Nonlinear axial-mode combustion instability remains a serious problem in the development of solid propellant rocket motors. Although the use of metal-loaded solid propellants which produce solid particles in the flow has reduced the occurrence of high frequency instabilities, it has not eliminated the axial-mode intermediate frequency (100 - 1000 Hz.) problem. If such an instability reaches a large amplitude limit cycle, it may lead to an increase in mean chamber pressure and burning rate, excessive heat transfer rates, and a severe vibration level. The objective of this report is to investigate the complex coupling between the chamber flow conditions and the solid propellant combustion process which may lead to large amplitude longitudinal instabilities. (Modified author abstract).

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 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 approximate theory based on the Galerkin method was developed to describe the nonlinear behavior of axial-mode combustion instability in solid-propellant rocket motors and T-burners. For motors with linear combustion driving and linear particle damping (gasdynamic nonlinearities only), growth rates, limiting amplitudes and waveforms were in reasonable agreement with available 'exact' numerical solutions and experimental data. For T-burners the predicted limiting amplitudes were considerably higher than the experimentally measured values. To assess the importance of combustion nonlinearities, a heuristic nonlinear combustion response model was introduced into the approximate analysis. REsults obtained with both the approximate model and the 'exact' analysis showed that nonlinear combustion effects may be important for moderate amplitudes and may account for pulsed instabilities in some cases. The higher Reynolds number correction to the Stokes Drag Law was also included in both the approximate and 'exact' analyses. Results show that nonlinear particle effects become increasingly important as particle size and/or frequency increases. Also, particle nonlinearities may have a significant effect on optimum particle size for maximum damping and may account for pulsed instabilities in some cases. (Author).