Flow simulations on an organ pipe foot model

Abstract

The present paper shows numerical simulations of the flow responsible for the sound generation in an organ pipe. Only the foot model of the organ pipe (i.e., with the resonator detached) is investigated by two-dimensional incompressible CFD simulations. It is shown that in spite of the moderately high Reynolds number (Re≈2350) no turbulence modeling is necessary. Free jet simulation (foot model without the upper lip) showed that the jet oscillates due to its natural instability. The velocity profile, the centerline and the width of the jet is determined at different heights above the flue. Edge tone simulations (foot model with the upper lip) were carried out having the upper lip at a constant height but at different x positions. It was found that the strongest and most stable edge tone oscillation occurs if the lower left corner of the upper lip is in the centerline of the jet (optimum position). When the upper lip is far from its optimum position the oscillation of the jet is rather due to the natural instability of the jet than the edge tone phenomenon. The results agree well with the experimental results of Außerlechner et al. [J. Acoust. Soc. Am. 126, 878–886 (2009)] and Außerlechner (Ph.D. thesis, Universität Stuttgart, Stuttgart, Germany) and with former results of the authors [Paál and Vaik, Int. J. Heat Fluid Flow 28, 575–586 (2007); Paál and Vaik, in Conference on Modelling Fluid Flow (CMFF'09), Budapest, Hungary].

The Dependence of Flue Pipe Airflow Parameters on the Proximity of an Obstacle to the Pipe’s Mouth

“…An organ pipe generates a sound only when the airflow is turbulent. Thus, the Reynolds number in this situation exceeds its critical value, hence R e > 2300 [ 5 ]. Additionally, since f 0 >> 1, the Reynolds number is very large.…”

“…The airflow remains turbulent even away from the mouth of the pipe [4]. Contemporary works on the generation of sound in labial pipes use models that take into account the phenomena related to the flow, and we also decided to follow this approach [4,5,27,29]. Expressions (11) and (12) in these papers are only treated as a starting point for further analyzes.…”

“…Our work is based on sound generation model taking flow into account [4,5,27,29], as we are interested in flow and fundamental frequency changes. Using the model described in equations from (11) to (14), it is possible to estimate the fundamental frequency of the organ pipe sound, but if there is an obstacle near the pipe's mouth, the difference between the frequency calculated using this model and the frequency measured from the signal (using the Fourier transform) can be even about 100 cents, i.e., a semitone.…”

“…The state-of-the-art research in the area of sound generation in organ pipes raises various aspects, e.g., airflow analysis [ 4 , 5 , 6 ], or transient state in the process of sound initiation [ 7 , 8 , 9 ]. The experiments and simulations of sound formation in pipes are reported in literature as well [ 10 , 11 , 12 ].…”

Pattern Recognition in Music on the Example of Reconstruction of Chest Organ from Kamień Pomorski

“…Research into the phenomenon has been largely experimental, as shown in works [ 10 , 11 ], or presented by organ builders, e.g., Astride Cavaillé-Coll “De la Détermination des Dimensions des Tuyaux par rapport à leur Intonation”, Paris, 23 January 1860 [ 12 ]. Modern-day research into the phenomena occurring in organ pipes focuses mainly on air flow modeling during sound generation, as well as on the experimental testing of simulation results [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ].…”