Stability of Rockets with Headwall Injection

Abstract

We investigate the hydrodynamic instability of the full-length, cylindrical models of solid and hybrid rockets with headwall injection. Our baseline is the rotational incompressible flowfield proposed in a recent study (Majdalani, J. and Vyas, A. B., Inviscid Models of the Classic Hybrid Rocket, AIAA Paper 2004-3474). The local non-parallel approach (LNP) is implemented in which the amplitude functions are assumed to be radially dependent at fixed streamwise locations. The usual singularity along the chamber axis is eliminated using Taylor series expansions. As a result, three compatibility relations are derived and substituted for the local boundary conditions along the axis. These depend on whether the tangential wave number q is 0, 1 or larger. Our rotational model is shown to exhibit a range of instability that broadens with successive increases in headwall injection. The lowest frequency below which the flow remains unconditionally stable is observed at ω = 28.5 regardless of the headwall injection rate. As usual, the zeroth order tangential mode is found to be the most amplified. Using a representative headwall injection velocity for hybrid rockets, we identify a range of frequencies along which large excursions in pressure and velocity amplitudes are possible. These surges signal the presence of a resonant-like mechanism that is akin to an acoustic instability response. The most excited frequencies vary between 387 and 415 in the vicinity of the headwall. These frequencies are spatially delayed and lowered to 93.8-163.5 when the headwall injection rate is reduced to the level associated with solid rockets. For the most critical streamwise stations, these resurging wave amplitudes are quantified and shown to exhibit spectra that mimic the waterfall data acquired in acoustic instability tests.