A general grid mapping and finite difference investigation of noise propagation in variable area ducts

The primary objectives of this work were to develop grid mapping procedures and numerical techniques required for the simulation of noise propagation in variable area ducts. The techniques developed are capable of handling soft wall boundaries as well as satisfying far field radiation conditions.

In order to simulate the noise propagation in variable area ducts, the effort was divided into two main parts. First, irregular geometries in the physical (X-Y) plane were transformed into a square grid in the (ξ - η) plane using a general numerical mapping procedure. Next, the noise equations were solved in the transformed plane using an explicit finite difference technique.

The work resulted in a general FORTRAN program that was tested for cases containing different boundary conditions including soft and hard wall top and bottom conditions, and plane wave and far field exit conditions. The results were compared to available numerical and experimental data.

The noise simulation was found to be successful when a plane wave exit condition was used, whereas problems were encountered when a far field exit was used. The problems were determined to be the failure of the explicit method to eliminate numerically generated erroneous "steady state reflections" in the noise solution, and the fact that the pressure wave did not expand exactly cylindrically in the vicinity of the far field exit boundary.

Recommendations for follow-up work include the use of an implicit scheme in place of the less sophisticated explicit methods, and the use of a free surface method at the far field exit boundary to insure correspondence between the physical shape of the exit boundary and the leaving pressure wave.