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SUMMARY:Analytic solutions for flows through cascades - Peter Baddoo\, Imp
 erial College London
DTSTART:20200128T150000Z
DTEND:20200128T160000Z
UID:TALK137389@talks.cam.ac.uk
CONTACT:Matthew Priddin
DESCRIPTION:Noise reduction is a principal aim of the aviation industry. P
 articular attention is devoted to reducing turbomachinery noise\, which is
  an important component of overall aero-engine noise during the take-off a
 nd landing stages. This talk therefore presents analytic investigations in
 to turbomachinery flows with the aim that the resulting solutions be used 
 by aircraft designers to produce quieter aircraft. In order to facilitate 
 exact solutions\, the turbine is unwrapped onto the two-dimensional plane\
 , resulting in a periodic array of blades commonly referred to as a “cas
 cade”. Previous research has been restricted to the case where the casca
 de consists of a single impermeable row of flat plates at zero angle of at
 tack. Consequently\, this talk considers three separate scenarios where th
 e cascades consist of (i) blades with realistic geometry\, (ii) blades wit
 h porosity gradients\, and (iii) multiple blades per period window. In eac
 h case\, we begin by solving the steady potential flow and proceed by inve
 stigating the effects of unsteady perturbations. This coupled approach pro
 vides analysis from both aerodynamic and aeroacoustic perspectives which i
 s essential for achieving practical noise reductions. In order to find ana
 lytic solutions\, sophisticated complex analysis is employed in the form o
 f singular integral equations\, Riemann--Hilbert problems\, the Wiener--Ho
 pf method and conformal mappings via the transcendental Schottky--Klein pr
 ime function. These methods are applied in the context of rigorous asympto
 tic expansions where the solution is expanded in terms of a small paramete
 r such as the amplitude of an unsteady incident disturbance or the size of
  the blades. The aerodynamic analysis generates exact expressions for the 
 surface velocity\, drag\, lift and deflection angle whilst the aeroacousti
 c solutions furnish exact expressions for the unsteady surface pressure\, 
 sound power output and far-field sound. These formulae are rapid to comput
 e compared to CFD simulations currently used in industry and\, moreover\, 
 they provide fresh insight into the roles played by blade spacing\, geomet
 ry and porosity for turbomachinery noise and aerodynamics. Although the so
 lutions in this talk are applied to turbomachinery\, they will also be use
 ful in other applications such as solid mechanics\, poroelasticity and bio
 logical fliers or swimmers operating in formation.
LOCATION:MR11
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