Linear Analysis of Erosive Burning in Solid Propellant Motors

Abstract

A theoretical investigation of the coupling between the core flow process and combustion sublayer process in a rocket chamber flow is presented. The focus of the investigation is on penetration of chamber disturbances into the sublayer and on the burn rate characteristic responses. Characteristic solutions to the local non parallel instability problem supported by gasifying propellant in a double slab geometry are sought. In the fully decoupled limit the only characteristic solution response is a pressure response, thus comparisons between coupled and decoupled pressure responses are presented. The propellant is typified by a set of burning characteristics, and their effect on the coupling is explored. The goal of the analysis is to clarify the extent strand burning characteristics (i.e., in zero cross flow conditions) can affect burn rate perturbations leading to the phenomenon of erosive burning. The findings of this research agree with experimental studies as it regards the effect of burning parameters on erosive behavior. Change in erosive sensitivity with propellant characteristics is thus correlated with a change in the core-sublayer interaction. n this paper we present an investigation of erosive burning in rocket motors by performing a linear analysis of the coupling between combustion sublayer and turbulent chamber flow. Erosive burning describes burn rate augmentation in solid rocket engines as a result of cross-flow conditions. Erosive burning is responsible for strong overpressure at the rocket firing stage. A better understanding of the influence of burning characteristics on erosive sensitivity can improve rocket design techniques and propellant choices. There have been many attempts to identify the mechanism responsible for the measured increase in burn rate over the zero-cross flow burn rate. “Flame bending”, “heat transfer from core to propellant surface”, “increase in heat flux due to turbulence” are classical examples. Most analyses have relied on empirical fits often based on turbulent profiles over a flat plate; none have been based on a rigorous analysis of the equations. Due to the large difference in length scales between combustion sublayer and chamber core flow, as discussed in more detail in §II of this paper, the development of the instability and the ensuing turbulent field are fairly independent of the burning characteristics. Therefore, the experimentally established link between erosive burning augmentation and propellant characteristics (e.g., King 3 ) cannot be resolved without hypothesizing an effect of the instability on the micron-size combustion profile; that is, hydro-dynamic considerations alone are not sufficient. Mukunda and Paul 2 argue that the effect of the burning characteristics can be taken into account by simply scaling the port mass flow rate by the strand value. Still, the proposed effect of the Reynolds number on erosive burning cannot be explained based on the relationship between the same parameter and the instability growth rate. The present paper attempts to provide a more rigorous analysis of the effect of burning parameters on the core flow-sublayer coupling by seeking characteristic solutions to the linearized and localized solid-gas fully-coupled problem. Although the linearized analysis does not provide a clear quantitative answer on the burning rate augmentation, burn rate eigenfunctions (fluctuation intensity) quantify the importance of