Numerical investigation of the pressure pulsation magnitude and natural aeroacoustic frequencies in the combustion chambers with a charge of a complex shape

The paper presents the results of numerical modeling of combustion product outflow in a gas-dynamic channel of the rocket engine. The pressure fluctuations have been determined in a gas cavity of combustion chamber. A numerical model is based on the Navier-Stokes equations for a single-phase compressible gas. The obtained solution of the Reynolds-averaged Navier–Stokes (RANS) equations with k-e turbulence model has been compared with that of the complete Navier–Stokes equations with large-eddy simulation (LES) model. The calculations have been implemented using the FLUENT package and GAMBIT CAD preprocessor.
The numerical simulations for a complex combustion surface have been performed to reveal a possible instability of the flow and pressure self-oscillations. The frequency-amplitude spectrum of the pressure fluctuations in the different regions of combustion chamber has been determined by the fast Fourier transform. Methodological calculations have been carried out for various configurations of the free volume in the gas cavity. The results of calculations made it possible to define more precisely the analytical formula for determining natural acoustic frequencies in the combustion chamber. Solutions in the framework of the RANS equations allowed one to determine accurately the positions of the acoustic modes in the combustion chamber. In combustion chambers of a complex shape, vortex disturbances generate sound waves and represent a strong source of the gas-dynamic perturbations. An approach based on the solution of the complete Navier–Stokes equations with LES turbulence model made it possible to determine the amplitude of the pressure oscillations taking into account a large-scale vortex generation. It has been shown that when the frequency of vortex generation is equal to the natural acoustic oscillations of combustion chamber, the frequency capture occurs accompanied with an increase in the pressure fluctuation magnitude.