Potential Flow Flashcards
Can you neglect friction effects of boundary layer for good approximation of pressure forces on bodies?
Yes
What is potential flow?
A flow where the velocity is the gradient of a potential u = nabla phi
What are the boundary conditions required for Laplace for potential flows?
- Fixed Potential at boundary (Derelict)
- Neumann Condition at boundary
- Infinite Domain Condition
Why do we need additional boundary conditions when calculating potential flow around an object?
For flow around objects, the domain is not simply connected, leading to non-uniqueness—this is why we need extra conditions like circulation or the Kutta condition.
What are the properties of the Bernoulli equation for potential flows?
It is valid for flows with irrotational velocity, constant density, and volume forces with potential with a unique Bernoulli constant for the entire field
What is the difference between 2D and 3D potential flow in terms of the analysis required?
3D requires matrix analysis, 2D requires complex analysis
How is the stream function psi for 2D potential flow defined?
It is defined such that the derivative wrt y gives us u and wrt x gives us - v.
This automatically satisfies the divergence free condition and also ensures constant value across streamlines
What are three observations unique to 3D potential flow?
Helical Flows
Vortex Stretching
Boundary later effects
What does the difference between two stream functions give us?
psi 1 - psi 2 gives us the volume flow rate between the two streamlines
If Psi 1 > Psi 2 then the fluid flows form S2 to S1
What do the velocity potential and the stream function represent?
The stream function is constant across streamlines and the velocity potential is constant across potential lines
What are the equations connecting velocity potential and stream function?
Cauchy Reimann Equations
What is a key observation about potential lines and stream lines?
They are always perpendicular to each other
What are the properties of the path integral of an analytic function?
- It is path independent
- It depends only on the endpoints
What is the residue theorem?
The Residue Theorem is a fundamental tool in complex analysis that allows you to compute complex integrals involving analytic functions by focusing on their singularities. By calculating residues and considering the winding numbers, you can efficiently determine the value of path integrals around closed contours.
Is conformal mapping angle preserving?
Yes
What is the advantage of using complex potential in 2D potential flows?
It allows us to combine stream and potential function into a single complex function
How do we arrive at the Laplace Equations form the Cauchy-Reimann equations?
By taking the derivative and adding the results.
What is complex velocity?
It is the term we obtain by derivating the complex potential
What is complex circulation?
It is the line integral of the complex velocity along a closed path
What are the characteristics of Sink/ Source Flows?
- Singularity at the origin
- Radial velocity field
- Decay with 1 / r
What are the properties of potential vortex flows?
- Singularity at the origin
- Tangential Velocity
- Decaying velocity with 1/r
What are the real and complex parts of the complex potential?
Real part is the potential function and imaginary part is the stream function
How do we construct dipole flow?
By superimposing a source and a sink
What is an interesting symmetry that dipole flows show?
The axis along which the source and sink approach each other is a mirror line of the streamlines
