Computation of Spinning Modal Radiation from an Unflanged Duct

Abstract

The radiation of high-order spinning modes from an unflanged duct with or without a mean flow is studied numerically. The application is to noise radiation from the intake duct of an aircraft engine. The numerical method is based on solutions of the linearized Euler equations (LEE) for propagation in the duct and near field and the acoustic analogy for far-field radiation. A formulation of the LEE is used for a single azimuthal mode, which offers an advantage in terms of computational efficiency: in the case of an axisymmetric mean flow-field, this model reduces computing costs connected with a three-dimensional model. In the solution process, acoustic waves are admitted from upstream into the propagation area surrounding the exit of an axisymmetric duct and the region immediately downstream. The wave admission is realized through an absorbing nonreflecting boundary treatment, which admits incoming waves and damps spurious waves generated by the numerical solutions. The wave propagation is calculated using a high-order compact scheme. Far-field directivity is estimated by solving the Ffowcs Williams-Hawkings equations. The far-field prediction is compared with analytic solutions, and good agreement is found.