Convergence of Two Analytical Flowfield Models Predicting a Destabilizing Agent in Rocket Combustion

In the combustion stability assessment of solid propellant rocket motors, several new destabilizing terms are introduced when rotational-flow effects are properly accounted for. Such effects must be included when the wave motion is parallel to the burning surface. A normal fluctuating velocity component then appears in a careful resolution of intrinsic fluid dynamics, including acoustico-vortical interactions that must satisfy mass and momentum conservation principles while accommodating the no-slip condition at the propellant surface. The source of this destabilizing term appears explicitly in two separate, independently derived, analytical formulations of the internal flowfield. Predictions generated by these analytical models are shown to agree with reliable computational data produced recently by a numerical code that solves the unsteady nonlinear Navier-Stokes equations. Verification of the analytical formulations by means of theoretical considerations, numerical comparisons, and global error assessments are also undertaken before examining the impact of the new time-dependent radial-velocity correction on rocket stability. The new radial-velocity fluctuations introduce a correction comparable in importance to the classical pressure coupling at the propellant surface. This effect along with several companion terms must be accounted for properly in the assessment of motor stability characteristics.