vertical axis wind turbine

[kanuk]

I wish to simulate a vertical axis wind turbine (2D) which will be centered in a circular boundary. As such I have 2 conceptual questions:

1) Will rotating the boundary conditions attain the same effect as rotating the entire geometry? Correct me if I'm wrong, but don't the Navier Stokes equations change for a different reference system, and if so, will I need to use the angular velocity body force condition??
2) I have heard that conditional boundary conditions exist, but am unable to find any solid examples in this regard for fluid flow. I've noticed that Elmer is much more stable with a velocity inlet condition and a pressure outlet condition - is this possible to implement using the conditional boundaries on a circular surface?

[raback]

Hi

1) Yes, you need to determine the angular velocity.
2) Yes you could create a condition that activates Dirichlet condition only when there is flow into the domain.
Note that if you set BC for "Velocity i", i=1,2,3. Then the corresponding condition is "Velocity i Condition".

-Peter

[kanuk]

Thanks for your quick response, Peter. What you said is basically what I expected.

So, to summarize, I understand that the body force section should be of the form:

Body Force 1
Velocity 1 = Variable Time, Coordinate 1, Coordinate 2
Real MATC "(cos(OMEGA*tx(0))-1)*tx(1)-sin(OMEGA*tx(0))*tx(2)+cos(OMEGA*tx(0))*VEL"
Velocity 1 Condition = Variable Time, Coordinate 1, Coordinate 2
Real MATC ????
Velocity 2 = Variable Time, Coordinate 1, Coordinate 2
Real MATC "(cos(OMEGA*tx(0)-1.0)-1)*tx(1)-sin(OMEGA*tx(0)-1.0)*tx(2)+cos(OMEGA*tx(0))*VEL"
Velocity 2 Condition = Variable Time, Coordinate 1, Coordinate 2
Real MATC ????
Pressure = Real 0
Pressure Condition = Variable Time, Coordinate 1, Coordinate 2
Real MATC ????
End

The reason for the ???? is because I am perplexed as to how to specify the coordinates for the dirichlet BCs. I am working on an unstructured cartesian mesh generated by gmsh, and my farfield boundary is circular. As such I can't simply perscribe R and a range of THETA (in polar coordinates) here (unless I'm mistaken).. I would use a mesh build in cylindrical coordinates, but ElmerGrid doesn't allow for unstructured meshes, which is a must for my case.

Am I missing something (very possible), or do I need to specify all node #s which will incorporate this dirichlet BC?

[raback]

Hi

I think you could use as the condition -\vec{n}\cdot\vec{v}, or equally well just -\vec{r}\cdot\vec{v}. This would set velocity if there is flow into the domain. It would be the same for both components.

Elmer does not that much like outlet pressure to be determined, so you could just drop that out.

I don't see any difference for the BCs on using structured vs. unstructured meshes. Elmer treats them internally just the same (except for some special solvers).

-Peter

[kanuk]

If we are specifying velocity at the boundaries using the conditional BC method described above, how do we ensure there is flow into the domain, except by using the regular "boundary condition" section, which would create dirichlet conditions both upwind and downwind (this is not what is desired)?

Basically, I am confused as to how to specify upwind velocity (dirichlet) and a zero natural bc downwind. So, I am confused as to how to implement your suggestion. Note that up until I stumbled upon the conditional BC method, I had been using the following:

Boundary Condition 1
Target Boundaries (4) = 1 2 3 4
Velocity 1 = Variable Time, Coordinate 1, Coordinate 2
Real MATC "(cos(OMEGA*tx(0))-1)*tx(1)-sin(OMEGA*tx(0))*tx(2)+cos(OMEGA*tx(0))*VEL"
Velocity 2 = Variable Time, Coordinate 1, Coordinate 2
Real MATC "(cos(OMEGA*tx(0))-1)*tx(1)-sin(OMEGA*tx(0))*tx(2)+cos(OMEGA*tx(0))*VEL"
End

However, this specifies downwind velocity, which is not physically realistic. Any suggestions on how to proceed??
Thanks,
D

[raback]

Hi

This requires some pen-and-paper when you have rotating coordinates. Without that the following might work:

Code: Select all

  Velocity 1 = Variable Coordinate 2
    Real MATC "-Omega*tx+VEL"
  Velocity 2 = Variable Coordinate 1
    Real MATC "Omega*tx"
  Velocity 1 Condition = Variable Coordinate 1
    Real MATC "-tx"
  Velocity 2 Condition = Variable Coordinate 1
    Real MATC "-tx"

Perhaps that gives you on idea. The velocity into the domain is proportional to the dot product between normal vector (n) and velocity vector (v). Now v=(-wy+v0)i+wxj and n=xi+yj and hence -n.v=-v0*x and thus the condition simplifies to just -x.

-Peter

[kanuk]

Thank you for the help. It seems to be working now.

I had no idea you could use the "velocity 1 condition = ..." in the boundary conditions section, this is what was troubling me.

regardless, I should be ok from here on in. thanks again.