AE 1350 Lecture 6-B

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AE 1350Lecture 6-B

• Compressible Flow

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Some definitions..

• Specific internal energy Energy stored in random
  (linear, rotational) motion of molecules, per
  unit mass. For diatomic molecules, e CvT 5/2
  RT, where Cv 5/2 R
• Specific enthalpy ep/r e RT 7/2RTCpT,
  where Cp 7/2 R
• Ratio of specific heats g Cp/Cv 7/5 1.4
  for air
• System A collection of particles of fixed
  identity.
• Properties of a system Quantifiable information
  such as p, r, T, Velocity Vector V, etc.
• Process An event that causes changes to the
  properties of the system e.g. flow of the
  particles over an airfoil will cause changes in
  velocity, pressure, density, and T.

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First Law of Thermodynamics

• Change in the specific internal energy of a
  system is due to heat added to the system, and
  work done on the system.
• This law can not be proved, but can be verified
  from observations.

Heat added per Unit mass
Work done on the System per unit mass due to
body forces Such as gravity, and Pressure forces
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First law continued..
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Adiabatic Process

• An adiabatic process is one in which there is no
  heat addition or removal.
• Examples of adiabatic flow are Flow over a wing,
  outside the boundary layer, flow through a
  propeller or a turbine, etc.
• In these cases, work is done by the pressure
  forces, but no heat is added.
• Example of a non-adiabatic flow Flow through a
  combustor or furnace, flow within the boundary
  layer where the wall is cooler or hotter than the
  fluid particles.
• First law becomes

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Integration of First Law forAdiabatic Inviscid
Flows

• Recall Eulers equation for conservation of
  momentum in a stream tube

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First Law, continued.
Generalization of Bernoullis Equation for
compressible flows
Kinetic Energy
Internal Energy
Pressure work
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Reversible Flow

• A reversible flow is one in which the system
  (i.e. collection of fluid particles moving over
  an airfoil or within a combustor, or through a
  turbine, or whatever) and the environment (i.e.
  surrounding particles), both may be restored to
  their original condition.
• Example Slow compression of air in a balloon
  does work on the air inside the balloon, and
  takes away energy from the surroundings. When the
  balloon is allowed to expand, the air inside and
  the surrounding air are both restored to original
  conditions.
• Example of an irreversible Process Heat flows
  from hot to cold, never in the opposite
  direction. Most conductive and viscous processes
  (i.e. flow inside the boundary layer) are
  irreversible.
• A second example of an irreversible process Flow
  across a shock wave where the Mach number
  abruptly decreases.

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Isentropic Flow

• A reversible adiabatic flow is called an
  isentropic flow.
• In such a flow,

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Isentropic Flow, continued..
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Isentropic Flow
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Summary

• We will deal with inviscid, reversible, adiabatic
  flows.
• For such flows, we get

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Further Simplifications