# Prevention of fluid vortex formation

I've been looking for a way to prevent Vortex (whirlpool) formation in a pressurized vessel as it drains, but I am not having any luck finding the parameters at which vortex formation occurs. Is there any way to prevent the formation of a vortex entirely?

• don't drain it at the center.. – philip_0008 Jun 15 '16 at 21:03
• @philip_0008 The drain doesn't need to be centered for a vortex to form -- ever drain a bathtub or a sink? Those definitely are not centered. – tpg2114 Jun 15 '16 at 21:08
• Yea, I just thought of that.. – philip_0008 Jun 15 '16 at 21:09
• Maybe use multiple holes, so that the spin of one vortex will counter the spin of the others.. assuming they all rotate in the same direction (which might be likely, because the origin of the vortex seems to come from the total angular momentum of the fluid).. – philip_0008 Jun 15 '16 at 21:13
• I can't tell you how many dividers, what hole size etc. it takes... hence my suggestion to look into the engineering literature. I am sure this is a well known and treated problem there. – CuriousOne Jun 16 '16 at 0:27

The vortex forms due to a process called vortex stretching. Essentially as soon as the plug is pulled and the tank begins draining, a vortex forms at the center of the drain where the length of the vortex line is increased, which in turn increases the rotation rate and the familiar tornado shape forms.

The only surefire way to ensure that the vortex does not form is to ensure there is no vorticity in the tank to begin with. If there is no initial vorticity, there are no vortex lines to stretch. In reality, this means you would have to have the tank sit, perfectly still, until all of the rotation disappears. This could take days, maybe longer, maybe not even possible if the environment isn't exactly consistent (ie. the temperature changes, or there's vibrations or an earthquake or something).

If the liquid is incompressible, a good assumption for oils or water, it may be possible for viscous effects to balance the production of vorticity due to stretching and prevent the vortex from forming. The vorticity transport equation for an incompressible fluid is:

$$\frac{D \vec{\omega}}{D t} = (\vec{\omega} \cdot \nabla) \vec{u} + \nu \nabla^2 \vec{\omega}$$

The first term on the RHS is the vortex stretching term and the second is the dissipation of vorticity by viscous forces. If you don't want a vortex to form, you would need $|\nu \nabla^2 \vec{\omega}| \geq |(\vec{\omega}\cdot\nabla)\vec{u}|$. You likely don't have much control over the viscosity -- your fluid is what it is, and you may not be able to change from water to oil or something. But, you can attempt to control the stretching term through careful design of the drain diameter, shape, etc..

How to actually complete such a design is beyond the scope of what we can do on this site. But given known conditions of your fluid, it should be possible to design a drain that does not produce large enough stretching terms such that viscosity will kill out any vortex that forms. Whether that design will be good for your purposes or not will depend on what you need to do.

• Thank you so much for this explanation, it was clear, concise, and helped me greatly with the problem I am working on. – Jeff O Jun 17 '16 at 18:46
• @JeffO Thanks, I'm glad it was helpful! You can mark it as "accepted" by clicking the little check mark under the vote buttons. – tpg2114 Jun 17 '16 at 18:58

There is a simple way to prevent vortex from occurring. Assuming the drain in the tank is on the bottom of the take, install a a horizontal plate several inches above the drain fully covering the drain. It should be such that any water traveling to the drain must travel in a horizontal motion to get under the plate to reach the drain. A simple way to think of it as a table sitting above the drain with short legs. This is done in many systems and is called "A Vortex Breaker".