Numerical computations of a fluid inside and around a recorder

We present the sound propagation and sound radiation inside and around a three dimensional recorder model. The fluid inside and in the near field of the instrument is meshed by second order Lagrangian tetrahedra elements. To present the effects in the far field, infinite elements are added to the finite elements. As infinte elements we use complex conjugated Astley-Leis elements. The goal of our studies is the computation of the eigenmodes of all playable notes, as well as the determination of the radiation behaviour for different fingerings. In a first step, the results obtained by considering a static fluid are presented. When playing a recorder, the inserted air flow leads to an oscillation of the air column inside the instrument. The musician is able to influence the frequency of the note by varying the blowing pressure and therefore a fine-tuning of the sound can be achieved. In rotation afflicted flows, the sound propagation can be described by the Galbrun equation. In a first instance, we present the influence of the flow velocity on the eigenfrequencies for simple geometries. Those results are compared to the frequencies obtained with Helmholtz equation for static fluids.