Principle Equations of Thermodynamics - Study Guide | AOE 4234, Study notes of Aerospace Engineering

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% ./  404  1 * 67689+ 0  287 67689 Principle Equations of Thermodynamics Continuity: Momentum: First Law: Δ>  ? @ A  B      CDEE  DFE G where   (  HI Second Law: Equation of State: %%  1  4  12 J $$  *1  4  12 J+ ,,-   *1  4  12 J+ ,-   $√4L0%JM 11  4  12 JN ,O ,-⁄ Q  1J R 14  1 *1  4  12 J+S,O ,-⁄ Compressible and Isentropic Equations (1D flow) Isentropic and adiabatic: Δ&  0, A  0, B  0 J  T U⁄ , U  L40%, 4  ./ .⁄ (V  U3.77Y  Z ! [\Z  ].Z  U3.77Y ^  _` ^a?b  ./%c  ./%  % de  fe∑fh Combustion i  j j k k  $j  $k j i  k l1  ^j  km  $j  $k j     j  h i  kn l1  ^jn  km  ko jo  k ik  j &Up] i  2qrs?b_j &Up] &  qt *uv+ ln *+?b8  *uv+ ln *+k8 i_ %w .  _i  _k l1  ^j  km Thrust and Efficiency Assumption of reversible external flow, thus P=U=const. Momentum equation is foundation and applies: One stream: Two streams (Hot flow “H” and Cold flow “C”, neglecting Pres): Efficiencies: Propulsive: q/  iDxy zO_D{E ⁄ - DyE ⁄ |  D{ Dy⁄OD{ Dy⁄ Thermal: qrs  xy lO_D{E ⁄ - DyE ⁄ mx} ~ , ^  x}xy Propeller: q/€  i‚Dƒ„  iDƒ{„ Overall: qt  q/qrs  iDx} ~  2qrs C Dy D{⁄ODy D{⁄ G qt  D{-DyDy_~ , max at k  j 2⁄ qt  C1  xy…xy† G D{‡‡‡‡-DyDy_~ (dual stream) j‡‡‡  xy†O_D{†Oxy… Dy…xy†O_Oxy… Takeoff Thrust: Range: Thrust Specific Fuel Consumption: %  %k *1  4  12 J+ $  $k R1  qˆ *%%k  1+S ,‰,‰- $  $$€ %  %l1  1q Š$€ ,‹-,‹  1Œm ^  %%Ž  1?b./%  %% $  $ [ $  $ *$$+ %Ž  %  %  % %f‘ U^(’[’f(’ $Ž  $ R1  1qr *1  %Ž%+S ,“,“-  $f‘ U^(’[’f(’ Tj  ”2q• 4•4•  10% –1  $k$ ,—-,— ˜ ’&k  l1  ^j  m %w .  ^1  ^j   Turbojet Compressor Inlet Compressor Outlet Burner Fuel-air Ratio Turbine Outlet Conditions Nozzle Exit Specific Thrust $™  $$€_ %™  % š1  1q_ Š$€ ,‹-,‹  1Œ› Tj_  ”2q_• 4_4_  10%™M1  $k$™ ,}-,} N %Ž  %  %  %  œ%™  %k $Ž  $ R1  1qr *1  %Ž%+S ,“,“- Tj  ”2q• 4•4•  10% –1  $$ ,—-,— ˜ Bp $  $k fV(&& ]‘6(
’&k  z1  ^j  1  œ  œj_| %w .  ^z1  ^j  1  œ  œj_| TurboFan Fan Outlet Fan Nozzle Exit Velocity Turbine Outlet Nozzle Out Thrust