Luke Edwards Abstracts

Luke Edwards

Ph.D. Candidate

Applied Mathematics GIDP

18th US National Congress for Theoretical and Applied Mechanics

Chicago, Illinois

June 4-9, 2018

The  receptivity  of  high-­‐speed  compressible  boundary  layers  to  kinetic  fluctuations  (KF)  is   considered  within  the  framework  of  fluctuating  hydrodynamics.  The  formulation  is  based  on   the  idea  that  KF induced  dissipative  fluxes  may  lead  to  the  generation  of  unstable  modes  in  the   boundary  layer.  Fedorov  and  Tumin  (AIAA  J.,  2017)  solved  the  receptivity  problem  using  an   asymptotic  matching  approach  which  utilized  a  resonant  inner  solution  in  the  vicinity  of  the   neutral  point  of  the  second  Mack  mode.  Here  we  adopt  a  slightly  more  general  inhomogeneous   multiple  scales  (IMS)  approach,  based  on  a  WKB  ansatz,  which  requires  fewer  assumptions   about  the  locus  of  primary  excitation.  The  approach  is  modeled  after  the  one  taken  by  Luchini   (AIAA  J.,  2017)  to  study  low  speed  incompressible  boundary  layers  over  a  swept  wing.  The  new   framework  is  used  to  study  examples  of  high-­‐speed,  high-­‐enthalpy,  flat  plate  boundary  layers   whose  spectra  exhibit  nuanced  behavior  near  the  generation  point,  such  as  first  Mack  mode   instabilities  and  near-­‐neutral  evolution  over  moderate  length  scales.    

Abstract for Lay Audience

This  research  is  motivated  by  the  desire  of  various  organizations  to  develop  aircraft  capable  of   traveling  at  extremely  high  speeds.  DARPA  (the  Defense  Advanced  Research  Projects  Agency),   for  example,  hopes  to  develop  an  aircraft  which  could  travel  between  any  two  points  on  the   globe  in  under  2  hours.  Critical  to  the  design  of  these  aircraft  is  a  detailed  understanding  of  how   the  air  would  flow  over  the  surface  of  such  a  vehicle.

Towards  the  front  of  the  aircraft,  the  air  tends  to  flow  in  a  smooth  and  predictable  manner,  a   desirable  state  referred  to  as  ‘laminar  flow’.  Farther  back  on  the  vehicle  body,  the  flow   transitions  to  a  highly  disordered  state  known  as  ‘turbulence’.  Turbulence  is  undesirable   because  it  causes  extreme  heating  on  the  surface  of  the  vehicle  which  necessitates  heavy  and   expensive  heat  shielding.  Transition  to  this  undesirable  state  is  often  inevitable,  and  thus  it  is  of   utmost  importance  from  a  vehicle  design  perspective  to  predict  where  the  onset  of  turbulence   occurs  on  the  body  of  the  aircraft.  This is known as laminar-­‐turbulent transition prediction.

 Transition  to  turbulence  is  typically  caused  by  external  disturbances  present  in  the  air  near  the   body  of  the  vehicle.  For  example,  turbulence  can  be  induced  by  particles  of  atmospheric  debris   colliding  with  the  vehicle  surface.  Our  recent  work  is  devoted  to  understanding  how  a  much   smaller  and  subtler  disturbance  might  similarly  lead  to  laminar-­‐turbulent  transition.  In   particular,  we  show  how  even  the  seemingly  insignificant  ‘jiggling’  of  molecules  in  the  air  near   the  aircraft  may  be  enough  to  cause  a  breakdown  of  laminar  flow  into  disordered  turbulence.      

 The  presentation  to  be  given  at  this  conference  describes  our  work  on  a  new  mathematical   approach  to  studying  this  process.  It  was  developed  to  facilitate  the  study  of  laminar-­‐turbulent   transition  for  a  broad  range  of  vehicle  types,  some  of  which  cannot  be  studied  using  other   methods.  The  talk  will  detail  the  new  mathematical  formulation  as  well  as  the  theoretical   background  necessary  to  understand  the  results.