Concise - Self Test 4

Question 1

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?

Answer 1

• Thin Aerofoil theory requires a continuous camber line
• Flaps and slats usually have a small gap
• Theory cannot predict stall
• Gap delays stall significantly

Question 2

What are the limitations of the aerofoil geometry obtained with the Joukowski transformation?

Answer 2

• Fixed thickness distribution; maximum thickness at c/4
• Camber line is a circular arc; maximum camber at midpoint
• Trailing edge is cusped and not physically realizable

Question 3

What are the key limitations of predictions of aerofoil performance obtained from either Juokowski or Thin Aerofoil analysis?

Answer 3

• Assumes inviscid flow
• Drag is predicted as zero
• Cannot predict stall and separation

Question 4

What are the key limitations of the predictions from thin aerofoil theory?

Answer 4

• Predicts constant pitching moment about 1/4 chord (aerodynamic center)
• Thickness moves aerodynamic center forward
• Pressure distribution disagrees with experiments near leading/trailing edge
• Aerofoil coefficients are reliable
• Drag predicted as zero

Question 5

What is the Kutta condition?

Answer 5

• Empirical rule based on trailing edge flow
• Flow leaves sharp trailing edge smoothly with finite velocity
• Consequences:
  • Velocities at trailing edge (upper & lower) are identical
  • Pressure difference between surfaces vanishes at trailing edge

Question 6

In general, will an aerofoil generate the circulation, and hence lift, indicated by the analysis of the Joukowski aerofoil? Explain why

Answer 6

• No circulation/lift as per Joukowski analysis
• Reasons:
  • Real fluid is viscous; boundary layer and wake affect flow
  • Physical trailing edge is rounded; separation point deviates from theoretical Kutta condition

Question 7

Explain why the Kutta condition is needed to analysis a Joukowski aerofoil

Answer 7

• Avoids infinite velocity at trailing edge
• Determines appropriate circulation for lift
• Provides additional constraint for streamline flow around aerofoil

Question 8

Explain how a flap with a gap between it and the main aerofoil helps to delay the onset of stall.

Answer 8

• Gap allows high pressure, high momentum fluid to leak into boundary layer
• Reduces momentum deficit in boundary layer
• Avoids boundary layer separation (stall)