Chapter Summaries Flashcards
What is a vortex?
A coherent motion of fluid particles around some common axis
What is rotational and irrotational flow?
Rotational flow is a flow where the fluid particles rotate around their individual axes, irrotational is the converse
Is a solid body vortex rotational?
yes
Is a potential vortex rotational?
No, except on axis
What is circulation?
An integral measure of the velocity or the vorticity field connected by Stokes theorem
What are vortex lines?
Integral curves of vorticity field
What is the Biot-Sarvat Law?
It allows us to compute the velocity at an arbritrary pint induced by a simply connected path of vorticity
What do the velocities in a straight vortex tube depend on?
We obtain rotationally symmetric velocities that depend inversely proportionally on the normal distance and on the two aspect angles
What do induced velocities in an infinite straight vortex tube depend on?
Only inversely proportionally on the normal distance
What is a general vortex sheet?
An infinite or finite arrangement of infinite or finite parallel straight or curved potential vortices
What are the properties of velocities for an infinite vortex sheet?
The velocities above and below are uniform and have a jump across
What is the mirror principle?
The mirror principle serve to generate suitable streamlines /surfaces as models for walls in inviscid flows
How can vorticity be produced and destroyed?
By positive or negative vortex stretching and by baroclinic production
What is Prandtl’s hypothesis?
Prandtl’s hypothesis enables to split flow domain into potential flow and boundary layer
What is potential flow?
Potential flow is a flow whose velocity field is irrotational and thus can be generated by a gradient of scalar potential functions
What is the superposition principle?
The superposition principle arises from linearity of the Laplace equation and allows to generate new potentials from summation of potentials
Where does the normal derivative of potentials vanish?
At impermeable walls
For what kind of Flows is the Bernoulli equation valid?
For potential flows with irrotational velocity (except at isolated singularities), constant density, and volume forces with potential with a unique Bernoulli constant for the entire field
How is the divergence free condition satisfied?
By using the streamfunction
What is the volume flux between two streamlines equal to?
The difference in respective stream functions at iso level
What is a property of streamlines and Equipotential lines?
They are orthogonal to one another except at singularities
What is a property of conformal mapping?
It is angle preserving
What do real and imaginary parts of complex potential represent?
Real part is potential function, imaginary part is stream function
How can complex vorticity be derived from complex potential?
By taking the first derivative
What are the components of complex circulation?
Real part is circulation, imaginary part is volume flux along closed integration part
What is parallel flow characterized by?
Velocity vectors of constant direction and magnitude
What is source / sink flow characterized by?
Velocity vectors pointing radially from / into origin with magnitude decaying inversely proportionally to distance
What is potential vortex flow characterized by?
Velocity vectors pointing tangentially to circumcircles around the origin with magnitude decaying inversely proportionally to distance
How does a dipole flow occur?
From the distinguished limit of superimposing source and sink where their strength increases inversely proportionally to their distance
What does a wedge flow represent?
A wedge flow can represent a whole range of interior/ exterior flows in and around corners, limit cases are flat plate and sharp tip
What do free stream and source result in?
An open body to compensate for the source volume flux rate which is fed into the body
How can a body be closed?
By adding a sink of equal and opposite strength
What is constructed using superposition of dipole and parallel flow?
A potential flow around an infinitely long straight cylinder with circular cross section
What is the Kutta-Joukowski theorem?
The resulting force in a 2D potential flow around a closed body is proportional to circulation, density and incoming velocity
What is the Joukowski map?
It maps a circle onto a flat plate
Are potential flow solutions around closed bodies unique?
No
