Third-Order Nonlinear Acoustic Instabilities in Combustion Chambers, Part II: Transverse Modes

An analytical analysis has been developed to investigate the behavior of unsteady transverse pressure oscillations in combustion chambers. The model extends the previous analysis for the second-order standing wave motions and accommodates spinning oscillations and third-order nonlinearities. The influences of various parameters and initial conditions on the limit cycles and triggering of pressure oscillations are discussed. Results indicate that the existence of spinning oscillations depends strongly on the number of modes included in the analysis and on the initial conditions. The third-order acoustics has little influence on the triggering of instability. It only modifies the characteristics of limiting amplitudes.