Aerodynamics – exam 20-06-2014

Advanced part

1. Provide general mathematical formulation of a 2D stationary potential flow

past an airfoil immersed in a stream of incompressible fluid, uniform at
infinity. Explain in details how to construct the solution so that the Kutta-
Joukovsky can be accounted for.

2. Write the Prandtl Equation for the turbulent boundary layer in the form

which contains explicitly the Reynolds stress term. Then, explain the essence
of the idea of the turbulent viscosity. Finally, write the Prandtl Equation in
the form containing turbulent viscosity. Also, make a neat plot showing a
typical distribution of the turbulent viscosity across the turbulent boundary
layer.

3. Make a careful and precise plot of the oblique shock polar. Using this plot

explain how the angle of inclination of the shock wave is determined if the
angle of flow deflection is given. Mark on the picture the case of flow
corresponding to the maximal inclination angle.

4. Make a precise plot (and comment it properly) showing how the drag

coefficient C

D

depends on the Mach number M

∞

.

Time: all problems – 40 minutes, problems 3

rd

and 4

th

– 20 minutes.