Flow around Cylinder and Aerofoil Flashcards
What are the three characteristics of potential flow?
- Inviscid
- Incompressible
- Irrotational
What elementary flows represent flow around a cylinder?
Uniform flow and doublet
What are the two components of the velocity field around a cylinder?
- v(theta)
- v(r)
What does v(theta) represent?
The velocity component that’s always tangent to a streamline
What does v(r) represent?
The velocity component that’s always perpendicular to the circle
What is it called when both v(theta) and v(r) are both ZERO?
A stagnation point
How can the pressure distribution be calculated around the cylinder?
Modified bernoulli equation to find p.
What does inviscid flow mean in terms of lift and drag?
Pressure is the only contributing factor, there are no shear forces
Where can the equations for v(theta), v(r), lift and drag per unit span be found?
Lecture slides or notes book.
What is the zero drag condition known as?
d’Alambert Paradox
Why is zero drag impossible with viscous flow?
There will always be frictional shear stress would generate seperation and wake
What is the name of drag arising from pressure?
Form Drag
What is the name of drag arising from shear force?
Skin Friction Drag
What are the names of the bodies dominated by form drag and skin friction drag?
Bluff body - Form drag dominated
Streamlined body - Skin friction drag dominated
Describe viscous flow at RE < 1
Stokes flow, very viscous
completely symetrical
flow remains attached as Re increases
Describe viscous flow at RE = 40
Flow seperates
Forms closed wake of recirculating flow
Flow is symetric about horizontal axis
Describe viscous flow at 100 < RE < 200
Von Karmen vortex street, periodical asymetric vortices on alternating sides of horizontal axis.
Gives rise the lift force alternating at shedding frequency
What is shedding frequency?
The frequency of the alternations in a Von Karmen vortex street
What is the Strohval number?
Characterises relationship between RE and shedding frequency.
Describe viscous flow at 400 < RE < 3e5
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.
Describe viscous flow at 3e5 < RE < 1e6
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.
Describe viscous flow at RE > 1e6
No seperation bubble and sepeeration moves rearward. Cd slowly increases as RE increases further.
What is the Kutta-Joukowski Theorem?
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
What is the Kutta condition?
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.
Why must there be a starting vortex?
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.
Define the circulation term used in the Kutta-Joukowski Theorem.
The sum of the circulations induced by all the vortices.
How does the panel method work?
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.
Why is the inviscid aerfoil theory beneficial and widely used?
To predict lift forces and pressure distribtutions.
What are the limitations of inviscid aerfoil theory?
- 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.
How does XFOIL work with viscosity?
Xfoil combines the panel method and boundary layer equations in a inviscid/viscous coupling approach. This means Xfoil can manage moderate seperation.
What is aerodynamic stall?
It’s when the boundary layer fully seperates from the aerfoil surface.
How does camber affect the lift curve?
Translates curve upwards and to the left, reducing angle of attack required for same lift coefficient. Lower stall angle
How does the RE number affect the lift curve?
Increases the maximum coefficient of lift. High RE flows are more resistant to stall.
How does the thickness affect the lift curve?
Increased thickness increases the maximum coefficient of lift but when too bulky (>12%) can have the inverse affect.
Do aerofoil parameters have different affects at low RE numbers?
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.
What is the Prandlt-Glauert formula?
a formula that accounts for compressibility. However it generally underpredicts experimental findings.
What formulas should be used in compressibility corrections?
The Karman-Tsien formula and Laitone formula as they are most widely used.
When can compressibility corrections be made?
Only when there are no shock waves. So at mach number less than 0.85.
