Inviscid fluid flow past a square cylinder.

In summary, the conversation discusses the study of inviscid incompressible fluid flow around a circular cylinder, as well as the challenges and complexities of simulating flow around sharp edges and boundaries. The potential for vortex shedding and the difference between viscous and inviscid flow are also mentioned. The conversation concludes with the acknowledgment that truly inviscid flow is nonphysical and may not have a solution.
  • #1
tarnhelm
17
0
The flow of an inviscid incompressible fluid around a circular cylinder is commonly studied in fluid dynamics courses. There's a wikipedia article about it here: http://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder.

However, what about a square cylinder? There seem to be issues with simulating such flow across sharp edges or boundaries like the corners of squares. Can somebody tell me what you expect with such a scenario?
 
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  • #2
Actually a colleague of mine is about to publish a paper in the Journal of Fluid Mechanics on the viscous flow past a square cylinder. It is a very similar flow field to a circular cylinder but te vortex shedding is more complex. I'd say keep an eye on JFM for it, but it will probably be a year before it is actually published.
 
  • #3
Thanks for that. I think there's a lot of stuff out there about viscous flow past a square cylinder. However, inviscid flow presents a problem because it may be the case that vortices are produced at the corners, which I don't think should be the case in inviscid flow. At the very least, finite difference simulations seem to produce this effect. As I understand it, steady incompressible inviscid flow shouldn't spontaneously develop rotation like this. I'm wondering if anybody has any more info about it, because google isn't turning up much!
 
  • #4
The problem is that a truly inviscid flow can turn around an arbitrarily sharp corner, which causes infinite acceleration of the fluid. This is clearly nonphysical. There isn't really a solution to this, which is why it is mostly ignored. If you decide to allow infinite acceleration, it would be qualitatively similar to the circular cylinder in terms of streamlines, but the corners would effectively be singularities in the flow. As for simulations, they have to have some inherent damping in order to converge, so they will never simulate truly inviscid flow.

Out of curiosity, why the interest in inviscid flow around corners? It's quite far from any physically realizable flow.
 
  • #5
A square cylinder? Someone will have to explain what that means to me.
 

1. What is an inviscid fluid?

An inviscid fluid is a theoretical concept in fluid mechanics that refers to a fluid with zero viscosity, meaning it has no resistance to shearing forces or internal friction. This type of fluid is often used in simplified models to study fluid flow without the complication of viscosity.

2. What is the significance of studying inviscid fluid flow past a square cylinder?

Studying inviscid fluid flow past a square cylinder allows scientists to understand the fundamentals of fluid dynamics and how different shapes can affect the flow of a fluid. This knowledge can be applied to various real-world scenarios, such as designing more efficient airfoils for airplanes or optimizing the performance of underwater vehicles.

3. How is inviscid fluid flow past a square cylinder different from other types of fluid flow?

Inviscid fluid flow past a square cylinder differs from other types of fluid flow, such as viscous or turbulent flow, in that it does not take into account the effects of viscosity. This simplifies the analysis and allows for easier mathematical calculations, but it may not accurately represent real-world scenarios where viscosity plays a significant role.

4. What factors affect the behavior of inviscid fluid flow past a square cylinder?

The behavior of inviscid fluid flow past a square cylinder is affected by several factors, including the shape and size of the cylinder, the velocity of the fluid, and the density of the fluid. Other factors, such as the angle of attack and the presence of other objects in the flow, can also have an impact.

5. How is the study of inviscid fluid flow past a square cylinder relevant to everyday life?

While inviscid fluid flow past a square cylinder may seem like a purely theoretical concept, it has practical applications in various industries. For example, understanding the behavior of air flow around a car or airplane can help improve their design and efficiency. It can also be applied to study the flow of water around ships, dams, or other structures in fluid environments.

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