Compressible Biglobal Stability of Rocket Internal Flowfields

Abstract

Combustion instability remains one of the most persistent challenges in rocket propulsion, where the nonlinear interaction between hydrodynamic structures and acoustic resonances can precipitate severe performance degradation or structural failure. To address this problem, a fully compressible biglobal stability framework is developed to predict hydrodynamic and vorticoacoustic instabilities in both porous solid-rocket-motor chambers and bidirectional vortex engines. Unlike traditional methods that rely on separate modal decomposition, the present formulation preserves compressibility so that acoustic and vortical branches emerge naturally. In the quiescent limit, the solver reproduces the classical Helmholtz eigenfrequencies and mode shapes, thereby confirming the embedded wave dynamics within the compressible Navier–Stokes system.

Applied to the compressible Taylor–Culick mean flow, the solver yields a comprehensive eigenspectrum that captures hydrodynamic and vorticoacoustic responses while differentiating between longitudinal, radial, and mixed-frequency structures across tangential orders. Increasing the Mach number produces a systematic detuning of vorticoacoustic frequencies, quantifying the convective influence on modal selection. The analysis further demonstrates how wall injection and flow turning regulate the penetration of acoustic vorticity into the core, shaping the growth rates and topology of the unstable modes.

The same framework is extended to the bidirectional vortex engine, representing a class of strongly swirling, injection-driven configurations relevant to liquid and hybrid propulsion. Through the use of complex-lamellar mean flow, the solver captures coupled axial–radial oscillations and delineates stability trends. Collectively, these results provide a unified physics-based foundation for predicting and interpreting modal behavior in compressible rocket flows, thereby advancing the understanding of combustion instability and informing strategies for mitigating flow–acoustic coupling in next-generation propulsion systems.