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SUMMARY:Acoustic resonances and trapped modes in unbounded domains - Werne
 r Koch\,  Gottingen
DTSTART:20080516T150000Z
DTEND:20080516T160000Z
UID:TALK11725@talks.cam.ac.uk
CONTACT:Nigel Peake
DESCRIPTION:Resonances are of importance in many fields of physics and eng
 ineering. In \nthis lecture we limit ourselves to acoustic resonances in d
 omains which are \nopen to infinity in at least one direction and are exci
 ted mainly by unstable \nshear layers. Using perfectly matched layer absor
 bing boundary conditions in \nthe form of the complex scaling method of at
 omic and molecular physics to \napproximate the radiation condition the re
 sonance problem is transformed into \na large eigenvalue problem which is 
 solved numerically. Of particular interest \nare resonances with zero radi
 ation loss (trapped modes) or very small \nradiation loss (nearly trapped 
 modes). Such trapped modes can enhance or even \ndominate the shear layer 
 instabilities causing high intensity tonal noise or \nstructural damage. I
 n domains which are open on all sides resonances \nare damped due to radia
 tion losses. In laterally bounded domains\, such as \nfinite length struct
 ures or cavities in channels or pipes\, trapped modes \nwith zero radiatio
 n loss are possible. \nA well known example are the Parker modes in compre
 ssor cascades. Special \nattention will be paid to trapped modes in single
  and tandem plate cascades in \nan annular duct modelling the situation in
  axial flow compressors. All \nresonances are computed for zero mean flow 
 approximating low Mach number \nflows. The \ndependence of the resonant fr
 equency on various cascade parameters\, such as \nblade length\, blade num
 ber\, blade stagger\, blade sweep or gap between \ncascades is demonstrate
 d.
LOCATION:MR2\, Centre for Mathematical Sciences
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