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Stream function along solid boundary

by TomBolton10
Tags: boundary, function, solid, stream
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TomBolton10
#1
Jun5-14, 08:14 AM
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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/que...ream-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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Chestermiller
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Jun5-14, 10:14 PM
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Quote Quote by TomBolton10 View Post
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/que...ream-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


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