Ballistics of solid rocket motors with spatial burning rate variations

Abstract

Introduction T HE solid rocket motor (SRM) ballistician has the job of predicting the chamber pressure and thrust history for both new and existing motors utilizing propellant burning rate and grain geometry, ambient conditions, and nozzle geometry. For motors which do have a test history, ballisticians introduce a constant to force predictions to match actual burn times of test units as well as a time varying multiplier to improve matching of the pressure history. This pointwise burning anomaly rate factor, or BARF, is usually established as a function of web distance since it is generally acknowledged that the factor accounts for spatial burning rate variations within the grain. This ubiquitous quantity has gone by several names through the years: factor, surface burn rate error (SBRE), and residual error to name a few. Since the scale factor forces the average burning rate to match that in the test, the net integration of the BARF curve should have no effect on burning time. For most motors, the result takes on a hump-shaped appearance with maximum errors in burning rate usually being between 2-10%. Burning rate errors of this magnitude translate to errors in pressure of 3-15% due to the nonlinear dependence of pressure on this parameter. Errors introduced due to the present technique for predicting ballistic response can require grain redesign and additional static tests. In addition, initial uncertainties in the ballistic prediction of maximum chamber pressure impacts the design of motorcase, nozzle, and insulation components since these parts must be designed for worst predictions. Even if initial tests are deemed to be adequate, thrust history variations from the optimal design can cause losses in payload capability. Finally, spatial burning rate variations not normally considered by the ballistician can lead to changes in insulation exposure times when compared with current prediction methodologies. This Note will investigate means to improve ballistic predictions by determining the contribution of spatially dependent burning rate variations to the BARF effect for a simple cylindrical-port motor. Background associated with research into BARF effects is provided in the next section, followed by a description of the technical approach. An analysis of a simple ballistic test motor follows this discussion, along with conclusions from the study. While propellant strain, grain deformations during pressurization, local gas velocity effects, and possible migration of propellant constituents have all been theorized to contribute to BARF effects, the primary influence appears to be attributable to spatial variations in the local burning rate within the propellant grain. We make this assumption because the hump shaped character of the curve seems to be consistent across many motors of varying grain geometry, case deformations, and propellant formulations. In nearly all cases, spatial burning rate variations are attributed to one of two effects resulting from the rheological processes undertaken in loading