Simulation of large non-linear thermo-acoustic vibrations in a pulsating combustor

Abstract

This paper concerns the modeling and numerical simulation of pulse combustion. As the title highlights, focus is on self-sustained acoustic vibrations, the cause of self-excitation being an unstable feedback loop closed by the combustion process. A Helmholtz-type mechanical-valve pulsating combustor was considered. Numerical models were two-dimensional axis-symmetrical, and efforts were made to model the elementary steps of the unstable feedback loop (valve opening, injection of reactants, turbulent mixing and combustion, etc.) as well as possible, to provide a realistic description of the self-excitation mechanism as a whole. Simulations were carried out the analyse the effects of several design and operation parameters on the feedback loop (from injection of reactants to turbulent combustion rate to history of heat release) and ultimately on the growth rate and frequency of vibrations. Results of simulations were post-processed to extract the time evolution of the total mechanical enery (sum of pressure and kinetic energy) of vibrations. Finite-amplitude self-sustained periodic oscillations in the combustor are completely reproduced and the limit cycle (at which dissipated energy per cycle is equal to amount of mechanical energy furnished by the combustion process) found. The software used was ‘Fluent,” a commerical CFD (Computational Fluid Dynamics) code [13] incorporating a reaction rate model accounting for turbulent mixing. A general purpose CFD code instead of classical linearized models was chosen to preserve the nonlinearity of the original equations, thus allowing us to carry out non-linear instability analysis (not only initial growth rate) and to find the limit cycle of the system.