A

ERODYNAMICS

–

EXAM

26-06-2014

Basic part

1. Consider stationary, 2D and potential flow past an airfoil described by the potential

( , )

x y

 



. The

flow domain (exterior of the airfoil) is



, a contour of the airfoil is



. Write: fully expanded form of

the partial differential equation fulfilled by the function



in



, the boundary conditions formulated for

this function at



and the asymptotic condition at infinity. Explain how – knowing

( , )

x y

 



- to

find the velocity and pressure at arbitrarily chosen point (x,y) in the flow domain (velocity and pressure in
the far field are equal, respectively,

V



and

p



)? Are above conditions sufficient for determination of a

unique flow? It not, formulate an additional condition (or conditions) and explain what important quantity
it determines.

2. Define center od pressure and the aerodynamic center of an airfoil. Make a careful drawing of typical

(like for NACA 4415) plot of

( )

L

L

C

C





. Make also a neat polar plot for such airfoil and mark the

point of maximal aerodynamic efficiency.

3. Write the Prandtl and continuity equations for 2D laminar boundary layer (incompressible case). What

case of the boundary layer flow is described by the Blasius self-similar solution? How does the
displacement thickness (DT) of the Blasius boundary layer change with the distance from the front
stagnation point? How – in the same geometric and exterior flow conditions – does the DT change in the
turbulent boundary layer?

4. Calculate the induced angle and drag coefficient for the elliptic wing with the aspect ratio equal 8 and

zero geometric twist. The aerodynamic coefficients of the wing section are C

D

= 0.06 and C

L

=0.4.

5. Make a careful drawing of a compressible flow pattern in the vicinity of the convex corner. How does the

entropy changes in this flow?

6. Write linearized equation of small disturbances potential function. What simplification with respect to

the general theory of inviscid compressible flows are necessary to derive this equation?

7. What is the critical Mach number in the compressible flow past an airfoil?
8. Make a precise plot of variations of the lift force coefficient as a function of Mach number

M



in real

flows.

Advanced part

9. Using the potential-flow aerodynamic properties of the Youkovsky airfoils, describe briefly how the

slope of the line

( )

L

L

C

C





depends on the airfoil’s thickness and camber

10. Make a neat drawing of the streamlines pattern and velocity profiles in the region of a laminar bubble in

the boundary layer. Next, make a careful and precise plot of a typical distribution of the pressure
coefficient along the upper part of the airfoil with the separation bubble. On this plot, mark the location
of the bubble. Finally, make a plot of variation of the shape factor H inside and close vicinity of the
separation bubble..

11. What case of the compressible boundary layer is described by the Crocco integral? Draw an appropriate

plot and provide a brief description.

12. What is a supercritical airfoil? Describe briefly its main properties and explain difference in the

distribution of the pressure coefficient while compared to a classical airfoil.

Time: 120 minutes

Attention: student who passed the midterm exam are should provide correct answers
to the problem 5,6,7 and 8 from the basic part. In the advanced part, these student are
expected to solve only the problems 11 and 12. Time – 60 minutes.