Download Linear Algebra

Interview Subject: Fluid Mechanics - MAE551 (Compressible Flow)
- MAE552 (Viscous Flows and Boundary Layers)
Interviewer: Dr. Clarence (Clancy) Rowley
Date: February 2002
Subsonic Flow
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What is the Boundary Layer Equation and the assumptions made during the derivation:
u
u
dU
 2u
o u v
U
 2
x
y
dx
y
o Assumptions: Variations across the boundary layer are much faster than variations along the
layer  x  y and  2 x 2  2 y 2 . Distances in the x direction over which the velocity
varies appreciably are of order L, but those of the y direction are of order δ, which is much
smaller than L.
o u v
Schematic of airfoil without and with circulation:
What’s happening to the streamlines near the leading edge?
o They are converging and the fluid velocity is increasing.
Draw the velocity profile in this region (near the leading edge where flow is accelerated) and
extended it to freestream?
What’s the Kutta-Joukowski (ҖУХOВСКИ in Russian) condition?
Where does circulation come from?
With the airfoil at an angle of attack, what happens to the streamlines?
How does the airfoil (wing) generate lift?
What does the pressure distribution over the airfoil look like?
What is potential flow?
      0
o
      0
Use Leibnitz theorem to prove.
Method for solving boundary layer equation?
o δ* (displacement thickness) is needed for solving the boundary layer equation, therefore, the
first approximation is to neglect the existence of the boundary layer and calculate the
irrotational p x over the body surface. Then a solution of the boundary layer equation
gives δ*, and then, the body surface is displaced outward by this amount and a next
approximation of p x is found from a solution of the irrotational flow, and so on….
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Supersonic Flow
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If there is a small disturbance on a wing surface and the flow is supersonic, what happens?
o Mach Wave
Supersonic flow about a flat plate?
a1
Ma = 2
a2
a3
o What is the value of angle a1? a1  sin 1 1 Ma 
o Is a1 > a2? No. Mach number increases as flow goes through expansion fan, hence
sin 1 1 Ma1   sin 1 1 Ma 2  . How does the expansion fan total deflection angle compare to
a3? They are equal.
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Draw the figure that relates shock angle versus deflection angle for different Mach numbers.
o Talk about detached shock and attached shock
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For supersonic wedge flow:
o What happens to a1 as Ma is increased? a1 decreases because Man (normal Mach number)
decreases.
o What happens to a1 as a2 is increased (constant Mach number)? a1 increases because Man
(normal Mach number) increases.
a1
Ma > 1
a2
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