Large-Eddy simulation of vortex shedding and pressure oscillations in solid rocket motors

A three-dimensional high-fidelity numerical simulation of a small-scale solid rocket motor is carried out adopting the implicit large-eddy simulation (ILES) approach to investigate the coupling between vortex shedding and the acoustic modes of the motor chamber. The ONERA C1xb laboratory-scale model is considered at a firing time close to ignition, corresponding to a 3-mm-grain burned layer. The analysis focuses on the characterization of the unsteady pressure signature on the motor wall, with emphasis on the role played by turbulence on the level of pressure oscillations. It is found that the root mean square of the wall-pressure fluctuations obtained by ILES along the motor wall is in excellent agreement with the experimental data, which is contrary to the prediction of axisymmetric simulations. Fourier spectral analysis reveals that, for this grain geometry, the first three longitudinal modes are weakly excited at the motor head end and most of the energy is concentrated in the shear layer detaching from the grain edge, whose development in the motor chamber is characterized by the rollers breakup with subsequent transition to fine-scale turbulence. The spectrum highlights that the coupling between vortex shedding and pressure oscillations is locked on the third acoustic mode, in agreement with previous experimental observations and with the frequency predicted by a simple acoustic feedback loop model.