Examination of jet growth and jet-drive in the recorder by means of linearized numerical and lumped models

Abstract

Physical modeling of the sound generation in recorder-like instruments is a challenging task due to the complex interaction of the air jet and the acoustical field occurring in the mouth region of the instrument. On one hand, simplified, lumped models were shown to capture some of the key properties of the process, while on the other hand, well-resolved direct computational fluid dynamic (CFD) simulation of the sound production is becoming more and more feasible thanks to the increasing computational capacity being available at hand. In this paper, the results of two-dimensional CFD simulations are combined with a one-dimensional acoustical system and a lumped jet-drive model as an attempt to bridge the gap between fully lumped models and direct CFD computations. A linearized model of the propagation of perturbation waves along the jet is proposed which takes the real velocity profile of the jet into account. Then, the Orr–Sommerfeld equation is solved for attaining the growth rate and phase speed of the perturbations in the frequency domain. The results are inserted into state-of-the-art lumped jet-drive models and are coupled to an acoustical waveguide. One novel model also accounts for the transient growth. Finally, the coupled system is utilized for predicting the playing frequencies of a tenor recorder as a function of the blowing pressure in the case of both steady-state and transient operation. Comparisons with experimental results show the validity of both the flow and acoustical models and also demonstrate the capabilities of the proposed fully linear model with respect to the prediction of the sounding frequencies and register change thresholds.