Stream function along solid boundary

In summary, the conversation discusses the concepts of slip and no-slip boundaries in fluid mechanics and their corresponding conditions. It also raises the question of whether the stream function is constant for both types of boundaries. The conclusion is that the stream function is constant for both slip and no-slip boundaries, despite what the lecturer may have stated.
  • #1
TomBolton10
1
0
Hi, I am studying fluid mechanics and I am trying to get to grips with slip and no-slip boundaries.

I know that:

Slip ---> Occurs when fluid is inviscid so no viscous stress at boundary.
No-slip ---> Viscous effects mean the the tangential velocity must be zero, relative to the boundary.

Also, for both slip and no-slip boundary conditions you have no normal flow if the boundary is solid and impermeable.

However, the problem I have is that some say that if you have the no normal flow condition, then the stream function is constant regardless of whether it is a slip/no-slip boundary (http://scicomp.stackexchange.com/qu...non-symmetric-obstacle-using-stream-functions). My lecturer however said that the stream function is constant only when it is a slip boundary. Any thoughts? Who is correct?
 
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  • #2
TomBolton10 said:
Hi, I am studying fluid mechanics and I am trying to get to grips with slip and no-slip boundaries.

I know that:

Slip ---> Occurs when fluid is inviscid so no viscous stress at boundary.
No-slip ---> Viscous effects mean the the tangential velocity must be zero, relative to the boundary.

Also, for both slip and no-slip boundary conditions you have no normal flow if the boundary is solid and impermeable.

However, the problem I have is that some say that if you have the no normal flow condition, then the stream function is constant regardless of whether it is a slip/no-slip boundary (http://scicomp.stackexchange.com/qu...non-symmetric-obstacle-using-stream-functions). My lecturer however said that the stream function is constant only when it is a slip boundary. Any thoughts? Who is correct?

Your lecturer is wrong, and what "some say" is correct. Just look at the relationship between stream function and velocity to see this. unormal=-∂ψ/∂x, where x is the coordinate along the wall.

Look up in the literature the solutions for inviscid- and viscous flow past a sphere. In both cases, the stream function is constant on the sphere.

Chet
 

1. What is a stream function along a solid boundary?

A stream function along a solid boundary is a mathematical function that describes the flow of a fluid along a solid boundary. It is used to visualize and analyze the movement of fluids, such as air or water, as they flow over a solid surface.

2. Why is the stream function along a solid boundary important?

The stream function along a solid boundary is important because it allows scientists and engineers to understand the behavior of fluids as they interact with solid surfaces. This information is crucial for designing and optimizing various systems, such as aircraft wings or water dams.

3. How is the stream function along a solid boundary calculated?

The stream function along a solid boundary is calculated using mathematical equations that take into account the fluid's velocity and the shape and orientation of the solid boundary. These equations are derived from the principles of fluid dynamics and can be solved using various numerical methods.

4. What are some applications of the stream function along a solid boundary?

The stream function along a solid boundary has many practical applications. It is often used in aerodynamics to study the flow of air around objects, in hydrodynamics to analyze water flow in rivers and oceans, and in heat transfer to understand how fluids carry heat along solid surfaces. It is also useful in the design of wind turbines, heat exchangers, and other engineering systems.

5. Are there any limitations to using the stream function along a solid boundary?

While the stream function along a solid boundary is a powerful tool in fluid dynamics, it does have some limitations. It assumes that the fluid is incompressible and inviscid, which may not always be the case in real-world scenarios. Additionally, it cannot accurately predict turbulent flows, which are common in many applications.

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