An approximate method for calculating the noise generated by a turbulent flow within a semi-infinite duct of arbitrary cross section is developed. It is based on a previously derived high-frequency solution to Lilley's equation, which describes the sound propagation in transversely-sheared mean flow. The source term is simplified by assuming the turbulence to be axisymmetric about the mean flow direction. Numerical results are presented for the special case of a ring source in a circular duct with an axisymmetric mean flow. They show that the internally generated noise is suppressed at sufficiently large upstream angles in a hard walled duct, and that acoustic liners can significantly reduce the sound radiated in both the upstream and downstream regions, depending upon the source location and Mach number of the flow.Goldstein, Marvin E. and Leib, Stewart J.Glenn Research CenterSOUND PROPAGATION; EMISSION; COMPUTATION; TURBULENT FLOW; APPROXIMATION; UPSTREAM; TURBULENCE; SHEAR FLOW; MACH NUMBER; LININGS; DUCTS; AXISYMMETRIC FLOW...