Stability Analysis of the Swirling Majdalani–Fist Mean Flowfield in Solid Rocket Motors

Abstract

Numerous studies have been performed to show the effects of spinning and swirling flows on increased flight stability characteristics, higher propellant consumption, increased burn rate, greater chamber pressures, and many more. The focus of this work is to understand and quantify the stability characteristics of the “swirling Majdalani–Fist” mean flowfield for solid rocket motors. The study is motivated by the need to quantify the hydrodynamic instability of the flow in cylindrically shaped solid rockets. The aforementioned mean flow profile has been adapted to the current biglobal stability framework. The biglobal stability framework developed here is not limited to a stream function formulation; instead it uses the complete Navier–Stokes equations to the extent of resulting in a linearized eigenproblem, which can be readily solved using a pseudo-spectral method. The governing equations are derived for a two-dimensional spatial wave with sinusoidal temporal dependence. Here a fully two-dimensional biglobal study is carried out using realistic boundary conditions that are consistent with solid rocket chambers. The swirling Majdalani–Fist profile results are compared with results found using the same framework with the well-known Taylor–Culick profile. Finally, future applications and areas of investigation such as headwall injection, multiphasic flow, and compressibility effects are then reviewed.