Aerofoil Theory (Week 7 and 8)

Question 1

What three types of flow are used to model the flow over a spinning circular cylinder using superposition?

Answer 1

1. Uniform flow
2. Doublet - defines cylinder contour
3. Vortex - adds effect of rotation of cylinder

Question 2

What are the equations for Kutta-Joukowski Theorem and d’Alembert paradox

Answer 2

Lift per unit span = densityvelocitycirculation

Drag per unit span = 0

Question 3

What is the Kutta condition?

Answer 3

States that the circulation around the aerofoil is just the right amount to ensure the flow leaves the trailing edge smoothly.

Question 4

What is Kelvins circulation Theorem?

Answer 4

The time rate of change of circulation around a closed curve remains constant.

This does not mean there is no change at all. It means that a
change of circulation in time also requires a change in space

Question 5

Explain the setup of a vortex sheet?

Answer 5

• Aerofoil of zero thickness (amber line only)
• Many vortices on the camber line
• coordinate along camber line is “s” and gamma(s) is the variable strength of the vortex sheet per unit length along s.
• circulation around aerofoil is sum of strengths of vortex sheet such that flow is tangential to camber line.

Question 6

What is the centre of pressure?

Answer 6

Point along chord where the resulting aerodynamic force acts and moment is zero

Question 7

What is the aerodynamic centre?

Answer 7

Point long chord where pitching moment is independent of lift (angle of attack)

Question 8

At what range of mach number can we not rely on linear theory or compressibility corrections

Answer 8

Transonic range (0.8<M<1.2)