The acoustic boundary layer in porous walled ducts with a reacting flow

Abstract

An analysis of the acoustic boundary layer in a porous walled duct containing a primixed, laminar flame adjacent to the duct walls is presented. The reactants are injected through the sidewalls and an overall one step chemical reaction is assumed. The theory finds applications in studies of propellant response and stability analyses of solid propellant rocket motors. The formulation, valid for low injection Mach numbers, is two dimensional and includes effects of viscosity, thermal conductivity, axial and transverse velocities and unsteady combustion in the flame. It is shown that increasing the flow injection rate increases the boundary layer thickness at a given frequency and its tendency to damp acoustic motions in the duct also increases. However, the unsteady reaction rate and associated unsteady heat release rate tend to enhance acoustic motions within the duct and generally dominate the damping processes. Furthermore, the analysis shows that the unsteady expansion in the unsteady reaction region is the, mechanism responsible for the observed acoustic driving. Finally, the analysis shows that the acoustic admittance at the boundary layer edge depends upon axial location within the duct, varying most rapidly near an acoustic pressure minimum.