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14 Cards in this Set

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The linearized potential eqn. is a 2nd order partial differential equation:

2 boundary conditions are
required.
The perturbation must die away as we move far from the source (from the airfoil).

There can be no flow through the surface of the airfoil. The normal component of the velocity is zero at the surface.
What is the local flow velocity at the surface?
The local flow velocity at the surface must be tangential to the surface.
Planar Wing Approximation

What does not make much
difference whether the boundary surface is taken at the airfoil surface or at the y=0 plane.
For thin wings and airfoils with small camber, at small angles of attack
Pressure coefficients:

In order for the pressure distributions to be the same at m=1....?
The compressible flow airfoil must have a lower surface slope than the incompressible-flow airfoil
"How does the pressure distribution over a given airfoil change
as the Mach # is increased?"
cp increases with Mach #.

Prandtl-Glauert Transformation:

c_p=c_po/(sqrt(1-M_inf^2)
For incompressible flow conditions what is unknown
The unknowns are velocity and pressure.
Pressure difference between upper and lower surfaces must vanish at tips of the wing. There are two effects of this,
a ) Loss in lift, compared to 2-D airfoils.

b) Induced drag, i.e. drag induced by the force vector tilting backwards as a result of the induced downwash.
No induced drag on 2-D airfoils in what conditions?
Steady conditions
Ideal elliptic lift distribution implies?
Minimum induced drag , i.e,
spanwise efficiency e = 1.
At low Mach numbers drag on well designed aircraft is primarily due to?
Induced drag
Note: In the 2-D limit (airfoil) there is no lift-induced drag in incompressible flow.

But there is drag due to:
There is always “profile” drag due to viscous effects (friction drag) and flow separation (pressure drag).
Substantial Derivative

The Eulerian Frame of Reference is the one fixed to a?
Control volume.
Substantial Derivative

The Lagrangian frame of
reference is the one fixed to a
Packet of fluid (a fluid element)
Substantial derivative

The rate of change D()/Dt is for two reasons:
1. Things are changing at the point through which the element is moving (unsteady, local)

2. The element is moving into regions with different properties.