A

ERODYNAMICS

–

EXAM

20-06-2014

Basic part

1. Formulate the Kutta-Joukovsky condition. Explain the meaning of this condition, in

particular by drawing the streamlines pattern of flow past an airfoil. Mark the location of
points of the maximal pressure and provide the value of this maximum (free-stream
velocity, density and pressure are, respectively,

,

,

V

const p









). Write the Kutta-

Joukovsky formula for the lift force and transform it to the formula for the lift force
coefficient C

L

(the airfoil chord length is equal c).

2. Define the pressure center and the aerodynamic center. How – within the framework of

the thin airfoil theory – does the airfoil camber affect the location of these points along the
airfoil’s chord.

3. Make a careful plot of the velocity profiles and the streamline pattern of the laminar

boundary layer flow near its separation point. Define the displacement and momentum
thickness. Write the von Karman equation at the point of separation.

4. Draw a typical shape of the lift/drag polar plot for a laminar airfoil. Mark the points of

maximal lift and maximal aerodynamic efficiency. Assuming that for some airfoil
C

D

= 0.06 at C

L

=0.4, evaluate – using the results from the lifting-line theory – the drag

coefficient of an elliptic wing with the aspect ratio equal 10.

5. Define an isentropic process. Provide the relation between pressure and density in the

isentropic process.

6. In the density/pressure plane, draw the plot of the thermodynamic process corresponding to

a shock wave. Can an expansion (rarefaction) shock wave appear in real flows? Explain
your answer.

7. Make a careful plot of velocity and temperature profiles in the laminar compressible

boundary layer at the thermally isolated wall.

8. Make a careful and precise plot of a supersonic flow past a flat plate at nonzero angle of

incidence.

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: 120 minutes