Computation of spinning modal radiation from an unflanged duct

The radiation of high-order spinning modes from an unflanged duct with or without a mean flow is studied numerically. The issues involved have applications to noise radiation from the inlet duct of an aircraft engine. The numerical method is based on solutions of linearised Euler equations (LEE) for propagation in the duct and near Held and the acoustic analogy for far Held radiation. A formulation of a Linearised Euler equation model is proposed to accommodate a single azimuthal mode (2.5D equations) which has an advantage in terms of computation efficiency. In the case of an axisymmetric mean flow fleld, this model reduces computing cost associated with a 3D model. In the solution process, acoustic waves are admitted into the propagation area surrounding the exit of an axisymmetric duct and its immediate downstream area. The wave admission is realised through an absorbing non-reflecting boundary treatment which admits incoming waves and damps spurious waves generated by the numerical solutions. The wave propagation is calculated through solutions of linearised Euler equations, using a high-order compact scheme. Far fleld directivity is estimated by solving the Ffowcs-Williams Hawkings equations. The far fleld prediction was compared with analytic solutions and good agreement was found. The work described in the paper contributes to the completeness and accuracy of the numerical method.