Aerodynamics (copy)

Fluid particle

A relatively small mass of the fluid, containing a large number of molecules that will provide a meaningful statistical averages

Kutta Condition

The strength of the vortex sheet at the trailing edge must be zero

Streakline

a line connecting fluid particles that has passed from the same point (Eularian)

Streamline

imaginary lines, which are tangent to flow direction at a given instant of time

Pathline

a trajectory traced out by a fluid particle moving in a flow field (Lagrangian)

Reynolds number

a dimensionless number used in fluid mechanics to indicate whether fluid flow past a body or in a duct is steady or turbulent.

Ratio of inertial forces to viscous forces

When calculating similitudes between a model and prototype the Reynolds number for each must be the same

Kutta-Joukowski Theorem

the lift per unit length of a spinning cylinder is equal to the density (r) of the air times the strength of the rotation (G) times the velocity (V) of the air.

dynamic similarity

all forces in the model flow scale by a constant factor to corresponding forces in the prototype flow

Stagnation point

a point in a flow field where the local velocity of the fluid is zero

Boundary layer thickness

the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity

Separation

reduced lift and increased pressure drag, caused by the pressure differential between the front and rear surfaces of the object

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A region of recirculating flow

Wall shear stress

expresses the force per unit area exerted by a solid boundary on a fluid in motion (and vice-versa) in a direction on the local tangent plane.

𝛁×𝑽

Curl

𝛁∙𝑽

Divergence

Dividing streamline

The part of the flow that separates the recirculating flow and the flow through the central region of the duct

Elementary flow

a collection of basic flows from which it is possible to construct more complex flows by superposition.

Laminar, Source/Sink, Vortex

Buckingham Pi Theorem

Dimensional analysis is used to formulate a physical phenomenon as a relation between a set of nondimensional (unitless) groups

No-slip condition

assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary

Circulation

the line integral of velocity around a closed curve in the flow

Vorticity

a region in a fluid in which the flow revolves around an axis line

Magnus effect

fluid pressure decreases at points where the speed of the fluid increases

d’Alembert’s Paradox

Body immersed in Fluid, There is no net drag, There is no net lift

Eularian

Fixed in the flow field and you observe the variation of properties at the point (spatial description)

Lagrangian

Identified fluid particles are followed in the course of time

Source/sink

fluid moves radially inward/outward towards a point known as sink, and fluid disappear at sink/source at a constant rate.

Doublet

a result of construction of a flow field using the superposition of a source and a sink that are placed very close to each other

Mean free path

The average distance a molecule travels before it collides with another molecule

Continuum

Fluid (gas or liquid) is continuously distributed along the region of interest.

Wake

the region of disturbed flow (often turbulent) downstream of a solid body moving through a fluid, caused by the flow of the fluid around the body.

What are the 4 thin aerofoil assumptions?

The aerofoil is thin (thickness and camber are small compared to the chord)
2\. The angle of attack is small
3\. Camberline is a streamline
4\. Aerofoil only slightly disturbs the freestream

Ideal Fluid characteristics?

Incompressible

No internal resistance to flow (zero viscosity)

Irrotational

Pressure

Force per unit area acting normal to the surface

Shear Stress

Stress component acting tangential to the surface

Normal stress

Stress component acting normal to the surface

When is a fluid incompressible and when is it compressible?

Incompressible when Mach number is < 0.3

Compressible when > 0.3

Steady Flow

Velocity and density are constant over time

scalar field

A scalar quantity given as a function of coordinate space and time “t“

dot product

Multiplying the matching components of two vectors together and adding them

Cross product

The one where you the grid with the components and crossing out a column

what does ∇ 𝑓 give and what type of field can you do it on

Can only do it on a scalar field and gives the gradient (which is a vector field)

∇ ∙ 𝑓

Works for vector field, gives divergence (scalar field)

∇ × 𝑓

Works for vector field, gives curl (scalar field)

Where is the centre of pressure on a symettrical aerofoil if the angle of attack is small?

coefficient of pressure equation

Kinematic Similarity

Flow fields in the prototype and the model must have the geometrically same set of streamlines

Fundamental units of: viscosity 𝜇, fluid density, 𝜌

Fundamental units of: Drag D

Displacement thickness

Imaginary increase in the thickness of the wall seen by the outer flow due to the reduced u velocity within the boundary layer

OR

the distance by which the solid boundary would have to be displaced to maintain the same mass flow rate in an imaginary frictionless flow

Momentum thickness

Distance by which the solid boundary would have to be displaced to maintain the same momentum transport rate at the actual mass flow rate in an imaginary frictionless flow

Streamlined body

A body where most of the drag is pressure drag

Blunt body

A body where most of the pressure is skin friction drag

What are Helmholtz 3 vortex theorems

The strength of vortex filament is constant along its length

A vortex filament can not enter a fluid

Vortex filament must extend up to the boundaries of the fluid/solid/infinity/form a closed path

What is kelvins circulation theorem

That there is no change in circulation around a closed curve consisting of the same fluid elements.