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SUMMARY:Green's function of pressure in both free space and a duct - James
  Mathews (CCA/DAMTP)
DTSTART:20140430T150000Z
DTEND:20140430T160000Z
UID:TALK52347@talks.cam.ac.uk
CONTACT:Vittoria Silvestri
DESCRIPTION:In this talk I will look to develop an understanding of the no
 ise in an aircraft engine due to interactions with the fan blades and lini
 ng of the engine casing\, which are the main contributions to the engine n
 oise.\n\nWe use a model of an infinite duct as the engine casing and consi
 der the fan blades as some rotating surface\, although more sophisticated 
 models could be considered as a later date. To understand the noise\, we d
 erive a differential equation for pressure in the duct and then we can use
  the formula L = 20log10(prms/pref) to calculate the sound level in decibe
 ls\, where pref is usually 20dB and prms is the root mean square of unstea
 dy pressure.\n\nAlthough we can solve the differential equation numericall
 y\, we would like some analytic results\, so we introduce the Green’s fu
 nction. By assuming the frequency to be large we can make progress towards
  an analytic solution using standard asymptotic methods. The pressure is t
 hen calculated by integrating the Green’s function against the source te
 rms\, which will be done in the future and not in this talk.\n\nThe assump
 tion of an infinite duct adds significantly more complications than free s
 pace\, so we first calculate the Green’s function in free space\, which 
 is discussed in the first half of the talk. In the second half of the talk
  I will point out the difficulties with an infinite duct and how I have ov
 ercome most of them to analytically calculate the Green’s function in an
  infinite duct. \n\nKey words: Partial differential equations\, Green’s 
 functions\, asymptotics\, fluid dynamics. 
LOCATION:MR14\, Centre for Mathematical Sciences
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