Flow around Cylinder and Aerofoil

Question 1

What are the three characteristics of potential flow?

Answer 1

• Inviscid
• Incompressible
• Irrotational

Question 2

What elementary flows represent flow around a cylinder?

Answer 2

Uniform flow and doublet

Question 3

What are the two components of the velocity field around a cylinder?

Answer 3

• v(theta)

- v(r)

Question 4

What does v(theta) represent?

Answer 4

The velocity component that’s always tangent to a streamline

Question 5

What does v(r) represent?

Answer 5

The velocity component that’s always perpendicular to the circle

Question 6

What is it called when both v(theta) and v(r) are both ZERO?

Answer 6

A stagnation point

Question 7

How can the pressure distribution be calculated around the cylinder?

Answer 7

Modified bernoulli equation to find p.

Question 8

What does inviscid flow mean in terms of lift and drag?

Answer 8

Pressure is the only contributing factor, there are no shear forces

Question 9

Where can the equations for v(theta), v(r), lift and drag per unit span be found?

Answer 9

Lecture slides or notes book.

Question 10

What is the zero drag condition known as?

Answer 10

d’Alambert Paradox

Question 11

Why is zero drag impossible with viscous flow?

Answer 11

There will always be frictional shear stress would generate seperation and wake

Question 12

What is the name of drag arising from pressure?

Answer 12

Form Drag

Question 13

What is the name of drag arising from shear force?

Answer 13

Skin Friction Drag

Question 14

What are the names of the bodies dominated by form drag and skin friction drag?

Answer 14

Bluff body - Form drag dominated

Streamlined body - Skin friction drag dominated

Question 15

Describe viscous flow at RE < 1

Answer 15

Stokes flow, very viscous
completely symetrical
flow remains attached as Re increases

Question 16

Describe viscous flow at RE = 40

Answer 16

Flow seperates
Forms closed wake of recirculating flow
Flow is symetric about horizontal axis

Question 17

Describe viscous flow at 100 < RE < 200

Answer 17

Von Karmen vortex street, periodical asymetric vortices on alternating sides of horizontal axis.
Gives rise the lift force alternating at shedding frequency

Question 18

What is shedding frequency?

Answer 18

The frequency of the alternations in a Von Karmen vortex street

Question 19

What is the Strohval number?

Answer 19

Characterises relationship between RE and shedding frequency.

Question 20

Describe viscous flow at 400 < RE < 3e5

Answer 20

Transition to turbulence is close to laminar speration point. If in the first half then a large wake is produced which means a high form drag.

Question 21

Describe viscous flow at 3e5 < RE < 1e6

Answer 21

Flow transitions to turbulent almost immediately after seperation however the incresed mixing re-energises the flow and it re attaches created a seperation bubble. It then seperates creating a narrow wake. These are the critical RE numbers.

Question 22

Describe viscous flow at RE > 1e6

Answer 22

No seperation bubble and sepeeration moves rearward. Cd slowly increases as RE increases further.

Question 23

What is the Kutta-Joukowski Theorem?

Answer 23

That a 2D aerofoil in inviscid incompressible flow generates a lift directly related to the circulation about the object. L = rho x V x circulation

Question 24

What is the Kutta condition?

Answer 24

For the Kutta-Joukowski Theorem to be applied the velocities on the upper and lower surface of the trailing edge should have the same magnitude and direction.

Question 25

Why must there be a starting vortex?

Answer 25

There must be a vortex with equal magnitude but negative sign before the aerofoil to counteract that at the trailing edge. This is to abide by Kelvins circulation theorem.

Question 26

Define the circulation term used in the Kutta-Joukowski Theorem.

Answer 26

The sum of the circulations induced by all the vortices.

Question 27

How does the panel method work?

Answer 27

Diving a surface into finite panels, employing elemental solutions and the Kutta-Joukowski Theorem produces potential functions which can used in the bernoulli equation to find presssure and therefore forces and moments.

Question 28

Why is the inviscid aerfoil theory beneficial and widely used?

Answer 28

To predict lift forces and pressure distribtutions.

Question 29

What are the limitations of inviscid aerfoil theory?

Answer 29

• No drag prediction
• Circulation is required for lift
• Based on big assumptions, inviscid, incompressible and irrotational.
• Lack of viscosity means it can’t deal with seperation/frictional forces.

Question 30

How does XFOIL work with viscosity?

Answer 30

Xfoil combines the panel method and boundary layer equations in a inviscid/viscous coupling approach. This means Xfoil can manage moderate seperation.

Question 31

What is aerodynamic stall?

Answer 31

It’s when the boundary layer fully seperates from the aerfoil surface.

Question 32

How does camber affect the lift curve?

Answer 32

Translates curve upwards and to the left, reducing angle of attack required for same lift coefficient. Lower stall angle

Question 33

How does the RE number affect the lift curve?

Answer 33

Increases the maximum coefficient of lift. High RE flows are more resistant to stall.

Question 34

How does the thickness affect the lift curve?

Answer 34

Increased thickness increases the maximum coefficient of lift but when too bulky (>12%) can have the inverse affect.

Question 35

Do aerofoil parameters have different affects at low RE numbers?

Answer 35

Yes, thickness at low RE decreases the lift curve and theres a drag penalty.
Camber still increases the lift curve but also increases the minimum coefficient of drag.

Question 36

What is the Prandlt-Glauert formula?

Answer 36

a formula that accounts for compressibility. However it generally underpredicts experimental findings.

Question 37

What formulas should be used in compressibility corrections?

Answer 37

The Karman-Tsien formula and Laitone formula as they are most widely used.

Question 38

When can compressibility corrections be made?

Answer 38

Only when there are no shock waves. So at mach number less than 0.85.