AdvancedTopic 81 of 105Thermodynamics & Fluids
Potential flow
Idealised inviscid, irrotational flow modelled with stream functions.
In depth
Assuming inviscid and irrotational flow gives velocity potential φ with ∇²φ=0 (Laplace). Elementary flows (uniform, source, sink, vortex, doublet) superpose to model flow around cylinders and aerofoils (Kutta-Joukowski lift L=ρVΓ). Fails to predict drag (d'Alembert's paradox).
Key points
- Stream function
- Superposition
- Valid outside boundary layers
ExampleUniform flow plus a doublet models flow past a cylinder.
What is Potential flow?
Idealised inviscid, irrotational flow modelled with stream functions.
Why is it important to understand potential flow?
Potential flow is an idealised model with no viscosity or rotation, which is simple to solve and useful for lift and flow around bodies away from walls.
What is potential flow?
Flow that is inviscid and irrotational, so it can be described by a velocity potential or a stream function.
Where does potential flow fail?
Near walls and in separated regions, where viscosity and vorticity matter, so boundary layer effects must be added.
How is Potential flow used in practice?
Typical applications include estimating the flow around a cylinder in an ideal fluid, modelling the lift on a thin airfoil with a potential flow model and calculating the flow field around a sphere for an early design study.
What should I learn before Potential flow?
Study "Navier-Stokes equations" first (topic 80 of 105 in Thermodynamics & Fluids). It covers the groundwork this topic builds on.
What are the key points of Potential flow?
Stream function. Superposition. Valid outside boundary layers.
Can you give an example of Potential flow?
Uniform flow plus a doublet models flow past a cylinder.
What comes after Potential flow?
The next topic is "Turbulence modelling", which builds directly on this one.
How difficult is Potential flow?
It is classed as Advanced in Thermodynamics & Fluids (topic 81 of 105). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Thermodynamics & Fluids.