Fluid Dynamics: Vortex Question

[Mag]

Just a simple question.

 

Say we have 2 tubes.

Air goes through a normal tube at a certain rate.

 

Then we have another one, with a device to create a vortex - and the air goes through it at the same rate.

 

Will air in the one with the vortex go faster [in the tube]?

and

Will it go through more smoothly?

 

thank you

[Norman Albers]

If you say the air moves through the same then velocity along the tubes is the same, but vorticity means that the spinning one has sideways velocity also, so the total velocity will be larger; there will be more friction and chaos, I would guess. If not, tell me! Friction and eddies go by total velocity relative to the wall.

[Mag]

hmm.

 

Im not sure myself! im trying to picture it, and it would seem as though that the vortex tube's air would flow easier.

maybe not faster, but easier. (?)

[Norman Albers]

As often we are looking for the right question. Listen carefully to your assumptions. You said air is 'going through' at the same rate. You have spent fan energy making it rotate. Maybe air being sucked in the center of a vortex manifests a situation where there is magnified flow rate at the center compared to at the wall; is this what you sense? You spent energy creating this, though.

[Bignose]

 

Then we have another one' date=' with a device to create a vortex - and the air goes through it at the same rate.

 

Will air in the one with the vortex go faster [in the tube']?

 

Well, firstly, these two statements are completely incompatible. "Air goes through at the same rate" would mean (at least to me) that there is the same volumetric flow rate, which would be the same average axial velocity. Axial velocity is a key phrase there, since there would be a swirl velocity as well, but in terms of fluid through the pipe it should be the same.

 

Next, air through a tube at any significant speed is probably turbulent. At a still wall, the turbulent kinetic energy (k) goes to 0, but when the wall is moving k at the wall will not be zero. I am not 100% sure, but I think that this would mean an increase in k across the entire pipe. Even a static mixer would add a theta velocity component, which would lead to a higher k. A higher k, would mean a higher turbulent viscosity, and a higher turbulent viscosity (total apparent viscosity of the flow would be the sum of the intrinsic and the turbulent viscosities) means that it would take more energy to push the fluid through. So, no, the swirl would not make the flow easier. (Not to mention, as above, the extra energy needed to swirl the pipe)

 

I can think of two reasons, however, to do this. 1) increasing the turbulence does increase the mixing in the pipe, good if you want the air to be a more uniform temperature if you are heating the walls or something. Or if you are mixing methane or something with the air. or 2) the swirl will keep the flow a little more coherent, in that the vortex will persist for some distance after leaving the pipe. It should persist longer than if the pipe just sprays in a jet straight out. A swirled outflow is probably easier to control that just a straight jet out. I think that this is done for flames, for example.

[Mag]

hmm, thank you.

 

and sorry for the misunderstanding, but: you dont swirl the tube, you put a stationary object in the begining of the tube to swirl the air.

I should have made that more clear.

 

maybe this would help with some difficulties.

[Bignose]

Even a static mixer would add a theta velocity component' date=' which would lead to a higher k. [/quote']

 

Yes, the stationary object to make the air swirl is what I have always heard called a static mixer.

 

Again, the added swirl will increase the turbulent kinetic energy and then all the consequences I said above.

[Mag]

ah ok, thank you