## Friday, September 15, 2017

### What The Heck Is That?

Consider the gizmo in my hand below. It's called a vortex tube and is around 4 inches long and weighs maybe half a pound. I had never heard of these until recently. Had you?

There are no moving parts. You connect the inlet near my thumb to an ambient (room) temperature air supply. Really, really hot air comes out the end near my forefinger. Really, really cold air comes out the other end near the base of my palm. That little orange label says "CAUTION: Hot and cold surfaces" and it's not kidding. If the air supply is 8 cubic feet per minute at 100 psi, the hot end is over 100F hotter than the input air temperature and the cold end is over 100F colder than the input air temperature and can provide over 500 BTUs of cooling.

That's a pretty neat trick for something with no moving parts. Another neat trick is that until recently folks were still debating the physics behind how it works:
...for a long time the empirical studies made the vortex tube effect appear enigmatic and its explanation – a matter of debate.
In fact, the science wasn't totally settled until 2012:
This equation was published in 2012; it explains the fundamental operating principle of vortex tubes. The search for this explanation began in 1933 when the vortex tube was discovered and continued for more than 80 years.
So I don't feel bad that I'd never heard of it and had no idea how it worked. And I'll admit when I read the explanation that I still only have a vague notion of how it works.

Why did I discover it now? We have robotic machines that work in agricultural environments. Those machines have computers. We use computers and systems that can withstand up to about 105 (Fahrenheit). 99.8% of the time, the ambient temperature is below that. Unfortunately, 0.2% of the time, it gets hotter than that but the crops still need to be tended to and the machines fail and even die if they're run at a temperature hotter than 105. Yet for 0.2% of the time, it's expensive, bulky, and makes the system less robust due to complexity to add cooling via air conditioning to every single computer cabinet.

On the other hand, putting a vortex tube in each system isn't expensive, bulky, or complex. On those days when it's really hot, the grower can just attach an air supply from a compressor to the vortex tube and voila!, they can run our systems even when it's ridiculously hot. Most growers have compressors available, but even if they don't, it's straightforward to rent one on short notice. Problem solved!

Wow, thnaks Bret, you made my day. I really, really love to see basic physics directly being put to technological applications.

If you can ever post a picture of this working with your robots, I will be much obliged.

Bret said...

Clovis,

Can you explain the physics to a layman (well, um, to me)?

I especially don't get this part: "As it passes its way to the cold outlet, its heat energy is transferred to the peripheric flow."

Why does the colder inner vortex transfer heat to the hotter peripheric vortex? Heat transfer usually goes from hot to cold, no?

I mean I sorta kinda get that on the way to the hot end, the "hotter" and therefore faster moving air molecules would tend to migrate to the outside because, um, well, I'm not sure, perhaps their greater inertia? But after that I'm totally lost.

Bret,

You are far from a layman, but you were surely not helped by that Wikipedia article, it is very badly written, not to mention inaccurate.

When it comes to flows with vortex and turbulence, beware of too nice graphs, that vortex pattern drawing in the Wikipedia article can't be the real thing. It looks like much more something like this, maybe better visualized by this cross section. Those are simulations, but you can see the experiment with injected dye, here and here, or tracing particles, is close.

As for an intuitive understanding of the phenomena, it usually asks for you to first accept the flow pattern - which by itself can often be very non-intuitive and asks for solving the fluid equations, but in this case, it is not hard to accept that injecting air at the periphery of the pipe and perpendicular to it, like shown here, will lead to formation of vortex patterns.

Now you only need to remember what happens when you pump air into a ballon (it heats), or when you let air out of it (it cools) (more technically, in an adiabatic expansion air cools, while adiabatic compression heats it).

So, given the helical motion of the flow along the pipe, and that air is compressible, the centrifugal forces will compress its outwards regions (hence heat it), and expand its inwards regions (hence cooling it). IOW, the flow leads to a pressure gradient, which leads to a temperature gradient - leading to that apparent paradox you mention, "Heat transfer usually goes from hot to cold, no?". It usually does, but the radial pressure gradient here turned tables.

Now, most of the outward heated gas will escape at conical nozzle in the heated end, while the inward cold one will reflec back to escape at the opposite end. But, with all those vortex mixing, it is not so neatly separated as that wikipedia link may lead us to believe. A more realistic picture of the temperature distribution is shown here.

It is a beautiful little piece of work, this pipe. Where did you buy it? I will try to get a few myself too...

Bret said...

Clovis,

Thanks for the explanation. It does seem that wikipedia was pretty far off with their explanation.

I get the pressure gradient/temperature gradient part EXCEPT that it would seem to me that the cooler air when it escapes would only be cooler than ambient if it was at a lower pressure than ambient OR there is some sort of heat transfer or separation. Same for the hotter part.

Anyway, we specifically bought this kit so we could try different flow and cooling rates:

https://www.grainger.com/product/EXAIR-Vortex-Tube-4LCK1

Ultimately, we're going with the 2 cfm configuration because we don't actually need 100F degrees of cooling, 20F is enough and there's less issue with moisture condensation and a much smaller compressor can be used. (If you go for 8 cfm, get ready for it to drip like crazy!).At the 2 cfm rate, it still drips but re-evaporates in the hot computer enclosure.

Bret,

The pressure of reference in that explanation is the compressed air injected at the vortex tube. The helical outer layers of air insite the tube will be compressed, and the inner layers rarified, in comparison with the injected pressured air - in the end, both the hot and cold expelled air will be at higher pressure than ambient air.

A pity I can't draw here, but I guess you still remember how isothermal and adiabatic lines are in a P x V diagram. Now imagine an adiabatic line crossing three isothermal lines, the upper one being at Th (T-hot) of the expelled air, the bottom one at Tc (T-cold) of the opposite end, and th emiddle one at Ta (T-ambient), which is both the temperature of the air around the setup and the temperature of the pressurized air inside a chamber that will be used to cool your machine.

Now draw two lines of constant pressure, Pc (P-chamber) and Pa (P-atmosferic, or P-ambient, and obviously Pc >> Pa), along the same middle (Ta) isothermal line.

Now the point marked by Pc in that isothermal line Ta will, when you open the chamber, follow two opposite paths, depending if you are observing the inner layers of gas or the outer one. The inner layers will go down along the adiabatic line, until it reaches the bottom isothermal line Tc. The outer layers will go us along the adiabatic line, until it reaches the upper isothermal line Th.

If you draw all those lines, you will see it is not hard to find caes where the pressure of the cold air is still greater than the ambient pressure Pa in that initial Ta isothermal line.

Gee, a single image would be worth, and better, than all the owrds above, but I hope you can see it.

---
https://www.grainger.com/product/EXAIR-Vortex-Tube-4LCK1
---

Hmm, pretty expensive for such a little piece of metal, isn't it?

I did a search and found prices far lower in China websites (50\$ - 80\$ as opposed to \$200 - \$350 at your link), would you know if the difference in quality could justify that?

I don't need it for better purposes than pictoric demonstration, so I guess I'll go with the cheaper ones anyway.

Bret said...

Clovis,

I can sorta see it now from your explanation - I may draw it out at some point. Thanks.

Yeah, we bought an expensive one and I'm guessing the Chinese ones work and are very likely good enough for our purposes (and your purposes), especially at 2 cfm. We chose the Grainger one because Grainger has always delivered quality stuff in a timely fashion and sometimes in business, especially when coupled with the cost of expensive engineers investigating something, it's best to reduce risk and go for the reliable vendor. Especially since we didn't really understand how the vortex tubes work.

Ultimately, our plan, once we verified operation was to buy some less expensive ones and see how they were built and worked. So please do let me know if whatever one you get seems to work and be of good quality. Agricultural environments are very harsh, so probably the most important thing is the quality of the stainless steel and interior components, though 304 is adequate for the cabinets and cabinet components for us.

Bret said...

I scratched out the diagram. I see it now. You have to remember I'm mostly a software and algorithms guy and isothermal and adiabatic graphs are not something I encounter with any regularity!

You must be a pretty good teacher.

And this little tube thingy does produce quite interesting effects.