3D Flows

Question 1

Describe the bound vortex.

Answer 1

This is used a hypothetical system to model a physical wing. The bound vortex is not a real physical structure but is equivalent to the circulation around a wing, as created by a starting vortex.

Question 2

Describe the horseshoe vortex.

Answer 2

This is modelled by the bound vortex and two trailing vortices at the wingtips. A starting vortex is shed, which dissipates due to viscosity.

Question 3

How can the horseshoe vortex be modelled to include tip effects?

Answer 3

With a reduced effective wingspan.

Question 4

Describe the lifting line theory.

Answer 4

The horseshoe vortex is represented by superimposing an infinite number of horseshoe vortices each with a bound-vortex of differing lengths and strengths, but all being centred on the same lifting-line (wing).

Question 5

What is the state of the bound vortex near the tips compared to the centre for lifting line theory?

Answer 5

It is weaker - or the sum of the filaments is lesser at the tips.

Question 6

What happens to the lost vortex strength/lost filaments?

Answer 6

They are shed as a vortex sheet all along the TE, rather than as two vortices at the tips. The sheet coalesces downstream.

Question 7

How do the infinite vortex filaments affect lift along the wingspan?

Answer 7

The lift at each point along the span of a wing is L = – rhoUgamma, where gamma is the total circulation of each vortex filament. The maximum lift occurs at the mid-span because each vortex filament is superposed.

Question 8

Why are there fewer bound vortices OBD than IBD?

Answer 8

The vortices begin to move from bound to trailing positions.

Question 9

How can lift be increased considering the bound and trailing vortices?

Answer 9

If fewer bound vortices become trailing vortices, less lift is lost.

Question 10

Describe the coalescence of the trailing vortices.

Answer 10

As they propagate downstream, the vortices formed at the wingtips move IBD and the vortices formed close to the centreline move OBD. The migration stops once the vortices reach the centroid, and they remain at this 2y/S distance until they dissipate.

Question 11

How can a Cp vs 2y/S plot be used to show where the trailing vortex pair will form for a single element wing?

Answer 11

If the line of Cp = peak is traced to 2y/S = 1, the lost bound vorticity, or the trailing vorticity can be found. The 2y/S position where the trailing vortices area to its left is equal in magnitude to the area on the right shows where the vortices will form.

Question 12

For a multi-element full-span wing, how does the position of the trailing vortices change?

Answer 12

It does not. There will be more trailing vorticity, but the position will be the same.

Question 13

For a multi-element part-span wing, how does the position of the trailing vortices change?

Answer 13

If the part-span flaps are positioned in the centre, they will move the trailing vortices IBD.

Question 14

How can the centroid of the trailing vortex positions be manipulated?

Answer 14

They will move IBD with IBD loading and vice versa.

Question 15

What are the highest lift, lowest drag, and most efficient spanwise lift distributions?

Answer 15

Elliptical for all.

Question 16

For a wing with an elliptical distribution of lift, how does the down/upwash vary with spanwise location?

Answer 16

It is constant.

Question 17

How can an elliptical lift distribution be obtained with planform area shape?

Answer 17

Using an elliptical planform.

Question 18

What other methods of obtaining an elliptical lift distribution are there?

Answer 18

Aerodynamic or geometric twist and taper ratio.

Question 19

Why elliptical distributions have the smallest induced drag?

Answer 19

They lose the fewest bound vortices as trailing vortices, making the trailing vortices smaller and decreasing the down/up wash induced.

Question 20

Why do trailing vortices form at part-span flap tips on an aeroplane?

Answer 20

That’s where the largest spanwise circulation gradient is. Vorticity along the span is pulled to this location. There is still vorticity at the full-span tips but it is too low to cause condensation.

Question 21

Describe the velocity distribution normal to the axis of a potential vortex.

Answer 21

Velocity increases to infinity at the centre.

Question 22

Describe the velocity distribution normal to the axis of a Rankine vortex.

Answer 22

Within the core, velocity increases linearly with distance from the centre. Outside the core, velocity decreases with the square of distance from the centre.

Question 23

What are the names of the two distinct regions of a Rankine vortex?

Answer 23

The rigid core, and the free vortex.

Question 24

What are the two main causes of vortex breakdown?

Answer 24

Swirl ratio and external pressure gradient.

Question 25

Define swirl ratio.

Answer 25

The ratio of the swirl velocity to the axial velocity.

Question 26

How do external pressure gradients cause vortex breakdown?

Answer 26

They can cause breakdown when adverse.

Question 27

What effect do external pressure gradients have on the pressure gradient along the vortex axis?

Answer 27

The pressure gradient along the vortex axis varies with the square of the circulation of the vortex. So the external pressure gradient is amplified at the vortex axis, making the vortex more sensitive to small changes in external pressure gradient.

Question 28

If more energy is used to form a vortex, what effect will this have on its health?

Answer 28

It will need to recover more Cp to return to freestream, so it has a steeper gradient.

Question 29

What two ways can a vortex be made stronger downstream?

Answer 29

With a favourable pressure gradient, and by creating it in a region of high CpT.

Question 30

Describe the transient development of a vortex.

Answer 30

Its circulation increases with time, and therefore its vorticity. Therefore, the pressure in the free vortex decreases. When the swirl ratio is too large, the vortex is shed from the shedding edge (or the edge runs out first) which allows the vortex to form a stable structure and conserve its circulation.

Question 31

How do co-rotating vortices affect each others normal Cp distributions?

Answer 31

They increase each others circulation. They increase the equivalent of their dumping velocities at their adjacent sides, since they don't need to recover to freestream.

Question 32

Describe the shear field of a co-rotating vortex pair.

Answer 32

There is increased shear between them, which causes them to rotate about each other in a spiralling motion (if equal strength).

Question 33

Describe the shear field of a counter-rotating vortex pair.

Answer 33

The inner sides of the vortices have the same velocity, so no shear is developed. The outer sides develop shear, which downwashes the vortices.

Question 34

What happens to the migration of a counter-rotating vortex pair in presence of as ground plane?

Answer 34

Their outwash thickens to BL, and further OBD their upwash raises the BL. The BL separates from the GP to form a secondary counter-rotating vortex which induces an upwards and OBD motion of the primary.

Question 35

What is the strength of tip vortices related to?

Answer 35

Wing lift.

Question 36

What do trailing vortices represent/are equivalent to?

Answer 36

They contain rotational Ek which is not useful to the wing and therefore appear as drag.

Question 37

On a lifting wing, what effect do the trailing vortices have on the flowfield?

Answer 37

They induce a downwash.

Question 38

What effect does the trailing vortices' induced down or up wash have on the wing?

Answer 38

They reduce the effective AoA.

Question 39

On what types of wing do trailing vortices cause the largest loss in lift?

Answer 39

Short aspect ratio wings (short span).

Question 40

What does the term Cl[alpha] refer to?

Answer 40

The gradient of a Cl vs AoA graph.

Question 41

Aspect ratio affects wing lift. How does it affect Cl[alpha]?

Answer 41

The higher the AR, the steeper the gradient in the attached region.

Question 42

What effect does AR have on induced drag?

Answer 42

Increasing AR decreases Di.

Question 43

What effect does AR have on lift, drag, and wing efficiency?

Answer 43

Increasing AR increases lift and decreases Di, so efficiency increases.

Question 44

What effect does aft (backwards) wing sweep have on Cl[alpha]?

Answer 44

It reduces.

Question 45

What effect does aft (backwards) wing sweep have on spanwise loading?

Answer 45

It OBD loads the wing.

Question 46

How does taper ratio affect spanwise loading?

Answer 46

For small taper ratios, the local tip Cl will increase.

Question 47

Name another method of affecting spanwise loading.

Answer 47

Geometric or aerodynamic twist.

Question 48

What effect does wing dihedral have outside of ground effect?

Answer 48

It reduces Cl[alpha].

Question 49

Draw a graph to describe induced drag.

Answer 49

Key points: effective AoA decreased, tilting lift vector which is always normal to onset flow, creating Di.

Question 50

How can induced drag be reduced by adding geometry?

Answer 50

Adding a neutral aerofoil endplate.

Question 51

How does adding a neutral aerofoil endplate reduced induced drag?

Answer 51

The tip vortex generates a crossflow which induces an AoA on the endplate, which creates lift. A component of the lift acts opposite to drag.

Question 52

How does a hang glider descend?

Answer 52

They roll, tilting their lift vector. The lift increases, balancing gravity but there is now a horizontal component making the glider yaw. The lift has increased, which increases the induced drag by square. Therefore they decelerate and lose lift.

Question 53

Why are endplates used?

Answer 53

To counteract wing pressure equalisation will occur, which decreases the lift generated.

Question 54

Draw the Cl vs 2y/b of wings with and without endplates.

Question 55

Draw the Cd and Cl vs AoA of wings with and without endplates.

Question 56

Why does drag increase due to endplates?

Answer 56

Due to the decreased pressure equalisation caused by endplates, there is a larger pressure difference between the two surfaces. This also increases lift.

Question 57

How does ground effect change lift on an aeroplane?

Answer 57

Lift increases with ground effect until stall.

Question 58

Explain the mechanism of ground effect on aeroplanes.

Answer 58

The wingtip vortices are upwashed by the secondary vortices. Therefore, the downwash at the wingtips is reduced. This means that the lift vector becomes more vertical and the effective AoA increases, creating more lift. The induced drag decreases for the same reason, therefore, the aeroplane requires less thrust to maintain the same airspeed.