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AE 1350 Lecture 6-B

AE 1350 Lecture 6-B. Compressible Flow. Some definitions. Specific internal energy: Energy stored in random (linear, rotational) motion of molecules, per unit mass. For diatomic molecules, e = C v T = 5/2 RT, where C v = 5/2 R

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AE 1350 Lecture 6-B

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  1. AE 1350Lecture 6-B Compressible Flow

  2. 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: e+p/r = e + RT = 7/2RT=CpT, 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.

  3. 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

  4. First law continued..

  5. 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:

  6. Integration of First Law forAdiabatic Inviscid Flows • Recall Euler’s equation for conservation of momentum in a stream tube:

  7. First Law, continued. Generalization of Bernoulli’s Equation for compressible flows Kinetic Energy Internal Energy “Pressure work”

  8. 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.

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

  10. Isentropic Flow, continued..

  11. Isentropic Flow

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

  13. Further Simplifications

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