a Mapped Finite Difference Study of Noise Transmission in Nonuniform Ducts

The primary objective of this work was to study a class of problems involving noise propagation in acoustically lined variable area ducts with or without mean fluid flow. The method of study was numerical in nature and included body -fitted grid mapping procedures in conjunction with implicit finite difference techniques. The work resulted in several general FORTRAN programs that were tested for cases with or without mean fluid flow, including soft wall or hard wall acoustic liner conditions, and plane wave or far field exit conditions. The results were compared to available theoretical and experimental data. The automated, body-fitted grid mapping procedure was found to be robust, simple to use, and capable of mapping very complicated geometries simply by defining the grid distribution on the boundaries. In general, the solution of the wave equation was found to be successful when using a plane wave exit condition, whereas a problem was encountered with reflections from the particular far field exit condition being applied. The problem was determined to be the result of the proximity of the far field boundary to the noise source as well as its applicability to exactly cylindrical wave expansions only. The fully-coupled solution of the linearized gas dynamic equations was successful for both positive and negative Mach numbers as well as for hard and soft wall conditions. The mean fluid flow considered was two-dimensional, inviscid, irrotational, incompressible, and nonheat conducting. The factored-implicit finite difference technique used did give rise to short wavelength perturbations, but these were dampened by the introduction of higher order artificial dissipation terms into the scheme. In the different problems that this study considered, the finite difference theory was found to be well-suited for the simulation of noise transmission in nonuniform ducts.