Propagation of Sound through a Variable-Area Duct with a Steady Compressible Flow

The equations governing the progagation of sound in a nonconstant area duct with a one-dimensional fluid flow are derived by a linearizing perturbation technique. The governing equations are transformed successively into two decoupled linear ordinary differential equations with a variable coefficient. By the appropriate choice of duct shape, the variable coefficient is made constant. The duct shape chosen is semi-infinite, diverging from the sonic throat. Solutions are obtained for several choices of the parameter ωL/2as, which relates frequency, duct shape, and speed of sound. The solutions exhibit standing-wave characteristics and reveal certain aspects of energy transfer between the mean flow and sound. The study bears on noise growth and decay in the input and output ducts of certain fluidic amplifiers.