# Smoke rings to the tune of AC/DC

So I’ve been spending quite a bit of time thinking about vortex rings. Probably more than I should! I decided I wanted something that shot vortex rings filled up with smoke, but in a way that can last for very long periods of time. I came up with this idea that if I had an ultrasonic mist maker, I would be able to generate virtually endless fog that I could use for this. As a tease, this is what I came up with:

So hopefully you also found this cool! To be honest, I don’t know how this isn’t a thing yet – this could very well be a product. (i.e., it still performs the function as a room humidifier, but vortex rings are just cooler!). Ok, so how did I do it?

### What’s a vortex ring?

A vortex ring is a (rather important) fluid mechanical structure. It is present in pretty much all realistic flows and plays an important role in turbulence. Generating one is simple: When fluid is squeezed through a round nozzle, it forms a temporary jet that “curls” around the edges of the nozzle. Since the nozzle is round in shape, the curling happens all around, like a ring of spinning fluid. If the “squeezing” stops, the curling continues, though, through inertia. One thing we learn in fluid mechanics is that a vortex (this curled fluid structure) induces a velocity everywhere in the flow field – i.e., it tries to spin everything around it. If the nozzle blows upward, the left-hand side vortex core induces an upward speed on the right-hand side. The same happens from the right-hand side vortex core, it also induces an upward speed on the left-hand side. It actually happens all around the circle, meaning the vortex ends up propelling itself upward.

If the flow of the vortex ring is somewhat laminar and we seed it with smoke, we can see the vortex ring propelling itself as a traveling ring (as in the video) because it persists for quite a long time. Eventually, it becomes unstable and stretches until it twists and crosses itself, rapidly breaking down to tiny vortices and spreading itself in a turbulent cloud.

### How do I make one?

You need a means of generating smoke. Smoke machines used in stages / parties is generally the easiest way to get started. You fill a bucket with smoke, have a hole about 1/4 of the bucket diameter on one end, and then tap the opposite end. This replicates the “squeezing” process described before. It is not really an ideal solution, though, because the smoke fluid has to be replenished quite often. Plus, routing the smoke from the machine to this device that produces the smoke rings is not really easy (the smoke condenses in the walls of a pipe and forms a lot of oil in it).

So this idea struck me. If I use an ultrasonic fog generator (like this one), then I can produce ungodly amounts of smoke from a relatively small water tank. This smoke can last for hours and be stored in the water tank to increase its density. This is what I came up with:

A speaker is connected to a little water bucket (an ex-ice cream container) through this funky-looking black 3d-printed part. It’s just a duct that adapts the size of the speaker to the size of the orifice in the bucket. The bucket has about 120mm height, and the water level is about 70-100mm. The ultrasonic transducer is simply submerged in the bucket, generating tiny water droplets (a mist). The mist will mostly stay in the container, since gravity makes the droplets rain back to the water eventually. The tank lid has a nozzle, which is the only exit available for the air and the mist, once it is pushed by the speaker’s membrane. Thus, the speaker acts as a piston, an electromechanical actuator, and displaces air inside the bucket. In the forward stroke, it squeezes the air out, forming a vortex ring. In the return stroke, it draws the air back in. The waveform has to be asymmetric, such that the suction power is less than the blowing power. Otherwise, the vortex rings are sucked back into the nozzle, and though they do propel, a lot of their niceness is destroyed.

The figure above shows the best waveform shape I found for driving the speaker. It is quite important to get the waveform right! Even more importantly, it is crucial to DC-couple the driver. If you AC couple this waveform, it will not work at the low frequencies (i.e. 1-2Hz).It’s easy to test with a function generator, since the waveform is already DC coupled. In the end application, however, I ended up building a Class-D amplifier, without the output filter stage. The speaker itself removes the high frequency content due to its inductance.

I would share my design (mechanical drawings, etc). But this is such a custom-built device to fit a random ice cream container I found that there’s no point in doing that. I’m sure if you are determined enough to make this, you’ll find your way! A few tips:

• Fog height between water level and top of the tank is somewhat important. The particular fog machine I used generates 30-50mm of fog height above the water level. If the fog is not to the top of the tank, when the speaker pumps the fluid out there will be no fog carried with it, which will result in an un-seeded vortex ring, ruining the visual effect. I found that the fog doesn’t overflow through the nozzle even when the tank lid is closed, even with a high water level.
• The displaced volume is important. The larger the speaker size (I used a 4″ speaker with a 20mm nozzle), the less it has to displace to produce a nice vortex. A ratio between speaker diameter and nozzle diameter of 5 seemed to work well to me.
• Remember, velocity is dx/dt. This means when you increase the frequency of the signal, the velocity increases linearly (2x frequency, 2x velocity). This means that, as you increase the frequency of the signal, you don’t need as much amplitude to generate the same exit velocity. Since exit velocity roughly determines the vortex circulation and, therefore, the vortex Reynolds number, you want to keep that number the same in your experiment. Say, if you double the frequency keeping the amplitude of the voltage signal, you’ll get twice the exit velocity, which will make the vortices shoot twice as fast (i.e., they’ll go further) and with twice the Reynolds number (i.e., they will become turbulent and break down earlier). There’s a balance to strike here.

I hope this gives you some ideas!