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Flows in Complex Systems

Numerical Investigations of the Gas Flow Inside the Bassoon

[+] Author and Article Information
Andreas Richter

Research Associate CIC VIRTUHCON,  Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germanya.richter@vtc.tu-freiberg.de

J. Fluids Eng 134(4), 041104 (Apr 20, 2012) (10 pages) doi:10.1115/1.4006247 History: Received October 14, 2011; Revised February 21, 2012; Published April 19, 2012; Online April 20, 2012

This work is devoted to the numerical investigation of the gas flow inside a bassoon while it is played. The digitized geometry for the simulations is taken from measurements using laser scan techniques in combination with image processing. Pressure time series measured at the bell and reed were used to define adequate boundaries. Additional pressure measurements inside the musical instrument helped to validate the calculations. With this approach, it was possible to model the characteristics of a bassoon which plays the lowest note. The results of the three-dimensional simulations showed that the acoustic velocities and the underlying mean flow exhibit the same order of magnitude. The calculations indicate that the flow in curved sections such as the crook and the 180 deg bend is considerably different from a steady-state flow. For example, in bends the time-averaged flow features chains of small, alternating vortex pairs, and the pressure distribution differs significantly from a plane wave solution.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Pressure measurement at the reed (a) and the the bell of the bassoon (b) [22]

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Figure 3

Details of the geometry discretization

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Figure 4

Difference between the measured and calculated transient pressure, time domain, forte. (thick line) measurement, (thin line) calculation. (Measured data by Grothe [22])

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Figure 5

Measured and calculated transient pressure, frequency domain, forte. (thick line) measurement, (thin line) calculation [22]

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Figure 9

Pressure isosurfaces at different time levels, forte. (a) inside the crook, p′ = −10... −8kPa. (b) inside the 180 deg bend, ppref  = −3.0…−2.4kPa. The smaller figure illustrates the pressure distribution at the inflow.

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Figure 10

Snapshot of the velocity field along the midplane while the negative pressure peak passes the crook (a) and the 180 deg bend (b). (small figure) pressure at the inlet of the crook. The long arrows illustrate the mean flow direction.

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Figure 11

Mean flow field (a) and steady-state velocity field (b) inside the crook

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Figure 12

Helicity isosurfaces inside the crook. (a) mean flow, (b) steady-state flow. |H|=500m/s2

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Figure 13

Mean flow field and steady-state velocity field inside the 180 deg bend. (a) mean flow, (b) steady-state flow

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Figure 14

Helicity isosurfaces inside the 180 deg bend. (a) mean flow, (b) steady-state flow. |H|=25m/s2

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Figure 15

Turbulent viscosity ratio ν t /ν

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Figure 1

Digitization of the bassoon. Model Wolf S2000, crook model Grundmann. (a) original, (b) digitized bore. The red arrow marks the inflow, and the blue arrow indicates the outflow of the instrument.

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Figure 8

Pressure time series (ppref ) at different time levels, forte. The starting and endpoints p1 − p4 are defined in Fig. 7.

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Figure 7

Pressure field ppref in kPa at different time levels, forte. The smaller figure illustrates the pressure distribution at the inflow.

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Figure 6

Pressure ppref versus time measured inside the bassoons double reed (a) and the outlet (b). (thick line) forte, (thin line) piano. The sampling rate was 35.7 kHz. The smaller figure illustrates the pressure distribution at the inflow [22]).

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