The present report is part of a two volume set which describes a nonlinear solid rocket motor instability analysis and computer program. The primary objective of the current effort was the development and solution of a nonlinear analytical longitudinal instability model, which would allow all of the various governing phenomena to be accounted for in a coupled manner. The two primary elements of the current instability analysis are a method of characteristics solution of the two phase flow in the combustion chamber of the motor, and a coupled calculation of a transient burning rate. It is based on an extension of the most popular, linear, harmonic combustion response model. The current method allows the calculation of propellant burning response to a pressure disturbance of arbitrary waveform, for all time, including the period immediately following the initiation of the disturbance. The analysis also includes a model for velocity coupled response. The nonlinear effects of velocity coupling on the growth of pressure waves in a combustion chamber can be computed.

The present report is part of a two volume set which describes a nonlinear solid rocket motor instability analysis and computer program. This volume of the set describes the computer program and serves as a user's manual.

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An existing nonlinear instability model has been extended and improved to allow it to more realistically treat the longitudinal shock wave type of combustion instability frequently encountered in tactical solid rocket motors. Results obtained utilizing this model to investigate limiting amplitude and velocity coupling phenomena in solid rocket motors are presented. An advanced finite difference integration technique capable of accurately describing shocks and contact discontinuities has been incorporated into the computer program, as well as an improved heat conduction solution, an heuristic velocity coupling model, and a spectral analysis capability. Solutions of wave propagation and shock formation and propagation in a variable area duct and a solid propellant rocket motor are presented; as are a number of solutions demonstrating that limiting amplitude is independent of the characteristics of the initial disturbance. Results of a preliminary study of nonlinear velocity modulated limit cycles are presented, as are results that demonstrate the primarily traveling wave nature of nonlinear wave propagation in solid rocket motors, and the complexity of the phase relationships between pressure, burning rate, and velocity oscillations are presented. Finally, the effect of a threshold velocity on non-linear velocity coupled instability was explored, and some of the results are also presented. (Author).

This book contains selected papers prepared for the NATO Advanced Study Institute on "Unsteady Combustion", which was held in Praia da Granja, Portugal, 6-17 September 1993. Approximately 100 delegates from 14 countries attended. The Institute was the most recent in a series beginning with "Instrumentation for Combustion and Flow in Engines", held in Vimeiro, Portugal 1987 and followed by "Combusting Flow Diagnostics" conducted in Montechoro, Portugal in 1990. Together, these three Institutes have covered a wide range of experimental and theoretical topics arising in the research and development of combustion systems with particular emphasis on gas-turbine combustors and internal combustion engines. The emphasis has evolved roughly from instrumentation and experimental techniques to the mixture of experiment, theory and computational work covered in the present volume. As the title of this book implies, the chief aim of this Institute was to provide a broad sampling of problems arising with time-dependent behaviour in combustors. In fact, of course, that intention encompasses practically all possibilities, for "steady" combustion hardly exists if one looks sufficiently closely at the processes in a combustion chamber. The point really is that, apart from the excellent paper by Bahr (Chapter 10) discussing the technology of combustors for aircraft gas turbines, little attention is directed to matters of steady performance. The volume is divided into three parts devoted to the subjects of combustion-induced oscillations; combustion in internal combustion engines; and experimental techniques and modelling.