3D Flows Flashcards
Describe the bound vortex.
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.
Describe the horseshoe vortex.
This is modelled by the bound vortex and two trailing vortices at the wingtips. A starting vortex is shed, which dissipates due to viscosity.
How can the horseshoe vortex be modelled to include tip effects?
With a reduced effective wingspan.
Describe the lifting line theory.
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).
What is the state of the bound vortex near the tips compared to the centre for lifting line theory?
It is weaker - or the sum of the filaments is lesser at the tips.
What happens to the lost vortex strength/lost filaments?
They are shed as a vortex sheet all along the TE, rather than as two vortices at the tips. The sheet coalesces downstream.
How do the infinite vortex filaments affect lift along the wingspan?
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.
Why are there fewer bound vortices OBD than IBD?
The vortices begin to move from bound to trailing positions.
How can lift be increased considering the bound and trailing vortices?
If fewer bound vortices become trailing vortices, less lift is lost.
Describe the coalescence of the trailing vortices.
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.
How can a Cp vs 2y/S plot be used to show where the trailing vortex pair will form for a single element wing?
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.
For a multi-element full-span wing, how does the position of the trailing vortices change?
It does not. There will be more trailing vorticity, but the position will be the same.
For a multi-element part-span wing, how does the position of the trailing vortices change?
If the part-span flaps are positioned in the centre, they will move the trailing vortices IBD.
How can the centroid of the trailing vortex positions be manipulated?
They will move IBD with IBD loading and vice versa.
What are the highest lift, lowest drag, and most efficient spanwise lift distributions?
Elliptical for all.
For a wing with an elliptical distribution of lift, how does the down/upwash vary with spanwise location?
It is constant.
How can an elliptical lift distribution be obtained with planform area shape?
Using an elliptical planform.
What other methods of obtaining an elliptical lift distribution are there?
Aerodynamic or geometric twist and taper ratio.
Why elliptical distributions have the smallest induced drag?
They lose the fewest bound vortices as trailing vortices, making the trailing vortices smaller and decreasing the down/up wash induced.
Why do trailing vortices form at part-span flap tips on an aeroplane?
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.
Describe the velocity distribution normal to the axis of a potential vortex.
Velocity increases to infinity at the centre.
Describe the velocity distribution normal to the axis of a Rankine vortex.
Within the core, velocity increases linearly with distance from the centre. Outside the core, velocity decreases with the square of distance from the centre.
What are the names of the two distinct regions of a Rankine vortex?
The rigid core, and the free vortex.
What are the two main causes of vortex breakdown?
Swirl ratio and external pressure gradient.
Define swirl ratio.
The ratio of the swirl velocity to the axial velocity.
How do external pressure gradients cause vortex breakdown?
They can cause breakdown when adverse.
What effect do external pressure gradients have on the pressure gradient along the vortex axis?
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.
If more energy is used to form a vortex, what effect will this have on its health?
It will need to recover more Cp to return to freestream, so it has a steeper gradient.
What two ways can a vortex be made stronger downstream?
With a favourable pressure gradient, and by creating it in a region of high CpT.
Describe the transient development of a vortex.
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.
How do co-rotating vortices affect each others normal Cp distributions?
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.
Describe the shear field of a co-rotating vortex pair.
There is increased shear between them, which causes them to rotate about each other in a spiralling motion (if equal strength).
Describe the shear field of a counter-rotating vortex pair.
The inner sides of the vortices have the same velocity, so no shear is developed. The outer sides develop shear, which downwashes the vortices.
What happens to the migration of a counter-rotating vortex pair in presence of as ground plane?
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.
What is the strength of tip vortices related to?
Wing lift.
What do trailing vortices represent/are equivalent to?
They contain rotational Ek which is not useful to the wing and therefore appear as drag.
On a lifting wing, what effect do the trailing vortices have on the flowfield?
They induce a downwash.
What effect does the trailing vortices’ induced down or up wash have on the wing?
They reduce the effective AoA.
On what types of wing do trailing vortices cause the largest loss in lift?
Short aspect ratio wings (short span).
What does the term Cl[alpha] refer to?
The gradient of a Cl vs AoA graph.
Aspect ratio affects wing lift. How does it affect Cl[alpha]?
The higher the AR, the steeper the gradient in the attached region.
What effect does AR have on induced drag?
Increasing AR decreases Di.
What effect does AR have on lift, drag, and wing efficiency?
Increasing AR increases lift and decreases Di, so efficiency increases.
What effect does aft (backwards) wing sweep have on Cl[alpha]?
It reduces.
What effect does aft (backwards) wing sweep have on spanwise loading?
It OBD loads the wing.
How does taper ratio affect spanwise loading?
For small taper ratios, the local tip Cl will increase.
Name another method of affecting spanwise loading.
Geometric or aerodynamic twist.
What effect does wing dihedral have outside of ground effect?
It reduces Cl[alpha].
Draw a graph to describe induced drag.
Key points: effective AoA decreased, tilting lift vector which is always normal to onset flow, creating Di.
How can induced drag be reduced by adding geometry?
Adding a neutral aerofoil endplate.
How does adding a neutral aerofoil endplate reduced induced drag?
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.
How does a hang glider descend?
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.
Why are endplates used?
To counteract wing pressure equalisation will occur, which decreases the lift generated.
Draw the Cl vs 2y/b of wings with and without endplates.
Draw the Cd and Cl vs AoA of wings with and without endplates.
Why does drag increase due to endplates?
Due to the decreased pressure equalisation caused by endplates, there is a larger pressure difference between the two surfaces. This also increases lift.
How does ground effect change lift on an aeroplane?
Lift increases with ground effect until stall.
Explain the mechanism of ground effect on aeroplanes.
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.
