Stability of the Taylor-Culick Profile with Headwall Injection and Particle Interactions

Abstract

In this work, we study the effects of particle addition on the hydrodynamic instability of the mean flow in a solid rocket motor. latter is modeled using Majdalani's extended representation of the Taylor-Culick profile (Majdalani, J., The Taylor-Culick profile with uniform headwall injection, AIAA Paper No. 2005-4534). Our mathematical idealization considers chemically inert particles that remain invariant in size. Interactions with the mean flow are entertained under incompressible, rotational, inviscid flow conditions. Linear instability theory is subsequently implemented following the approach used by Feraille and Casalis in investigating the stability of Taylor's profile in a porous channel (Feraille, T., and Casalis, G., Channel Flow Induced by Wall Injection of Fluid and Particles, Physics of Fluids, Vol. 15, No. 2, 2003, pp. 348-360). At the outset, the effect of varying particle mass concentrations on the stability characteristics is examined. Our solution enables us to assess the effects of particle damping on flow stability for a given particle concentration, Reynolds number, Stokes number, and headwall injection velocity. Despite the ability of the model to account for an inlet profile at the head end, the main results are shown for the internal burning rocket motor with non-reactive headwall conditions.