dc.contributor.author Khamis, Doran en dc.contributor.author Brambley, Ed en dc.date.accessioned 2017-01-12T10:54:47Z dc.date.available 2017-01-12T10:54:47Z dc.date.issued 2017-01-01 en dc.identifier.issn 0022-1120 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/261834 dc.description.abstract The effect of viscosity and thermal conduction on the acoustics in a shear layer above an impedance wall is investigated numerically and asymptotically by solving the linearised compressible Navier–Stokes equations (LNSE). It is found that viscothermal effects can be as important as shear, and therefore including shear while neglecting viscothermal effects by solving the linearised Euler equations (LEE) is questionable. In particular, the damping rate of upstream-propagating waves is found to be under-predicted by the LEE, and dramatically so in certain instances. The effects of viscosity on stability are also found to be important. Short wavelength disturbances are stabilised by viscosity, greatly altering the characteristic wavelength and maximum growth rate of instability. For the parameters considered here (chosen to be typical of aeroacoustic situations), the Reynolds number below which the flow stabilises ranges from 10$^{5}$ to 10$^{7}$. By assuming a thin but non-zero-thickness boundary layer, asymptotic analysis leads to a system of boundary layer governing equations for the acoustics. This system may be solved numerically to produce an effective impedance boundary condition, applicable at the wall of a uniform inviscid flow, that accounts for both the shear and viscosity within the boundary layer. An alternative asymptotic analysis in the high-frequency limit yields a different set of boundary layer equations, which are solved to yield analytic solutions. The acoustic mode shapes and axial wavenumbers from both asymptotic analyses compare well with numerical solutions of the full LNSE. A closed-form effective impedance boundary condition is derived from the high-frequency asymptotics, suitable for application in frequency domain numerical simulations. Finally, surface waves are considered, and it is shown that a viscous flow over an impedance lining supports a greater number of surface wave modes than an inviscid flow. dc.description.sponsorship E.J.B. gratefully acknowledges support from a Royal Society University Research Fellowship, and from a college lectureship from Gonville & Caius College, Cambridge. D.K. was supported by an EPSRC grant. dc.language eng en dc.language.iso en en dc.publisher Cambridge University Press dc.subject aeroacoustics en dc.subject boundary layer stability en dc.subject compressible flows en dc.title Viscous effects on the acoustics and stability of a shear layer over an impedance wall en dc.type Article prism.endingPage 534 prism.publicationDate 2017 en prism.publicationName Journal of Fluid Mechanics en prism.startingPage 489 prism.volume 810 en dc.identifier.doi 10.17863/CAM.7055 dcterms.dateAccepted 2016-10-24 en rioxxterms.versionofrecord 10.1017/jfm.2016.737 en rioxxterms.version AM en rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2017-01-01 en dc.identifier.eissn 1469-7645 rioxxterms.type Journal Article/Review en cam.issuedOnline 2016-12-01 en rioxxterms.freetoread.startdate 2017-06-01
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