Actuator Disk Pressure Boundary Condition?

Numerical methods and mathematical models of Elmer
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hola
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Actuator Disk Pressure Boundary Condition?

Post by hola »

I'd like to model a fan with an infinitely thin disk with a prescribed pressure jump (http://en.wikipedia.org/wiki/Actuator_disk). How can I set a pressure difference
boundary condition in Elmer?
hola
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Re: Actuator Disk Pressure Boundary Condition?

Post by hola »

In the meanwhile, I thought of specifying the pressure jump condition on a permeable surface by MATC.
Is it possible? Maybe in a tangential coordinate system, an expression takes the pressure a small
distance away in normal direction, and adds the pressure jump to it, then sets this new pressure as a pressure
condition? Does anybody know how to get the pressure in a given point and how the tangent coordinates are called?
tx, t.... like in the laminar step tutorial's parabolic velo. distr. intake?
raback
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Re: Actuator Disk Pressure Boundary Condition?

Post by raback »

Hi

1) If the pressures at the inlet/outlet may be assumed to be well settled you could set "Pressure 1" or "External Pressure" (normal pressure) to given value such that you get the desired dp.

2) If the pressures have a profile you should basically have a periodic profile with offset. Unfortunately I don't think this will work with the default discretization. You could set "Gradp discretization = Logical True" and then try setting periodic BCs for Pressure with an offset. Have never tried, but it could work.

-Peter
hola
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Re: Actuator Disk Pressure Boundary Condition?

Post by hola »

Hi,
many thanks for your help, I'll try them out. Actually, I've already found the External Pressure
and Pressure <1|2|3> options. I tried them, and they worked, albeit not perfectly.
I had a problem with discretization, just as you'd predicted. The meshing gave the
best result when the resolution was low, otherwise the flow pattern was something
like a bound vortex ring with the core on the edge of the disk. Oh, yeah, I
found another makeshift method to get this working: Acceptably thin slab
instead of a plane disk, with a body force boundary condition applied for the
whole body. The whole thing is for checking my idea about a non-planar
actuator "shell", like a hemispherical fan, or an umbrella . I think if an actuator shell would have the
same pressure, same diameter as an actuator disk(-> same axial force), then it should consume
less power, and induce a slower fluid current. Some kind of a "self-ground-effect".
The first results I saw in the post processor shows a noticeable velocity drop.
I will post the pictures as soon I get my system working again, since it crashed...(.

(It's not about a fan, by the way, but a lifting device.)
hola
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Re: Actuator Disk Pressure Boundary Condition?

Post by hola »

Hi,

here are the first images, crude mesh only. I had problems with finer resolution (really),
and I still have to find a workaround for the "leak" visible in the hemisphere version,
so these are just previews. I know that the momentum theory prescribes the neccessary
dI/dt for the given reaction force, so, according to this, there is no way decreasing
the mass transport rate. But maybe the force can be generated by another way than
the pure "rocket" momentum theory. For example, hovercrafts float entirely by fluid
mechanics means, yet they don't produce so much mass rate as a rocket would do, they use a choked flow.
The wireframe images show that the vertical velocity distribution of the hemisphere version
is somewhat slower (green strip is shorter, green for high speed, red for low speed).
Later, higher resolution images must be more conclusive. (Plus these are in 2D only,
in 3D things might change)

(fluid: air, fan diameter: 0.5 m, dp=30 Pa )
hemi_actuator.PNG
Hemispherical actuator disk, abs. velocity map, pressure contours
(362.13 KiB) Not downloaded yet
flat_actuator.PNG
Flat actuator disk, abs. velocity map, pressure contours
(312.89 KiB) Not downloaded yet
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