Remarks on the two-mode approximation to the nonlinear behavior of pressure oscillations in combustion chambers

This paper summarizes recent work on the approximation to nonlinear pressure oscillations using two modes. A large part of the effort has been concerned with the consequences of gasdynamic nonlinearities of second order in the fluctuations. It appears that the two-mode approximation is valid over a broad range of the linear parameters that govern the global qualitative behavior, particularly if the lower mode is the unstable mode. Exact solutions have been found for the existence and stability of limit cycles, allowing meaningful comparison with numerical solutions obtained with larger numbers of modes considered. The nonlinear analysis to second order does not contain "triggering" - nonlinear instability of a linearly stable system - because the nonlinear processes order terms involving the mean flow speed, or DC shifts in the amplitudes of oscillation do produce triggering.