Cones of silence, complex rays, & catastrophes: novel sources of high-frequency noise in jets

Abstract

As industrial design continues to look at less conventional jet engine nozzles that produce typically asymmetric mean flows, there is now a need for completely 3D noise prediction schemes. To date, most prediction schemes have been based on extensions of the acoustic analogy given by Lighthill. The most popular, due to Lilley for a parallel shear flow, proves too restrictive when considering the flows from complicated nozzle geometries. However, a generalised acoustic analogy based on an arbitrary mean flow with prescribed nonlinear source terms remains a viable method for industrial computations.

Since any source can be decomposed into a sum of point sources, a critical step in acoustic analogies is the construction of the mean field Green's function. In general the numerical determination of the Green's function still remains a major undertaking, and so much attention has been focused on the simplifications afforded to high-frequency ray approximations. Typically ray theory suffers from three main deficiencies: multiplicity of solutions, singularities at caustics, and the determining of complex solutions. The latter lying beyond-all-orders of the divergent ray expansion in the wavenumber parameter, but proving critical when computing the acoustic held in shadow zones such as the cone of silence.

The purpose of this thesis is to generalise, combine and apply existing methods of tackling these deficiencies to moving media scenarios for the first time. Multiplicities are dealt with using an equivalent two-point boundary-value problem, whilst non-uniformities at caustics are corrected using diffraction catastrophes. Complex rays are found using a combination of imaginary perturbations, an assumption of caustic stability, and analytic continuation of the receiver curve.

As a demonstration of the solver two problems are studied with increasing utility to jet noise. The most important is the application to Lilley's equation for an off-axis point source. This solution is representative of high-frequency source positions in real jets and is rich in caustic structures. Full utilisation of the ray solver is shown to provide excellent results.

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