Pressure–thrust oscillation characteristics and amplification mechanisms in a backward-facing step solid rocket motors under self-excited and forced conditions

To investigate the pressure–thrust oscillation characteristics and amplification mechanisms in solid rocket motors, unsteady numerical simulations under a fixed geometry assumption were performed for a backward-facing step C1xb motor. A two-dimensional axisymmetric scale-resolving framework was employed to capture unsteady vortex dynamics, acoustic wave propagation, and their coupling with thrust generation. Under self-excited conditions, the motor exhibits a bimodal response dominated by the first longitudinal acoustic mode and the vortex shedding component at about 735 Hz and 1420 Hz. Although the pressure fluctuations of these two components are comparable at the head-end, the vortex shedding component produces a much stronger thrust response, indicating a pronounced non-proportional pressure–thrust relationship associated with vortex–nozzle interaction. When periodic inlet perturbations are introduced, the oscillation characteristics become strongly frequency-dependent. For a perturbation amplitude of 5%, the most intense response occurs at 750 Hz, where the dimensionless thrust fluctuation reaches 17.49%, indicating a near-resonant amplification in the first longitudinal resonance region. As the perturbation frequency departs from this region, the dominant high-response zone shifts from the head-end toward the aft cavity and nozzle entrance, while the vortex shedding component remains concentrated near 1400 Hz. At a fixed perturbation frequency of 1000 Hz, increasing the perturbation amplitude mainly strengthens the forcing fundamental and suppresses the first longitudinal mode, whereas the vortex shedding component retains a relatively stable amplification level of about 9.0. These results indicate that thrust oscillations in solid rocket motors are governed jointly by acoustic resonance, modal competition, and vortex–nozzle interaction.