Vortical perturbations in shear flow, scattered at a hard wall - pressure release wall transition

S.W. Rienstra, D.K. Singh

Research output: Book/ReportReportAcademic

Abstract

An analytically exact solution for the problem of low Mach number (i.e. incompressible) incident vorticity scattering at a hard - to - pressure release (Z = 0 ) wall transition is obtained using the Wiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall transition, which results in a pressure-velocity field which is qualitatively different for low shear and high shear cases. The incompressible field produces an acoustic outer field, which can be determined for the low shear case, including a $U^4_0$ relation for the radiated power. The similar behaviour of this Z = 0 solution when compared with the asymptotic behaviour of the solution for finite impedance case confirms the validity of this last solution.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages8
Publication statusPublished - 2015

Publication series

NameCASA-report
Volume1513
ISSN (Print)0926-4507

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wall pressure
shear flow
shear
perturbation
Mach number
vorticity
velocity distribution
impedance
harmonics
acoustics
scattering

Cite this

Rienstra, S. W., & Singh, D. K. (2015). Vortical perturbations in shear flow, scattered at a hard wall - pressure release wall transition. (CASA-report; Vol. 1513). Eindhoven: Technische Universiteit Eindhoven.
Rienstra, S.W. ; Singh, D.K. / Vortical perturbations in shear flow, scattered at a hard wall - pressure release wall transition. Eindhoven : Technische Universiteit Eindhoven, 2015. 8 p. (CASA-report).
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Rienstra, SW & Singh, DK 2015, Vortical perturbations in shear flow, scattered at a hard wall - pressure release wall transition. CASA-report, vol. 1513, Technische Universiteit Eindhoven, Eindhoven.

Vortical perturbations in shear flow, scattered at a hard wall - pressure release wall transition. / Rienstra, S.W.; Singh, D.K.

Eindhoven : Technische Universiteit Eindhoven, 2015. 8 p. (CASA-report; Vol. 1513).

Research output: Book/ReportReportAcademic

TY - BOOK

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AU - Singh, D.K.

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N2 - An analytically exact solution for the problem of low Mach number (i.e. incompressible) incident vorticity scattering at a hard - to - pressure release (Z = 0 ) wall transition is obtained using the Wiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall transition, which results in a pressure-velocity field which is qualitatively different for low shear and high shear cases. The incompressible field produces an acoustic outer field, which can be determined for the low shear case, including a $U^4_0$ relation for the radiated power. The similar behaviour of this Z = 0 solution when compared with the asymptotic behaviour of the solution for finite impedance case confirms the validity of this last solution.

AB - An analytically exact solution for the problem of low Mach number (i.e. incompressible) incident vorticity scattering at a hard - to - pressure release (Z = 0 ) wall transition is obtained using the Wiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall transition, which results in a pressure-velocity field which is qualitatively different for low shear and high shear cases. The incompressible field produces an acoustic outer field, which can be determined for the low shear case, including a $U^4_0$ relation for the radiated power. The similar behaviour of this Z = 0 solution when compared with the asymptotic behaviour of the solution for finite impedance case confirms the validity of this last solution.

M3 - Report

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BT - Vortical perturbations in shear flow, scattered at a hard wall - pressure release wall transition

PB - Technische Universiteit Eindhoven

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Rienstra SW, Singh DK. Vortical perturbations in shear flow, scattered at a hard wall - pressure release wall transition. Eindhoven: Technische Universiteit Eindhoven, 2015. 8 p. (CASA-report).