propellant additives such as aluminum oxide, zirconium carbide and graphite, as well as aluminum, can also be incorporated in the propellant formulations modeled by the PEM. This report presents the results obtained by applying a small perturbation analysis to the equations representing the steady state PEM (including aluminum and erosive burning effects). Performing such an analysis yields nonsteady state models of both the pressure coupled response and the velocity pressure coupled response of composite solid propellants. Other historical pressure coupled response models such as the Dension and Baum mode, the Cohen model, and the Zeldovich/Novozhilov model are also briefly described. Finally, a second velocity coupled response model based on the Zeldovich/Novozhilov methodology coupled to the erosive burning PEM is presented. (Author).
The objective of this program was to develop a computerized mathematical model of the combustion response function of composite solid propellants, with particular attention to the contributions of the solid phase heterogeneity. A one-dimensional model was developed which treats the solid phase as alternating layers of AP and binder, with an exothermic melt layer at the surface. Solution of the Fourier heat equation in the solid provides temperature and heat flux distributions with space and time. The problem is solved by equating the heat flux at the surface to that produced by a suitable model of the gas phase. An approximation of the BDP flame model is utilized to represent the gas phase. By the use of several reasonable assumptions, it is found that a significant portion of the problem can be solved in closed form. A method is presented by which the model can be applied to tetramodal particle size distributions. A computerized steady-state version of the model was completed, which served to validate the various approximations and lay a foundation for the combustion response modeling. It is concluded that some other mechanism associated with the propellant heterogeneity must be incorporated into the theory to account for observed behavior.
An analytical model for the linearized velocity-coupled combustion response function was developed. The model combines elements of response to velocity perturbations, pressure perturbations, and compositional perturbations due to the heterogeneity of composite propellants. The important effects of AP size distribution are accounted for in terms of effects on ballistics properties and in terms of periodic fluctuations in propellant composition. Properties of the response function have been calculated theoretically over a range of the governing variables. There are two facets of the crossflow problem: the response to velocity perturbations, and the effect of crossflow velocity on the various response elements. The crossflow mechanism is heuristically based upon the so-called 'Soderholm erosive burning law, ' but which has been given physical significance in the theoretical work of Kuo. Significant results are described. In addition, the triggered non-linear instability experiments performed at CARDE were reviewed and shown to depend upon the achievement of a formulation-dependent critical velocity in the rocket motor. Progress was made in the measurement of the pressure-coupled response functions of propellants formulated to seek out the effects of AP particle size. Progress was made toward formulating a high frequency combustion response model applicable to nitramine/minimum-smoke propellants.
Despite significant developments and widespread theoretical and practical interest in the area of Solid-Propellant Nonsteady Combustion for the last fifty years, a comprehensive and authoritative text on the subject has not been available. Theory of Solid-Propellant Nonsteady Combustion fills this gap by summarizing theoretical approaches to the problem within the framework of the Zeldovich-Novozhilov (ZN-) theory. This book contains equations governing unsteady combustion and applies them systematically to a wide range of problems of practical interest. Theory conclusions are validated, as much as possible, against available experimental data. Theory of Solid-Propellant Nonsteady Combustion provides an accurate up-to-date account and perspectives on the subject and is also accompanied by a website hosting solutions to problems in the book.
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