Stability of acoustic oscillations in a model helmholtz-type pulse combustor

Abstract

The leading-order fluid motions and frequencies in combustion chambers and resonance tubes are generally found to be strongly related to those governed by linear acoustics. The present work considers the nonlinear stability of such motions in the context of a model pulse combustor with applications to moisture removal, or drying. In this model, the flow from the combustion chamber supplies energy to the acoustic motions through inertial effects, while the action of viscosity and vaporization of moisture from the initially wet particles, which are injected at the entrance to the resonance tube, are examples of potential damping processes. For small mean-flow Mach numbers and particle densities, the equations of linear acoustics emerge as a first approximation, but are then perturbed by processes such as those just described. Introducing a formal perturbation expansion for the nonsteady motions, evolution equations for the amplitudes of the classical acoustic modes are determined from solvability conditions at various orders in the analysis. Focusing on the linear stability of the basic flow, conditions are derived for the growth or decay of acoustic oscillations as a function of parameters such as viscosity and those that describe the coupling of pressure and velocity perturbations at the entrance to the resonance tube. The combination of inertial, viscous and coupling processes is then seen to provide an effective mode-selection mechanism that inhibits the growth of all but a few lower-frequency acoustic modes from among the infinite number predicted by linear acoustics alone.