Aerofoil Lift

Question 1

Why is there no net force on an object in potential flow if there is no circulation?

Answer 1

Due to Kelvins theorem dK/dt = 0

Question 2

What does the diagram of potential flow around an aerofoil look like when tilted front end downwards?

Answer 2

Flow over top and flow on bottom turns back then forwards, with stagnation points at back and front still.

Question 3

What does the boundary separation diagram of flow over an aerofoil look like?

Answer 3

Flow over top and bottom and then flow goes back round front and then continues forward: flow reversal due to adverse pressure.

Question 4

What does the flow reversal section look like on the boundary for the wings trailing edge?

Answer 4

Reversed flow leads to detached/separated vortex anticlockwise.

Question 5

Using Kelvins theorem in 2D, what does the diagram for flow around the aerofoil look like when it is at rest?

Answer 5

Just a square with flow moving clockwise around aerofoil.

Question 6

Using Kelvins theorem in 2D, what does the diagram for flow around the aerofoil look like when it starts moving?

Answer 6

Same loop with with 2 loops inside - one loop around aerofoil and the other around the vortex, all travelling in clockwise direction.

Question 7

Using Kelvins theorem, what is the integral of v.dl around the big loop equal?

Answer 7

integral around loop 1 of v.dl = integral around loop 2 of v.dl + integral around loop 3 of v.dl (K1 = K2 + K3, hence K2 = -K3)

Question 8

What does K2 act as on the aerofoil?

Answer 8

A clockwise vorticity, and using the magnus effect force, we can see it is an upwards force causing lift.

Question 9

What is the vortex pattern like in 3D?

Answer 9

Has a vortex line through wing tips and vortex flows around these lines pointing inwards.

Question 10

What is the equation for the air displaced by the plane in time t?

Answer 10

V = ρAv*t

Question 11

What is the equation for the downward momentum of the air pushed down by the plane?

Answer 11

ρAvtu, where u is the speed the air is pushed down by, = upward momentum imparted on plane due to pushing air down

Question 12

What does dp/dt equal for an aeroplane without flow? What does the change in momentum therefore equal?

Answer 12

dp/dt = mg, so Δp = mgt

Question 13

What is the equation for the momentum needed in air to keep flight?

Answer 13

mgt = ρAvtu, therefore u = mg/Aρv

Question 14

What does u equal for potential flow?

Answer 14

u = 0 for potential flow, so no lift.