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

• Published in: Journal of sound and vibration 2022-06, Vol.527, p.116857, Article 116857
• Main Authors: Nagy, Péter Tamás, Rucz, Péter, Szabó, András
• Format: Article
• Language: English
• Subjects: Air jets; Aircraft; Blowing pressure; Fluid dynamics; Frequencies; Jet-drive; Linearization; Lumped model; Mathematical models; Orr-Sommerfeld equations; Orr–Sommerfeld equation; Perturbation; Phase velocity; Propagation; Recorder model; Simulation; Sound; Sound generation; Transient operation; Velocity distribution; Wave propagation; Waveguides
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2022.116857

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. •The speed and growth of the jet oscillations account for the real recorder geometry.•The windway losses are modeled accurately by CFD simulation.•The mouth radiation impedance model is improved by 3D finite element simulation.•The sounding frequencies estimated by linear models agree well with measurements.•A change in frequency in the attack is observed both in models and experiments.