External Flows

Question 1

What does g_o corespond to

Answer 1

to a suction peak at the lower surface, causing an adverse pressure gradient, increasing drag

Question 2

Explain Boundary Layers and seperation

Answer 2

Turbulent boundry layers are dominated by unsteady mixing pricess and are thicker and fuller in profile than laminar layers

Seperation occurs when a boundary layer is subjected to adverse pressure gradients. Turbulent layers, with their fuller profile, are less prone to seperation than laminar. Transition from laminar to turbulent is inhibited by favourable and encouraged by adverse pressure gradients

Question 3

Explain Seperation bubbles

Answer 3

WHen the near- wall velocity is unable to support the adverse pressure gradient then serperation can occur

Often on airfoils laminar seperation is followed by turbulent reattachment (a seperation bubble) visible as a flat in the Cp plot.

Question 4

Explain stall mechanisms in two dimension aerofoil flow.

Answer 4

At high reynolds numbers there are two main types of stall:

Leading edge stall
Trailing edge Stall

Leading edge stall is typically associeated with thin airfoils and is linked to the seperation bubble which forms after the suction peak as the angle of attack is increased. Eventually the bubble bursts and abrupt stall takes place

Trailing edge stall is typically associated with thick airfoils and occurs when the cumulative effect of the suction side adverse pressure gradient causes a seperation to start near the trailing edge and then move progressively upstream as the angle of attack increases leading to gradual stall

Question 5

Explain remedial measures for stall

Answer 5

fixes for stall are based on re energising the new wall b;layer in safa way and use combinations of vortex generators, blowing and suction

Question 6

Explain the role of spanwise loading distribution on stalling behaviour

Answer 6

Question 7

What is boundary layer cross flow?

Answer 7

Takes place on swept wings as b’layer fluids deflect with greature curvature than free-stream fluid in the same spanswise pressure gradient (v²/r _~ V²/R) therefore r < R

on a finite wing this leads to the accumulation of low energy fluid towards the wing tips- this leads to a greater succeptibility to stall near the tip. This can be controlled to some extent by installing “Chord-wise boundary layer fences”

Question 8

Prove C_P = - ρuγ

Answer 8

Show that γ = velocity jump acrooss boundary layer

use bernoulii to find C_p for small pertubations

FInd difference between upper and lower pressure

Question 9

derrive camber flow

Answer 9

The model is based on representing the velocity jump across the aerofoil by a vortex sheet distributed along the camber line (which is taken as being the y=0 axis as the camber is small)

The y-wise velocity is found by summing the effects of each element of circulation

Question 10

Explain Pitching moment solution

Answer 10

Question 11

Exaplain the thickness contribution

Answer 11

The thickness represents “blockage” and is modelled by a set of line sources:

Question 12

Explain 2d lumped parameter modelling

Answer 12

First, lift and circulation are connected via a simple “2π” lift slope law:

Given that the lift acts at the quarter chord point (x=c/4) the downwash just balances the upwash at the so- called “collocation point” x=3c/4 – as demonstrated to the right. This is the key modelling assumption

Question 13

Describe the use of horsehoe vortices in lifting line theory

Answer 13

Question 14

DErive expression for the downwash and downwash angle in lifting line therory

Answer 14

Question 15

Explain the physcal orgines of induced drag, explain key stpes in derrication of downwasg angle

Answer 15