Combustion stability analysis of rocket engines with resonators based on nyquist plots

The paper is concerned with the formulation and validation of an efficient, flexible, and reliable method to assess the influence of resonator rings on combustion dynamics in rocket thrust chambers. The chamber is modeled as a network of low-order acoustic elements that describe three-dimensional waves in cylindrical duct segments with nontrivial boundary conditions and mean flow. The main elements responsible for (thermo)acoustic driving and damping, such as time-lagged fluctuating heat release, injector plate, and short exit nozzle are considered. Particular attention is given to the formulation of a semianalytical resonator ring model, which is capable of handling transverse waves, mode coupling, and mode scattering. A Nyquist plot method based on control theory, which is considerably more efficient than classical root finding techniques, is used to identify the eigenmodes and growth rates of the system. After validating the Nyquist method against analytical results, the stabilizing influence of resonator rings is demonstrated through a representative test case. The key mechanisms induced by the resonator ring that lead to stabilization are also discussed. The proposed method is capable to predict linear stability and give insight in the threedimensional pressure distribution with very moderate computational effort that allows parametric studies.