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Acoustics in a two-deck viscothermal boundary layer over an impedance surface
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Khamis, Doran and Brambley, Edward J. (2017) Acoustics in a two-deck viscothermal boundary layer over an impedance surface. AIAA Journal, 55 (10). pp. 3328-3345. doi:10.2514/1.J055598 ISSN 0001-1452.
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WRAP-acoustics-two-deck-viscothermal-boundary-layer-Brambley-2017.pdf - Accepted Version - Requires a PDF viewer. Download (821Kb) | Preview |
Official URL: http://dx.doi.org/10.2514/1.J055598
Abstract
The acoustics of a mean flow boundary layer over an impedance surface or acoustic lining is considered. By considering a thick mean flow boundary layer (possibly due to turbulence), the boundary-layer structure is separated asymptotically into two decks, with a thin weakly viscous mean flow boundary layer and an even thinner strongly viscous acoustic sublayer, without requiring a high frequency. Using this, analytic solutions are found for the acoustic modes in a cylindrical lined duct. The mode shapes in each region compare well with numerical solutions of the linearized compressible Navier–Stokes equations, as does a uniform composite asymptotic solution. A closed-form effective impedance boundary condition is derived, which can be applied to acoustics in inviscid slipping flow to account for both shear and viscosity in the boundary layer. The importance of the boundary layer is demonstrated in the frequency domain, and the new boundary condition is found to correctly predict the attenuation of upstream-propagating cut-on modes, which are poorly predicted by existing inviscid boundary conditions. Stability is also investigated, and the new boundary condition is found to yield good results away from the critical layer. A time-domain formulation of a simplified version of the new impedance boundary condition is proposed.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) |
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| Library of Congress Subject Headings (LCSH): | Viscous flow, Shear flow, Navier-Stokes equations | ||||||||
| Journal or Publication Title: | AIAA Journal | ||||||||
| Publisher: | American Institute of Aeronautical and Astronautics | ||||||||
| ISSN: | 0001-1452 | ||||||||
| Official Date: | October 2017 | ||||||||
| Dates: |
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| Volume: | 55 | ||||||||
| Number: | 10 | ||||||||
| Page Range: | pp. 3328-3345 | ||||||||
| DOI: | 10.2514/1.J055598 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 3 November 2017 | ||||||||
| Date of first compliant Open Access: | 7 November 2017 | ||||||||
| Funder: | Royal Society (Great Britain). University Research Fellowship, Engineering and Physical Sciences Research Council (EPSRC) |
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