Vortices

Question 1

For a wing with a full-span element and two part-span elements joined at the endplate, describe the three vortices created.

Answer 1

1) IDB edge of part-span elements
2) higher p pressure surface and lower p OBD face of endplate, forms on UPR OBD edge of endplate
3) lower p suction surface and higher p OBD face of endplate, forms on LWR IBD edge of endplate

Question 2

State and describe which of the three vortices is strongest on a full-span and two part-span element wing.

Answer 2

The one on the LWR IBD edge of the endplate.
If that edge moves further away in z from the suction surface of the wing as x increases, the low pressure on the wing will decrease downstream.

Question 3

What happens to the vortex system of a full-span and two part-span element wing downstream of the wing?

Answer 3

The two iso-rotating vortices formed on the endplate spiral about each other. Since the OBD vortex is weaker than the IBD vortex, it is gradually sucked into the OBD and they merge together.

Question 4

Describe the bound vortex.

Answer 4

Used as a hypothetical system to model a physical wing.
It represents the circulation around a wing.

Question 5

Describe briefly the horseshoe vortex.

Answer 5

Modelled by the bound vortex and two trailing vortices at the wing tips.

Question 6

Describe the lifting line theory.

Answer 6

Same as the horseshoe vortex but considers tip effects. The trailing vortices are shed as “sheets”.

Question 7

Describe how the simple horseshoe model can be used.

Answer 7

Adjusted by reducing the effective span of the wing to account for tip effects.

Question 8

How does a Cp plot change when vortices are co-rotating?

Answer 8

It has the circulation effect, so the Cp plot is stretched.

Question 9

How does the vorticity of three co-rotating vortices of vorticity, d, change when they merge? Assume no viscous effects.

Answer 9

d+d+d = 3d = D

Question 10

What effect does adding endplates to a wing have on drag?

Answer 10

It better maintains the pressure differential between the shedding edges, thereby decreasing pressure equalisation, meaning the suction surface continues to have a large component of pressure force in the drag direction, increasing drag.
However, it can move the tip vortex away from the surface of the wing thereby decreasing the effect of the vortices it creates on the wing.