Self Test 4 - Aerofoil Theory Flashcards
As an arbitrary camber line shape can be specified in thin aerofoil theory, the effect of flaps and slats can be assessed. Why is this problematic theoretically?
Thin Aerofoil theory requires that the camber line is continuous (i.e. there’s no gaps in the aerfoil). However, typically flaps and slats have a small gap between them and the main aerofoil section. This works out as the theory cannot predict stall, and in a real flap, the gap allows stall to be significantly delayed.
What are the limitations of the aerofoil geometry obtained with the Joukowski transformation?
The thickness distribution cannot be changed only the thickness, and the maximum thickness is at c/4.
The camber line shape is a circular arc with the maximum camber at the midpoint.
The trailing edge is not physically realizable as it the upper and lower surface are both cusped (i.e. the upper and lower surfaces meet tangentially at the trailing edge).
What are the key limitations of predictions of aerofoil performance obtained from either Juokowski or Thin Aerofoil analysis?
Because the flow is inviscid:
The drag is predicted to be zero with this type of analysis.
No prediction of stall and separation is possible.
What are the key limitations of the predictions from thin aerofoil theory?
Theoretically, a constant pitching moment about the 1/4 chord is predicted, indicating that this is the location of the aerodynamic
center. In fact, the effect of thickness is to move the aerodynamic center slightly forward.
The theoretical pressure distribution does not agree well with experimental values especially close to the leading and trailing edge.
However the aerofoil coefficients are found to be reliable predictions.
Drag is predicted as zero.
What is the Kutta condition?
The Kutta condition is an empirical rule based on experimemtal observation of the flow in the trailing edge region. It states that the flow leaves a sharp trailing edge of an aerofoil smoothly and the velocity in this region is finite.
There are two consequences:
the velocities at the trailing edge on the upper and lower surfaces are identical (both magnitude and direction).
The pressure difference between the upper and lower surfaces vanishes at the trailing edge.
In general, will an aerofoil generate the circulation, and hence lift, indicated by the analysis of the Joukowski aerofoil? Explain why
No.
For two reasons:
The real fluid is viscous, so the flow near the trailing edge is effected by the presence of the boundary layer and wake.
For a physical structure, the trailing edge must be rounded to some degree. This allows the separation point at the trailing edge to deviate from the theoretical position postulated by Kutta.
Explain why the Kutta condition is needed to analysis a Joukowski aerofoil
Without the Kutta condition, the Joukowski transformation of the flow field predicts a non-zero velocity at the trailing edge and so generally an infinite acceleration there.
Alternatively, the choice of circulation strength does not affect the constraint that the aerofoil is a streamline on the flow, and so to revolve what is the appropriate circulation, and hence lift, and additional constraint is needed.
Explain how a flap with a gap between it and the main aerofoil helps to delay the onset of stall.
A small gap allows high pressure, high momentum fluid to “leak” into the boundary layer on the upper side. Thus, the momentum deficit in the boundary layer is reduced and boundary layer separation (stall) is avoided.
