Instability of oscillatory flow in ducts and applications to solid-propellant rocket aeroacoustics

Prior research has shown that oscillatory or modulated flows can achieve a significant increase in heat transfer relative to the corresponding steady flow, providing that a critical or threshold amplitude is achieved. The threshold condition is associated with the production of near-surface turbulence by the oscillatory motion. A similar process is hypothesized as a mechanism of high-amplitude acoustic instability in solid propellant rockets, wherein finite amplitude acoustic motions can produce near-surface turbulence and lead to an enhanced propellant burning rate that couples with the chamber acoustics. Prediction of the threshold acoustic amplitude of propellant response requires prediction of the conditions leading to turbulent transition from near-laminar to a turbulent flow in the vicinity of the propellant surface as a prerequisite condition, and is thus a problem of hydrodynamic instability. In the present approach, linear stability theory together with pseudo spectral method is used to obtain unstable flow regimes for ducted flows with injection and acoustic oscillations. Results are first obtained for benchmark problems involving steady injection-induced flow, and oscillatory and modulated noninjected duct flows. The present results compare favorably with prior theoretical and experimental results for the benchmark flows. For simulated solid rocket chamber flows, a periodic burst behavior is noted near the surface as in the purely oscillating flow, with flow disturbances capable of resonance with longitudinal acoustic modes. The key parameters affecting the unsteady laminar motion and the stability results have been identified through an approximate analysis and are calculated at the conditions of several pulsed instability experiments. The most critical modes typically occur within a thickness characterized by the first maximum of axial velocity in the acoustic boundary layer. For higher chamber pressures, this thickness decreases appreciably, leading to a predicted decrease in stability threshold amplitude. Significant axial mean flow in the chamber is found to have a slight stabilizing effect on acoustically induced instability when acoustic amplitudes are relatively large. The wavelengths of acoustically-induced disturbances are qualitatively consistent with the wavelengths of surface ripples observed on extinguished samples of propellant acquired during high-amplitude instability.