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A numerical method for prediction of acoustic spinning mode radiation from turbofan inlets is presented. Sound propagation is modeled by the linearized mass conservation equation for irrotational flows and solved in the frequency domain. The mean flow through the inlet is obtained as a solution of the full potential equation. Both the mean-flow and the acoustic problem are approximated by Galerkin projection in spectral element spaces of continuous piecewise polynomials defined on the same grid. The Gauss--Chebyshev--Lobatto points within the elements are generated via transfinite interpolation and CAD projection procedures embedded within the code. The linear algebraic systems obtained are then solved using either direct or sparse iterative solvers based on the message passing interface standard for interprocessor communication. The singularity appearing in the acoustic integrals on the symmetry axis is treated by the use of a collocation operator based on the Gauss-Chebyshev, instead of the Gauss--Chebyshev--Lobatto, points. To eliminate reflections from the radiation boundaries, a novel frequency-domain formulation of the matched-layer technique, wherein waves entering the layer are exponentially damped, is proposed. The overall computing procedure is first validated on a tone radiation problem from a semi-infinite cylinder and then applied to an experimental JT15D turbofan inlet setup.

An essentially nonoscillatory (ENO) scheme was extended via extrapolation to develop a higher-order ENO formulation for the Euler equations on unstructured meshes. A piecewise polynomial reconstruction of the formulation from its cell averages was used to achieve a higher-order accuracy. The method was found to be very effective and competitive with other ENO methods of the same accuracy.