Theoretical Estimation of the Acoustic Energy Generation and Absorption Caused by Jet Oscillation

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We investigate the energy transfer between the fluid field and acoustic field caused by a jet driven by an acoustic particle velocity field across it, which is the key to understanding the aerodynamic sound generation of flue instruments, such as the recorder, flute, and organ pipe. Howe’s energy corollary allows us to estimate the energy transfer between these two fields. For simplicity, we consider the situation such that a free jet is driven by a uniform acoustic particle velocity field across it. We improve the semi-empirical model of the oscillating jet, i.e., exponentially growing jet model, which has been studied in the field of musical acoustics, and introduce a polynomially growing jet model so as to apply Howe’s formula to it. It is found that the relative phase between the acoustic oscillation and jet oscillation, which changes with the distance from the flue exit, determines the quantity of the energy transfer between the two fields. The acoustic energy is mainly generated in the downstream area, but it is consumed in the upstream area near the flue exit in driving the jet. This theoretical examination well explains the numerical calculation of Howe’s formula for the two-dimensional flue instrument model in our previous work [Fluid Dyn. Res. 46, 061411 (2014) ] as well as the experimental result of Yoshikawa et al. [ J. Sound Vib. 331, 2558 (2012) ].

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