Abstract:
The complexity of airfoil shapes has brought di culties in modeling the
uid
ow around an
airplane. This di culty is based on
uid interactions around aircraft and generally on the
aspect that one wants a solution of the practical part of aerodynamics. To model this, a lot of
simpli cations must be done. Conformal mapping technique is widely used to transform complicated
uid
ow problems into simpler
uid
ow problems. In our thesis, we reviewed and
implemented the model used to model the ideal
uid around a circular cylinder. This model
was constructed by a superposition of elementary potential
uid
ows including uniform
ow, doublet
ow and vortex
ow. The Conformal mapping technique known as Joukowsky
transformation was used to map the
uid
ow around the circular cylinder into the
uid
ow
around the airfoil. This transformation was implemented in MATLAB to be able to visualize
the streamlines around the circular cylinder and the corresponding airfoil. The lift force was
calculated versus the angle of attack using the Kutta-Joukowsky formula. It was found that
there is a strong linear dependence between the lift force and the angle of attack. Again, the
lift coe cient as a function of the angle of attack of the Joukowsky airfoil was compared to
the lift coe cient for the NACA 0012 airfoil and these almost match better as the maximum
absolute error in the lift coe cient for the two airfoils is in the range of 0 to 12 degrees was
found to be 2:8%.
