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CATEGORIES:Waves Group (DAMTP)
SUMMARY:Analytic solutions for flows through cascades - Pe
ter Baddoo\, Imperial College London
DTSTART;TZID=Europe/London:20200128T150000
DTEND;TZID=Europe/London:20200128T160000
UID:TALK137389AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/137389
DESCRIPTION:Noise reduction is a principal aim of the aviation
industry. Particular attention is devoted to redu
cing turbomachinery noise\, which is an important
component of overall aero-engine noise during the
take-off and landing stages. This talk therefore p
resents analytic investigations into turbomachiner
y flows with the aim that the resulting solutions
be used by aircraft designers to produce quieter a
ircraft. In order to facilitate exact solutions\,
the turbine is unwrapped onto the two-dimensional
plane\, resulting in a periodic array of blades co
mmonly referred to as a “cascade”. Previous resear
ch has been restricted to the case where the casca
de consists of a single impermeable row of flat pl
ates at zero angle of attack. Consequently\, this
talk considers three separate scenarios where the
cascades consist of (i) blades with realistic geom
etry\, (ii) blades with porosity gradients\, and (
iii) multiple blades per period window. In each ca
se\, we begin by solving the steady potential flow
and proceed by investigating the effects of unste
ady perturbations. This coupled approach provides
analysis from both aerodynamic and aeroacoustic pe
rspectives which is essential for achieving practi
cal noise reductions. In order to find analytic so
lutions\, sophisticated complex analysis is employ
ed in the form of singular integral equations\, Ri
emann--Hilbert problems\, the Wiener--Hopf method
and conformal mappings via the transcendental Scho
ttky--Klein prime function. These methods are appl
ied in the context of rigorous asymptotic expansio
ns where the solution is expanded in terms of a sm
all parameter such as the amplitude of an unsteady
incident disturbance or the size of the blades. T
he aerodynamic analysis generates exact expression
s for the surface velocity\, drag\, lift and defle
ction angle whilst the aeroacoustic solutions furn
ish exact expressions for the unsteady surface pre
ssure\, sound power output and far-field sound. Th
ese formulae are rapid to compute compared to CFD
simulations currently used in industry and\, moreo
ver\, they provide fresh insight into the roles pl
ayed by blade spacing\, geometry and porosity for
turbomachinery noise and aerodynamics. Although th
e solutions in this talk are applied to turbomachi
nery\, they will also be useful in other applicati
ons such as solid mechanics\, poroelasticity and b
iological fliers or swimmers operating in formatio
n.
LOCATION:MR11
CONTACT:Matthew Priddin
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