Stream function along solid boundary

[TomBolton10]

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?

 

[Chestermiller]

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. u_normal=-∂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