Simulation studies of a recorder in three dimensions

Abstract

The aeroacoustics of a recorder are explored using a direct numerical simulation based on the Navier–Stokes equations in three dimensions. The qualitative behavior is studied using spatial maps of the air pressure and velocity to give a detailed picture of jet dynamics and vortex shedding near the labium. In certain cases, subtle but perhaps important differences in the motion of the air jet near the edge of the channel as compared to the channel center are observed. These differences may be important when analyzing experimental visualizations of jet motion. The quantitative behavior is studied through analysis of the spectrum of the sound pressure outside the instrument. The effect of chamfers and of changes in the position of the labium relative to the channel on the tonal properties are explored and found to be especially important in the attack portion of the tone. Changes in the spectrum as a result of variations in the blowing speed are also investigated as well as the behavior of the spectrum when the dominant spectral component switches from the fundamental to the second harmonic mode of the resonator tube.