Numerical study of a French horn mouthpiece accompanied by vibrating lips and an oral cavity with compressible direct numerical simulation

A two-dimensional model of a French Horn mouthpiece is numerically studied with a 2D direct numerical simulation (DNS) of the compressible Navier-Stokes equations to investigate the sound generation mechanism from the viewpoint of aeroacoustics. That is, we consider the sounding mechanism of buzzing, when the mouthpiece without a bore is played. Our numerical tool is highly accurate due to the minimum mesh size of the order of the micro-meter, and details of fluid motion and acoustic oscillation inside and near the mouthpiece are successfully reproduced. In particular, we focus on the roles of vibrating lips and an oral cavity in the sound generation mechanism. When the mouthpiece without lips and an oral cavity is driven by a periodic flow with a certain frequency, a single tone without overtones is observed. On the other hand, when the mouthpiece is driven by vibrating lips with an oral cavity, a generating sound includes rich overtones and its waveform is similar to that observed experimentally. Since the bore is a linear element and cannot generates overtones from a single tone by itself, the sound of a horn including rich overtones is generated by a mouthpiece with the vibrating lips and oral cavity.