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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Scattering by a periodic array of slits with compl
ex boundaries via the Wiener--Hopf method - Peter
Baddoo (University of Cambridge)
DTSTART;TZID=Europe/London:20190823T153000
DTEND;TZID=Europe/London:20190823T160000
UID:TALK128989AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128989
DESCRIPTION:The interaction of a plane wave with a periodic ar
ray of slits is an important problem in fluid dyna
mics\, electromagnetism and solid mechanics. In pa
rticular\, such an arrangement is commonly used as
a model for turbomachinery noise. Previous work h
as been restricted to the case where the slits pos
sess a Neumann (no-flux) boundary condition. Con
sequently\, in this work we consider "complex" bou
ndary conditions including Robin (e.g. compliance)
\, oblique derivatives (porosity) and generalised
Cauchy conditions (impedance). We employ generalis
ed derivatives and Fourier transforms to recast th
e Helmholtz equation as an integral equation amena
ble to the Wiener--Hopf method. Although the slits
are of finite length\, we are able to avoid a tru
e matrix Wiener--Hopf problem by assuming the stru
cture of the scattered field. Since the Wiener--
Hopf kernel is meromorphic\, the Fourier transform
may be inverted analytically to obtain the scatte
red field. The Wiener--Hopf analysis shows that an
effect of modifying the boundary conditions is to
perturb the zeros of the kernel function\, which
correspond to the "duct modes" in the near field.
In aeroacoustic applications\, this result shows t
hat blade porosity can dramatically reduce the uns
teady lift\, which has implications for turbomachi
nery design.

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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