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Acoustic boundary layers as boundary conditions
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0003-0473-3263
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0001-8329-8348
Umeå University, Faculty of Science and Technology, Department of Computing Science.
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 371, p. 633-650Article in journal (Refereed) Published
Abstract [en]

The linearized, compressible Navier-Stokes equations can be used to model acoustic wave propagation in the presence of viscous and thermal boundary layers. However, acoustic boundary layers are notorious for invoking prohibitively high resolution requirements on numerical solutions of the equations. We derive and present a strategy for how viscous and thermal boundary-layer effects can be represented as a boundary condition on the standard Helmholtz equation for the acoustic pressure. This boundary condition constitutes an O (delta) perturbation, where delta is the boundary-layer thickness, of the vanishing Neumann condition for the acoustic pressure associated with a lossless sound-hard wall. The approximate model is valid when the wavelength and the minimum radius of curvature of the wall is much larger than the boundary layer thickness. In the special case of sound propagation in a cylindrical duct, the model collapses to the classical Kirchhoff solution. We assess the model in the case of sound propagation through a compression driver, a kind of transducer that is commonly used to feed horn loudspeakers. Due to the presence of shallow chambers and thin slits in the device, it is crucial to include modeling of visco-thermal losses in the acoustic analysis. The transmitted power spectrum through the device calculated numerically using our model agrees well with computations using a hybrid model, where the full linearized, compressible Navier-Stokes equations are solved in the narrow regions of the device and the inviscid Helmholtz equations elsewhere. However, our model needs about two orders of magnitude less memory and computational time than the more complete model. 

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 371, p. 633-650
Keywords [en]
Acoustics, Visco-thermal boundary layers, Helmholtz equation, Wentzell boundary condition, Compression driver
National Category
Fluid Mechanics and Acoustics Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-150643DOI: 10.1016/j.jcp.2018.06.005ISI: 000438393900031Scopus ID: 2-s2.0-85048401964OAI: oai:DiVA.org:umu-150643DiVA, id: diva2:1244262
Funder
Swedish Research Council, 621-2013-3706Swedish Foundation for Strategic Research , AM13-0029Available from: 2018-08-31 Created: 2018-08-31 Last updated: 2018-08-31Bibliographically approved

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Berggren, MartinBernland, AndersNoreland, Daniel

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