Juliette Chabassier | Viscothermal models for wind musical instruments

I co-advised the PhD of Alexis Thibault with Thomas Hélie and Henri Boutin around viscothermal effects in wind instruments. One highlight of the thesis was to review the reduced model including those effects used in musical acoustics, and contribute with new models of porosity, roughness and viscothermal effects in conical instruments.

References

JSV

Transmission line coefficients for viscothermal acoustics in conical tubes

Thibault, Alexis, Chabassier, Juliette, Boutin, Henri, and Hélie, Thomas

Journal of Sound and Vibration Oct 2022

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Viscothermal acoustic propagation in gases contained in rigid straight or conical tubes is considered. Under the assumption that the wavelength is much larger than both the boundary layer thickness and the tube radius, pressure and flow are shown to be solutions of a pair of coupled 1D differential equations, formulated as transmission line equations involving complex loss coefficients. The derivation of these loss coefficients, which is usually accomplished in cylinders, is generalized here to conical geometries. In the well-kown case of circular cylinders, the Zwikker–Kosten (ZK) theory is recovered. For circular cones, the expression of the loss coefficients is derived. It involves complex-order spherical harmonics, instead of Bessel functions for circular cylinders, and makes the hydraulic radius appear as a natural relevant geometrical parameter. We show that replacing the classical radius by the hydraulic radius in the ZK theory provides an affordable and accurate approximation of the analytic model derived for cones. The proposed formulas are used to compute the input impedance of a cone, and compared with a 3D reference. In an ideal setting, using the spherical harmonics or the hydraulic radius in the 1D method accurately approximates the full 3D method, and allows to increase accuracy by approximately two orders of magnitude compared to the ZK theory.

JASA

Dissipative time-domain one-dimensional model for viscothermal acoustic propagation in wind instruments.

Thibault, Alexis, and Chabassier, Juliette

Journal of the Acoustical Society of America Aug 2021

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Accurate modeling of the acoustic propagation in tubes of varying cross section in musical acoustics must include the effects of the viscous and thermal boundary layers. Models of viscothermal losses are classically written in the frequency domain. An approximate time-domain model is proposed in which all of the physical parameters of the instrument, the bore shape or the wave celerity, are explicit coefficients. The model depends on absolute tabulated constants, which only reflect that the pipe is axisymmetric. It can be understood as a telegrapher’s equations augmented by an adjustable number of auxiliary unknowns. A global energy is dissipated. A time discretization based on variational approximation is proposed along with numerical experiments and comparisons with other models.

@article{thibault:hal-03328715,
  title = {{Dissipative time-domain one-dimensional model for viscothermal acoustic propagation in wind instruments.}},
  author = {Thibault, Alexis and Chabassier, Juliette},
  url = {https://hal.archives-ouvertes.fr/hal-03328715},
  note = {Copyright 2021 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.The following article appeared in Thibault, A., \\& Chabassier, J. (2021). Dissipative time-domain one-dimensional model for viscothermal acoustic propagation in wind instruments. The Journal of the Acoustical Society of America, 150(2), 1165-1175 and may be found at https://doi.org/10.1121/10.0005537 .},
  journal = {{Journal of the Acoustical Society of America}},
  publisher = {{Acoustical Society of America}},
  volume = {150},
  number = {2},
  pages = {1165-1175},
  year = {2021},
  month = aug,
  doi = {10.1121/10.0005537},
  pdf = {https://hal.archives-ouvertes.fr/hal-03328715/file/Manuscript%20%281%29.pdf},
  hal_id = {hal-03328715},
  hal_version = {v1},
  bibtex_show = {true},
  html = {https://doi.org/10.1121/10.0005537},
  abbr = {JASA}
}

ICSV 2021

A low reduced frequency model for viscothermal wave propagation in conical tubes of arbitrary cross-section

Thibault, Alexis, Chabassier, Juliette, Boutin, Henri, and Hélie, Thomas

In ICSV27 - 27th International Congress on Sound and Vibration Jul 2021

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RR

Viscothermal models for wind musical instruments

Chabassier, Juliette, and Thibault, Alexis

Research Report Aug 2020

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WAVES 2022

Thermoviscous acoustic propagation in thin rough tubes

Boutin, Henri, Chabassier, Juliette, Hélie, Thomas, and Thibault, Alexis

In WAVES Jul 2022

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Thermoviscous acoustic propagation in a tube with corrugated isothermal rigid walls is considered. At long wavelengths, it amounts to a 1D transmission line equation, in which the coefficients depend on the solution to a 2D diffusion problem. These coefficients are shown to display predictable behaviors at low, high, and intermediate frequencies. These results are demonstrated on a numerical example.
CFA 2022

Modélisation de l’influence d’une paroi rugueuse sur la propagation acoustique dans un instrument à vent

Thibault, Alexis, Chabassier, Juliette, Boutin, Henri, and Hélie, Thomas

In CFA 2022 - 16ème Congrès Français d’Acoustique Apr 2022

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FA 2023

Viscothermal effects in ducts at audible frequencies. Application to wind musical instruments

Chabassier, Juliette, and Thibault, Alexis

In Forum Acusticum 2023 - 10th Convention of the European Acoustics Association Sep 2023

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