Velocity Coupling from Pulse-Test Firings

Abstract

There has been much dispute about triggering of non-linear combustion instability(CI). The norm has been to use ad hoc models to include second order combustion terms most notably velocity coupling. This term arose due to classical linear analyses predicting stable motors necessitating another driving function. However there is no practical universally accepted experimental method that can obtain the velocity coupling response function. The solid rocket motor (SRM) designer is left to his own devices as to what the contribution of velocity coupling may be. This has led to much confusion and rocket motors that have been predicted stable but in practice were not. Flandro and co workers provide an alternative interpretation into the cause of non-linear combustion instability by including rotational terms into the linear analysis. This has been shown to improve the linear stability prediction by predicting unstable systems i.e. CI is always present but at low amplitudes growing too slowly to form a steep fronted wave. A pulse in this context needs to be of high enough amplitude to induce rapid growth. No criterion exists to predict such an amplitude. This study uses a newly developed analysis methodology using tubular grain SRMs to investigate both interpretations i.e. a linearly stable system with velocity coupling or linearly unstable system. This method when combined with response data can be used to obtain a velocity coupling response function from pulse tests. From this analysis it was possible to obtain reasonable velocity coupling response function. When using these constants to predict it was possible to predict a trigger point. Interestingly this point changes significantly with the initial higher order mode amplitudes. It then becomes vital to understand the likely wave structure of a pulse and what influence it has on the triggering amplitude. The system dynamics did not follow that of the experimental data but this may be due to truncation errors and assumptions made in the mathematical model. However the limiting amplitude is predicted correctly. The Flandro interpretation can be evaluated using this new method and applying a systematic study to evaluate criteria for the triggering amplitude. The linearly unstable values seem to capture the system dynamics better. However, in theory any pulse should cause CI. Regardless whether it is true or perceived triggering there seems to be an amplitude value at which non-linear CI is induced. The boundary layer pumping term here seems to be the key to interpreting triggering. The boundary layer acts as a piston that drives the acoustic oscillations when in phase. Thus for non-linear CI to occur the pulse must be of such an amplitude to cause the boundary layer to oscillate and maintain a high enough amplitude until the boundary layer starts to oscillate in phase. Regardless of interpretation this method shows great promise in allowing SRM designers to obtain quantitative response data and investigate triggering quickly and cheaply.