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.

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.

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).

The solution of problems of combustion instability for more effective communication between the various workers in this field is considered. The extent of combustion instability problems in liquid propellant rocket engines and recommendations for their solution are discussed. The most significant developments, both theoretical and experimental, are presented, with emphasis on fundamental principles and relationships between alternative approaches.