Inviscid flow around cylinder in presence of wall

In summary, the conversation discussed a potential flow theory problem involving a cylinder moving at a constant velocity through a stagnant fluid in the presence of a wall. The presence of the wall causes a "ground effect" and results in a lift force. The person inquiring has two questions: how to find the flow field and how to find the force as a function of distance from the wall. The solution suggested is to use the method of reflections by placing an identical cylinder on the other side of the wall and observing from the frame of reference of the cylinders.
  • #1
Armin1986
1
0
Hi there,

Is there someone who would know how to solve the following potential flow theory problem:

How to find the flow field and resulting force on a cylinder moving at a constant velocity through a stagnant fluid in the presence of a wall. The motion of the cylinder is parallel to the wall.

Without the wall it can be found that there is no force due to the inviscid nature of the flow.
However, due to the wall, "ground effect" occurs and therefore there will be a lift force.

I have two questions:
- How to find the flow field (e.g. streamlines or vector field)
- How to find the force as a function of the distance from the wall

I would be very thankfull if someone could help me with this problem.
 
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  • #2
You can use the method of reflections by placing an identical cylinder at an equal distance on the other side of the wall (and removing the wall). You would also have the observer moving along with the cylinders, so that, from his frame of reference, the cylinders are stationary and the fluid is flowing. Very straightforward.
 

1. What is meant by "inviscid flow"?

"Inviscid flow" refers to the theoretical scenario of fluid flow where the fluid is assumed to be frictionless and have no viscosity. In other words, there is no energy loss due to internal friction as the fluid moves. This simplifies the mathematical analysis of fluid flow and is often used as a starting point for more complex models.

2. How does the presence of a wall affect the flow around a cylinder?

The presence of a wall near a cylinder can significantly alter the flow pattern. The wall acts as a boundary that redirects the flow, causing vortices and eddies to form. This can greatly impact the pressure distribution and drag force on the cylinder.

3. What is the significance of studying the flow around a cylinder in the presence of a wall?

The study of inviscid flow around a cylinder in the presence of a wall has practical applications in fluid dynamics, aerodynamics, and engineering. It helps us understand the behavior of fluids in various scenarios and can aid in the design of structures and vehicles that need to move through or interact with fluids.

4. How can the flow around a cylinder in the presence of a wall be modeled mathematically?

This type of flow can be modeled using the Navier-Stokes equations, which describe the motion of a fluid. In the case of inviscid flow, the equations can be simplified by assuming that the viscosity term is zero. This results in the Euler equations, which can then be solved using numerical methods or analytical techniques.

5. What are some real-world examples where understanding inviscid flow around a cylinder in the presence of a wall is important?

Some examples include the aerodynamics of airplane wings, the flow of water around a ship's hull, and the behavior of fluids in pipes and channels. It can also be applied to the design of wind turbines, racing cars, and other vehicles that need to minimize drag and maximize performance.

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