The objective is to find accurate methods for calculating the transmission of sound in flow ducts. To get numerically stable procedures, operator methods, including splitting techniques, are employed. As a first step the acoustic transmission is determined for curved ducts with varying cross sections. General two-dimensional and technically important classes of three-dimensional ducts are treated.

Three-dimensional duct handled with the operator method

Then the transmission in sheared two-dimensional ducts are studied using methods that can be generalized to include an axial variation of the flow. Of particular interest is the expansion of a jet in a duct. Critical to this study are the potential presence of the Kelvin-Helmholtz instability and the incorporation of both quiescent and moving zones in the flow. While the problem is conveniently described with partial differential equations when the entire flow has a non zero mean velocity, a differential algebraic formulation is required to include both quiescent and moving zones.

Recently, efficient algorithms have been developed for numerical conformal mappings to be used in the procedure described above.

Axial flow field of an expanding jet with a quiescent zone.